Relationship Deformation Cracking

Technical Report

Understanding the Interaction Between LocalizedDeformation in Materials and EnvironmentallyAssisted Cracking

Effective December 6, 2006, this report has been made publicly available in accordance with Section 734.3(b)(3) and published in accordance with Section 734.7 of the U.S. Export Administration Regulations. As a result of this publication, this report is subject to only copyright protection and does not require any license agreement from EPRI. This notice supersedes the export control restrictions and any proprietary licensed material notices embedded in the document prior to publication.

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EPRI Project Manager J. Hickling

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Understanding the Interaction Between Localized Deformation in Materials and Environmentally Assisted Cracking

1011789

Final Report, January 2006

Cosponsor EDF R&D Site des Renardières Avenue des Renardières Ecuelles 77818 Moret sur Loing France

Project Manager J. Boursier

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ORGANIZATION(S) THAT PREPARED THIS DOCUMENT

EDF R&D

Institut National Polytechnique de Grenoble

NOTE

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CITATIONS

This report was prepared by

EDF R&D Site des Renardières Avenue des Renardières Ecuelles 77818 Moret sur Loing France

Principal Investigators T. Couvant J. Massoud

Institut National Polytechnique de Grenoble Laboratory of Thermodynamics and Metallurgical Physico-Chemistry France

Principal Investigator Y. Brechet

This report describes research sponsored by the Electric Power Research Institute (EPRI), and EDF R&D.

The report is a corporate document that should be cited in the literature in the following manner:

Understanding the Interaction Between Localized Deformation in Materials and Environmentally Assisted Cracking. EPRI, Palo Alto, CA, and EDF R&D, Moret sur Loing: 2006. 1011789.

iii

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PRODUCT DESCRIPTION

This report sets out to develop an understanding of the interaction between localized mechanical deformation in reactor structural materials (such as nickel-base alloys, austenitic stainless steels, or carbon and low-alloy steels) and their susceptibility to degradation by environmentally assisted cracking (EAC) after long-term exposure to light water reactor coolant. The main emphasis is on stress corrosion cracking (SCC), with and without the influence of irradiation, in the pressurized water reactor (PWR) primary side environment; but reference is also made to intergranular SCC in boiling water reactors and to corrosion fatigue. The report identifies key gaps in knowledge and recommends areas where additional experimental work and advanced modeling techniques are likely to produce useful outcomes for proactive management and mitigation of materials degradation by EAC.

Results & Findings Evidence of strain localization / EAC interactions has been identified in the laboratory for various environments, materials, and loads. These interactions occur at different stages in the degradation process, and the exact contribution of strain localization to EAC is often not defined. The development of a quantitative model for EAC / strain localization interactions will require additional experiments in order to define local and individual processes of oxidation, transport, deformation, and rupture, as well as to deal with their coupling. Investigations should focus on improved prediction of the “industrial” initiation time for EAC, including the effects on the incubation and slow cracking regimes of strain localization due to:

• Initial micro- and macrostructural discontinuities, such as grain boundary sliding, or heterogeneities in weld regions

• Strain softening, due to substructure instabilities, resulting in a change of strain path

• Fatigue instabilities, such as persistent slip bands.

Challenges & Objectives EAC modeling is difficult because interactions between oxidation and strain localization are confined to a narrow region ahead of the crack tip. An analytical solution seems inadequate here, and it is recommended that the coupled equations described in the report should be solved numerically for steady-state cracking. Development of numerical simulations would allow hypotheses to be tested on physical models and would provide insight into the interplay between local oxidation, diffusion, plastic flow and rupture. Numerical simulations should also lead to better planning for experiments; better understanding of EAC phenomena; and, ultimately, better design of components for light water reactors.

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Applications, Values & Use Understanding and preventing EAC / strain localization interactions in structural materials may offer an attractive and economic path to maintaining the integrity of light water reactor components throughout their service lives. Consequently, efforts should be focused on better understanding and modeling of such phenomena. The approach recommended in this report will be of primary interest to material specialists in the nuclear industry engaged in planning and monitoring research programs on EAC.

EPRI Perspective This report represents an ambitious attempt to advance our understanding of what is widely thought to be a key factor influencing the susceptibility of reactor structural materials to EAC. The authors have drawn heavily on both field experience and the advanced materials research carried out over many years within the R&D department of Électricité de France, the utility that co-sponsored the project. The authors also benefited from theoretical insights into the physics of material deformation, as well as from suggestions provided by industry and academic peers during a dedicated meeting on this topic towards the end of the project.

The project results will be used by the EPRI Primary Systems Corrosion Research Program to identify and prioritize additional experimental work on EAC to be carried out during the next few years in the context of the U.S. Industry Materials Initiative. The results are expected to be of considerable importance in moving to a more proactive approach for dealing with materials degradation as the existing LWR fleet ages and enters the license renewal phase of operation.

Approach The project team was familiar with ongoing worldwide efforts studying the degradation of materials through EAC and had direct access to both theoretical and experimental resources, as well as to extensive experience of the field behavior of PWR components in French reactors. The team drew on their own knowledge and interactions with technical peers to assemble a comprehensive, state-of-the-art assessment of what is known about the localization of mechanical deformation in a wide variety of reactor structural alloys and its interaction with EAC. The focus throughout was on identifying important gaps in both understanding and data, as well as in making detailed recommendations for appropriate testing and modeling to resolve key issues.

Keywords LWR materials degradation Environmentally assisted cracking Stress corrosion cracking Corrosion fatigue Crack initiation Testing techniques Numerical modeling

EXTENDED ABSTRACT

Environmentally assisted cracking (EAC) in the nuclear industry has been studied for 50 years. As a result of improving practices in nuclear power plants, such as optimizing operational procedures or the replacement of components using better materials, the susceptibility of pressurized water reactors (PWR) and boiling water reactors (BWR) to EAC has been considerably reduced. Nevertheless, repairs and further aging now lead us to consider the possibility of a more delayed appearance of EAC resulting from the long-term interactions between mechanisms such as oxidation and strain localization.

The tendency to undergo localized deformation in materials appears as a key contributor to induce or increase the susceptibility to stress corrosion cracking (SCC), irradiation assisted stress corrosion cracking (IASCC), and corrosion fatigue (CF). In this context, and because plastic deformation is always localized in metals (e.g. along slip planes), the current concern consists of identifying possible common physical domains in terms of temperature, load, or microstructure that could favor interactions between the mechanisms of EAC and strain localization in nuclear power plant components.

The present study has four main objectives:

• To identify possible strain localization mechanisms in materials used in nuclear power plants.

• To review the different types of EAC/strain localization interactions already identified in PWR and BWR environments.

• To focus on gaps in understanding and to identify the main issues for the possible contribution of strain localization to EAC susceptibility.

• To propose recommendations to clarify these key gaps: firstly by identifying advanced tools both to quantify strain localization/EAC interactions and to assess the validity of existing models, and secondly by proposing a strategy for future experiments and modeling.

This document is focused on possible strain localization in LWR structural materials at different scales of observation. Conditions for the occurrence of strain localization and its effect on EAC are considered as input and output data, respectively, as shown in the following diagram:

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Nature of loading:

• Strain/stress

• Temperature

• Irradiation…

Loading “kinetic”:

• Monotonous, cyclic…

• Frequency

• Strain path…

Material:

• Composition (SS, Nickel-based alloys, ferritic steel…)

• Manufacturing

• Surface conditions

• Cold-work rate…

Macro ( )1

Meso ( )2

Micro (3)

Polycrystalline:

• Deformation incompatibilities from one grain to the other (or due to a second phase)…

Intercrystalline:

• Grain disorientation,

• Grain boundaries slid,

• Soft grain boundaries with hardened grains…

Transcrystalline:

• Dislocation channeling

• Deformation bands

• Dislocation cells

• Dislocation pinned by solute interstitial atoms (dynamic and static aging)…

Evidence of interactions:

• Ni-based alloys in PWR

• Strain hardened SS in LWR

• Sensitized SS in BWR

• Irradiated SS in LWR

• LAS in BWR

How to understand the interactions at the different stages of EAC:

• Incubation

• Slow propagation of short cracks

• Rapid propagation

Recommendations:

• Strategy to model interactions

• Possible experiments to evaluate the interactions…

Following an introductory chapter, the report is organized into four main sections:

• Section 2 describes the different types of strain localization in nuclear materials, at different scales, using phenomenological and modeling approaches. Throughout this section, efforts were made to illustrate each case of plastic flow instability with examples from the nuclear industry.

• Section 3 reviews cases of EAC with evident, or possible, correlation with strain localization in LWR environments (for various nickel-based alloys, austenitic stainless steels, and low-alloy steels).

• Section 4 discusses the possible synergies between EAC and strain localization that may occur during the different stages of EAC.

• Recommendations for further work are reported in Section 5. Several tasks are suggested in order to improve understanding of EAC/strain localization interaction mechanisms, and to develop methods for quantitative prediction of EAC based on the identified mechanisms.

Some of the key findings are summarized in tabular form as follows:

( )1 The macroscopic scale is the scale of the component or sample in the laboratory.

( )2 The mesoscopic scale is related to the collective material behavior (e.g., dislocation substructures) which requires inputs from both macroscopic and microscopic levels.

( )3 The microscopic scale is at the scale of the primary “actors” (precipitates, dislocations, slip systems).

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Environment Material EAC Stage Key-Gaps

Incubation Effect of strain localization (especially due to strain path and grain boundary sliding) on chemical surface reactivity.

Initiation Consequences of strain localization associated with cyclic loading on time to initiation of PWSCC.

Austenitic stainless steel

Slow propagation of short cracks

Effect of plastic flow instabilities due to solute atoms/dislocations interactions on the CGR. Effect of strain incompatibilities due to localization on the crack growth path.


Initiation Consequences of strain localization (due to strain path and GBS) on time to initiation of PWSCC.

Relevance of ctε and low K as mechanical parameters for coupling with internal oxidation mechanism.

Correlation between precipitation and strain localization at grain boundaries.

Correlation between transport (oxygen) and strain localization at grain boundaries.


Identification of the local rupture criteria due to the internal oxidation process.

Wrought Alloy 600

Rapid propagation Effect of loading on strain localization at the crack tip.Consequences of plastic flow instabilities for the CGR.

Incubation Effect of strain localization (due to material heterogeneity) on the surface reactivity.

Initiation Effect of strain localization (due to material heterogeneity) on time to initiation.

HAZ in wrought Alloy 600

Propagation Effect of strain localization (due to material heterogeneity) on the CGR.


Initiation Consequences of strain localization (due to periodic reverse strain path) on time to initiation of PWSCC.

Weld metal 182


Correlation between transport (oxygen) and strain localization at grain boundary.

PWR

Wrought Alloy 690 Initiation

Consequences of high strain localization (due to complex or periodic reverse strain path) on time to initiation of PWSCC.

The three main tasks identified for future studies are summarized in the following table, together with an indication (on an increasing scale of 1 to 3) of the expected level of difficulty and the timeframe involved:

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Task Description Difficulty Time Scale

Qualitative techniques for characterization of the cracks

1 1

SEM observation of in-situ deformation in corrosive environment

3 3

Quantitative characterization of strain localization

1 1

Development of specific tests to characterize EAC/strain localization interactions

2 2

– 1 –

Tools of investigation

Numerical simulation of propagation of EAC 3 3

Experimental quantification of the effect of strain localization rate on EAC propagation

2 3

Experimental quantification of the effect of strain localization rate on EAC initiation in austenitic stainless steels

1 2

Modeling the effect of strain localization on EAC in austenitic stainless steels

3 3

Experimental quantification of the effect of strain localization rate on EAC initiation in Ni base alloys

1 2

– 2 –

Quantification of the effect of strain

localization rate on EAC

Modeling the effect of strain localization on EAC in Ni base alloys

2 2

Substructure instabilities due to fabrication process

2 2 – 3 –

Experimental evaluation of possible EAC/strain localization synergy for

components

Material heterogeneities due to fabrication process 2 2

At each step, experimental and modeling work is recommended in two simultaneous directions:

• To advance understanding of the physical mechanisms. In particular, it is essential to identify the contribution of local mechanics (plastic flow and/or brittle fracture) and thereby better understand the process of crack initiation and advance. Physical parameters controlling crack initiation and propagation are not the same in the case, for example, of local brittle fracture and in the case of disruption of the protective layer leading to dissolution.

• To develop quantitative models of initiation and propagation phenomena, based on physical mechanisms. Firstly, empirical modeling should permit experimental results to be integrated more directly into industrial applications. Then, equations predicting the material behavior should be implemented into large-scale computational codes so as to model the structural response for environmentally assisted rupture.

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ACRONYMS

AFM Atomic Force Microscopy

BWR Boiling Water Reactor

CBB Cell Block Boundary

CEPM Corrosion Enhanced Plasticity Model

CERT Constant Extension Rate Test

CGR Crack Growth Rate

CIR Cooperative IASCC Research Program

DDD Discrete Dislocation Dynamics

EAC Environmentally Assisted Corrosion

FCC Face-Centered Cubic

FEM Finite Element Model

GBS Grain Boundary Sliding

HAZ Heat Affected Zone

HCF High Cycle Fatigue

HWC Hydrogen Water Chemistry

IASCC Irradiation Assisted Stress Corrosion Cracking

IGSCC Intergranular Stress Corrosion Cracking

LAS Low-Alloy Steel

LCF Low Cycle Fatigue

LRO Long Range Ordering

NWC Normal Water Chemistry

PFZ Precipitate Free Zone

PLC Portevin-Le Chatelier

PSB Persistent Slip Band

PWR Pressurized Water Reactor

RUB Reverse U-Bend

SCC Stress Corrosion Cracking

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SEM Scanning Electron Microscopy

SFE Stacking Fault Energy

SOC Self Organized Criticality

SRO Short Range Ordering

SS Stainless Steel

SSRT Slow Strain Rate Test

TEM Transmission Electron Microscopy

TGSCC Transgranular Stress Corrosion Cracking

Physical parameters

σ Stress

σ0 or YS Yield Stress

σm or UTS Ultimate Tensile Strength

ε Strain

εp Plastic Strain

ρ Volumic weight

b Burgers vector

d Grain size

E Young Modulus

El Elongation

F Faraday Constant

h Strain Hardening

K Stress Intensity factor

M Atomic weight

n Work hardening rate

Qi Quantity of current

S Strain rate

T Temperature

t time

z number of exchanged electrons during the oxidation

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CONTENTS

1 INTRODUCTION ....................................................................................................................1-1

1.1 Background .....................................................................................................................1-1

1.2 Objectives .......................................................................................................................1-2

1.3 Organization of the Report ..............................................................................................1-2

2 STRAIN LOCALIZATION IN LWR STRUCTURAL MATERIALS..........................................2-1

2.1 Introduction .....................................................................................................................2-1

2.2 Phenomenological Approach to Plastic Instabilities ........................................................2-2

2.2.1 Type O: Material Heterogeneity...............................................................................2-3

2.2.2 Type h: Strain Softening ..........................................................................................2-3

2.2.3 Type S: Strain Rate Softening .................................................................................2-4

2.2.4 Type F: Winter Instability in Fatigue ........................................................................2-5

2.3 Physical Causes for Localization and Examples in Nuclear Materials ............................2-6

2.3.1 Type O: Initial Structural Heterogeneities or Discontinuities ...................................2-6

2.3.1.1 Macroscopic Heterogeneities...........................................................................2-6

2.3.1.2 Intragranular Heterogeneities ..........................................................................2-7

2.3.1.3 Discontinuities: Grain Boundary.......................................................................2-8

2.3.2 Type h: Strain Softening (Lüders and Pseudo Lüders, Precipitate Shearing, Short Range Order) ........................................................................................................2-10

2.3.2.1 Dislocation Avalanche....................................................................................2-10

2.3.2.2 Destruction of Obstacles................................................................................2-10

2.3.2.3 Substructure Instability ..................................................................................2-11

2.3.3 Type S: Strain Rate Softening ...............................................................................2-12

2.3.4 Type F: Fatigue Localization .................................................................................2-15

2.3.5 Summary Tables ...................................................................................................2-17

2.4 Modeling and Limitations...............................................................................................2-21

2.4.1 Type O: Toward a Continuum Approach? .............................................................2-21

2.4.2 Type h: Use of Mesoscopic Dislocation Simulations .............................................2-22

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2.4.3 Type S: Internal Variable Models, Statistical Approaches.....................................2-24

2.4.4 Type F: Reaction Diffusion Approach....................................................................2-25

2.5 Consequences of Localization on Fracture Behavior....................................................2-27

2.5.1 Effect of Heterogeneities on Ductility.....................................................................2-27

2.5.2 Effect of Strain Localization on Toughness ...........................................................2-32

2.5.3 Effect of Damage Percolation on Fatigue Life .......................................................2-33

2.6 Conclusions...................................................................................................................2-34

3 ENVIRONMENTALLY ASSISTED CRACKING.....................................................................3-1

3.1 Introduction .....................................................................................................................3-1

3.1.1 Materials ..................................................................................................................3-1

3.1.1.1 Nickel-Based Alloys .........................................................................................3-2

3.1.1.2 Austenitic Stainless Steels...............................................................................3-3

3.1.1.3 Low-Alloy Steels ..............................................................................................3-4

3.1.2 Environments...........................................................................................................3-5

3.1.2.1 The PWR Primary Environment (Primary Water) ............................................3-6

3.1.2.2 BWR Environment ...........................................................................................3-6

3.1.3 Investigation of Environmentally Assisted Cracking ................................................3-7

3.1.3.1 Definitions ........................................................................................................3-7

3.1.3.2 Experimental Tests ..........................................................................................3-8

3.2 SCC of Nickel-Based Alloys in the PWR Primary Environment ......................................3-8

3.2.1 IGSCC in Wrought Alloy 600 ...................................................................................3-9

3.2.1.1 Phenomenology...............................................................................................3-9

3.2.1.2 Evidence of EAC/Strain Localization Interactions..........................................3-14

3.2.1.3 Main Issues....................................................................................................3-17

3.2.2 IGSCC in Wrought Alloy 690 .................................................................................3-18

3.2.2.1 Phenomenology.............................................................................................3-18

3.2.2.2 Evidence of EAC/Strain Localization Interaction............................................3-19

3.2.2.3 Main Issues....................................................................................................3-19

3.2.3 IGSCC in Wrought Alloy X750...............................................................................3-19

3.2.3.1 Phenomenology.............................................................................................3-19

3.2.3.2 Main Issues....................................................................................................3-20

3.2.4 IGSCC in Wrought Alloy 718 .................................................................................3-20

3.2.4.1 Phenomenology.............................................................................................3-20

3.2.4.2 Evidence of EAC/Strain Localization Interactions..........................................3-21

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3.2.4.3 Main Issues....................................................................................................3-22

3.2.5 SCC in Weld Metals 182 and 82 ...........................................................................3-22

3.2.5.1 Phenomenology.............................................................................................3-22

3.2.5.2 Evidence of EAC/Strain Localization Interaction............................................3-23

3.2.5.3 Main issues....................................................................................................3-23

3.3 SCC of Austenitic Stainless Steels in LWR Environments............................................3-25

3.3.1 Context ..................................................................................................................3-25

3.3.2 SCC of Strain Hardened Austenitic Stainless Steels in the PWR Primary Environment ...................................................................................................................3-25

3.3.2.1 Phenomenology.............................................................................................3-25

3.3.2.2 Evidence of EAC/Localization Interactions ....................................................3-27

3.3.2.3 Main Issues....................................................................................................3-33

3.3.3 SCC of Sensitized Austenitic Stainless Steels in BWR Environment....................3-34

3.3.3.1 Phenomenology.............................................................................................3-34


3.3.3.3 Main Issues....................................................................................................3-40

3.3.4 IASCC of Austenitic Stainless Steels in PWR and BWR Environments ................3-40

3.3.4.1 Phenomenology.............................................................................................3-40


3.3.4.3 Main Issues....................................................................................................3-49

3.4 EAC of Low-Alloy Steels ...............................................................................................3-50

3.4.1 Phenomenology.....................................................................................................3-50

3.4.2 Evidence of EAC/Strain Localization Interactions .................................................3-51

3.4.2.1 Effect of DSA .................................................................................................3-52

3.4.2.2 Effect of Hydrogen .........................................................................................3-54

3.5 Conclusion ....................................................................................................................3-54

4 DISCUSSION OF EAC AND STRAIN LOCALIZATION INTERACTIONS ............................4-1

4.1 Approach.........................................................................................................................4-1

4.2 Incubation, Slow and Rapid Propagation ........................................................................4-1

4.2.1 Incubation ................................................................................................................4-1

4.2.1.1 Oxidation Reactions: Case of Austenitic Ni-Base Alloys in PWR ....................4-2

4.2.1.2 Mechanical Dependence of Surface Reactivity ...............................................4-4

4.2.1.3 Main Issues......................................................................................................4-9

4.2.2 Slow Propagation of Short Cracks...........................................................................4-9

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4.2.2.1 Configuration ...................................................................................................4-9

4.2.2.2 Production and Diffusion of Species at the Crack Tip....................................4-10

4.2.2.3 Consequences of Oxidation on Brittle Rupture Criteria at a Crack-Tip..........4-14

4.2.2.4 Interactions Between Oxidation and Plastic Flow at a Crack-Tip ..................4-16

4.2.2.5 Main Issues....................................................................................................4-18

4.2.3 Rapid Propagation of Deep Cracks .......................................................................4-19

4.2.3.1 Configuration .................................................................................................4-19

4.2.3.2 Consequences of Crack Growth for Transport Mechanisms within the Crack .........................................................................................................................4-19

4.2.3.3 Consequences of Crack Growth on Oxidation Mechanisms..........................4-20

4.2.3.4 Consequences of Crack Growth on Plastic Flow at the Crack Tip ................4-20

4.2.3.5 Consequences of Crack Growth on Rupture Criteria.....................................4-20

4.2.3.6 Main Issues....................................................................................................4-20

4.3 Transitions in EAC Stages ............................................................................................4-21

4.3.1 True Initiation.........................................................................................................4-21

4.3.2 Slow/Rapid Propagation Transition .......................................................................4-22

4.4 Main Issues ...................................................................................................................4-22

5 RECOMMENDATIONS ..........................................................................................................5-1

5.1 Strategy for Investigations...............................................................................................5-1

5.2 Task 1: Tools of Investigation..........................................................................................5-4

5.2.1 Qualitative Techniques for the Characterization of Cracking ..................................5-5

5.2.2 Quantitative Characterization of Strain Localization................................................5-6

5.2.3 Development of Specific Tests to Characterize EAC/Strain Localization Interactions .......................................................................................................................5-6

5.2.4 Numerical Simulation of Environmentally Assisted Rupture....................................5-6

5.3 Task 2: Quantification of the Effect of Strain Localization Rate on EAC.........................5-7

5.3.1 Strain Localization Maps in an Inert Environment ...................................................5-8

5.3.2 SCC of Alloy 600 in the PWR Primary Environment .............................................5-10

5.3.2.1 Incubation and Initiation of IGSCC.................................................................5-10

5.3.2.2 Slow Propagation of Short Cracks.................................................................5-12

5.3.2.3 Rapid Propagation .........................................................................................5-13

5.3.3 IGSCC of Weld Metal 182 in the PWR Primary Environment................................5-14

5.3.3.1 Incubation and Initiation of IGSCC.................................................................5-14

5.3.4 Incubation and Initiation of IGSCC for Alloy 690 in the PWR Primary Environment ...................................................................................................................5-16

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5.3.5 SCC of Austenitic Stainless Steels 304L and 316L in the PWR Primary Environment ...................................................................................................................5-17

5.3.5.1 Incubation and Initiation of SCC ....................................................................5-17

5.3.5.2 Slow Propagation of Short Cracks.................................................................5-18

5.3.5.3 Rapid Propagation .........................................................................................5-18

5.4 Task 3: Experimental Evaluation of Possible EAC/Strain Localization Synergy for Components........................................................................................................................5-19

5.4.1 Substructure Instabilities Due to the Manufacturing Process ................................5-19

5.4.2 Material Heterogeneities Resulting from the Manufacturing Process....................5-19

6 CONCLUSIONS .....................................................................................................................6-1

7 REFERENCES .......................................................................................................................7-1

A DIFFUSION OF OXYGEN IN ALLOYS ................................................................................ A-1

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LIST OF FIGURES

Figure 1-1 Understanding EAC and Strain Localization Interactions.........................................1-3 Figure 2-1 DSA and PLC Regimes in Strain Rate Sensitivity Versus Temperature

Diagram..............................................................................................................................2-4 Figure 2-2 Serrated Flow (Left) and Localization Bands (Right) in Al Alloys .............................2-5 Figure 2-3 PSB at the Surface of a Fatigued Material in Pure Copper ......................................2-5 Figure 2-4 Localization of Plasticity in a Friction Stir Weld. Experiments Involved Digital

Image Correlation and FEM Calculations with a Spatially Dependent Constitutive Law.....................................................................................................................................2-6

Figure 2-5 Example of a Macroscopic Heterogeneity: Hardened Ferrite (Dark Phase) in Thermally Aged Duplex Stainless Steels ...........................................................................2-7

Figure 2-6 Precipitation at GB and Cr Depleted Zone Resulting in Sensitization ......................2-8 Figure 2-7 Irradiation Defects Free Zones Close to a Grain Boundary in an Austenitic

Stainless Steel Irradiated Up to 10 dpa [4].........................................................................2-8 Figure 2-8 Stress Concentration at a Triple Point in AISI 304L .................................................2-9 Figure 2-9 Intergranular Precipitates Emitting Dislocations in Alloy 600 [5]...............................2-9 Figure 2-10 Evidence of GBS in Alloy 600 at 360°C in an Inert Environment [6] ......................2-9 Figure 2-11 Stress Strain Curve Presenting a Lüders Plateau ................................................2-10 Figure 2-12 Stress-Strain Curves at 330°C for an Austenitic Stainless Steel Alloy After

Different Irradiation Doses Expressed in dpa [4]..............................................................2-11 Figure 2-13 Clear Bands in Neutron-Irradiated Copper ...........................................................2-11 Figure 2-14 Stress-Strain Curves for Different Strain Paths in 304L at 360°C (5.10–8 s–1)

[7]. The Strain Path is Characterized by Pre-Shearing γ and the β Parameter Defined by Schmitt [8] ......................................................................................................2-12

Figure 2-15 Physical Causes for DSA .....................................................................................2-13 Figure 2-16 Serrated Flow and Critical Strains ........................................................................2-13 Figure 2-17 Types of Serration and Stress Drop Statistics as a Function of the Strain

Rate and the Inverse Temperature for an Al-Mg Alloy .....................................................2-14 Figure 2-18 Effect of DSA on Tensile Strength for Different LAS [102] ...................................2-15 Figure 2-19 Dissolution of Precipitates During Fatigue in a Structural Hardening Al Alloys ....2-16 Figure 2-20 AFM Micrographs of the Surface Relief within a Grain of 316L Steel Cycled

at Constant Plastic Strain Amplitude (2×10–3) for Different Numbers of Cycles. The Scale is Identical on Both Micrographs ............................................................................2-16

Figure 2-21 Model of the Plastic and Damage Behavior of a PFZ...........................................2-21

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Figure 2-22 Modeling the Ductility Anisotropy in Textured Aluminum with a Grain Boundary PFZ ..................................................................................................................2-22

Figure 2-23 Strain Localization Diagram. ∆τ is the Amount of Softening, γ0 the Typical Strain for Full Softening, h the Hardening Coefficient. The Schematic Shows the Nature of Localization (Lüders Type or Random Nucleation of Bands) ...........................2-23

Figure 2-24 Prediction of the Band Velocity Using a “Spring-Block Model” .............................2-25 Figure 2-25 The “Ladder Structure” in a Copper Single Crystal Having Undergone Single

Slip Fatigue and its Schematics .......................................................................................2-26 Figure 2-26 Critical Energy Release Rate ...............................................................................2-28 Figure 2-27 Schematic of the Microstructure Around Grain Boundaries with PFZ ..................2-29 Figure 2-28 Competition Between the Different Failure Modes ...............................................2-30 Figure 2-29 Fracture Map ........................................................................................................2-31 Figure 2-30 Ductility Anisotropy Resulting from Textured Materials with Weak

Boundaries .......................................................................................................................2-32 Figure 2-31 Origin and Characterization of Strain Localization ...............................................2-35 Figure 3-1 Stages of SCC of Alloy 600 in PWR Primary Environment ....................................3-10 Figure 3-2 Effect of Stress on Time to Failure of Alloy 600 at Tube Sheet ..............................3-11 Figure 3-3 Effect of Stress on Time to Failure of Alloy 600 Vessel Head Nozzles ..................3-12 Figure 3-4 Effective Stress as a Function of the Applied Stress and the Thickness of the

Cold-Worked Surface Layer [34]......................................................................................3-13 Figure 3-5 Influence of the Applied Stress and the Effective Stress on SCC Initiation

Time [34] ..........................................................................................................................3-13 Figure 3-6 Comparison of Maximum Crack Depth for CERT (Tests 1 and 2) and a

Constant Load Test (Test 3) for Alloy 600 Tested in PWR Hydrogenated Environment at 360°C [28] ...............................................................................................3-15

Figure 3-7 CGR vs. Crack-Tip Strain Rate from CERT in the PWR Primary Environment at 360°C [34] ....................................................................................................................3-15

Figure 3-8 Dislocation Motion in Alloy 600 TT (0.75% El.) [37] ...............................................3-16 Figure 3-9 Dislocation Motion in Alloy 600 MA (0.75% El.) [37] ..............................................3-16 Figure 3-10 GBS at the Surface of an Alloy 600 Tube in [23]..................................................3-17 Figure 3-11 CGR vs. η in Alloys 600 and 690 from CERT (5.10–8 s–1) in the PWR Primary

Environment at 360°C [39] ...............................................................................................3-17 Figure 3-12 Stress–Strain Curves at Room Temperature of Hydrogen Pre-Charged and

Hydrogen Free Specimens Deformed at Various Strain Rates: (a) 5×10–7.s–1, (b) 5×10–5.s–1, and (c) 5×10–3.s–1 [49] ......................................................................................3-21

Figure 3-13 Highly Deformed Matrix and Localized Deformation Structure off Crack Walls. TEM Brightfield Image [55] ....................................................................................3-23

Figure 3-14 Micro-Hardness Threshold for Initiation and Propagation of SCC During CERT in the PWR Primary Environment (360°C, ε = 5 10–8 s–1) [7] .................................3-26

Figure 3-15 Stress Threshold for Initiation and Propagation of SCC During CERT in the PWR Primary Environment (360°C, ε = 5.10–8 s–1) [7] ......................................................3-26

xx

Figure 3-16 Initiation and Propagation Stages During CERT with Non Pre-Strained 304L in the PWR Primary Environment (360°C). Depth of the Main Crack vs. Strain at the End of the Test [7]............................................................................................................3-26

Figure 3-17 Creep Rate as a Function of Temperature in Austenitic Stainless Steels [62] .....3-27 Figure 3-18 GBS at a Triple Point. Cold Pressed Hump Specimen, CERT ( ε = 5.8 10–8 s–1)

[62] ...................................................................................................................................3-27 Figure 3-19 Microcracks on a Grain Boundary After Sliding. Cold Pressed Hump

Specimen, CERT ( ε = 5.8 10–8 s–1) [67] ............................................................................3-28 Figure 3-20 Transgranular Crack-Tip Examinations After CERT ( ε = 5.8 10–8 s–1) [62]............3-28 Figure 3-21 Intergranular Crack Depth Versus Pre-Shearing for Several Strain Paths.

CERT on Notched Specimens (360°C, ε = 5 10–8 s–1) [61] ...............................................3-29 Figure 3-22 Transgranular Crack Depth Versus Pre-Shearing for Several Strain Paths.

CERT on Notched Specimens (360°C, ε = 5 10–8 s–1) [61] ...............................................3-30 Figure 3-23 Strain Localization and Residual δ-Fe; CERT in the PWR Primary

Environment (360°C, ε = 5.10–8 s–1) [61]...........................................................................3-30 Figure 3-24 Cavities at a Grain Boundary. CERT in the PWR Primary Environment

(360°C, ε = 5 10–8 s–1). Detail of Figure 3-23 [61] .............................................................3-31 Figure 3-25 Martensite Localized Around Residual Ferrite [61]...............................................3-31 Figure 3-26 Transgranular Crack in Austenite, 100-200 nm from δ−γ Interface [61]................3-32 Figure 3-27 Pure TGSCC in 304L After CERT (5.10–8 s–1) in the PWR Primary

Environment at 360°C. Grain size ≈ 60 µm [61] ...............................................................3-32 Figure 3-28 IGSCC and TGSCC in 304L After CERT (5.10–8 s–1) in the PWR Primary

Environment at 360°C. Grain Size ≈ 20 µm [61] ..............................................................3-33 Figure 3-29 Effect of Corrosion Potential on SCC Susceptibility of Sensitized 304 in

BWR Environment at 288°C [77]......................................................................................3-35 Figure 3-30 Corrosion Potential vs. Dissolved Oxygen Concentration in BWR

Environment in the Range 100°C-288°C [76] ..................................................................3-36 Figure 3-31 Effect of Dissolved Oxygen on %IGSCC in BWR Environment for Sensitized

304 [78] ............................................................................................................................3-36 Figure 3-32 Effect of Dissolved Oxygen on Strain to Initiation for Sensitized 304 in BWR

Environment [78] ..............................................................................................................3-37 Figure 3-33 SCC Depth vs. Cold Work in 304 Tested in BWR Environment (CBB

Specimens) [82] ...............................................................................................................3-37 Figure 3-34 SCC Depth vs. Temperature of Thermal Treatment in Cold-Worked 304.

Tests in BWR Environment (CBB Specimens) [82]..........................................................3-38 Figure 3-35 Crack Growth Rate Versus Yield Strength in BWR Environment at 288°C

[79] ...................................................................................................................................3-38 Figure 3-36 Cracked Bolt .........................................................................................................3-41 Figure 3-37 Intergranular Fracture Surface of a Cracked Bolt .................................................3-41 Figure 3-38 Fracture Surface of a Constant Load Specimen (800 MPa) Tested in the

PWR Primary Environment (SA 304H Irradiated Up to 30 dpa).......................................3-42

xxi

xxii

Figure 3-39 Details of Intergranular Fracture Surface Zones of a Constant Load Specimen (700 MPa) in the PWR Primary Environment (SA 304 Irradiated Up to 30 dpa). Slip Lines on the Intergranular Surfaces........................................................3-42

Figure 3-40 Fracture Surface of a CERT Specimen. CW 316 Irradiated Up to 20 dpa. Brittle Area with Both Intergranular and Transgranular Zones.........................................3-43

Figure 3-41 Totally Intergranular Fracture Surface of an O-Ring Specimen of a Highly Irradiated CW 316 Material ..............................................................................................3-43

Figure 3-42 Results Obtained on CW Irradiated 316 and Annealed Irradiated 304 (6 dpa). CERT (ε ≈10–7 s–1) in the PWR Primary Environment..........................................3-44

Figure 3-43 Evolution of the Stress Required to Sensitize the Material to Intergranular SCC as a Function of the Irradiation Dose for Austenitic Stainless Steels (from IASCC Advisory Committee)............................................................................................3-45

Figure 3-44 Strain Localization and IASCC Initiation in a SA 304L Irradiated Up to 30 dpa. CERT at 360°C ...................................................................................................3-46

Figure 3-45 A Schematic Map of Strain Rate-Temperature-Fracture Morphology Dependencies ..................................................................................................................3-48

Figure 3-46 Summarizes the Main Mechanisms to Consider when Modeling the Stress-Corrosion Behavior and Resistance of Irradiated Stainless Steels (After Bruemmer) .....3-49

Figure 3-47 Crack Initiation Stages on Longitudinal Sections of Specimens After LCF Tests at 288°C in Water at (a) 0.1% s–1 (b) 0.001% s–1.....................................................3-51

Figure 3-48 S-N Curves of LAS in Simulated BWR Water and in Air at 288°C .......................3-52 Figure 3-49 Coincidence Between SCC (in Term of Crack Growth Rate in BWR

Environment) and DSA Susceptibility (in Term of Reduction of Area) [102] ....................3-52 Figure 3-50 Schematic Synergistic Effect of Different Parameters (Including DSA) for

SCC Crack Growth [102]..................................................................................................3-53 Figure 3-51 Schematic Synergistic Effect of Different Parameters (Including DSA) for

Corrosion Fatigue Crack Growth [102].............................................................................3-53 Figure 4-1 Compact Oxide Formed at the Surface of Electropolished Alloy 600 (Inner

Surface of a Tube) Exposed 1170 h to Primary Water at 325°C [110] ..............................4-5 Figure 4-2 Compact Oxide Formed at the Surface of Cold-Worked Alloy 600 (Inner

Surface of a Tube) Exposed 1170 h to Primary Water at 325°C [110] ..............................4-5 Figure 4-3 Number of Metastable Pits Formed on 304 Austenitic Stainless Steel, Tested

in 0.1 M NaCl at 25°C, for 0-70% of Pre-Straining [113]....................................................4-6 Figure 4-4 Free Potential at Initiation of SCC in 316L Tested in Boiling MgCl2 (117°C).

CERT [115] ........................................................................................................................4-7 Figure 4-5 Surface State After Oligocyclic Fatigue (10 Cycles) in Air of 316L. Inter-Slip

Spaces ≈ 10 µm [115] ........................................................................................................4-8 Figure 4-6 Surface State After Oligocyclic Fatigue (50 Cycles) in Air of 316L. Inter-Slip

Spaces ≈ 1 µm [115] ..........................................................................................................4-8 Figure 4-7 Example of Absorption and Diffusion Enhanced Strain Localization Process........4-16 Figure 4-8 Possible Strain Localization Enhanced by DSA at a Crack Tip ..............................4-17 Figure 4-9 Stress-Elongation Curve from CERT (5×10−7 s−1) Conducted in Air, First at

500°C up to 0.04 Plastic Strain and then at 470°C Up to Rupture. At 500°C, the

SRS of the Flow Stress is Slightly Positive and the Flow Stress is Continuous. At 470°C, the SRS of the Flow Stress Becomes Negative and the PLC Effect Occurs .......4-18

Figure 5-1 Etch Pit Patterns of Dislocations Emitted from Crack-Tip Sources Roughly a Distance of 5 µm Apart. The Sources are Envisioned to be Associated with Cleavage Ledges [140] ......................................................................................................5-5

Figure 5-2 Coupling Mechanisms for Environmentally Assisted Rupture (EAR) Simulation ..........................................................................................................................5-7

Figure 5-3 Reference Map for Strain Localization due to DSA and GBS in Inert Environment .......................................................................................................................5-8

Figure 5-4 Evolution of Reference Map with Intergranular Precipitation....................................5-9 Figure 5-5 Evolution of the Density of PSB Under Cyclic Loading with Strain Rate and

Temperature.......................................................................................................................5-9 Figure 5-6 Distribution of Vickers Micro-Hardness Along the HAZ. HSLA 100 Steel [144]......5-20 Figure 5-7 Mechanical Responses of Base Metal, Weld Metal and Boundary with the

HAZ in the Center of the Specimen. HSLA 100 Steel [144] .............................................5-20

xxiii

LIST OF TABLES

Table 2-1 Types of Instability in Nuclear Materials, with Examples .........................................2-18 Table 2-2 Examples of Instabilities in Nuclear Materials, Classified by Type of Materials.......2-20 Table 2-3 Plastic Instabilities, Physical Causes, Governing Parameters, Modeling Tools

and Critical Experiences ..................................................................................................2-37 Table 3-1 Materials and their Locations in Nuclear Power Plants .............................................3-1 Table 3-2 Chemical Composition of Materials ...........................................................................3-4 Table 3-3 Material Properties at 20°C for Materials Susceptible to EAC in Nuclear Power

Plants .................................................................................................................................3-5 Table 3-4 EAC/Strain Localization Interactions in Nuclear Materials/Environments................3-55 Table 4-1 Chemical Composition and Thickness of the Internal Oxide Layer Formed on

Alloy 600 Exposed to the PWR Primary Environment, as a Function of Dissolved Hydrogen. EDS Normalized Measurements ......................................................................4-2

Table 5-1 Main Issues and Identified Key Gaps from the Present Study ..................................5-2 Table 5-2 Difficulty and Time Scale for Identified Tasks............................................................5-3 Table 5-3 Prioritization of Investigations for the PWR Primary Environment .............................5-4

xxv

1 INTRODUCTION

The location of fracture in a material is a key issue. For ductile materials, rupture implies that, ultimately, plastic deformation will become spatially heterogeneous. For brittle materials, it means that the crack will run between essentially undeformed regions of matter. If strain localization is a consequence of the fracture process, and if the onset of the unstable plastic flow is rapidly followed by the final fracture, the localization becomes a secondary issue. But the reverse situation is also possible, and plastic localization may enhance locally damage processes and therefore play a crucial role in determining the ultimate conditions for failure. This is true for both simple damage and environmentally assisted damage. It is therefore relevant, in terms of a predictive approach to component failure in nuclear power plants, to address the issue of the effect of plastic localization, related with materials properties or triggered by irradiation, on cracking processes.

1.1 Background

Environmentally assisted cracking (EAC) in the nuclear industry has been studied for 50 years. As a result of improving practices in nuclear power plants, such as optimizing operational procedures or the replacement of components using better materials, the susceptibility of pressurized water reactors (PWR) and boiling water reactors (BWR) to EAC has been considerably reduced. Nevertheless, repairs and further aging now lead us to consider the possibility of a more delayed appearance of EAC resulting from the long-term interactions between mechanisms such as oxidation and strain localization.

The tendency to undergo localized deformation in materials appears as a key contributor to induce or increase the susceptibility to stress corrosion cracking (SCC), irradiation assisted stress corrosion cracking (IASCC), and corrosion fatigue (CF). Recent examples include:

• The influence of highly localized welding strains leading to SCC in unsensitized stainless steels in BWR.

• The possible effect of stacking fault energy in determining the response of different alloys to irradiation assisted stress corrosion cracking (IASCC).

• The effect of dynamic strain aging (DSA) in low-alloy steels on corrosion-fatigue cracking under slow cyclic loading in light water reactors (LWR) pressure boundary components, such as pressure vessels and piping.

1-1

Introduction

Some strain localizations involving EAC have been identified in the laboratory. Interactions between oxidation and deformation have been studied mostly for austenitic and low-alloy steels in simulated nuclear environments. Quantitative and qualitative models have been developed to describe environmental crack propagation, based for example on slip and dissolution at the crack-tip. This is especially true for austenitic stainless steels in BWR environment (slip dissolution model) or in boiling MgCl2 (corrosion enhanced plasticity model) [1, 2].

In this context, and because plastic deformation is always localized in metals (e.g. along slip planes), the current concern consists of identifying possible common physical domains in terms of temperature, load, or microstructure that could favor interactions between the mechanisms of EAC and strain localization in nuclear power plant components. The apparent gap between our knowledge of the conditions required to initiate and propagate stress corrosion cracking in laboratory tests and current nuclear power plant operating experience is particularly well illustrated by the case of cold-worked stainless steels in PWR primary coolant.

1.2 Objectives

This study has four main objectives:

• To identify possible strain localization mechanisms in materials used in nuclear power plants.

• To review the different types of EAC/strain localization interactions already identified in LWR environments.

• To focus on gaps in understanding and to identify the main issues for the possible contributions of strain localization to EAC susceptibility.

• To propose recommendations to clarify these key gaps: first by identifying advanced tools to quantify strain localization/EAC interactions and to assess the validity of existing models, and secondly by proposing a strategy for future experiments and modeling.

1.3 Organization of the Report

As shown in Figure 1-1, this document is focused on possible strain localization in LWR structural materials at different scales of observation. Conditions for the occurrence of strain localization and its effect on EAC are considered as input and output data, respectively. Following this introduction, the report is organized into four main sections:

• Section 2 describes the different types of strain localization in nuclear materials, at different scales, using phenomenological and modeling approaches. The title of the section is “strain localization in nuclear materials” and underlines the fact that this section is focused on nuclear applications; therefore plastic flow instabilities leading to strain localization are restricted to the four types appropriate for nuclear materials. Throughout this section, efforts were made to illustrate each case of plastic flow instability with examples from the nuclear industry. Nevertheless, some examples also refer to the aeronautical or automotive industries.

1-2

Introduction

• Section 3 reviews cases of EAC with evident, or possible, correlation with strain localization in LWR environments (for different nickel-based alloys, austenitic stainless steels, and low-alloy steels).

• Section 4 discusses the possible synergies between EAC and strain localization during the different stages of EAC.

• Recommendations are reported in Section 5. Several tasks are suggested in order to improve understanding of the EAC and strain localization interaction mechanisms, and to develop methods for quantitative prediction of EAC based on the identified mechanisms.

Conditions for the Occurrence of

Strain Localization (Input Data)

Strain Localization Mode

Effect on Environmentally

Assisted Cracking (Output Data)

Nature of loading: • Strain/stress • Temperature • Irradiation…

Loading “kinetic”: • Monotonous,

cyclic… • Frequency • Strain path…

Material: • Composition (SS,

Nickel-based alloys, ferritic steel…)

• Manufacturing • Surface conditions • Cold-work rate…

Macro ( )4

Meso ( )5 Micro (6)

Polycrystalline: • Deformation incompatibilities

from one grain to the other (or due to a second phase)…

Intercrystalline: • Grain disorientation, • Grain boundaries slid, • Soft grain boundaries with

hardened grains…

Transcrystalline: • Dislocation channeling • Deformation bands • Dislocation cells • Dislocation pinned by solute

interstitial atoms (dynamic and static aging)…

Evidence of interactions: • Ni-based alloys in PWR • Strain hardened SS in LWR • Sensitized SS in BWR • Irradiated SS in LWR • LAS in BWR

How to understand the interactions at the different stages of EAC: • Incubation • Slow propagation of short

cracks • Rapid propagation

Recommendations: • Strategy to model

interactions • Possible experiments to

evaluate the interactions…

Figure 1-1 Understanding EAC and Strain Localization Interactions

( )4 The macroscopic scale is the scale of the component or sample in the laboratory.

( )5 The mesoscopic scale is related to the collective material behavior (e.g., dislocation substructures) which requires inputs from both macroscopic and microscopic levels.

( )6 The microscopic scale is at the scale of the primary “actors” (precipitates, dislocations, slip systems).

1-3

2 STRAIN LOCALIZATION IN LWR STRUCTURAL MATERIALS

2.1 Introduction

The classical modeling approaches in continuum mechanics assume a homogeneous plastic response of loaded materials at the level of the microstructure. Many studies have aimed at predicting macroscopic localization using phenomenological constitutive models which assume a homogeneous response at the microstructural level. These investigations focus on the conditions for bifurcation or localization arising from a homogeneous response, considering the material has no internal length scales ( )7 . All these analyses lead to conditions of macroscopic localizations in terms of diffuse or localized necking. Localization results from a complex competition between material hardening versus softening, which is strongly linked to the geometry and loading configuration. Details of the constitutive models, such as vertices on the yield surface or anisotropy effects, are known to affect the onset of localization. The main application for engineering purposes is prediction of the forming limit diagram. Although the width of the localization band is set by the microstructure (typically the grain size), the condition for the onset of localization in this approach does not need directly to incorporate microstructural features. In addition, beside the conditions for unstable growth of infinitesimally small perturbations, one may consider the possible triggering via finite perturbation, such as the onset of necking for samples with different surface polishing. The problem of the onset of localization thus remains essentially macroscopic. This topic has been reviewed extensively by the solids mechanics community and documented in the literature during the last 3 or 4 decades.

The purpose of the present section is different. It addresses the problem of localization at the level of the microstructure and how it may affect the macroscopic properties of ductility and fracture toughness. Conditions for the occurrence of this type of localization cannot be formulated without taking into account the relevant microstructural characteristics and length scales. Of course, plastic flow is intrinsically localized when considered at the atomistic level, since it is related to the glide of dislocations, but when averaged on the scale where elementary damage events occur (some micrometers), it can often be considered as homogeneous, and is treated as such for fracture behavior modeling. However, the situation

( )7 In classical continuum mechanics, the constitutive laws for material behaviors have no length scale. Generalized

mechanics (such as Cosserat media or gradient plasticity theories) artificially introduce a length scale. Micromechanics, with which we are concerned in this report, considers the internal length scale of the material (grain size, interdislocation distance, inclusion size, precipitate spacings…) as crucial to understanding the mechanical properties and fracture behavior. In these approaches, the length scales of localization (such as band width) are consequences of the microscopic mechanics and are related to the internal length scales defined above.

2-1

Strain Localization in LWR Structural Materials

is substantially different when the flow is heterogeneous at this scale, e.g., because of the microstructure of the alloy studied. Plastic flow may be localized for the following reasons ( )8 :

• because the microstructure itself is spatially heterogeneous (Type O localization): it can be a heterogeneity in the hardening microstructure (such as precipitate free zones) or a discontinuity such as grain boundary sliding;

• because the plastic flow is unstable, due to:

– negative work hardening rate, as in the case of plastic deformation of irradiated materials (Type h localization);

– negative strain rate sensitivity, as in the alloys exhibiting the “Portevin-Le Chatelier” effect (Type S localization);

– insufficient removal of the heat produced by plastic deformation, as in the case of adiabatic localization (Type T localization);

• because, even though the microstructure is homogeneous, the nature of loading induces plastic localization, as is the case in fatigue (Type F localization);

• because the textural evolution leads to catastrophic softening: this issue is relevant mainly in forming operations and for large-scale deformations (Type θ localization).

These various types of localization are of different importance from the perspective of this report. Our attention will focus on type O, h, S, and F, which are likely to be encountered under the operating conditions in nuclear reactors and may couple with environmental effects.

It has to be stressed that, even in a microstructurally homogeneous material, plasticity leads to spatially heterogeneous dislocations structures (formation of subgrains, persistent slip bands, ladder structures and matrix vein structures in fatigue, intense shear bands in irradiated alloys). This aspect of the problem, namely dislocation patterning, is a difficult problem beyond the scope of this chapter. In this section, our attention will be focused on:

• the phenomenological description of localization (Section 2.2);

• the physical reasons for localization, such as loading and microstructure (Section 2.3);

• the available modeling tools (Section 2.4);

• the consequences of localization on fracture (Section 2.5).

2.2 Phenomenological Approach to Plastic Instabilities

The simplest definition of the phenomenon is: “homogeneous loading leading to heterogeneous deformation”. The most obvious reason for the non-homogeneous response is non-homogeneous local behavior. This instability is named “type O”.

( )8 These denominations are found in the works of Estrin and Kubin.

2-2


Analyzing the possible growth of an infinitesimally small fluctuation in a material with a differential constitutive law such as:

dσ = h dε + S dLn tε Equation 2-1

where εt is the total deformation, h is the strain sensitivity, and S is the strain rate sensitivity; Estrin and Kubin [3] derived a simple condition for unstable plastic flow:

(σ - h - S)/S > 0 Equation 2-2

The “natural case” for a material is that both the strain hardening h and the strain rate hardening S are positive. In this situation, the previous equation reduces to the Considere-Hart criterion for necking.

In some specific situations that will be analyzed below, the strain hardening is negative (type h) or the strain rate sensitivity is negative (type S): these are the most frequent “macroscopic reasons” for plastic localization.

Plastic localization has also been classified according to its macroscopic manifestation: the localization may be in specific places in the material (stationary) or in traveling plastic waves (propagative). It can be a transient regime or lead to persistent localization (type F).

A third way to build a relevant taxonomy is to consider the different localization scales: at the grain level, at the level of several grains, and at the macroscopic level.

In the following, the Estrin-Kubin classification is adopted, but the situation with respect to the two other classification approaches is also indicated.

2.2.1 Type O: Material Heterogeneity

Preexisting heterogeneities in the microstructure can be present at all scales, such as precipitate free zones (PFZ) at boundaries and heat affected zones (HAZ) in welds. The heterogeneities may also be internal surfaces at which the strain field becomes singular as in grain boundary sliding (GBS). By definition, these instabilities are stationary. In general they are also persistent. Depending on the scale of the microstructural heterogeneity, they can be either at the grain scale, or at the grain boundary scale (PFZ, GBS, …), or at the macroscopic scale (HAZ in welds).

2.2.2 Type h: Strain Softening

The resistance to plastic flow results from both microstructural obstacles to dislocation motion (precipitates) and dislocation accumulation in organized substructures (work hardening). The net effect is an increase of the resistance to plastic flow with deformation, which is a stabilizing phenomenon for plastic deformation: a very deformed region has more difficulty to further deform than a less deformed region. Two types of phenomena may reverse the situation:

• The destruction of intrinsic obstacles with the deformation.

• The instability of dislocation substructure for dislocation storage.

2-3


Such situations are observed when dislocations brutally unpin from obstacles (such as in the Lüders phenomena), when hardening features such as chemical order, precipitates, or irradiation loops are wiped out by dislocation motion (such as in alloys with shearable precipitates, or irradiated materials), and when dislocation substructure becomes unstable (such as in a severe change in strain path). Type h instabilities are generally characterized at the macroscopic level by a yield point and a plateau in the stress strain curve, and by localized bands (either propagating through the sample or localized at fixed positions). They can be either transient or persistent. The localization obtained by the destruction of obstacles, such as precipitate shearing and irradiation loop sweeping, are generally at the grain scale, even if some localization may be triggered from one grain into its neighbors. The localization due to brutal unpinning or to the destabilization of the dislocation substructure, as observed in Lüders bands or a change in strain path, are somewhat more violent and the bands generally involve groups of grains.

2.2.3 Type S: Strain Rate Softening

Usually, a stress increase is necessary to deform a material at a higher rate, due to the thermally activated nature of dislocation motion. The strain rate sensitivity reflects the temperature dependency, and, in general, an increase in strain rate is equivalent to a decrease in temperature. This situation may be reversed in the case where the resistance to plastic flow increases with time: if strain rate decreases, the dislocations move more slowly, and stay pinned longer at obstacles. If the resistance to their further motion increases as their arrest time increases, the flow stress is then larger. A typical example of this situation is when diffusing solutes tend to pin down moving dislocations: this is known as dynamic strain aging (DSA) and leads to the

“Portevin-Le Chatelier” phenomenon (PLC) when ∂∂Lnεσ

< 0 (Figure 2-1). PLC presents both

a spatial (propagating bands) and temporal (serrated flow) signature (Figure 2-2). These instabilities are in general persistent and propagative. Their macroscopic signature, which distinguishes them from h-type instabilities, is a negative strain rate sensitivity. The “Portevin-Le Chatelier” band’s scale is that of several grains.

σε

∂∂Ln

T

DSA

PLC

0

Figure 2-1 DSA and PLC Regimes in Strain Rate Sensitivity Versus Temperature Diagram

2-4


Figure 2-2 Serrated Flow (Left) and Localization Bands (Right) in Al Alloys

2.2.4 Type F: Winter Instability in Fatigue

Fatigue loading has to be treated separately. Indeed, even for a material as well-behaved as copper with a positive strain rate sensitivity and strain hardening, cyclic loading can lead, under certain conditions, to very severe intragranualar plastic localization at fixed positions (see Figure 2-3). On a steady-state basis, it is called the persistent slip band (PSB) phenomena and was discovered by Winter. The plastic strain amplitude in the bands is two orders of magnitude larger than that between the bands. The relevant parameter for this phenomenon is the plastic strain amplitude: at low plastic strain amplitudes, the plastic deformation is homogeneous within a grain, but beyond a certain amplitude, it localizes in the PSB. Finally, beyond a greater amplitude, the PSB fill the sample and deformation becomes homogeneous again.

Figure 2-3 PSB at the Surface of a Fatigued Material in Pure Copper

2-5


2.3 Physical Causes for Localization and Examples in Nuclear Materials

2.3.1 Type O: Initial Structural Heterogeneities or Discontinuities

2.3.1.1 Macroscopic Heterogeneities

The influence of macroscopic heterogeneities in the plastic behavior, such as the ones resulting from HAZ in welds (Figure 2-4), is straightforward and mainly requires a careful finite element modeling (FEM) approach to make sure that the issues of strain partitioning and triaxiality are dealt with in an appropriate manner.

Figure 2-4 Localization of Plasticity in a Friction Stir Weld. Experiments Involved Digital Image Correlation and FEM Calculations with a Spatially Dependent Constitutive Law

Examples in nuclear materials: different kinds of macroscopic heterogeneities are present at different scales in the microstructure of materials used in nuclear components. HAZ in the base metal adjacent to welds are the most common, but “ghost lines” (or segregation lines) in ferritic steels in reactor pressure vessels and hardened ferrite in thermally duplex stainless steels (Figure 2-5) are other types of macroscopic heterogeneities.

2-6


2-7

Figure 2-5 Example of a Macroscopic Heterogeneity: Hardened Ferrite (Dark Phase) in Thermally Aged Duplex Stainless Steels

2.3.1.2 Intragranular Heterogeneities

The heterogeneities inside the grain substructure are usually influenced by the grain boundary with respect to its chemical interaction with the solute and its nature as a sink and a source of vacancies. When intergranular precipitation occurs, the zone close to the boundary becomes solute depleted (Figure 2-6). Vacancies can also be absorbed near the grain boundary. Both phenomena create a heterogeneous precipitation microstructure close to the grain boundary: the Precipitation Free Zone (PFZ). A similar phenomenon is observed after irradiation, where the vicinity of grain boundaries may be depleted from irradiation loops (Figure 2-7). The net result is that the grains are “coated” with a soft layer, where plastic deformation localizes and damage often accumulates.

Examples in nuclear materials: chemical heterogeneities near the grain boundaries are often encountered in Ni-based Alloy 600, or in sensitized austenitic stainless steels (Figure 2-6), due to grain boundary precipitation or segregation resulting from fabrication treatments. Segregation of phosphorous at and near the grain boundaries due to temper embrittlement in ferritic steels is also a case of intragranular heterogeneity. Chemical heterogeneities can also be observed in austenitic stainless steels due to irradiation induced segregation at the grain boundaries: a significant depletion in chromium, molybdenum, and iron is reported, as well as an enrichment in silicon, nickel, and possible impurities such as phosphorus and sulfur [4]. In certain circumstances, zones depleted from irradiation loops near the grain boundaries can also be found in irradiated austenitic steels (Figure 2-7).


Figure 2-6 Precipitation at GB and Cr Depleted Zone Resulting in Sensitization

Figure 2-7 Irradiation Defects Free Zones Close to a Grain Boundary in an Austenitic Stainless Steel Irradiated Up to 10 dpa [4]

2.3.1.3 Discontinuities: Grain Boundary

Grain boundaries are surfaces of potential discontinuity in the material. Different grains may behave differently under a given macroscopic load, leading to incompatibilities and internal stresses. These stress gradients are observed at triple points, or close to intergranular precipitates, and they lead to diffusional flow (i.e. a flow of vacancies), which may result in grain boundary sliding (GBS). It is not, strictly speaking, a “plastic strain localization” phenomenon, but rather a “displacement discontinuity”, which may result in considerable damage if the grains are prevented from sliding, or if protective surface layers are locally damaged in a corrosive environment.

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Example in nuclear materials: stress concentrations are commonly observed at triple points in cold rolled materials (Figure 2-8). Figure 2-9 shows grain boundary carbides acting as a dislocation source in Alloy 600. Figure 2-10 shows evidence of GBS in Ni-based Alloy 600 at 360°C in an inert environment after grid deposit.

Figure 2-8 Stress Concentration at a Triple Point in AISI 304L

Figure 2-9 Intergranular Precipitates Emitting Dislocations in Alloy 600 [5]

Figure 2-10 Evidence of GBS in Alloy 600 at 360°C in an Inert Environment [6]

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2.3.2 Type h: Strain Softening (Lüders and Pseudo Lüders, Precipitate Shearing, Short Range Order)

2.3.2.1 Dislocation Avalanche

The dislocation avalanche phenomenon starts with a sudden increase in mobile dislocation density, leading to a very large plastic strain rate. To ensure a constant applied total strain rate, the load has to drop, which corresponds to the yield point phenomenon. This burst of “fresh dislocations” generated at a sufficiently high stress is the reason for the “Lüders” phenomena in steels, where the unpinning of dislocations from carbon leads to a yield point and the propagation of a transient plastic wave.

Example in nuclear materials: in the case of static strain aging of low-alloy steels, the unpinning of dislocations from interstitial atoms leads to a Lüders plateau (Figure 2-11).

El.

Load

Lüders band Unyielded metal

Figure 2-11 Stress Strain Curve Presenting a Lüders Plateau

2.3.2.2 Destruction of Obstacles

When obstacles are wiped out by moving dislocations, a strain increase then leads to a smaller resistance of the microstructure. This phenomenon is observed when short or long range chemical order is destroyed by moving dislocations, when precipitates are sheared, and when dislocation loops resulting from irradiation are wiped out. The resulting local softening leads to plastic localization. Depending on the magnitude of the softening, and on the incompatibility coupling between layers of material deformability, the plastic localization can be propagative or stationary at random positions.

Examples in nuclear materials: iron-chromium spinodal decomposition in thermally aged ferrite in duplex stainless steels, or possible short and long range ordering in thermally aged 690 nickel-base alloys, which are strong obstacles for dislocation motion could be at the origin of strain softening by obstacle destruction, as well as precipitates in 718 or X750 nickel-base alloys. Although it seems that the iron content of nickel-based alloys would prevent such ordering from occurring, very long-term aging experiments performed at higher temperatures showed this phenomenon and extrapolation suggests that its existence at service temperatures cannot be precluded.

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Neutron irradiation induces an overall hardening in austenitic stainless steels due to the accumulation of irradiation dislocation loops (Frank loops), which act as obstacles to the motion of the dislocations. The destruction of these Frank loops by the sweeping action of moving dislocations is expected to localize the deformation. Strain softening is clearly shown on the stress-strain curves in Figure 2-12. Experimental evidence of strain localization in these irradiated materials is generally associated with the “channeling” effect and the presence of clear bands (Figure 2-13).

Figure 2-12 Stress-Strain Curves at 330°C for an Austenitic Stainless Steel Alloy After Different Irradiation Doses Expressed in dpa [4]

Figure 2-13 Clear Bands in Neutron-Irradiated Copper

2.3.2.3 Substructure Instability

The dislocation substructure is destabilized by a change in strain path. Qualitatively, the physical reason for this is the development of dislocation substructures to accommodate a given state of plastic loading. For instance, the orientation of the bands and the shape of the dislocation cells result from a subtle interplay between the crystallography and the loading geometry. When the loading conditions are changed, a new microstructure has to develop. The more severe the change is, the more different the microstructure will be. A mild change in strain path can be adapted by a minor modification of the substructure, whereas a major change in strain path will require a total reshuffling of the dislocation substructure. This reshuffling will occur heterogeneously and lead to strain localization, at least in a transient regime.

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Example in nuclear materials: a case of substructure instability deals with the behavior of cold-worked austenitic stainless steels under complex mechanical loading Figure 2-14.

0

100

200

300

400

500

600

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14

Plastic strain

True

stre

ss (M

Pa)

γ = 0 , β = (+1)

γ = 0.4 , β = −1

γ = 0.4 , β = 0

γ = 0.4 , β = +1

Figure 2-14 Stress-Strain Curves for Different Strain Paths in 304L at 360°C (5.10–8 s–1) [7]. The Strain Path is Characterized by Pre-Shearing γ and the β Parameter Defined by Schmitt [8]

2.3.3 Type S: Strain Rate Softening

The Portevin-Le Chatelier (PLC) phenomenon is the most extensively studied case of spatio-temporal instability in mechanical behavior. In some alloys, a negative strain rate sensitivity is observed, leading to a serrated stress-strain curve and to spatial localization of the plastic deformation. This phenomenon has been interpreted as the interplay between diffusion of impurities toward dislocations and unpinning of dislocations (Figure 2-15). For a given applied strain rate, a given density of dislocations spends part of the time waiting at obstacles (other dislocations) and part of the time moving toward another obstacle. While stopped at obstacles, dislocations attract mobile impurities. The greater the concentration of impurities segregated at the dislocation core, the higher the stress has to be to unpin the dislocation. Therefore, two characteristic times have to be considered: the impurities diffusion time and the dislocations waiting time. When the diffusion time is very large compared to the waiting time, dislocations move with high mobility and almost no solute interaction: a positive strain rate sensitivity is then observed. When the diffusion time is very small compared to the waiting time, the dislocations are permanently loaded with solute; they have low mobility, but the strain rate sensitivity remains positive. When the two times are of the same order of magnitude, the longer the waiting time (lower strain rate), the greater the concentration of impurities that will segregate to the dislocation and the lower its mobility will be; a higher stress is then needed to make it move at a given velocity, which results in a negative strain rate sensitivity. Since the waiting time depends on the dislocation density and the applied strain rate, and the diffusion time depends on both the temperature and dislocation density, this simple analysis allows for a basic understanding of why the PLC effect is observed only in a closed domain of strain rates and temperatures, and only beyond a critical strain. The PLC effect has two characteristics: a serrated stress-strain curve and a localized deformation pattern (Figure 2-16). Three types of stress strain curves are commonly

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distinguished, based on three different types of spatial organization of plasticity (Figure 2-17). Type A serrations are associated with repetitive continuous propagation of deformation bands, nucleated at one end of the sample. Type B serrations correspond to a hopping propagation of localized bands in the axial direction of the sample. Type C serrations correspond to the nucleation of bands in a spatially non correlated manner. The statistical analysis of the stress drops in various situations can also lead to three types of histograms: the peak shaped distribution (type p), the asymmetric distribution (type as), and an intermediate distribution with both a peak and asymmetry (type i). It is worth noting that the statistical analysis of serrated flows provides a direct indication of the type of localized plastic waves.

Diffusing solute atom td ∝ D−1

Mobile dislocation tw ∝ (dε/dt)−1

Dislocation forest

Figure 2-15 Physical Causes for DSA

Figure 2-16 Serrated Flow and Critical Strains

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To a first approximation, the parameters controlling the characteristics of the PLC effect can be the strain rate and temperature. It is convenient to map the domain in which serrated yielding occurs in terms of the type of instability and the type of distribution. An example for the Al-Mg system is shown in Figure 2-17.

Figure 2-17 Types of Serration and Stress Drop Statistics as a Function of the Strain Rate and the Inverse Temperature for an Al-Mg Alloy

Examples in nuclear materials: low-alloy steels, C-Mn steels, and their associated welds are known to be sensitive to dynamic strain aging (DSA), when too many interstitial solute atoms remain in the microstructure [9]. DSA is also observed in nickel-based alloys [10] and austenitic stainless steels [11]. DSA is associated with an increase in flow stress, ultimate tensile strength (UTS), work hardening rate, and ductile to brittle transition temperature, as well as a decrease in ductility (elongation, reduction of area, strain rate sensitivity coefficient, fracture toughness, and low-cycle fatigue life) [12]. DSA can produce the Portevin-Le-Chatelier (PLC) effect [13] in a temperature range which is clearly dependent on the mobility of the solute atoms relative to the imposed dislocation velocity [14, 15]. In C-Mn steels, it is well established that the diffusing elements are interstitial carbon and nitrogen atoms. Moreover, due to its greater solubility limit, the nitrogen content seems to exert a more pronounced influence on strain aging than the carbon content. PLC can also be observed in austenitic stainless steels between 300 and 700°C [16].

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Depending on the diffusion coefficients, the chemical composition, the heat treatment, and the strain rate (generally less than 10–2 s–1;, DSA occurs in the temperature range 200-350°C (Figure 2-18), which is the temperature range of nuclear reactors. The range where it occurs is shifted to lower temperature with decreasing strain rate, ε .

All fabrication processes which reduce the amount of nitrogen in solid solution also reduce the sensitivity to DSA. In particular, the addition of nitrogen-trapping elements, such as Al, Ti, Nb or also Mn (for instance in nitrides or carbo-nitrides), is beneficial against DSA. In the case of welds where the oxygen level is higher, on the other hand, aluminum can be preferentially trapped in the oxides and is therefore less effective in trapping nitrogen.

Figure 2-18 Effect of DSA on Tensile Strength for Different LAS [102]

2.3.4 Type F: Fatigue Localization

The physical reasons for the localization of plastic flow are not clearly understood. A possible explanation is related to slip irreversibility. The strain amplitude governs the rate of irreversibility in the dislocation motion. When a dislocation moves backward following the same path, it eliminates some dislocation lines: this acts as an added driving force to its motion. At very low strains, reversibility is at a maximum. At intermediate strains, it is easy to go back the same way: reversibility acts as local negative strain hardening. At very large strain, the path traveled is long and reversibility becomes very low. This qualitatively explains why plastic localization occurs only in a limited range of strain amplitudes.

Note that this instability may be coupled to a type h instability, when there is a possibility of precipitate shearing: precipitate dissolution is enhanced by plasticity (Figure 2-19).

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Figure 2-19 Dissolution of Precipitates During Fatigue in a Structural Hardening Al Alloys

Example in nuclear materials: Atomic force microscopy was applied [17] to study the surface relief evolution at emerging persistent slip bands in 316L stainless steel cycled with constant plastic strain amplitude (Figure 2-20). The first persistent slip marks appeared after the initial hardening (0.1–0.25% of Nf). PSBs can be active for the whole fatigue life in grains where no cracks develop. The initial rapid growth of extrusions is followed by a period of stable linear growth up to the end of the fatigue life. The width of extrusions, corresponding to the thickness of the emerging PSBs quickly stabilizes and remains constant during the whole fatigue life.

Figure 2-20 AFM Micrographs of the Surface Relief within a Grain of 316L Steel Cycled at Constant Plastic Strain Amplitude (2×10–3) for Different Numbers of Cycles. The Scale is Identical on Both Micrographs

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2.3.5 Summary Tables

The following tables summarize the instability examples for nuclear components. Table 2-1 provides examples of relevant types of instabilities in nuclear components, their physical cause, and the governing parameters (microstructure, load…). Table 2-2 provides examples of instabilities for the main materials used in PWR and BWR: nickel-based alloys, stainless steels, and low-alloy steels.

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Table 2-1 Types of Instability in Nuclear Materials, with Examples

Type of Instability Physical Cause Governing Parameters Microstructure, Loading

Examples in Nuclear Materials

Type O: macrosopic heterogeneity

Heterogeneity at the mesoscopic or macroscopic level (Castings, weldings).

Scale and connectivity of the soft and hard zones, contrast between the zones. Direction of loading with respect to the heterogeneities.

• PWR primary coolant pipes: thermally aged cast stainless steels (hardened ferrite in austenite leading to mechanical embrittlement).

• Welds and heat affected zones.

• “Ghost lines”.

Type O: intragranular heterogeneity

Interaction of the GB with chemical species, vacancies (grain coated with a soft layer in which plastic deformation could localized).

Width of the PFZ and depleted zone, state of precipitation at the GB, direction of loading with respect to the grain morphological texture.

• Chemical heterogeneities due to grain boundary precipitation or segregation: Cr-carbides in Alloy 600 and sensitized stainless steels in BWR.

• Chemical heterogeneity due to in-service (irradiation or thermal aging) induced segregation at grain boundary (thermal aging of pressurizer leading to reversible temper embrittlement; irradiation of stainless steels internals).

Type O: GBS

Stress gradients, incompatibilities.

Grain size, misorientation of grain boundaries, state of precipitation at the grain boundary.

• Nickel-based alloy components in PWR primary circuit: influence of grain boundary sliding on Alloy 600 SCC.

Type h: Dislocation avalanches

Unpinning from obstacles or brutal multiplication of mobile dislocations.

Solid solution composition, prior static aging, state of recristallisation, temperature, strain rate.

• Corrosion fatigue of LAS components (static strain aging).

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Table 2-1 Types of Instability in Nuclear Materials, with Examples (Continued)

Type of Instability Physical Cause Governing Parameters Microstructure, Loading

Examples in Nuclear Materials

Type h: Obstacle destruction

Destruction of chemical order or localized obstacles by the motion of dislocations.

Strengthening effect of chemical order, density and size of precipitates, density and size of irradiation loops, wavelength of spinodal decomposition.

• Channeling in irradiated austenitic steels (internals, radial core support).

• Possible short and long range ordering in Alloy 690 (and stainless steels) in “hot” parts of components.

• Alloy 718, X750.

• Spinodal decomposition into ferrite phase of duplex stainless steels.

Type h: substructure instability

Destabilization of a well developed substructure by a strain path change.

State of organization of the substructure prior to the strain path change, severity of the change.

• Cold-worked stainless steels under complex mechanical loading.

Type S: PLC instability

Dynamic strain aging due to the interaction of dislocations with mobile solute atoms.

Solid solution composition, strain rate, strain and temperature.

• Alloy 718, X750 bolts.

• Low-alloy steels.

• Austenitic stainless steels and Ni-base alloys.

Type F: fatigue Local softening, partial plastic reversibility.

Strain amplitude, temperature, possible precipitation.

• Stainless steels fatigue.

• Fatigue corrosion of LAS.

• Fatigue of irradiated stainless steels.

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Table 2-2 Examples of Instabilities in Nuclear Materials, Classified by Type of Materials

Materials Range of Temperature (°C) Instabilities Condition for Instabilities Physical Cause Possible Solution to Avoid

Instabilities

Alloy 600 and 182

GBS,fatigue, heterogeneity of hardening, microstructure, PLC, SRO.

Range of T, loading, chemical ordering.

Microstructure evolution during heating cycle, DSA.

Grain boundary precipitates, surface treatment, post welding heat treatment.

Alloy 690 and 152

350 - 575 Obstacle destruction, PLC, LRO/SRO.

Range of T-ε , chemical ordering.

Disordering by dislocations, DSA.

Thermal treatment.

Alloy X-750

Obstacle destructionprecipitation, PLC.

Underaged precipitation state Precipitate shearing,DSA.

Overaging.

Alloy 718 PLC. Range in temperature and strain rate.

DSA. Change the solute content by heat treatment, T-ε out of the DSA range.

304(L) and 316(L)

250 - 650 PLC, obstacle destruction.

Critical dose, range of T-ε .

DSA assisted by pipe diffusion, channeling of irradiation defects.

Change the solute content by heat treatment, T-ε out of the DSA range.

LAS 200 - 350 PLC. ε < 10–2 s–1 DSA, material insufficiently killed (free N).

Change the solid content by heat treatment or by solute trapping elements.

Remark: all of the above materials are welded and therefore prone to resulting spatial heterogeneities in the microstructure which lead to a gradient in mechanical properties at the origin of the localization phenomenon.

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2.4 Modeling and Limitations

Many analytical and simulation modeling techniques have been developed over the years to analyze plastic localization phenomena. These various techniques are more or less capable of being adapted to each of the cases described earlier. In the following, an overview of the most suitable techniques is provided, together with a description of the relevant limitations.

2.4.1 Type O: Toward a Continuum Approach?

Behavior heterogeneity and grain boundary sliding must be distinguished. For heterogeneity of the local plastic behavior, two situations have to be considered. If these heterogeneities are at a macroscopic level, as for instance in castings and welds, then the obvious modeling tool is a standard finite element approach, based on continuum mechanics. The damage behavior associated with a non homogeneous plastic constitutive law can be described via a Gurson type of model.

If the heterogeneities are intergranular or close to the grain boundaries, as in precipitate free zones (PFZ), caution must be observed in using a continuum model: the scale of the heterogeneity is comparable to the scale of the microstructure and the details of the precipitates at the grain boundaries have to be taken into account (in a cell model for instance), as well as the plasticity contrast between the PFZ and the grain interior (Figure 2-21).

Figure 2-21 Model of the Plastic and Damage Behavior of a PFZ

An added complexity occurs when the morphological and crystallographic texture interfere, leading to damage anisotropy. The appropriate tools are then polycrystal plasticity and self-consistent models, coupled to a local approach for failure in the vicinity of the grain boundary (Figure 2-22).

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Figure 2-22 Modeling the Ductility Anisotropy in Textured Aluminum with a Grain Boundary PFZ

The case of grain boundary sliding (GBS) has been extensively studied in the literature and models to describe it in simple geometries are available. There is a considerable amount of confusion between GBS, diffusional flow, and dislocation accommodations, which are often presented as independent mechanisms. Coupling with the realistic geometry of grain boundaries still needs to be performed, but the basic tools to model GBS have been available since the work of Raj and Ashby [18, 19].

2.4.2 Type h: Use of Mesoscopic Dislocation Simulations

The occurrence of type h instabilities can be modeled with simple classical physical metallurgy models. The components of the model include an equation for the evolution of dislocation density, an associated work hardening law (usually the flow stress scaling with the square root of the dislocation density), and an equation for the evolution of the obstacle strength. These types of models have been applied to precipitate shearing, channeling in irradiated materials, etc. In order to predict the nature of localization (steady or propagative) and the width and velocity of the bands, recent work relies on mesoscale dislocation simulations. The principle of all simulations described below is first to compute the local stress on each dislocation segment using the applied stress and the interaction with other dislocations in the system. Under this local stress, a given dislocation will move at a given velocity. The simulations differ in the variety of local reactions allowed (multiplications, annihilation, junction formation), and in the degree of accuracy with which they are described. Concurrently, they also differ in the range of strains (or equivalent dislocation densities, or volume simulated) that can be processed with reasonable computing time. The most sophisticated ones are developed in 3D, but some refined 2D simulations may still be of interest for engineering purposes. This ambitious program has been developed over the years and finally led to the simulation of an emerging dislocation structure associated with a spatial patterning of the internal stress. It has been applied to the analysis of type h instability by introducing an evolution of the threshold stress in a plane according to the local plastic shear which has taken place in this plane (Figure 2-23).

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Figure 2-23 Strain Localization Diagram. ∆τ is the Amount of Softening, γ0 the Typical Strain for Full Softening, h the Hardening Coefficient. The Schematic Shows the Nature of Localization (Lüders Type or Random Nucleation of Bands)

The limitations are the plastic strain attainable within a reasonable computational time and the rather poorly defined cellular structure, which prevents testing of the scaling law for cell size as function of the flow stress (although the observed length scale is reasonable). The lessons to be learned from the 2D and the 3D simulations are that both long range stresses and short distance reactions are necessary to obtain patterning and that the short range reactions have to be described with sufficient accuracy as far as their spatial location is concerned. The fact that a source is unlikely to operate when dislocations in the surrounding zone are closely spaced has to be taken into account (for instance, distributing sources randomly cannot work). Revisiting 2D simulations, with the idea of incorporating information from the 3D simulations, in principle offers benefits from the rapidity of 2D calculations and the possibility to treat mechanical boundary conditions rigorously, together with the stated necessity to relate the local rules to the local environment. Improved 2D simulations are the obvious route to investigate the coupling between local strain softening, strain localization, and interaction with the grain boundaries, which is a crucial issue relevant to strain localization/environment interactions.

To date, the special case of strain localization associated with deformation path change has not received the attention it deserves from the viewpoint of modeling. Textural instabilities at large strains have been extensively studied, but the conditions both for the emergence of a dislocation substructure, and for its instability, are still unknown.

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2.4.3 Type S: Internal Variable Models, Statistical Approaches

The PLC phenomenon has been modeled using various strategies. The oldest technique is the use of internal variables (such as dislocation densities) whose evolution equations embody the dynamic strain aging phenomenon. This approach has been thoroughly explored, using rate equations for dislocation densities (mobile and stopped) and well established segregation kinetics for impurities at dislocations. The questions of which conditions lead to PLC in terms of strain rate, temperature and critical strain can be considered to be understood. The influence of precipitates concurrently with PLC instability has also been explored within the same framework. Similarly, a formal description of the range of negative strain rate sensitivity, together with spatial dependencies in gradients of stress or strain rate, have permitted a continuum description of the propagative plastic waves. Recent advances on this topic are related with non-periodic serrated flow, and with the associated spatial aspects of strain localization. Either a “spring-block” model, or techniques of deterministic chaos approaches, were used to investigate the detailed features of the spatial organization of plasticity and the statistics of serrated flow. These approaches have confirmed PLC as an example of self organized criticality (SOC) and as an example of deterministic chaos.

The “spring-block” models are able to describe not only the power law behavior of the stress drop distribution, but also the conditions under which it is observed (in terms of applied strain rate and test temperature). They also predict the type of spatial localization expected. The models are solved numerically and show the same types of behavior that are observed experimentally. When the strain rate increases, the stress-drop distribution changes from bell-shaped to continuously decreasing. The asymmetric distribution is, indeed, a power law and the exponent depends on the coupling constant between the blocks. The value of this coupling constant, which allows the retrieval of the correct exponent, is of the order of the elastic modulus and confirms the interpretation of coupling as resulting mainly from elastic incompatibilities. The plastic localization observed in the numerical simulation also evolves with an increase in applied strain rate from spatially uncorrelated (Type C), to spatially correlated, hopping or propagating (Types B and A). Figure 2-24 shows the prediction of the band velocity using a “spring-block” model. This quantity, together with the strain rate inside the band, governs the rate of blunting at a crack tip.

The second class of models are analyses of the set of coupled evolution equations for the internal variables (Ananthakrishna model) within the framework of deterministic chaos. The attractor, reconstructed from experimental data on Al-Mg polycrystals, and the prediction of the model proposed by Anathakrishna show striking similarities, indicating that the non-linearities of this set of equations are relevant to capturing the physics of the problem. The spatial features of the chaotic regime need further investigation to be fully understood, as do the mechanisms for the cross-over between chaos and SOC with increasing strain rate.

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Figure 2-24 Prediction of the Band Velocity Using a “Spring-Block Model”

2.4.4 Type F: Reaction Diffusion Approach

The modeling of plastic localization during fatigue is practically an unexplored field. A lot of work has been focused on analyzing the emergence of dislocation patterning within the “internal variable” framework, but a direct relation to macroscopic strain localization features (band width, band activity, band intensity) is still to be developed. The patterns observed in fatigue are very regular, much more so than the patterns obtained in monotonic plasticity. Since the discovery of the phenomenon of plastic localization in fatigue, the dislocation structures associated with intense localization have been extensively studied experimentally, both by conventional transmission electron microscopy (TEM) to characterize the structure, and by in-situ deformation to see their mode of operation. Since the motion of dislocations is responsible for pattern formation, the most relevant studies have been performed by applying a constant plastic strain amplitude to single crystals oriented for single slip. Below a threshold amplitude, the dislocation structure is formed of “veins”, rich in dislocations, separated by “channels” of equivalent volume fraction, low in dislocations. This is called the “matrix structure” and plastic deformation at the macroscopic level is homogeneous in space. When a threshold amplitude is reached, plastic deformation becomes strongly localized into the so called “persistent slip bands” (PSB), which exhibit a very regular “ladder structure”. This strikingly regular structure, as shown in Figure 2-25, has been thoroughly studied as one of the nicest and simplest example of dislocation patterning in plasticity. It is simpler than cellular patterns, since it is a structure built while single crystals are fatigued so that a single burgers vector is activated.

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Figure 2-25 The “Ladder Structure” in a Copper Single Crystal Having Undergone Single Slip Fatigue and its Schematics

This dislocation structure seems to be extremely efficient in carrying the important strains within the PSBs and it corresponds to a true steady state situation: in a constant, applied plastic strain amplitude test, it corresponds to saturation of the applied stress amplitude and to a steady state in the dislocation density. This implies that any creation of dislocation length has to be balanced by an equivalent annihilation process.

The overall functioning of the structure is now well understood. The walls in the ladder structure are of edge type and the dislocations moving in the channels are of screw type. The walls are formed by dislocation dipoles. Under the applied stress, the dipoles act as sources and emit dislocations into the channels. The screw dislocations moving in the channels leave new edge dislocations in the walls. The creation processes just described are counterbalanced by annihilation processes: dipoles in the walls can collapse by climb, annihilating edge dislocations, and two screw dislocations of opposite signs in the channels can annihilate by cross-slip. Annihilation by climb in the walls requires the emission of point defects, which are at the origin of the “swelling” of the PSB as a whole, creating extrusions and intrusions. The structure operating stress is governed by the stress necessary to emit a dislocation from the walls and to propagate it in the channel. Therefore, this structure operates at a stress amplitude which scales with the inverse spacing of the ladder rungs. In the domain of strain amplitude where the PSB are observed, the applied saturation stress amplitude is constant, and the volume fraction of PSB is proportional to the strain. This qualitative description of the functioning of the structure has been cast into a “chemical kinetics approach” for the density of dislocations in the walls and in the channels by Differt and Essmann.

If the functioning of the structure is well understood, its spontaneous emergence is still not clear. It has been studied in the framework of the “reaction diffusion approach” in a series of papers by Walgraef and Aifantis, which can be seen as the most developed example of this type of modeling in plasticity. Two dislocation populations, the fast ones and the slow ones, with two different “effective diffusion coefficients” (the slow dislocations diffusing less rapidly than the fast ones), are evolving in a coupled manner. In fact, the exact form of the reaction terms is more

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inspired by the so called “Brussellator” than by any precise dislocation mechanism. The control parameter in this model is the applied stress and a sequence of instabilities is predicted via a “Turing type” scenario: from a homogeneous distribution to a “rod like” distribution (identified as the so-called “vein structure”) to a “ladder like” distribution.

One of the features, specific to fatigue, is the existence of a large density of dipoles. These dipoles are naturally created by the back-and-forth motion of dislocations during fatigue loading. An attempt to propose a working mechanism to generate dipole clusters, as incipient features of pattern formation, has been proposed by Kratochvil. The basic idea is that a dipole drifts in a stress gradient generated by the moving screw dislocations. This drift tends to accumulate dipolar loops, which in turn enhance the bowing of the dislocations and cause further accumulation. This mechanism has been seen to operate in a 3D dislocation simulation, and a simulation of dipole clustering shows that it may be considered as a possible mechanism to generate structures. However, we are still far from the nice regular structures described for the PSB.

2.5 Consequences of Localization on Fracture Behavior

This section provides some examples of the consequences of strain localization on fracture. The first example is related to type O instability, the second to type S instability, and the third to type F instability. The goal of this section is not to provide an exhaustive list, but to provide examples of clear experimental evidence and of modeling attempts to explain these examples quantitatively.

2.5.1 Effect of Heterogeneities on Ductility

Many metallic alloys combine different phases or regions with different flow properties: duplex ferritic-austenitic steels and other multiphase steels, metal matrix composites, cast aluminum alloys made of solute rich α-Al dendrites within an eutectic matrix, Ni-based superalloys containing a γ-γ’ mixture, titanium dual-phase alloys. All types of welded joints present hardness gradients, pre-strained polycrystals present harder zones along the grain boundaries after some amount of loading (while the hardness was homogenous at the beginning), and age-hardenable aluminum alloys present softer precipitate free zones along grain boundaries.

Plastic localization will first occur in the softest phases or regions and leads, in some circumstances, to poor ductility of the composite material. One undesirable effect comes from the last example given in the previous list: aluminum alloys present zones around the grain boundaries that are weakened by a special state of intergranular precipitation, but remain strong enough so that failure in the vicinity of grain boundaries is still ductile. This situation, known as intergranular ductile failure, is well known in aerospace aluminum alloys, but is also observed each time a grain boundary is weakened by precipitates and is surrounded by a layer of soft ductile material (softer than the grain interior).

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The paradigm of this problem is given by the 7000 alloys (aeronautical aluminum alloys) in which an appropriate heat treatment leads to fine scale precipitates, which harden the material. Similar situations can be found in steels with structural hardening, but also in irradiated materials with a zone free from dislocation loops close to the boundaries. The yield stress first increases, then decreases with heat treatment duration. In parallel, the work-hardening rate decreases with precipitation. A slower quench rate favors coarse intragranular precipitates, which lower the toughness. The generic evolution of the critical energy release rate in a 7000 alloy, measured on a pre-cracked specimen (i.e. with relatively high triaxiality), is shown in Figure 2-26.

Figure 2-26 Critical Energy Release Rate

The possible ductile failure modes are intragranular or intergranular. The general trend for the dominance of one of the two failure modes is given in the previous figure. When such a situation occurs, the question arises as to the failure mode of the material. The key point in this problem is the persistence of the localization of plasticity around the grain boundary, depending on the mismatch of properties between the grain interior and the PFZ, and the intrinsic fracture resistance of the PFZ. The purpose of this section is to develop the relationships between the microstructure, the flow properties, the persistence of the localization, and the resulting fracture mode. A schematic of the microstructure is shown in Figure 2-27. The individual features controlling the fracture of aluminum alloys are well identified. The dispersoid particles used for avoiding recrystallization modify the grain structure and the plastic flow, and provide sites for ductile cavity growth. These microstructural features are essentially controlled by the chemical composition of the alloy and are unmodified by precipitation heat treatments. Therefore, the intragranular number and initial size of cavities has been considered constant. The influence of heat treatments on the grain interior behavior is lumped into an evolution of the yield stress and work-hardening behavior. The typical behavior of the grain interior after heat treatment is a high yield stress and a low work-hardening rate.

2-28


Figure 2-27 Schematic of the Microstructure Around Grain Boundaries with PFZ

Understanding the influence of PFZ characteristics on the failure mechanisms and rationalizing the complex interplay of microstructural features resulting from a change in process parameters requires a micromechanical model at the scale of the grain boundary structure.

The various length scales entering the problem (Figure 2-27-b) are the grain size d, the PFZ width h, the size and spacing of intergranular precipitates Dp and Lp (assumed to control the initial size and spacing of grain boundary nucleated cavities). In addition, the triaxiality ratio is known to be a central parameter for ductile fracture of macroscopically homogeneous materials and it will also be a key parameter in the present study. The uniaxial elastic and plastic tensile properties for the material in the grain interior and the PFZ interior are given by a simple, two-parameter description. The modulus E is the same for the PFZ and the grain interior. The values of the parameters σ0 (yield stress) and n (hardening exponent) are given with a subscript “g” or “p” for the grain interior and for the PFZ, respectively. The problem can be simplified further by assuming that the alloy is a multilayer material (such as a laminate), constituted of a stacking of soft and hard zones. The material response is thus completely modeled by the response of a bi-layer as the representative microstructural entity (Figure 2-27-c).

A quantitative analysis of this highly non-linear problem of plasticity and failure mode transition requires a detailed model for void growth and coalescence to be incorporated into each layer. Since the deformation process involves very significant changes of stress triaxiality, the void growth model should be able to encompass a large range in this parameter. It is well known that the stress state affects not only the growth rate of the voids, but also their shape (especially at low values of triaxiality).

The competition between intergranular and transgranular failure modes can be qualitatively understood in the following way (see Figure 2-28).

2-29


Figure 2-28 Competition Between the Different Failure Modes

The PFZ is soft and plasticity thus tends to localize along the grain boundary. The elastic grain imposes a strong constraint on the PFZ, involving large stress triaxiality. The large void growth rate in the PFZ leads to a rapid coalescence of the voids. However, in some circumstances, the stress in the grain, that keeps increasing with the overall deformation, reaches the yield stress before the onset of coalescence in the PFZ; then the stress triaxiality drops in the PFZ which, due to its higher hardening capacity, induces a slightly higher constraint within the grain. At this point, the plasticity stops being localized along the grain boundaries, which then act as a sort of hard shell around the grains. Voids then tend to grow more rapidly within the grain. Due to the low hardening capacity of the grain, a state of damage induced softening is rapidly attained until the voids finally coalesce within the grain. The transgranular failure mechanism is favored by a low global stress triaxiality, as it allows an increase of the stress in the grain without too much void growth within the PFZ. The influence of stress triaxiality on the failure mode can be experimentally probed either by using notched specimens, or by superimposing an external pressure during the tensile tests. For instance, transgranular fracture is favored by imposing a hydrostatic pressure to the exterior of the specimens. Transgranular failure is also favored by a low coverage of particles along grain boundaries (large L/D), because an increase in void spacing tends to delay the onset of coalescence.

Intergranular fracture is directly related to the persistence of plastic localization within the PFZ as the deformation proceeds. Other factors influencing the persistence of the localization along grain boundaries include the following. The larger the yield stress mismatch is, or the smaller the strain hardening mismatch between the grain interior and the PFZ is, the more prone the material is to intergranular fracture. Indeed, a low yield stress and a hardening exponent as low as possible for the PFZ prevent this zone from reaching the hardness of the grain interior, even at large strains. Another interesting prediction of the model is that the relative spacing

2-30


between the particles within the PFZ, i.e. the ratio of the particle spacing to the PFZ width λ, is an important factor regarding the persistence of the plastic localization, as it strongly affects the onset of void coalescence. It should be emphasized here that there is “localization cascade” with the coalescence process: the first plastic localization within the PFZ is followed by plastic localization between the voids growing in this zone.

Experimentally, the increase of the grain yield stress is accompanied by an increase in grain boundary failure and a decrease in fracture toughness. Studying the effect of the quenching rate leads one to conclude that here the intergranular failure mode increases with a decrease in quenching rate. Microstructural analyses have shown that decreasing the quench rate leads to larger grain boundary particles and thus to lower relative particle spacing Lp0/Dp0 values. These two effects can be understood in terms of a σ0g/σ0p versus Lp0/Dp0 map as proposed in Figure 2-29.

Figure 2-29 Fracture Map

Such a locus can be obtained when running the model with a large stress triaxiality typical of the fracture process zone (i.e., a triaxiality of about 3). This map shows the locus for failure mode transition and gives a qualitative picture of the combined effect of the quench rate and the aging time on the fracture toughness through the persistence of the plastic localization along grain boundaries.

In the same family of alloys, it is observed that the ductility is anisotropic (Figure 2-30). This is mainly a consequence of the morphological textures which result from rolling. Coupling a local criteria for grain boundary failure in shear with a polycrystalline plasticity approach of the self-consistent type allows the ductility anisotropy to be predicted.

The strain localization effect is present in this type of model, but “hidden” in the local criteria for failure of the grain boundary. The detailed micromechanical approach presented here explicitly encompasses microstructural features in the definition of the local criteria.

2-31


Figure 2-30 Ductility Anisotropy Resulting from Textured Materials with Weak Boundaries

2.5.2 Effect of Strain Localization on Toughness

When negative strain rate sensitivity is observed, plastic flow is localized into propagative bands, and the stress stain curve exhibits serrated flow. The occurrence of localized plastic flow in a tensile sample also coincides with appearing of plastic waves ahead of cracks in a notched sample. Each plastic wave carries some dissipation process, but also is responsible for blunting at the crack tip. With homogeneous flow, in contrast, the existence of traveling waves makes both blunting and dissipation localized in time. A simple way of describing the effect is to consider that the local stress concentration factor is the nominal one (imposed by the geometry of the sample and the notch) corrected by this blunting effect. While the experimentalist tries to develop macroscopically a stress concentration K, the effective stress concentration is reduced due to blunting. Unstable crack propagation will occur when the effective local stress intensity factor Keff reaches a critical value Kc. At this point, the macroscopically applied concentration faction has a value which is the toughness of the material. The more the crack is blunted, the larger is the discrepancy between the nominal stress intensity factor and the local one: this is a very simple way of describing the increase of toughness associated with easier plastic flow. Of course, this qualitative description is valid for “quasi brittle materials” for which the blunting effect dominates over the extra dissipation effect introduced by plastic flow. When plastic flow is localized into bands of width w and spacing L traveling at a velocity V, the blunting takes place only when the band is traveling across the crack tip, which will last a time w/V.

2-32


When loaded at constant .K , the increase in applied toughness during this time is:

VwK /.

Equation 2-3

The plastic strain introduced during this time will be proportional to where the strain rate is the one carried by the deforming band only. From these considerations, we can deduce that each band traveling ahead of the crack tip will lead to a drop in local stress concentration

factor proportional to . This quantity, which is characteristic of the features of localized plastic flow, can be measured experimentally on tensile specimens tested with a double extensometer (one for the macroscopically applied strain rate and one for a local measurement): when the band enters the local gage and travels through it, the characteristics of the plastic wave can be measured. This approach is able to rationalize the drop in toughness observed for overaged 2091 Al Li Cu Mg alloys (by a factor 2) but could also be applied to any materials showing dynamic strain aging and PLC, such as low-alloy steels. For relevant heat treatments, the yield stress changes by less than 10% and ductility or work-hardening behavior are basically unchanged: the main modifications are to the strain rate sensitivity (negative since the material is loaded in the regime where PLC bands are generated) and also the localization characteristics of the PLC bands. With increasing aging time, their velocity is increased and the local strain rate is decreased, so that the blunting effect is less efficient for alloys which have been overaged. This example shows a direct macroscopic consequence (on toughness) of the features of strain localization.

Vwb /.

ε

22.

/. Vwbε

2.5.3 Effect of Damage Percolation on Fatigue Life

The persistent slip bands (PSB) characteristic of fatigue localization have a crucial importance on fatigue life. Damage in these situations appears in the form of multiple cracks located at the surface, often at the intersection of the PSB and the surface, either within grains or at grain boundaries. In the low-cycle fatigue (LCF) regime, these cracks appear after 10% of the fatigue life, whereas in the high-cycle (HCF) regime, more than 60% of the fatigue life is necessary for nucleation. In addition, the surface density of cracks in the LCF regime is one or two orders of magnitude larger than in HCF. Because of this fact, it seems reasonable to deal with damage accumulation in the LCF regime through a statistical analysis of microcrack population. The specific role of PSB in crack nucleation is probably related to the incompatibilities emerging from the forced coexistence of a highly deformed material (as in PSBs) and a non-deformed one (matrix). An interesting feature of this self organized structure is that the PSB spacing is related to the inverse of the plastic strain amplitude (1/∆εp). At the macroscopic level and in low cycle fatigue, the number of cycles to fracture is related to the plastic strain amplitude by the Manson Coffin law:

NR(∆εp)b = K Equation 2-4

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Although the constant K depends strongly on the material, the exponent b for single phase materials is, surprisingly, always close to 2. This is to be contrasted with the other power law used in fatigue, in the high cycle regime, for which the exponent is very material dependent. We are facing two universal behaviors: the patterns of plastic localization and the life-time dependency with applied plastic strain. The relation between these two features can be sorted out as follows. The length of an elementary crack is the grain size of the material. Such elementary cracks accumulate at the surface, progressively connecting with each others through a kind of percolation process, until somewhere a critical length is reached which leads to crack propagation in the volume and final fracture. Since the specific characteristics of PSB lead to short-range stress fields, it is reasonable to assume that damage nucleation is uncorrelated from one grain to another. It is expected that the number of elementary cracks scales linearly with the number of cycles. This has been shown via cautious quantitative metallography in a 316L alloy.

Since crack nucleation occurs at PSBs, the number of sites for crack nucleation is proportional to ∆εp and one expects that the number of microcracks after N cycles should scale as N.∆εp. Connection between two cracks in neighboring grains occurs when the PSBs on which they have been nucleated have some kind of overlap at the boundary level. Since the width of the PSB is independent of ∆εp and their spacing scales as 1/∆εp, the number of microcracks likely to be connected after N cycles scales is N.(∆εp)

2. If φ is the grain diameter, and p the probability to have an elementary crack connected to a crack in the neighboring grain, then the probability to have a macrocrack of length L (i.e. formed from L/φ connected microcracks) for a sample surface S, is given by:

2/

φφ SpP L

L = Equation 2-5

The length of the largest crack Lmax is obtained when this probablity reaches 1. Final fracture occurs when Lmax reaches a critical value, which means that pL reaches a critical value. As a consequence, the number of cycles to fracture NR is expected to scale as 1/(∆εp)

2, which is precisely the Manson Coffin law. The universality of the Manson Coffin law in polycrystalline single-phase materials can be interpreted as a consequence of the scaling behavior of the PSB spacing with the applied plastic strain amplitude, and of the necessity to connect microcracks together to reach a critical macrocrack length.

2.6 Conclusions

This chapter was a review of strain localization physics in metals. The authors have attempted to relate this to nuclear structural materials as much as possible, in order to argue that deformation modeling should help the understanding and predictability of EAC.

Strain localization can result from non-homogeneous loading, or from a non-homogeneous response of the material (Figure 2-31). This section was focused on the non-homogeneous response of the material due to material heterogeneities and plastic flow instabilities. The intensity of strain localization, its length scale, and its evolution in space and time appear to be essential characteristics of this strain localization.

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Non homogeneous loading (crack, notch…)

Non homogeneous response (heterogeneous material, plastic

instabilities…)

Strain localization

• Intensity

• Characteristic Length scale

• Stationary / propagative

• Transient regime / persistent

Figure 2-31 Origin and Characterization of Strain Localization

Plastic flow instabilities leading to strain localization have been identified in nuclear materials such as austenitic stainless steels, nickel base alloys, and low-alloyed steels (Table 2-1). Heterogeneities due to welding, precipitation, irradiation, or grain boundary sliding are the main physical causes for strain localization. Furthermore, they are characterized on the macroscopic length scale with respect to the following issues. Strain softening is directly correlated to the interactions of mobile dislocations with obstacles resulting from the chemical composition (solute atoms), the microstructure (short range ordering), or previous well developed substructures of dislocations (due to cold-work). Strain rate softening is mainly due to dynamic strain aging. Dynamic interactions between solute atoms and mobile dislocations can be suspected in austenitic steels and LAS under specific loading conditions. The consequences of such instability at the surface of materials, or at a crack tip, could be an important issue in the presence of an aggressive environment. For the same reasons, the partial plastic reversibility of materials under cyclic loading needs to be considered with respect to the environment. Strain softening and strain rate softening operate at the intragranular scale. Their manifestations in the nuclear industry are not necessarily obvious. Table 2-3 summarizes the different types of plastic flow instabilities presented in this section, as well as the physical causes, governing parameters, modeling tools, and critical experience.

Plastic localization, beside its consequence on the overall mechanical behavior of materials (and especially on damage processes), is expected to have a profound influence on corrosion behavior. Indeed, these localizations trigger the development of surface roughness, which is likely to interact with protective oxide or passive layers, and possibly damage them, thus reducing their protective character. This is even more important at crack tips, where the strain is already naturally localized.

The localization of plastic deformation has two main consequences: on the one hand, the plastic incompatibilities between the deforming and non deforming zones might be responsible for stress concentrations; on the other hand, the more intense local plastic deformation can lead to accelerated cracking because of local plasticity damaging the passive film layers, and consequently promoting hydrogen ingress into the material. In conclusion, situations where the deformation is heterogeneous generally correspond to premature failure of materials.

2-35


For additional information, the reader is encouraged to consult the following, further references:

• [20, 21], for a review of the various types of instabilities;

• [22], for a review of fatigue localization;

• [23], for a review of PLC instabilities;

• [24], for a review of instabilities related to fracture.

2-36


Table 2-3 Plastic Instabilities, Physical Causes, Governing Parameters, Modeling Tools and Critical Experiences

Type of Instability

Physical Cause Governing Parameters Microstructure, Loading

Critical Experience Modeling Tools

Type O: macrosopic heterogeneity

Heterogeneity at the mesoscopic or macroscopic level (casting, welding)

Scale and connectivity of soft and hard zones, differences of behavior between the different zones, direction of loading with respect to heterogeneities

- Continuum mechanics using FEM.

- Non homogeneous plastic constitutive law (Gurson type)

Type O: intragranular heterogeneity

Interaction of the GB with chemical species and vacancies

Width of the PFZ, GB precipitation, direction of loading with respect to the grain morphological texture, width of the PFZ and depleted zone

- PFZ: by thermal treatments, their geometrical features can be modified in a controlled manner

- Damage accumulated in the area near the GB

- Continuum model used with caution (plastic contrast between PFZ and grain interior, precipitates at GB to be taken into account)

- Polycristal plasticity and self consistent models coupled to a local approach for failure in GB vicinity

Type O: GBS

Stress gradients, incompatibilities

Grain size, precipitation at the GB

GBS observed and quantified on wires with a Bamboo structure loaded in shear

Raj and Ashby models

Type h: Dislocation avalanches

Unpinning from obstacles or brutal multiplication of mobile dislocations

Solid solution composition, prior static aging, recristallisation, T, ε

Type h Obstacle destruction

Destruction of chemical order or localized obstacles by the motion of dislocations

Strengthening effect (LRO, SRO), density and size of precipitates and irradiation loops

Type h: substructure instability

Destabilization of a well developed substructure by a change path

State of organization of the substructure prior to the strain path, severity of the change

- Yield point and plateau in the stress strain curve

- Lüders Bands and pseudo-Lüders

- Localization at the grain level

- Localized bands either propagating or localized at fixed positions

- Both transient and persistent effects

- Classical models of physical metallurgy (evolution of dislocation density associated with work-hardening law)

- Advanced models, using mesoscale dislocation simulations (DDD): computing on each dislocation segment the local stress coming from the applied stress and from the interaction with other dislocations

2-37


Table 2-3 Plastic Instabilities, Physical Causes, Governing Parameters, Modeling Tools and Critical Experiences (Continued)

Type of Instability

Physical Cause Governing Parameters Microstructure, Loading

Critical Experience Modeling Tools

Type S: PLC instability

DSA due to the interaction of dislocations with mobile solute atoms

Solid solution composition, T, ε , ε

- T and ε dependence

- Spatial (propagating bands) and temporal (serrated flow) signature

- PLC bands at the scale of many grains

- Classical use of internal variable models (dislocation densities)

- Statistical approaches as “spring block model” (technique of deterministic chaos as Ananthakrishna model…)

Type F: fatigue

Local softening partial plastic reversibility

Strain amplitude, T, precipitation

Control of the volume fraction of PSB via the plastic strain amplitude, and width of PSB controlled by changing the loading temperature

Reaction diffusion approach to simulate PSB (Walgraef and Aifantis)

2-38

3 ENVIRONMENTALLY ASSISTED CRACKING

3.1 Introduction

Environmentally Assisted Cracking (EAC) is the key aging degradation mechanism for a number of major components in nuclear reactors. In this section, some examples of EAC/strain localization interactions are presented for Ni-based alloys, austenitic stainless steels, and low-alloy steels exposed to LWR environments. The section starts with a brief presentation of the materials, the environments, and types of EAC. After this introduction, the phenomenology of EAC, the evidence for EAC/strain localization interactions, and the main EAC issues are described for several material/environment combinations.

3.1.1 Materials

A large variety of structural materials potentially affected by EAC are used in the components of LWR (Table 3-1).

Table 3-1 Materials and their Locations in Nuclear Power Plants

Reactor Component Carbon/Low -Alloy Steel

Stainless Steel Cast Stainless Steel

Nickel-Based Alloys

Reactor pressure vessel

Pressurizer

Steam generator shell & internals

Reactor internals

Piping

PWR

Steam generator tubes

Pressure vessel

Reactor internals BWR

Piping

Presence of the material somewhere in the component. Absence of the material in the component.

3-1

Environmentally Assisted Cracking

3.1.1.1 Nickel-Based Alloys

Alloy 600 (15% chromium) is still( )9 present in many nuclear plant components: steam generator (SG) tubes, vessel head and bottom nozzles, pressurizer taps, SG partition plates, radial core supports in PWR, and in reactor internals and piping in BWR. This austenitic alloy shows a variable resistance to stress corrosion cracking in the primary medium, depending in part on its microstructure, which is characterized primarily by the location of the carbide precipitates. These differences in microstructure result mainly from differences in thermo-mechanical treatments during the component manufacturing process. The parameters determining the microstructure are the carbon content, the heating temperature before hot working, and the temperature of the final heat treatment, which depends on the yield stress of the raw material after hot working. A structure with continuous or semi-continuous intergranular carbides is beneficial for resistance to stress corrosion cracking. The corresponding weld metals are Alloys 82 (wire or strip/flux, TIG wire, 18-22% chromium) and 182 (coated manual electrode, 15-16% Cr). Alloy 82 is used, e.g., in repairs, for SG tube sheet coating, and welding SG tubes to the tube sheet.

Alloy 690 (30% chromium) is being used for the development of a new generation of units and is the replacement material for most of the previous Alloy 600 parts (vessel top and bottom head penetrations, SG partition plates, etc.). Its excellent resistance to stress corrosion cracking in the primary medium is due to the increased chromium content and has been demonstrated for various products (especially SG tubes). The manufacturing procedures for Alloy 690 are based on those of Alloy 600, with a few adaptations (in particular, a higher final heat treatment temperature), even when using a different hot process. An order-disorder transformation can occur in Alloy 690 [25]. The matrix phase in these materials could induce a short-range ordering (SRO) structure, which could transform into a long-range ordered (LRO) structure when exposed to neutron irradiation( )10 , or for long durations at temperature below 575°C (the actual critical temperature depends on the composition). The SRO can transform into a LRO by nucleation and growth. The microstructure in this condition consists of a dispersion of highly ordered particles in a disordered matrix. The degree of LRO depends on Cr content, the LRO kinetics depends on the Ni/Cr ratio and the Fe content [26]. Commercial products with Fe above 8% do not seem to be sensitive to LRO [27]. The weld metals corresponding to Alloy 690 are Alloys 52 (wire/flux, 30% Cr) and 152 (coated manual electrode, 30% Cr).

Nickel-based Alloy X-750 (14-17% chromium) is a precipitation hardening, austenitic nickel-chromium-iron alloy. In nuclear power plants, it is used where high general corrosion resistance (similar to that of Alloy 600) is required combined with higher strength and greater fatigue resistance. It has been widely used in core internals applications, such as for fuel assembly hold-down springs, control rod guide tubes, support pins, etc. Alloy X-750 is supplied in a variety of heat treatments or thermo-mechanical processing conditions, which result in very different strength and SCC resistance properties. For PWR applications, after solution annealing (880 to 1100°C), the material is age-hardened at a lower temperature (≈ 700°C) to produce second phase γ’ precipitation and carbides, which increase strength.

( )9 It is increasingly being replaced by Alloy 690 or stainless steel.

( )10 Alloy 690 can be exposed to neutron irradiation in High Flux Reactors.

3-2


Alloy 718 (17-21% chromium) is present in highly stressed components in PWR primary water. Alloy 718 offers high strength, resistance to stress relaxation and good resistance to initiation of SCC in the temperature range of LWR. In PWR, Alloy 718 is used for fuel assembly hold-down springs and fuel grid springs ( )11 . In BWR, Alloy 718 is mainly used for jet-pump components and high strength bolts. Alloy 718 is a nickel-based superalloy, which derives its strength from precipitation of the γ’’ phase Ni3Nb (DO22 structure). γ’’ precipitates are disc shaped (tens of µm in diameter), and their volume fraction can be tens of %. Grain boundaries can be decorated by a continuous film of δ phase, but needle-shaped δ phase can also precipitate locally, growing into the grain or at grain boundaries. It seems impossible to prevent delta-phase formation.

3.1.1.2 Austenitic Stainless Steels

Primary 300-series stainless steels are iron-based alloys containing at least 12% Cr. They achieve their stainless characteristics through the natural formation of a very thin and adherent chromium-rich oxide surface layer (passive film) for temperatures below 100°C ( )12 . Stainless steels are commonly divided into five groups: martensitic stainless steels, ferritic stainless steels, austenitic stainless steels, duplex (ferritic-austenitic) stainless steels, and precipitation-hardened stainless steels. AISI 304 has the base chemical composition for austenitic stainless steels, containing less than 0.07% of carbon. AISI 304L requires a very low carbon content (below 0.03%). To improve corrosion resistance, AISI 316(L) stainless steel has a Mo content in the range 2-3%. AISI 321 (Ti-stabilized) and 347 (Nb- (Ta-) stabilized) are sometimes used because of their greater resistance to thermal sensitization (e.g., during welding). Si content is increased up to 2% to improve hot cracking resistance in AISI 302. Finally, both hot cracking and creep resistance are improved by increasing the Cr and Ni content in AISI 309 and 310. Stainless steels are available in the form of plate, sheet, strip, foil, bar, wire, semi-finished products, pipes and tubing. Stainless steel castings are usually classified as either corrosion-resistant or heat-resistant castings, with the usual distinction here being based on the carbon content.

Some elements extend the γ-loop in the iron-carbon equilibrium diagram, e.g. nickel and manganese. When sufficient alloying element is added, it is possible to preserve the face-centered cubic austenite at room temperature, either in a stable or meta-stable condition. The presence of chromium greatly improves formation of a thin, stable, oxide film on the surface, so stainless steels are now widely used materials in a range of corrosive environments (both at room and elevated temperatures), as in coolant systems, safety and auxiliary systems for piping, internals, pressure vessel cladding, and various components of LWR.

Cast duplex stainless steels are used for applications like large diameter, primary coolant piping, cast pump casings, fittings, and cast valve bodies.

( )11 About 40 million fuel grid springs are currently in service in any one year, e.g., for Framatome fuel elements.

( )12 Above ~150°C, the oxide films are thicker and less protective (much higher passive current density in pure water).

3-3


3.1.1.3 Low-Alloy Steels

Low-alloy steels (LAS) are defined as those steels that:

• contain manganese, silicon or copper in quantities greater than the maximum limits (1.65% Mn, 0.60% Si, and 0.60% Cu) for carbon steel; or

• that have specified ranges or minima for one or more other alloying additions.

Thus LAS are those steels containing alloying elements, including carbon, up to a total alloy content of about 8%. LAS with suitable compositions have greater hardening capability than structural carbon steels and can thus provide high strength and good toughness in thicker sections by heat treatment. Their alloy contents may also provide improved heat and corrosion resistance.

LAS are widely used in reactor vessels, pressurizers, SGs and reactor coolant system piping of nuclear power plants because of their low cost, good mechanical properties, good weldability, and acceptable resistance to corrosion in high-temperature water/steam environments. In many applications, LAS are clad with more corrosion-resistant, austenitic steels.

Table 3-2 and Table 3-3 summarize the main characteristics of the alloys presented in this section.

Table 3-2 Chemical Composition of Materials

Type Material Fe Ni Cr C Mo Mn Si

600 6-10 > 72 14-17 < 0.05 < 0.5 < 0.5

690 7-11 > 58 27-31 < 0.05 < 0.5 < 0.5

X-750 5-9 > 70 14-17 < 0.08 < 0.5 < 0.5

718 Bal. 50-55 17-21 < 0.08 < 0.35 < 0.35

Wrought Ni-based

alloys

800 Bal. 30-35 19-23 < 0.10 < 1.5 < 1

304L Bal. 8-12 18-20 < 0.03 < 2 < 1 Austenitic stainless

steels 316L Bal. 10-14 16-18 < 0.03 2-3 < 2 < 1

3-4


Table 3-3 Material Properties at 20°C for Materials Susceptible to EAC in Nuclear Power Plants

Materials E (GPa)

Sy (MPa)

UTS (MPa)

El. (%) n Tl (°C) Precipitation

Alloy 600 219 200-450 550 30 0.74 if TT 1354-1413

M7C3

M23C6

(inter and intra)Ni2Cr (aging)

Alloy 690 219 240-400 550 30 0.59 if TT 1340-1375

M23C6

TiC (inter and intra)

Ni2Cr (aging)

Alloy 718 200 1030-1380 1240-1480 6-20 1260-1330 Ni3Nb (δ, γ″) Ni3(Al,Ti) (γ’)

C(Ti,Nb)

Alloy X-750 200 600-1200 1000-1400 16-30 0.34 1400-1425

Ni3(Al,Ti) γ’) M7C3

M23C6

M5B3

304L-316L 195 175-200 480-500 45 0.4-0.5 1400-1450 No precipitation when annealed

LAS 210 278-400 480-544 20-35 0.10-0.30 1300-1400 MnS

TT = thermal treatment, n = strain hardening coefficient, Tl = temperature of the liquidus.

3.1.2 Environments

Only LWR primary environments ( )13 are considered in the present section. The main differences between BWR and PWR reactor coolant are:

• the temperature (~288°C for BWR and typically ~325°C for PWR ( )14 )

• coolant additives (shifting the pHT from 5.6 for pure water in BWR to ~7.2 for PWR)

• hydrogen content (~50 ppb for BWR on hydrogen water chemistry (HWC) ( )15 as opposed to ~3000 ppb for PWR).

( ) 13 Secondary side chemistries are important from the steam generator point of view. Nevertheless, because of

the apparent unbalance with regard to correlations between strain localization and EAC in PWR primary and secondary coolant systems, only the former are considered in this report.

( ) 14 340°C in the pressurizer; as low as 290°C in the “cold leg”.

( ) 15 Only trace amounts (from radiolysis) in BWR on “oxygenated” normal water chemistry (NWC).

3-5


3.1.2.1 The PWR Primary Environment (Primary Water)

Pressurized Water Reactors were originally designed by Westinghouse Bettis Atomic Power Laboratory for navy applications, then by the Westinghouse Nuclear Power Division for commercial applications. The first commercial PWR plant in the United States was Shippingport. In addition to Westinghouse, Asea Brown Boveri-Combustion Engineering (ABB-CE), Framatome, Siemens, and Mitsubishi have typically built this type of reactor throughout the world. Babcock & Wilcox (B&W) built PWR power plants using vertical once-through SGs, rather than the U-tube recirculation design used by the rest of the suppliers. The PWR has three separate cooling systems, but only the primary reactor coolant system is expected to have radioactivity.

The reactor coolant system consists of 2, 3, or 4 cooling loops connected to the reactor, each containing a reactor coolant pump and a steam generator. The reactor heats the water that passes upward past the fuel assemblies from a temperature of about 286°C to a temperature of about 325-330°C. Apart from nucleate boiling, leading to minor bubbles on some highly rated fuel rods, boiling is suppressed. Pressure is maintained by a pressurizer (345°C), connected to the reactor coolant system, at approximately 155 bar (through a heater and spray system in the pressurizer). The water from the reactor is pumped to the steam generator and passes through tubes before being returned to the reactor pressure vessel.

The chemistry of the reactor coolant system is composed of:

• Pure water: demineralized water with a conductivity below 0.2 µS cm–1 at 25°C.

• Boric acid: the isotope of boron is a neutron poison. Boric acid is a weak acid at 25°C (pH25°C = 4 for concentrated solutions) and a very weak and stable acid at higher temperatures. After refueling, its concentration is close to 1200 ppm. Lithium hydroxide is introduced to maintain the pHT slightly alkaline (pH300°C ~7.2, pHneutrality = 5.6 at 300°C) in order to limit generalized corrosion and thus to control the activity level in the primary circuit. LiOH is stable and has a limited ability to concentrate where nucleate boiling occurs (on some fuel rods and in the pressurizer). LiOH concentration is adjusted to the boric acid concentration (typically 2.2 ppm at the beginning of a cycle with 1200 ppm of B).

• Hydrogen: introduced to limit the water radiolysis. Hydrogen concentration is maintained between 25 and 50 ml kg–1.

• Impurities: the maximum concentration of impurities is defined so as to limit stress corrosion cracking (oxygen < 100 ppb, chlorides, sulfates and fluorides < 150 ppb), or the formation of insoluble deposits on the cladding (leading to hot spots). Silica is currently acceptable up to 1 ppm, but there are moves to raise this limit to 3 ppm.

3.1.2.2 BWR Environment

Boiling Water Reactors (BWR) represent 30% of the nuclear power plants in the world and were originally designed by both Allis-Chambers and General Electric (GE), but nowadays all Allis-Chambers units are shut down. The first GE U.S. commercial plant was Humboldt Bay (California). Other suppliers of the BWR design world-wide include ASEA-Atom, Kraftwerk Union, Hitachi, and Toshiba. Commercial BWR reactors are found in USA, Finland, Germany, India, Japan, Mexico, Netherlands, Spain, Sweden, Switzerland, and Taiwan.

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Water circulates through the reactor core, picking up heat as the water moves past the fuel assemblies. The water eventually is heated enough to convert it into steam. Steam separators and dryers in the upper part of the reactor remove water and moisture from the steam. The steam then passes through the main steam lines to the turbine-generators. The steam typically goes first to a smaller high pressure turbine, then passes through moisture separators, then to the 2 or 3 larger low pressure turbines. It then condenses in the condenser, which is depressurized and cooled by various means (sea, lake, or river water). Then, the condensed steam is pumped to low pressure feedwater heaters, passing to the feedwater pumps, which, in turn, pump the water to the reactor and start the cycle all over again. A basic advantage of the BWR concept is that power level can be controlled simply by the cooling water flow rate.

In the most common condition, the recirculation system water contains ~200 ppb of oxygen. With Normal Water Chemistry (NWC), oxygen levels vary between ~30 ppb in BWR feedwater up to ~20 ppm in the steam condensate and the metal is protected by a duplex oxide layer (magnetite/hematite). Passivation of stainless steels and Ni-based alloys and protection of LAS by formation of magnetite can still occur, however, at very low oxygen levels (e.g., as found in various areas of the system when using Hydrogen Water Chemistry (HWC)). No soluble neutron absorber can be used in BWR, because of the boiling water and fixed gadolinium is therefore used. In the control rods, the primary absorber is B as B4C. The temperatures at the entrance and the exit of the core are 274°C and 288°C, respectively, with the pressure being 71 bar. Due to radiolysis, stable oxidant species are produced (NO2

–, NO3

–), accompanying OH– and H2O2 into the steam.

With HWC, hydrogen is introduced into the feedwater (typically 450-1350 ppb, with lower levels being used in conjunction with catalysis by noble metals) to avoid intergranular corrosion and converts oxidant species (NO2

–, NO3

–) into N2 and NH3. At high H2 addition rates, when N16 becomes volatile, turbine radiation levels rise (turbine shine).

For either chemistry, the extent to which BWR water is oxidising depends in a complex way on location within the reactor circuit and is influenced, e.g., by the radiolytic formation of H2O2.

3.1.3 Investigation of Environmentally Assisted Cracking

3.1.3.1 Definitions

In the current report, environmentally assisted cracking (EAC) refers to environmentally assisted rupture (EAR) and mechanically assisted corrosion (MAC).

Environmentally assisted rupture is a step by step rupture resulting from localized interactions between the environment (oxidation, ingress of dissolved hydrogen) and the mechanical loading, and occurs via transport mechanisms (of hydrogen, vacancies, oxygen…). Examples of such mechanisms are the internal oxidation model for Alloy 600 in PWR or the corrosion enhanced plasticity model for austenitic stainless steels in boiling MgCl2 media.

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On the other hand, mechanically assisted corrosion (MAC) refers to the localized dissolution of metal that is bare due to plastic glide. The slip dissolution model for austenitic stainless steels exposed to BWR environments is a good example of MAC.

EAC includes an incubation period, a true initiation phase (formation of a chemical or mechanical or metallurgical defect), an initiation period including previous periods (slow propagation of a short chemical or mechanical or metallurgical undetectable defect) and a rapid propagation period of a detectable chemical and mechanical and metallurgical crack. In the laboratory, the propagation period includes slow, then eventually rapid propagation. In industry, the initiation is taken to include both the incubation phase and the entire slow propagation period.

3.1.3.2 Experimental Tests

Mechanical loading plays an important role in stress corrosion cracking tests and is classified in three categories: constant displacement, constant load, and constant extension rate.

The least severe test is the constant displacement test (CDT). It permits stress relaxation during an eventual crack propagation and, consequently, crack arrest. The interpretation of the test is supported by anisothermal relaxation tests. The main disadvantage of this technique is the possible very long duration of the test and the stress relaxation.

Constant extension rate tests (CERT) are extremely severe because both stress and strain hardening increase continuously during the test. These tests do not allow evaluation of the incubation time for initiation of EAC, but are relevant when the EAC mechanism is strongly dependent on the crack tip strain rate. During the test, dislocations are continuously created and emitted at the crack tip(s).

Constant load tests (CLT) are usually long, but they are relevant for crack growth rate evaluations, because stress increases over a short range during the test (no relaxation). The use of notched or pre-cracked specimens permit control of the stress concentration and partial, periodic unloading can be applied in order to destabilize the oxide at the crack-tip or to promote strain activity. CLT can be used to evaluate initiation times. Usually, stress threshold or stress concentration thresholds (above which no initiation or propagation are observed) are sought. Crack growth rates, with or without partial, periodic unloading, can be derived from CLT.

Each kind of test provides specific information with respect to the main stages of cracking. CDT on U-bend and reverse U-bend specimens are dedicated to initiation studies, as are CLT on tensile specimens. CDT and CLT on pre-cracked specimens (CT, WOL) are dedicated to (rapid) propagation studies. Finally, CERT on tensile specimens allow investigation of both true initiation and slow propagation periods.

3.2 SCC of Nickel-Based Alloys in the PWR Primary Environment

The cracking of components (SG tubes and plugs, pressurizer nozzles, vessel head penetrations, and more recently bottom vessel penetrations) made of Alloy 600 in contact with the primary

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environment is a generic phenomenon that now affects practically all PWR. Considerable knowledge has been acquired concerning the behavior of this alloy with regard to SCC in water at high temperature at EDF, CEA, EPRI, Framatome-ANP, Westinghouse, B&W, and in various laboratories (Universities, American National Laboratories), and by plant operators abroad.

The recent field experience is related to the base metal and to weld metal with no stress relief ( )16 .

All the available results seem to indicate that the materials resisting SCC in water have to have a chromium content higher than 25%. For very severe tests (CERT) on alloys containing intragranular carbides, sensitivity can be detected even for 30% chromium. Nevertheless, for an identical microstructure (grain boundary, precipitation), an increased chromium content reduces the risk of SCC.

The influence of carbon on SCC is mainly related to carbide precipitation. However, a significant effect of interstitial free carbon can also be its consequences for creep properties and plastic flow instabilities (DSA). The influence of other elements in the alloy (boron, sulphur, niobium) is less significant. Niobium probably has more influence than most other elements on the interdendritic deformation between dendrite domains (grain boundaries) in weld metals.

3.2.1 IGSCC in Wrought Alloy 600

3.2.1.1 Phenomenology

Figure 3-1 shows the successive stages of the EAC mechanism. The stress corrosion cracks in Alloy 600 appear after an incubation phase. Its duration can vary from a hundred hours to several thousands of hours, depending on the sensitivity of the material to stress corrosion cracking [28].

After an incubation period, the true initiation of stress corrosion cracks begins when the electrochemical conditions are locally favorable, or when oxides have been significantly developed at critical grain boundaries. In the case of internal oxidation of Alloy 600 in the PWR primary environment, true initiation corresponds to the development of oxidized grain boundaries before the formation of the first microcrack. The cracks are detected when their size exceeds the detection limit of the employed experimental technique.

The initiated cracks then propagate in a slow regime. In the laboratory, the slow propagation period can vary from a few hundred hours to a few thousand hours, depending on the applied load. The propagation rate of the largest cracks then increases by an order of magnitude. The rapid propagation rates have the same order of magnitude as those measured on pre-cracked specimens.

( )16 A heat treatment at 600°C is mainly used for stress relieving the welds of components in low-alloy steels.

It also has a favorable influence on the SCC behavior of Ni-based alloys by reducing the surface residual stresses induced during the manufacturing operations. It has no effect on the intrinsic resistance of welds (except surface effects).

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Incubation Rapid

propagation

Detectable crack

Critical crack

Crack depth

Time

Initiation

Slow propagation

True initiation

Figure 3-1 Stages of SCC of Alloy 600 in PWR Primary Environment

Under static loading conditions, the initiation of SCC depends on three main parameters: the temperature, the applied stress, and the microstructure of the material. The influence of these factors was quantified [29] by the sensitivity indexes iθ, iσ and im, which relate to the temperature, the microstructure and the applied stress, respectively. In modeling, these indexes are assumed to be independent. Water chemistry and corrosion potential are additional parameters affecting the initiation time.

The reference configuration (global index of 1) corresponds to a tube of “susceptible Alloy 600”, subjected to a mechanical stress of 450 MPa, at a temperature of 325°C. Under these conditions, the minimum crack initiation time is about 10,000 hours. Consequently, the relation expressing the minimum initiation time tf (in hours) depends on the indexes as follows:

σθ iiit

mf ..

000,10= Equation 3-1

Temperature is the dominant parameter of the environment (in addition to redox potential) on SCC suceptibility. The following law is retained for the relation of cracking time to the temperature, and consequently iθ has been defined as:

⎟⎠⎞

⎜⎝⎛−×=

RTQi exp1049.9 15

θ Equation 3-2

with the temperature T expressed in K, the activation energy Q = 185 kJ.mol–1, and R = 8.315 J.mol-1.K–1.

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Microstructure also has an important effect on SCC susceptibility. The resistance of Alloy 600 to SCC in the mill-annealed condition is clearly improved by the presence of intergranular carbides. Because a 16 hour at 700°C thermal treatment favors intergranular precipitation, it also improves the resistance to SCC, except in the case of significant cold-work before this heat treatment. Materials (SG tubes) with an intragranular precipitation of carbides lined up on the former austenite grain boundaries are the most sensitive to SCC. The chemical composition near the grain boundaries (Cr-depletion) has little influence in the reducing conditions encountered in PWR. High mechanical strength characteristics and small grains are detrimental to SCC resistance. The material index im measures the intrinsic sensitivity of the material to the industrial initiation of SCC. Two methods are used to determine the material indices of the studied products:

1. Based on corrosion tests: this method consists of conducting a stress corrosion test on samples of the considered material, with surface and core stress characterization. The cracking time of the test pieces and the application of the index method allow im evaluation.

2. From manufacturing data: for a given manufacturing process (forging, rolling, drawing, etc.) and for a given type of product, correlations have been established between the manufacturing process, the heat treatment parameters, and the sensitivity to SCC, both in service and in laboratory. The microstructure of the product, resulting from the manufacturing parameters is then taken into consideration.

The maximum material indexes determined by these methods are as follows [30]:

• Vessel head materials: im = 2.5.

• Bottom vessel penetration materials: im = 0.6.

• Partition plate materials: im = 1.

• Radial core support materials: im = 1.

Finally, Equation 3-1 also depends on the applied stress σ (see Figure 3-2 and Figure 3-3). The stress index, iσ , is defined as:

4111044.2 σσ−×=i Equation 3-3

Figure 3-2 Effect of Stress on Time to Failure of Alloy 600 at Tube Sheet

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Figure 3-3 Effect of Stress on Time to Failure of Alloy 600 Vessel Head Nozzles

Rapid propagation of the larger cracks can be linked to both the crack depth and the applied load. Propagation rates have undergone several evaluations for SG tubes and for thick materials (representative or not of the various components). The principal parameters relating to the propagation rates are the temperature and the stress intensity:

• The most commonly accepted value for the activation energy is about 110 kJ.mol–1 for SG tubes and 130 kJ.mol–1 ± 20 kJ.mol–1 for crack growth in thick materials, between 290°C and 360°C.

• The crack growth rate is a function of stress intensity, K (in MPa. m ):

– For the roll transition of SG tubes in Alloy 600 MA, the crack growth rate law accepted by the international community at 325°C is [31]:

meana = 2.23 10–12 (K–9)1.16 Equation 3-4

– The crack growth rate case of thick materials at 325°C is a controversial point. EDF [32] retained the CGR law of the fastest crack described by Equation 3-5, with an α coefficient depending on the material. The international EPRI-MRP Group has proposed the law described by Equation 3-6, using data from different heats and loading procedures [33].

maxa = α.(KTini – KISCC)0.3 Equation 3-5

( ) 16.112 959811130000exp10.67.2 −⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−= − K

TRamean Equation 3-6

Strain hardening has been identified as promoting both initiation and propagation of stress corrosion cracking: superficial cold work can be taken into account in Equation 3-3, by replacing σ with an effective stress σeff, which corresponds to the stress level which would induce the same SCC initiation time on an electropolished specimen as on the specimen with a cold-worked surface layer under an applied stress σ. Le Hong [34] expressed σeff as:

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16.3/1

0

9.116.12 )(

−

−−⎥⎦

⎤⎢⎣

⎡×= ∫

ca

coreISCC

eff daaWDK

σπσ Equation 3-7

In Equation 3-7, σcore is the stress in the core material, WD(a) is the width of the X-ray diffraction peak, a is the depth, and ac is the critical crack depth. Figure 3-4 shows the effective stress as a function of the applied stress and the thickness of the cold-worked layer. The evaluation of the effective stress leads to higher stress levels, but the slope of the curve remains close to

(4−effσ Figure 3-5). The effect of surface condition on SCC can be taken into account when the

applied stress is higher than the yield strength of the core material.

Figure 3-4 Effective Stress as a Function of the Applied Stress and the Thickness of the Cold-Worked Surface Layer [34]

Figure 3-5 Influence of the Applied Stress and the Effective Stress on SCC Initiation Time [34]

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Finally, strain hardening has a highly aggravating effect on CGR for yield strength σ0.2 less than 400 MPa or for hardening rates C below 5%, with an amplification factor (1+C1.25). The effect of σ0.2 is moderate for materials with σ0.2 greater than 450 MPa and for hardening rates greater than 5% (amplification factor 3 to 4 for C = 25%).

3.2.1.2 Evidence of EAC/Strain Localization Interactions

Based on the initiation model proposed by EDF (Equation 3-1), it is possible to predict the time to failure for different types of specimens such as reverse U-bends (RUBs) or tensile specimens. When the tests are performed on the same material, at the same temperature, and at the same stress level in different types of specimens, a significant difference is observed in the time to initiation: tf is significantly longer for the tensile specimens than for the RUBs [35]. This difference could originate in the loading difference between the two types of specimens: the uniaxial stress in the tensile specimen versus the complex strain path at the location of SCC initiation in the RUBs.

Strain rate is a relevant parameter to describe the damage occurring during the slow propagation regime (Figure 3-6) during CERT [28]. The propagation rate during a CERT depends on the applied strain rate (in the range 5.10–9 < appε < 2.5.10–7 s–1) according to the following law:

58.0.

ε×= Ca Equation 3-8

Equation 3-9 has been established for Alloy 600 to describe the damage occurring during the rapid propagation phase. The expression of the crack growth rate as a function of applied strain rate

aappε and the crack-tip strain rate CTε is [36]:

ad appCT ×+×= 1.215 εε Equation 3-9

In Equation 3-9, d is the average distance between two cracks, defined as:

cracks ofNumber lengh Gauge=d Equation 3-10

Using these two last equations, a relationship is obtained (Equation 3-11), linking the CGR to the crack tip strain rate CTε , as shown in Figure 3-7.

6.0.

CTCa ε×= Equation 3-11

Therefore, the crack tip strain rate is a relevant parameter to quantify the crack propagation rate. Consequently, strain localization (at the crack tip) is a relevant parameter in PWSCC mechanism.

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Figure 3-6 Comparison of Maximum Crack Depth for CERT (Tests 1 and 2) and a Constant Load Test (Test 3) for Alloy 600 Tested in PWR Hydrogenated Environment at 360°C [28]

Figure 3-7 CGR vs. Crack-Tip Strain Rate from CERT in the PWR Primary Environment at 360°C [34]

Since the cracking of Alloy 600 is intergranular, the crack growth rate in CERT has been shown to follow the following function of the grain boundary viscosity η:

76.0.

' −×= ηCa Equation 3-12

where C’ is a constant andη is expressed as:

Stb

πση 4

= Equation 3-13

where S represents the extent of grain boundary sliding (Figure 3-10).

Equation 3-12 takes into account the SCC propagation obtained during CERT on Alloys 600 and 690 from different suppliers (Figure 3-11). Concerning initiation, CDT on RUB specimens have led to the conclusion that the initiation time of Alloy 600 is also proportional to the grain boundary viscosity, η, which itself depends on the creep constant k and the microstructure (fs is the surface fraction occupied by intergranular carbides and d is the grain size), as shown in Equation 3-14:

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η = Ci k-1

dhf is )/exp(

Equation 3-14

with .ε creep = k (

2.0

2.0

RpRp−σ

)0.86 t-0.47 exp(-RT

180000) Equation 3-15

The good correlation between strain localization, induced by grain boundary sliding, and crack initiation and propagation shows that such plastic instability is a relevant parameter for PWSCC quantification.

Alloy 600 SCC changes from an intergranular to a transgranular mode with grain boundary precipitation carbide content increase and lead concentration increase in high temperature water (1 M NaOH, 340°C). IGSCC is delayed by stress relaxation at grain boundaries. TGSCC in thermally treated (TT) alloys results from crack blunting at grain boundary carbides [37]. Dislocations in Alloy 600 TT seem to be preferentially emitted from the grain boundary carbides (Figure 3-8), locally reducing the stress concentration, and improving IGSCC resistance. On the contrary, a tangled dislocation structure appears in Alloy 600 mill annealed (MA) near the grain boundary [38] (Figure 3-9).

Figure 3-8 Dislocation Motion in Alloy 600 TT (0.75% El.) [37]

Figure 3-9 Dislocation Motion in Alloy 600 MA (0.75% El.) [37]

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Figure 3-10 GBS at the Surface of an Alloy 600 Tube in [23]

Figure 3-11 CGR vs. η in Alloys 600 and 690 from CERT (5.10–8 s–1) in the PWR Primary Environment at 360°C [39]

Finally, it is important to mention that partial, periodic unloading of specimens in the laboratory has a significant, detrimental effect on the CGR for materials with a low susceptibility to stress corrosion cracking. In contrast, susceptible materials are not affected by partial, periodic unloading. This observation suggests that there is an effect of strain localization at the crack tip, probably with oxide growth during loading and oxide cracking during unloading.

3.2.1.3 Main Issues

The potential mechanisms for IGSCC of wrought Alloy 600 have been essentially focused on either film rupture with oxidation/repassivation models, or local hydrogen embrittlement models. Creep was mentioned in the past, but appears only as the driving force for depassivation and not as a damaging process in itself. The injection of vacancies as a damaging process appeared in the Jones model [40] and in a precursor of the Corrosion Enhanced Plasticity Model (CEPM) [2] based on local softening at the crack tip, but with the role of hydrogen not yet clearly explained.

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Since the 1990s, a very important evolution of ideas can be noted. The film rupture model has almost been abandoned, while models involving a local concentration of hydrogen (CEPM, Hall model) and internal oxidation (at grain boundaries) have emerged. Nevertheless, for creep behavior, grain boundary sliding, and effects of hydrogen on accelerated transport (Cr, O), this modeling still needs to be improved. The oxidation vs. hydrogen models remain fiercely debated, even with a shift towards the local hydrogen effects at the crack-tip and the consideration of substrate induced damage (intergranular oxidation, selective oxidation, vacancies, etc.) regarding oxidation.

Initiation continues to remain a key issue for most of the models and damage processes, particularly for the mechanisms based on hydrogen and creep. Most of these mechanisms are reasonably adequate to describe the SCC propagation phase, but no current model presents convincing arguments to account for all the observed parameter effects, or presents satisfactory, quantitative, predictive aspects.

Concerning the EAC/strain localization interactions in Alloy 600 in the PWR primary environment, the main issues are:

• Is strain localization necessary for IGSCC initiation?

• How can strain localization (induced by the complex strain path in RUBs for example) enhance the initiation mechanism? How can initiation prediction incorporate strain localization? This point is especially important for safety in service investigations.

• How do crack tip examinations supporting the internal oxidation mechanism as proposed by Scott [53] reconcile with experimental evidence demonstrating the effect of local strain at the crack tip, grain boundary sliding, and grain boundary precipitation?

• Does DSA play any role in crack propagation?



A survey program was set up simultaneously at EDF and at CEA. It showed an absence of stress corrosion cracking in RUB specimens after 90,000 h in the environment at 360°C. This result confirmed the absence of cracking observed by Framatome on kiss-rolled transition mock-ups after 100,000 h. This duration at higher temperature is considered sufficient to ensure the absence of cracking risk in 40 years at operating temperature.

This program also implemented an approach based on the “Strain-Rate Damage Model”, allowing extrapolation of the behavior obtained during CERT to deformation rates close to creep rates [41, 42]. Results have confirmed the very large margins obtained with Alloy 690 compared to Alloy 600. Margins were the largest for industrial tubes of Alloy 690 with intergranular carbides and moderate mechanical characteristics: from an engineering perspective, these components are not sensitive to stress corrosion under laboratory conditions.

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Regarding corrosion-fatigue (∆ε = 0.008, ε =10–3 s–1), the primary environment has a significant impact on the S-N fatigue curves of Alloy 690 at 315°C [43, 44]:

[Log(N25)]air = [Log(N25)]pwr + 0.401 Equation 3-16

No increase in propagation rate should be obtained within 1500 h under trapezoidal loading (R = 0.7 and frequency 2.8.10–4 Hz), although these conditions can generate an increase in GBS and SCC of Alloy 600.

3.2.2.2 Evidence of EAC/Strain Localization Interaction

Some IGSCC initiation has been observed in sensitive cold-worked Alloy 690 in CERT specimens [45]. Cold work was obtained by manufacturing either cold pressed hump specimens or shot peened specimens. For cold pressed hump specimens, the strain is localized at the hump in the specimens, initially due to cold-working in air and then due to straining in the PWR primary environment (high localized strain triaxialty).

3.2.2.3 Main Issues

It has been shown that strain localization can promote IGSCC in Alloy 690, justifying an investigation of different plastic flow instabilities in this material. An order-disorder transformation based on the formation of a Ni2Cr ordered phase can occur under specific conditions of temperature, time and irradiation [25]. This could lead to hardening of the material and the potential for an increased sensitivity to EAC. The occurrence of long range ordering at the PWR operating temperature is very unlikely for a 9% iron Alloy 690, but such a transformation could take place in an alloy with less than 7% iron.


• How can the detrimental effect of cold work on EAC initiation be explained?

• What could the effect of the possible ordered phase on the heterogeneity of plasticity be at different stages of deformation?

• What could the consequence of plastic flow instabilities, such as strain softening (due to change of strain path), DSA, and possibly that induced by ordered phases, be on SCC?

3.2.3 IGSCC in Wrought Alloy X750


Alloy X-750 is susceptible to SCC in LWR environments and this susceptibility depends on the thermal treatment and the microstructure. A higher temperature solution anneal followed by a single step aging treatment increases the resistance to SCC. A coarse grain structure coupled with a fine and semi-continuous intergranular precipitation of M23C6 carbides, in epitaxy with the matrix, and with a homogeneous distribution of fine γ’ precipitates (10 to 15 nm) leads to the

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best resistance to SCC in the PWR primary environment. On the contrary, microstructures with η phase at the grain boundaries and coarse γ’ precipitates resulting from low temperature annealing exhibit strong susceptibility to SCC. In this case, it appears that this high susceptibility to SCC is related to the distribution and morphology of the hardening phases and carbides. There are different set of concerns for BWR, including sensitization for example.

Even with the recommended heat treatment conditions to get the suitable microstructure ( )17 , Alloy X-750 is still highly susceptible to SCC in LWR environments when peak stresses are high and surface damage is present. The susceptibility of Alloy X-750 to SCC strongly depends on the surface conditions and particularly on the sequence of heat treatment, machining, and surface finishing.

3.2.3.2 Main Issues

Despite the increased resistance to SCC due to heat treatment and surface state optimization, Alloy X-750 remains susceptible to SCC. The mechanistic reasons for the high susceptibility of X-750 to SCC are related to the distribution and morphology of the hardening phases and carbides.

Finally, investigations [46] have show that low boron heats experience rapid SCC, while heats with boron content in the range 25–40 ppm provide the best resistance to SCC. On the other hand, other tests [47] have indicate that boron content increases the IASCC susceptibility for fluences above 1019 n.cm–2. Thus, the effect of boron content should be more thoroughly investigated.

Concerning the EAC/strain localization interactions in Alloy X-750 in the PWR primary environment, the main issues are:

• What is the effect of trace alloying elements such as boron on the nature of precipitation?

• Does precipitation induced strain localization correlate to EAC initiation? Grain boundary carbides could have an effect on both grain boundary plasticity and oxidation.



Superalloy 718 is usually highly resistant to IGSCC in PWR primary water, but exceptionally it can be sensitive to IGSCC ( )18 . Like other nickel base alloys, it was shown to be highly susceptible to both gaseous and cathodic hydrogen induced cracking at room temperature, and hydrogen is often invoked to explain SCC at 360°C. Foucault [48] performed CERT at 80°C in simulated PWR primary water after pre-exposure of the specimens for 141 h at 300°C in the same environment. The author observed a cleavage-like fracture surface restricted to a

( )17 Material solution annealed at 1100°C for 1 hour, rapidly cooled and aged at 700°C for 20 hours. ( ) 18 There are extremely few service failures among the tens of millions of Alloy 718 springs and tens of thousands

of bolts in service.

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peripherical band at the surface. This observation provides evidence for the role of hydrogen in EAC of Alloy 718 in PWR primary water. Hydrogen can have consequences either on crack initiation or on crack growth. Fournier [49] has shown that internal hydrogen ( )19 leads to multiple surface cracks during a CERT at 25°C (5×10–7 s–1), as opposed to external hydrogen ( )20 . Internal hydrogen leads to both hydrogen induced crack initiation and hydrogen assisted crack propagation, while external hydrogen leads only to accelerated crack propagation. Nevertheless, both internal and external hydrogen lead to a brittle fracture mode characterized by 1 µm planar cleavage micro-facets, indicating that the mechanisms of hydrogen embrittlement are similar.

3.2.4.2 Evidence of EAC/Strain Localization Interactions

EDF performed tests on Alloy 718 in the PWR primary environment at 360°C. Cracking was observed under pure static loading (RUB specimens) after 4,000 h, while no SCC was observed on CERT specimens. Furthermore, DSA was observed at 400°C for ε = 5.10–7 s–1. CERT performed by Fournier show that fracture in air is more rapid in hydrogen precharged specimens (19) than in hydrogen free specimens for ε = 5.10–5 s–1 and ε = 5 10–7 s–1 (Figure 3-12) [49]. In contrast, the times to failure are identical for ε = 5.10–3.s–1.

Figure 3-12 Stress–Strain Curves at Room Temperature of Hydrogen Pre-Charged and Hydrogen Free Specimens Deformed at Various Strain Rates: (a) 5×10–7.s–1, (b) 5×10–5.s–1, and (c) 5×10–3.s–1 [49]

( )19 Hydrogen introduced by cathodic precharging at room temperature, for an applied current of –100 mA cm–2 in 1N

H2SO4. ( )20 Hydrogen introduced during CERT by cathodic charging for an applied current of –100 mA cm–2 in 1N H2SO4.

3-21


3.2.4.3 Main Issues

Creep and low frequency fatigue tests performed on compact tension specimens of Alloy 718 at 650°C showed that crack growth rates in air were several orders of magnitude higher than in vacuum [50, 51, 52]. Scott [53] has suggested that intergranular oxygen penetration may be involved in the IGSCC process of nickel-based alloys in PWR primary water. Such a mechanism could explain the CGR increase in air at 650°C compared to vacuum and can be suspected to operate at lower temperatures in the PWR primary environment.

Sheth has qualitatively correlated the CGR increase to the amount of δ precipitation at the grain boundaries. Burke has employed high solution annealing temperature (1093°C) prior to aging at 718°C to eliminate δ phase formation and to produce a very uniform γ’’ and γ’ microstructure. It appeared that δ phase (Ni3Nb) and Ni2Nb are not required for IGSCC in Alloy 718. But SCC resistance is improved when Ni3Nb and Ni2Nb are not present at the grain boundaries. A possible correlation to strain localization should be investigated (strain softening due to obstacle destruction).


• How can the paradoxical influence of DSA on EAC in air at 650°C be explained?

• Do DSA and PLC instabilities play a role on SCC susceptibility (initiation and propagation) in the PWR primary environment?

3.2.5 SCC in Weld Metals 182 and 82


Grades of Alloy 182 with high contents of Si and C are more susceptible to SCC initiation. In addition, the higher the mechanical strength characteristics are, the greater the sensitivity to SCC. Initiation results may be described by an Arrhenius law, with an apparent activation energy of 185 kJ mol–1 (similar to Alloy 600) and a stress dependence of σ–7. The stress threshold for initiation is near 350 MPa at 350°C.

There are experimental difficulties in determining the SCC CGR of Alloy 182, due to the heterogeneous nature and anisotropy of weld metal. Results obtained by CEA, ETH Zürich, EDF, Studsvik and Westinghouse have demonstrated the following effects [54]:

• Temperature increases the CGR, with an activation energy between 130 and 230 kJ mol–1 depending on the laboratories.

• CGR is reduced by a factor of 2 to 3 after a heat treatment (6 h at 610°C).

• Strain hardening (El. = 10%) increases the CGR by a factor of 2.

• CGR depends on the crack growth path, which is correlated to the orientation of the dendrites in the specimen.

3-22


• Under cyclic loading, CGR in the direction parallel to the dendrites is two or even five times more rapid than in the perpendicular direction.

• The weld chemical composition has a limited influence on the CGR.

Alloy 82 is susceptible to cracking, but shows a better resistance to both PWSCC initiation and propagation than Alloy 182. Alloy 82 initiation times are at least six times longer than those for Alloy 182. It should be noted however that few results are available.

3.2.5.2 Evidence of EAC/Strain Localization Interaction

Bruemmer [55] observed only intergranular attack (IGA) ( )21 on the crack-wall dislocation structure in Alloy 182 (Figure 3-13), even with high dislocation density (as opposed to findings for Alloy 600).

Figure 3-13 Highly Deformed Matrix and Localized Deformation Structure off Crack Walls. TEM Brightfield Image [55]

3.2.5.3 Main issues

Because the welding process leads to heterogeneities in the weld (microstructure, chemical composition), the mechanical behavior of a weld is also heterogeneous and anisotropic. Consequently, strain localization can be suspected in a weld, with possible consequences for EAC mechanisms. The EDF PWR field experience currently suggests that the weld metals are less affected by EAC than the base alloys.

( ) 21 At the crack tip, whereas no clear distinction has been observed between IGA and IGSCC in Alloy 600 in primary

water.

3-23


Hot cracking is a consequence of segregation during solidification. No correlation has been established between hot cracking and subsequent EAC.

Furthermore, Charpy tests and resistivity measurements did not show any effect of aging. No long term ordering after 30,000 hours at 400°C and 60,000 hours at 360°C has been observed in 82/182/52/152 alloys [56]. Therefore, no strain softening in ordered zones due to aging is expected in these materials.

Results obtained by EDF [54] and Framatome [57] have shown a strong correlation between the orientation of the dendrites with respect to the load axis and preferential sites for both initiation and propagation. Initiation occurs in areas where the dendrites are perpendicular to the surface exposed to the environment, at the interface between grains with and without strain localization (strain localization seems correlated to Nb and Mn segregation) [57]. Consequently, the effect of segregation on plastic flow instabilities is a main issue in order to understand the initiation and propagation of PWSCC in Alloy 182.

The SCC growth rate increases by a factor 3 when the weld metal 182 is cold-worked to 12% of reduction of thickness, compared to the as-welded condition [58]. Therefore, the effect of strain hardening of anisotropic weld metals could be a main issue for quantitative prediction of initiation and CGR.

Finally, crack propagation tests have shown the deleterious effect of unloading-reloading (R = 0.7) on susceptible weld materials (as opposed to low sensitivity welded material), while unloading-reloading is strongly detrimental for Alloy 600 with low sensitivity to PWSCC and without any effect on Alloy 600 with high susceptibility to PWSCC. This major difference in behavior is still not explained.

Concerning the EAC/strain localization interactions in Alloys 182/82 in the PWR primary environment, the main issues are:

• What are the possible mechanisms of strain localization in a complex weld microstructure with a complex microchemistry?

• How can the difference in behavior between the base metal and the weld metal with the loading cycle be explained?

• How can the paradoxical fact that the (heterogeneous) weld Alloys 182/82 seem more resistant to SCC in reactors than Alloy 600 base materials be explained?

• How can the good resistance to PWSCC of 152/52 weld metals be explained, despite the locally unfavorable microstructure/chemical composition associated with plastic instability?

3-24


3.3 SCC of Austenitic Stainless Steels in LWR Environments

3.3.1 Context

Austenitic stainless steels are characterized by a good resistance to general corrosion at elevated temperature, which is the main reason for their widespread use in LWR. However, numerous studies have demonstrated the susceptibility of austenitic stainless steels to SCC in BWR environments [1]. Most SCC tests have been conducted to find threshold values for SCC occurrence and to clarify the effect of plastic pre-deformation. Some components also suffer SCC under neutron irradiation [59]. Irradiation assisted SCC (IASCC) is the main reason for intergranular cracking in core components made of stainless steels in PWR, where the degradation could result from the increase of hardness that occurs because of irradiation. In order to avoid complex and costly corrosion research, irradiation hardening is commonly approximated by applying strain hardening to non-irradiated material prior to stress corrosion cracking tests [60]. However, no attempt to simulate irradiation hardening by work-hardening stainless steels has satisfactorily reproduced their behavior in the PWR primary environment. Thus, specific deformation modes of irradiated stainless steels must be considered. Furthermore, SCC of austenitic stainless steels in this environment is relatively poorly understood, mainly because of the restricted conditions for the occurrence of the phenomenon. Currently, the main cause for initiation of SCC in the PWR primary environment is thought to be related to highly pre-strained materials [61, 62, 63, 64, 65, 66].

3.3.2 SCC of Strain Hardened Austenitic Stainless Steels in the PWR Primary Environment


Initiation tests (17,000 h), CERT, and crack growth tests performed by EDF [62] confirm the idea that strain hardening is a prerequisite condition for SCC initiation and propagation. No SCC is observed for micro-hardness below 240 HV0.1, and no propagation under 310 HV0.1

(Figure 3-14). An equivalent stress close to 700 MPa also seems necessary for propagation (Figure 3-15). The transition between the slow and rapid regimes is observed with CERT for a crack depth of ~50 µm (Figure 3-16). Nevertheless, exceeding these thresholds is not a guarantee that SCC initiation or propagation will be observed.

3-25


0

50

100

150

200

250

300

350

180 220 260 300 340

Vickers microhardness at the crack-tipC

rack

dep

th (µ

m)

Figure 3-14 Micro-Hardness Threshold for Initiation and Propagation of SCC During CERT in the PWR Primary Environment (360°C, ε = 5 10–8 s–1) [7]

0

50

100

150

200

250

300

350

160 260 360 460 560 660 760

Equivalent V.M. Stress (MPa)

Cra

ck d

epth

(µm

)

Figure 3-15 Stress Threshold for Initiation and Propagation of SCC During CERT in the PWR Primary Environment (360°C, ε = 5.10–8 s–1) [7]

y = 3736,3x - 940,09

y = 311,19x - 32,746

0

50

100

150

200

250

300

350

400

450

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40

Strain

Dep

th o

f the

dee

pest

cra

ck (µ

m)

Initiation of TGSCCPropagation of TGSCC

Figure 3-16 Initiation and Propagation Stages During CERT with Non Pre-Strained 304L in the PWR Primary Environment (360°C). Depth of the Main Crack vs. Strain at the End of the Test [7]

3-26


3.3.2.2 Evidence of EAC/Localization Interactions

Test results confirmed the assumption that a positive strain rate (eventually sharply localized at a crack tip) is a necessary condition for both initiation and propagation of SCC in 304L in the PWR primary environment (360°C). This hypothesis is supported by the correlation between the creep resistance of austenitic stainless steel and their good resistance to SCC under static loading. Figure 3-17 shows that creep rates measured on annealed 304L are negligible at 360°C (3.10–12 s–1) for true stresses in the range 250–400 MPa [62]. Consequently, assuming that the SCC mechanism strongly depends on strain rate, the very good resistance of austenitic stainless steels to SCC in PWR could result from their reduced ability to creep, due to interactions between solute atoms (N and C) and mobile dislocations. Nevertheless, the possible contribution of localized grain boundary sliding to the cracking process when the material is stressed for very long periods of time should be mentioned (Figure 3-18 and Figure 3-19) [62].

1E-121E-111E-101E-091E-081E-071E-061E-051E-041E-031E-021E-01

0 200 400 600 800 1000

Tempérarure (°C)

Vite

sse

de fl

uage

(1/s

)

50 MPa - 316LN (Usami)



250-400 MPa - 304L (EDF-MMC)

170 MPa - 304 (Frost)

340 MPa - 304 (Frost)

Figure 3-17 Creep Rate as a Function of Temperature in Austenitic Stainless Steels [62]

Figure 3-18 GBS at a Triple Point. Cold Pressed Hump Specimen, CERT ( ε = 5.8 10–8 s–1) [62]

3-27


Figure 3-19 Microcracks on a Grain Boundary After Sliding. Cold Pressed Hump Specimen, CERT ( ε = 5.8 10–8 s–1) [67]

Evidence for localized deformation is observed as a series of micro-twins at the crack-tip as shown in Figure 3-20 (bright field tilt). Thus, at 360°C, micro-twinning is an important mechanism of deformation. A large number of dislocations are accumulated, especially on the twin boundary, about 250 nm ahead of the crack-tip. The crack-tip and the twin boundary are also linked by a pile-up of dislocations, which could represent crack nucleation. Such observations allow the assumption that localized deformation could promote transgranular SCC propagation. Furthermore, it can be mentioned that a residual stress field spread over 1 µm2 is present ahead of the tip. Finally, a small area extending for 200 µm, and with few dislocations, could correspond to the crack process zone.

DFZ

Area under residual stress

Twin boundary

Pile-up of dislocations

Figure 3-20 Transgranular Crack-Tip Examinations After CERT ( ε = 5.8 10–8 s–1) [62]

3-28


CERT on pre-strained hardened 304L have demonstrated the important effect of the strain path on the crack growth path (Figure 3-21 and Figure 3-22) [62]. Monotonic strain paths lead to pure TGSCC, while complex strain paths (reverse and cross-directional SCC tests) favor IGSCC. Furthermore, IGSCC increases with strain hardening, while TGSCC is first favored by strain hardening, but then decreases when strain hardening becomes excessive. Therefore, mechanical consideration of strain path changes could highlight some SCC aspects. During plastic strain, the most highly-stressed slip systems are activated, leading to dislocation motion in these planes. After a sufficient amount of monotonic deformation (β = +1), the dislocation structures evolve toward steady-state configurations as cell block boundaries, where dislocations are stored. Generally, in FCC structures, such boundaries are formed along the most active {111}-crystallographic slip planes. In a reverse test (β = –1), most of the slip systems that are active during pre-strain are also active during the second loading, but are operating in the opposite direction. The beginning of the reverse loading leads to the rapid disappearance of unstable dislocation pile-ups, which implies an asymmetry of slip resistance. In a cross test (β = 0), the active slip systems from the first deformation path remain latent, while new slip systems are activated. A high resistance to dislocation motion is obtained because the dislocation structures formed during the first stage operate as obstacles for the new slip systems. Consequently, strain path changes could have two major effects on SCC. First, dislocation structures formed during pre-deformation could lead to strong obstacles to dislocation motion and increase SCC, in agreement with corrosion enhanced plasticity models [2]. Second, short-term transient behavior, such as the Bauschinger or cross effects, resulting from micro-plasticity, could have major implications on the enhancement of SCC mechanisms in 304L. One of the noticeable features is that the effects resulting from reverse and cross tests appeared to vanish after an equivalent tensile strain of 0.15-0.20. Afterwards, the initial plastic anisotropy is completely replaced by the anisotropy induced by the new deformation mode. In accordance with SCC observations, it may be assumed that TGSCC is dramatically reduced in the cross-directional SCC test because the motion of dislocations into the grains, during the second straining, is slowed by the dislocation forest previously induced by the pre-strain hardening. Furthermore, TGSCC could be favored by planar glide and micro-twinning at the crack-tip, while IGSCC would tend to be enhanced by the strain incompatibilities. Additional tests and observations should be carried out to check these hypotheses.

0

20

40

60

80

100

120

140

160

0 0,1 0,2 0,3 0,4γ

Max

. IG

SCC

dep

th (µ

m)

β = −1

β = 0

β = +1

Figure 3-21 Intergranular Crack Depth Versus Pre-Shearing for Several Strain Paths. CERT on Notched Specimens (360°C, ε = 5 10–8 s–1) [61]

3-29


0

200

400

600

800

1000

1200

0 0,1 0,2 0,3 0,4γ

Max

. TG

SCC

dep

th (µ

m)

β=−1

β=0

β=+1

Figure 3-22 Transgranular Crack Depth Versus Pre-Shearing for Several Strain Paths. CERT on Notched Specimens (360°C, ε = 5 10–8 s–1) [61]

SEM examinations have shown the effect of microscopic strain localization in the material. Residual ferrite is harder than austenite, leading to strain localization around δ-Fe strips (Figure 3-23). Consequently, in the earlier stages of deformation (few % in elongation), strain incompatibilities are observed between grains close to residual δ-Fe. Furthermore, precise examination of the boundaries separating deformed and undeformed grains revealed small intergranular cavities lined up with the slip bands of the deformed grains (Figure 3-24). Therefore, it can be assumed that microscopic strain localization and strain incompatibilities promote IGSCC.

Figure 3-23 Strain Localization and Residual δ-Fe; CERT in the PWR Primary Environment (360°C, ε = 5.10–8 s–1) [61]

3-30


Figure 3-24 Cavities at a Grain Boundary. CERT in the PWR Primary Environment (360°C, ε = 5 10–8 s–1). Detail of Figure 3-23 [61]

Furthermore, when the material is strained at room temperature, strain-induced martensite is formed around residual ferrite, as revealed in Figure 3-25. Rho [68] has shown that ferrite-austenite interfaces in 304L are favorable sites for the initiation of fatigue cracks, due to stress concentration. In spite of the similar stress concentrations observed in an EDF study [61], none of the interfaces examined showed any SCC. Nevertheless, a strong correlation is observed between crack path and localized deformation around δ-Fe. Figure 3-26 is an example of transgranular stress corrosion propagation in austenite, along a residual ferrite strip, after testing under trapezoidal loading in the PWR primary environment. Even if the crack propagates particularly close to the ferrite strip, sometimes less than 100 µm away, the δ-γ interface itself never fails.

500 nm

δ-Fe

α’-Fe

Figure 3-25 Martensite Localized Around Residual Ferrite [61]

3-31


δ-Fe

γ-Fe

Figure 3-26 Transgranular Crack in Austenite, 100-200 nm from δ−γ Interface [61]

This hypothesis of the effect of strain incompatibilities on IGSCC susceptibility can be validated by CERT performed on the same material, but with a finer grain size. In order to reduce the grain size, a thermal treatment (TT) consisting of one hour at 900°C, followed by cooling in a furnace, was applied to a 40% cold-rolled sample. The resulting grain size was close to 20 µm. CERT performed on flat-notched specimens removed from TT 304L exhibit an increase in IGSCC susceptibility (both initiation and propagation), as shown in Figure 3-27 and Figure 3-28: pure TGSCC is observed for a structure with a grain size of ≈ 60 µm, and a mixed morphology (predominantly TGSCC, but with some IGSCC) is observed for a structure with a grain size of ≈ 20 µm.

Figure 3-27 Pure TGSCC in 304L After CERT (5.10–8 s–1) in the PWR Primary Environment at 360°C. Grain size ≈ 60 µm [61]

3-32


Figure 3-28 IGSCC and TGSCC in 304L After CERT (5.10–8 s–1) in the PWR Primary Environment at 360°C. Grain Size ≈ 20 µm [61]

3.3.2.3 Main Issues

The same composition and structure of oxides are observed at the surfaces of transgranular and intergranular cracks, and for both short (~10 µm) and long cracks (~100 µm). Consequently, the environment and the electrochemical conditions are probably quite similar for initiation and propagation, regardless of the crack morphology (IGSCC or TGSCC). Conversely, significant corrosion and deformation interactions are noticed, which do not directly support an internal oxidation mechanism [69]. On the other hand, the corrosion enhanced plasticity model [2] was originally derived from detailed observations of the TGSCC of austenitic stainless steels in chloride environments. It relies on corrosion/deformation interaction mechanisms and on the alteration of crack shielding by dislocations in the presence of environmental effects on crack tip plasticity. In this framework, the increase of CGR induced by pre-straining could be considered as the result of the increased density of strong obstacles to deformation at the SCC crack tip. However, this model does not contain sufficient elements to explain quantitatively the observed TGSCC/IGSCC transition.

3-33


Concerning EAC/strain localization interactions in austenitic stainless steel in the PWR primary environment, the main issues are:

• Is the “corrosion enhanced plasticity model” a good approach for future quantitative prediction of PWSCC in strain hardened austenitic stainless steels?

• What is the contribution of GBS to IGSCC in strain-hardened austenitic stainless steels?

• What is the quantitative contribution of DSA at the crack tip to TGSCC and IGSCC crack growth rates?

• What are the critical conditions in terms of temperature, strain rate, and solute atoms content which allow sufficient unpinning of the mobile dislocations (at the crack tip) for PWSCC propagation?

• Does the transition from transgranular to intergranular mode observed during a decrease of the applied strain rate correspond to the start of the DSA regime?

• Are there common mechanisms here between SCC and corrosion fatigue?

3.3.3 SCC of Sensitized Austenitic Stainless Steels in BWR Environment


IGSCC of austenitic stainless steels in BWR environments has been extensively investigated and is considered to proceed primarily by a slip dissolution mechanism, modeled in terms of parameters such as crack tip strain rate, corrosion potential, conductivity, material composition, and microstructure.

SCC usually occurs above a critical electrochemical potential (ECP) corresponding to a certain amount of dissolved oxidants (e.g., ten to one hundred ppb of oxygen), or with pollutants such as chlorides. It is often influenced by sensitization of the material, leading to chromium depletion at the grain boundaries. The two main parameters controlling the CGR of SCC in BWR environments are the ECP and the crack-tip strain rate CTε [70]. Studies often focus on the heat affected zones of welds (AISI 308 weld metal) and on thermally treated stainless steels at the temperature of 450 – 550°C. Sensitization is a key parameter in the laboratory, even though various cases of SCC initiation have been observed in non-sensitized materials [71]. In this case, cold work, surface state, and segregation of impurities at the grain boundary (sulphur, phosphorus) are of special interest.

Austenitic stainless steels are particularly susceptible to IGSCC if they are sensitized during heat treatment or welding. Chromium carbide precipitation along the grain boundaries results in chromium depletion in the regions adjacent to the grain boundaries. The lower chromium concentration makes the depleted zone anodic with respect to the rest of the grain and the chromium carbides, and these localized regions are preferential sites for initiation of IGSCC. Nevertheless, IGSCC readily occurs in austenitic stainless steels without Cr depletion, whether in oxidizing or reducing conditions. Under oxidizing conditions, Cr depletion accelerates SCC, but this has been clearly shown to be a continuum response starting at no depletion and

3-34


becoming worse as Cr depletion increases by even very small amounts [72]. The IGSCC threshold of Cr content from sensitization is very dependent on the test environment and mechanical conditions, even at lower temperature. For example, below 13.5% chromium, 100% intergranular cracking is observed in oxygenated high purity water at 288°C [73].

Grain size and grain boundary misorientation have an effect on cracking susceptibility. These parameters affect the degree of sensitization, but also the dislocation density at the grain boundaries [74]. High-angle grain boundaries are more susceptible to cracking than low-angle grain boundaries [75]. It was found that sensitized 304 with a large grain size (~100 µm) was not very sensitive to IGSCC, compared to the same steel with smaller grain size (20-65 µm). The effect of grain size can be correlated to the Hall-Petch relationship, indicating that flow stress varies as the inverse of the square root of the grain size of the material. Furthermore, strain incompatibilities increase, when the grain size decreases.

IGSCC also depends on the corrosion potential (Figure 3-29) or on the amount of dissolved oxygen (Figure 3-30) [76]. High CGRs (>5.10–8 m.s–1) are often observed for oxygen contents above 2000 ppb (>200 mVNHE), and much lower CGRs (<10–8 m.s−1) for oxygen contents below 200 ppb (<160 mVNHE) [77].

Figure 3-29 Effect of Corrosion Potential on SCC Susceptibility of Sensitized 304 in BWR Environment at 288°C [77]

Oxygen content has an effect on the strain threshold for SCC initiation (sensitized AISI 304 [78]). Propagation of IGSCC increases for oxygen content above 200 ppb (Figure 3-31). Strain threshold for initiation of IGSCC decreases, when oxygen content increases (Figure 3-32). Below 100 ppb, the strain threshold is between 30 and 40%. Above 200 ppb, the strain threshold is in the range of 10 to 20%. Results obtained for very low oxygen contents can be linked to results obtained in the PWR primary environment: IGSCC is only observed for a strain hardening above 40% with 1-10 ppb O2.

3-35


Figure 3-30 Corrosion Potential vs. Dissolved Oxygen Concentration in BWR Environment in the Range 100°C-288°C [76]

Figure 3-31 Effect of Dissolved Oxygen on %IGSCC in BWR Environment for Sensitized 304 [78]

The strain hardening effect is often associated with martensite and/or sensitization. The strong increase in IGSCC sensitivity with strain hardening is common to both sensitized and non sensitized stainless steels. For the same yield stress, the similarity of CGRs between 304L, 316L and 348 demonstrates that the effect of strain hardening is predominant in the cracking mechanism (Figure 3-35), compared to the effect of the material (amount of interstitial atoms, proportion of martensite) [79].

3-36


Figure 3-32 Effect of Dissolved Oxygen on Strain to Initiation for Sensitized 304 in BWR Environment [78]

Globally, IGSCC CGRs increase with the yield stress (288°C, 200 ppb O2) [79]. Under constant extension rate testing, strain hardening enhances TGSCC with respect to IGSCC (304) [80]. Under constant displacement, strain hardening of 5% is required to initiate SCC in 500 h in crevice bent beam type specimens [81]. The crack depth and the CGR increase with the level of prestrain-hardening (Figure 3-33). The time to failure under constant load is delayed when the material is cold or warm worked by uniaxial tension (20%) [82]. The roughness resulting from the prestrain hardening by traction has no significant effect on the initiation of IGSCC. Martensite slightly increases CGR. Moreover, according to Kuniya [81], the elimination of martensite by heat treatment above 500°C may prevent initiation of SCC under constant load (Figure 3-34).

Figure 3-33 SCC Depth vs. Cold Work in 304 Tested in BWR Environment (CBB Specimens) [82]

3-37


Figure 3-34 SCC Depth vs. Temperature of Thermal Treatment in Cold-Worked 304. Tests in BWR Environment (CBB Specimens) [82]

0,0

0,1

1,0

10,0

0 200 400 600 800 1000

Yield strength (MPa)

CG

R (µ

m/h

)

304L

304L WR

304L CR

316L WR

348 WR

Figure 3-35 Crack Growth Rate Versus Yield Strength in BWR Environment at 288°C [79]


Several microstructural and microplasticity observations have shown that strain localization promotes IGSCC in BWR environment.

In 304 stainless steel exposed for 48 h to 1,000 ppm Na2S2O3 solution, nucleation sites have been observed at grain boundary triple points and at grain boundary/twin boundary intersections, which are subject to highly localized stress/strains. Hirth and Lothe demonstrated that the dislocation density in grain boundary regions increases with increasing misorientation. Although

3-38


in theory grain boundaries do not produce long-range stress fields, the stress fields of individual dislocations near grain boundaries can be significant. If the grain boundaries are sensitized, they are decorated with carbides that block dislocation motion through the metal. Hwang [83] showed that localized plastic deformation and relative misorientation have an important effect on the intergranular crack nucleation process.

The electrochemical reactivity of localized areas on the specimen surface is controlled by the distribution of the surface potential. Using a scanning Kelvin probe (maximum resolution of 50 µm), Mansfeld showed that the local potential distribution changed over the area of maximum applied stress on the surface of indented 304 and 600 specimens after their exposure to a 1,000 ppm sodium thiosulfate solution for 20 h.

Ford has demonstrated that the crack-tip strain rate evaluation is a necessary condition for quantitative prediction of IGSCC propagation in BWR environment. The mechanism described by Ford is based on the localized dissolution induced by the rupture of the passive layer. The model describes quantitatively the crack propagation of austenitic stainless steels in BWR environment [1] and is based on a removal of material by anodic dissolution. The periodic propagation of the crack results in the repetition of three successive steps:

1. Rupture of the passive layer;

2. Dissolution of the bare metal;

3. Repassivation.

The CGR depends on the frequency of rupture of the layer, governed by the crack tip strain rate, as well as the dissolution kinetics and the repassivation kinetics. The mechanism is possible only if the depassivation rate and repassivation rate are of the same order of magnitude. Indeed, if repassivation is too fast, propagation is negligible. If repassivation is too slow, generalized corrosion blunts the crack tip and finally stops the propagation. Quantification of the crack advance is described by the Faraday relationship, correlating the average CGR fV to the

quantity of current Qf consumed between two successiveruptures of the passive layer:

f

ff tFz

QMV

....

ρ= Equation 3-17

with

layer passive theof rupture of period:constantFaraday :

metal of atoman ofoxidation theduring electrons exchanged ofnumber : metal theof weight volumic: metal theof weight atomic:

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

ftFzρM

By definition, the quantity of consumed current Qf is a function of the density of the repassivation current i:

∫ft

f 0Q = i.dt Equation 3-18

3-39


Transients of current obtained during depassivation tests provide the repassivation kinetics:

i = i0.t–n Equation 3-19

Consequently,

nf

f tni

FzMV 1

1..0 ×

−×=

ρ Equation 3-20

assuming that:

f

CT

ft εε

=1

Equation 3-21

with ⎩⎨⎧

==

layer passive theof rupture strain to ratestrain crack tip

f

CT

εε

Finally, a relationship between the CGR and the crack-tip strain rate is obtained:

nCTf AV ε.= Equation 3-22

Consequently, quantitative prediction of the average CGR requires the knowledge of the crack tip strain rate including the effect of the oxidation process on hydrogen and vacancy diffusion at the crack tip.

3.3.3.3 Main Issues

Concerning EAC/strain localization interactions in sensitized austenitic stainless steels in BWR environments, the main issues are:

• How to quantify the crack-tip strain rate?

• How to quantify the contribution of strain localization to EAC initiation?

3.3.4 IASCC of Austenitic Stainless Steels in PWR and BWR Environments


Intergranular cracking without visible plastic deformation has been detected in baffle-former bolts in earlier French PWR (see Figure 3-36 and Figure 3-37) [84, 85, 86].

3-40


Figure 3-36 Cracked Bolt

Figure 3-37 Intergranular Fracture Surface of a Cracked Bolt

In laboratory tests at temperatures of around 320°C in the PWR primary environment using different types of loading (CLT, CERT and CDT) on materials ( )22 irradiated above 3 dpa, the sample fractures generally show a significant proportion (up to 100%) of intergranular features (Figure 3-38, Figure 3-39). These features usually appear in initiated cracks, while the final fracture may be ductile with dimples. The initiation of IASCC can eventually be transgranular (Figure 3-40). Multiple secondary cracks are always observed, and the number of cracks increases with the stress. Many slip lines appear on the intergranular features and on the flank of the specimens, near the secondary cracks (Figure 3-41).

( )22 Solution annealed 304 or cold-worked 316.

3-41


Figure 3-38 Fracture Surface of a Constant Load Specimen (800 MPa) Tested in the PWR Primary Environment (SA 304H Irradiated Up to 30 dpa)

Figure 3-39 Details of Intergranular Fracture Surface Zones of a Constant Load Specimen (700 MPa) in the PWR Primary Environment (SA 304 Irradiated Up to 30 dpa). Slip Lines on the Intergranular Surfaces

The relative importance of the main factors influencing cracking of pre-irradiated materials in the PWR primary environment have been well established for cracked bolts [87]. In fact, the analysis of field experience confirms that a critical irradiation dose of 2-3 dpa is required to make the bolts susceptible to intergranular cracking; it also confirmed that the applied stress and the component temperature are other significant factors.

3-42


Figure 3-40 Fracture Surface of a CERT Specimen. CW 316 Irradiated Up to 20 dpa. Brittle Area with Both Intergranular and Transgranular Zones

Figure 3-41 Totally Intergranular Fracture Surface of an O-Ring Specimen of a Highly Irradiated CW 316 Material

3-43


These conclusions suggest to use predictive laws similar to those for SCC of Alloy 600 (Equation 3-1), depending on temperature (Equation 3-23), stress (Equation 3-24), irradiation dose (Equation 3-25) and material.

⎟⎠⎞

⎜⎝⎛∝

RTQt f exp Equation 3-23

ασ −∝ft Equation 3-24

mft φ∝ Equation 3-25

An analysis of instances of intergranular cracks developing in field bolts [87], and also in thimble tubes and control rods, suggests that a critical fluence for sensitivity to intergranular cracking exists at around 1-2.1021 n.cm–2 (E > 1 MeV), or a dose of approximately 2-3 dpa. This value agrees with levels deduced from various laboratory corrosion tests in the PWR primary environment [88, 89, 90, 91].

The percentage of intergranular cracking then increases with dose to reach 100% intergranular cracking above 40 dpa (Figure 3-42) [92, 88].

Reported results [88] indicate that the critical dose for sensitivity to cracking decreases when the temperature increases from 290 to 340°C. This result agrees well with in service experience: cracked bolts are generally the hottest and most irradiated. From this, it is possible to deduce the apparent activation energy Q of the phenomenon (Q ≈ 70 kJ.mol–1 for laboratory materials, and 100 < Q < 180 kJ.mol–1 for in-service materials).

0

10

20

30

40 50

60

70

80

90

100

1,0E+20 1,0E+21 1,0E+22 1,0E+23 1,0E+24

Fluence (n/cm 2 , E>0,1 MeV)

T . T ube Suzuki 316 E, 340°CT . T ube Suzuki 316E, 320°C T . T ube Suzuki 316E, 290°C T T ube 316E, 320°C T . T ube 316E, 340°C, 316 - E irradiated - 340°C Bolt , 340°C

% Intergranular

Figure 3-42 Results Obtained on CW Irradiated 316 and Annealed Irradiated 304 (6 dpa). CERT (ε ≈10–7 s–1) in the PWR Primary Environment

3-44


Mechanical parameters which control the sensitivity of materials to intergranular cracking are also being sought. Most information about the effect of stress is from tests at constant displacement (C-rings and O-Rings) on thimble tubes [92]; and from tests at constant load on bolts [86] and Chooz A (French PWR) internals. Results show that intergranular cracking can be fast even when the load is below the yield strength. Time to fracture is a function of the applied stress (proportional to σ−α). There also appears to be a stress threshold (around 40% of the yield strength) below which cracking is not initiated. It is widely accepted that the stress required to sensitize the material to intergranular corrosion changes as a function of the irradiation dose as shown in Figure 3-43, but the experimental data is still insufficient to quantify this behavior: area A in Figure 3-43 corresponds to the material’s work-hardening stage (where the yield strength increases), during which the material is sensitive only for stresses above the yield strength. Area B shows the competition between the increase in yield strength and the beginning of susceptibility to IASCC in the material. This area also corresponds to the start of localized deformation, extending throughout area C and making the material increasingly sensitive up to the saturation level in area D.

Figure 3-43 Evolution of the Stress Required to Sensitize the Material to Intergranular SCC as a Function of the Irradiation Dose for Austenitic Stainless Steels (from IASCC Advisory Committee)

Under certain conditions, hydrogen ( )23 could play a role in a hypothesis explaining SCC. Hydrogen mobility is high at PWR temperatures, but the quantity of hydrogen that actually remains within the steel is difficult to measure because it depends on how effectively it is trapped, particularly by defects created during irradiation (bubbles, dislocations, any martensitic phase created by strain, etc.). At low temperatures (below 100°C), hydrogen is known to embrittle austenitic steel, and in particular unstable steels (such as 304L, where martensitic

( )23 Hydrogen can be generated within components internal to the PWR, by:

• cathodic reactions from surface corrosion;

• transmutation reactions in volume: transmutation could produce up to about 1,500 atomic ppm of hydrogen at 100 dpa;

• water radiolysis;

• collision recoil between a neutron and hydrogen in the water.

3-45


transformation occurs during plastic deformation) [93]. The risk is increased by segregation, which occurs near grain boundaries during irradiation. Sensitivity to hydrogen-induced weakening will decrease with temperature increasing, but sensitivity to hydrogen at PWR temperatures is not known. Tests intended to measure the effect of hydrogen at PWR operating temperatures have been performed and the results do not show any specific effect. Currently, apart from a few experimental results in this area, there are few objective indications that hydrogen-induced embrittlement is really among the mechanisms for IASCC in PWR.


Initiation observed on irradiated 304L illustrates the interaction between EAC and strain localization, as shown in Figure 3-44.

Figure 3-44 Strain Localization and IASCC Initiation in a SA 304L Irradiated Up to 30 dpa. CERT at 360°C

Irradiation-Induced Grain Hardening

Irradiation by neutrons is known to induce an overall hardening, i.e. an increase of the yield stress, associated with the accumulation of irradiation damage (mainly dislocation loops which act as obstacles to the motion of dislocations). This hardening is held responsible for the embrittlement of the steels and is suspected to contribute to the stress increase. A yield strength above 600 MPa is generally required for the material to be sensitive to intergranular cracking.

Hardening is clearly a necessary condition for steel sensitization, but it is not sufficient to explain the behavior of these steels in the PWR primary environment. In fact, no attempt to simulate irradiation hardening (by work-hardening to a level similar to that of the irradiated materials) has satisfactorily reproduced their behavior in the PWR primary environment. However, the mechanisms for irradiation hardening and work-hardening are very different: irradiation hardening is accompanied by strong localized deformation and premature necking, even before the hardening saturation level is reached. Thus specific deformation modes must be considered.

3-46


In addition, sensitivity to irradiation-assisted SCC seems to continue to increase with irradiation dose ( )24 , whereas hardening stabilizes at around 10 dpa, indicating that other secondary mechanisms are involved. These could be segregation at grain boundaries or additional embrittlement by helium or hydrogen, etc.

Localized Deformation Leading to Stress Concentrations at Grain Boundaries in Irradiated Materials

The evolution of work hardening due to irradiation defects has received less attention than the evolution of hardening generally.

Specific deformation modes (or changes in deformation modes from uniform to heterogeneous) are observed in irradiated austenitic stainless steel. After irradiation (to 2 or 3 dpa), and apart from considerable hardening, strong localized deformation and premature necking is observed (see Figure 2-12 & Figure 2-11). This dose of 2 or 3 dpa can be compared to the threshold dose after which the material becomes sensitive to IASCC.

Dislocation channeling is often evoked as a specific deformation mode in irradiated austenitic steels. As an example, proton irradiated 304 samples exhibit well defined, widely spaced steps on the surface within individual grains [94]. Defect-free zones are observed within the matrix deformation bands, indicating that dislocation channeling occurs in these proton irradiated materials. Even if there is no strong evidence for neutron irradiated stainless steels, deformation may be also localized in channels and these may cause very high stress concentrations at grain boundaries. Dislocation channeling could concentrate the deformation in coarse slip bands separated by nominally undeformed material. As a result, plastic instability could be reached in local regions, although the macroscopic strain may be low. In terms of the stress-strain curve, this premature localized instability is manifested in a decrease in the apparent rate of work hardening and the uniform elongation.

In addition, results from the CIR Program (and particularly tests of IASCC after proton irradiation) show increased sensitivity to IASCC in materials that easily undergo localized deformation e.g. materials with low stacking-fault ( )25 energy [96].

The change in the microstructure under irradiation in a material with a low stacking-fault energy can then cause highly-localized deformation. The deformation channels formed in this way (which are observed mainly at high temperatures - around 300°C) can, when they intercept grain boundaries, cause large-scale deformation, which may fracture the oxide layers and hence initiate and propagate intergranular cracking.

( )24 This point is still being debated.

( )25 There are a number of formulae expressing stacking-fault energy as a function of the non irradiated steel’s chemical composition. The best known is Pickering’s formula: γ (mJ/m2) = 25.7 + 2 (%Ni) + 410 (%C) – 0.9 (%Cr) - 77 (%N) - 13 (%Si) – 1.2 (%Mn).

3-47


Possible Effect of Strain Rate on Crack Morphology

The percentage of intergranular cracking appears to increase as the strain rate decreases. For strain rates in the range 10–8 to 10–9 s–1, intergranular rupture can be observed. However, interpretation of this result in a purely mechanical way (the PWR primary environment acting simply as an accelerator) is still controversial. Figure 3-45 correlates strain rate, temperature and fracture morphology. Based on this map, containing many assumptions and uncertainties, the cracking morphology could be a function of strain rate, temperature and irradiation dose; but also depend on parameters like stacking fault energy, constraint and environment.

Figure 3-45 A Schematic Map of Strain Rate-Temperature-Fracture Morphology Dependencies

Mechanisms (see Figure 3-46) that could contribute to a significant increase in stress at grain boundaries of irradiated steels and thus weaken their resistance to IASCC are:

• grain hardening during irradiation (due to Frank loops) increasing stress at boundaries,

• localized deformation, leading to high stress concentrations at grain boundaries,

• changes in the composition of the boundaries, increasing the difference between grain and boundary behaviors, and

• possible precipitation and (still debated) the existence of bubbles of helium at the boundaries.

These mechanisms all make irradiated materials possibly sensitive to intergranular cracking. Very large amounts of deformation at grain boundaries may fracture the oxide layers and hence help initiate and propagate intergranular cracking. The relative effect of each of these different mechanisms is not yet fully quantified, but grain hardening and localized deformation could be the most effective.

3-48


Figure 3-46 Summarizes the Main Mechanisms to Consider when Modeling the Stress-Corrosion Behavior and Resistance of Irradiated Stainless Steels (After Bruemmer)

3.3.4.3 Main Issues

Chemistry of the materials appears to have an effect on IASCC, but it is not clearly defined and the underlying factors remain unknown. Cold-worked 316 and solution-annealed 304 and 347 materials behave in roughly the same way [95]. However, differences in their intergranular cracking behavior are sometimes observed and attributed to a possible “material effect”. Factors influencing this (such as their chemical composition or thermal treatment) are rarely uniquely identified. One factor often invoked is stacking-fault energy: low values lead to strongly localized deformation and increased sensitivity to intergranular cracking [96]. However, little experimental evidence on neutron irradiated materials is available to support this hypothesis. The negative effects of either martensite formation (in some type 304 steels), or of silicon or phosphorus concentration at grain boundaries are also sometimes put forward.

It has been shown that strong segregation could occur at grain boundaries during irradiation, reducing the levels of chromium and increasing those of nickel. Removing chromium from the grain boundaries could explain instances of cracking observed in the BWR-NWC (oxygenated) environment, but is not sufficient to explain cracking in BWR-HWC (hydrogenated) environments or in the PWR primary environments [97]. In the PWR primary environment, segregation at grain boundaries does not really seem to be the main cause of sensitivity to intergranular cracking. However, changes to the composition near the grain boundary could serve to increase the difference in grain/boundary behavior and contribute to increasing the boundary stress, leading to strain localization. Segregation may also have a chemical role on EAC, e.g. Cr depletion in BWR and (perhaps) Si enrichment in PWR.

3-49


The mechanisms for irradiation creep are not damaging and do not themselves change the grain boundaries. However, it is sometimes reported in the literature that the effects of irradiation creep are highly dependent on the loading method, since they can be either positive (relieving stress from imposed deformation) or negative (causing cracking at constant load in the PWR primary environment) [98]. For very highly irradiated steel, it is also considered possible that very small helium bubbles could be precipitated at the grain boundaries [99], which could weaken them mechanically. Although still controversial, this hypothesis would explain why intergranular cracking increases with dose, while hardness remains constant. It would also explain intergranular cracking in highly-irradiated materials in an inert environment. At low doses (around 5 dpa), however, helium levels have not been observed to have any effect on the sensitivity to intergranular cracking [100].

Concerning EAC/strain localization interactions in irradiated austenitic stainless steel in PWR and BWR environments, the main issues are:

• What is the relative contribution of irradiation hardening, irradiation-induced segregation and irradiation induced strain localization to IASCC?

• What are the thresholds in irradiation hardening, segregation and strain localization for IASCC?

• Is there any irradiation saturation effect on IASCC?

• Is there an effect of the stacking fault energy of the material (related to chemical composition) on its sensitivity to IASCC?

3.4 EAC of Low-Alloy Steels

3.4.1 Phenomenology

SCC in carbon and low-alloyed steels, while not likely to occur in most reactor coolant environments, is possible in oxygenated BWR coolant at high stress levels, and corrosion fatigue also occurs in the PWR primary environment, primarily because of the presence of sulfide inclusions in the steels. Factors that tend to increase the likelihood of SCC include high stress and stress intensity levels, increases in oxygen concentration or other species that increase the electrochemical potential, increases in temperature and in MnS inclusion content [101].

Simultaneous high sulphur-anion activity, low pH and positive crack-tip strain rate are required for EAC in LAS. Then, EAC crack growth is governed by the crack-tip strain rate and by sulphur-anion content and pH in the electrolyte at the crack tip [102]:

• Sulphur content: S-anion content in crack-tip environment depends on sulfur content of the steel and impurities in the bulk environment, but also on dissolution of MnS-inclusions in crack crevices, and mass transport (diffusion, migration, convection).

• Size, shape and spatial distribution of MnS also seem to influence EAC in LAS. In an inert environment, the ductile damage mechanism of LAS is mainly governed by second phase particles such as manganese sulphides.

3-50


• Yield stress (hardness): generally a moderate effect of yield stress on SCC and corrosion fatigue crack growth is observed in high temperature water from 200 to 600 MPa, while a strong effect of yield strength is observed above 800 MPa (350 HV).

A common crack propagation model is based on the interrelation between CGR and crack tip strain rate as expressed by Equation 3-26:

.a = A n

.ε Equation 3-26

where A and n depend on S content in the crack tip chemical environment.

3.4.2 Evidence of EAC/Strain Localization Interactions

Pressure vessel LAS can be subject to corrosion fatigue in high-temperature water environment (see Figure 3-47 and Figure 3-48). The fatigue resistance of LAS in simulated BWR water at 288°C depends on cyclic strain rate, which is related to a change in the environmental assisted cracking mechanism [103]. The strain rate effect observed for LAS in BWR coolant could have to do with oxidation kinetics relative to deformation rates, or with DSA. Generally, it has not been established that DSA is a major actor in all these examples of corrosion fatigue.

Figure 3-47 Crack Initiation Stages on Longitudinal Sections of Specimens After LCF Tests at 288°C in Water at (a) 0.1% s–1 (b) 0.001% s–1

3-51


Figure 3-48 S-N Curves of LAS in Simulated BWR Water and in Air at 288°C

3.4.2.1 Effect of DSA

DSA is observed in the range 100°C-350°C and is promoted by the diffusion of interstitial atoms such as N and C. Earlier data revealed the enhancement of EAC when DSA operates [104, 105]. However, EAC can also occur in LAS under operating conditions where no, or only minor, DSA effects are present. Thus DSA is not a pre-requisite for EAC, but there is obvious coincidence of DSA and EAC susceptibility in terms of temperature and strain rate conditions (Figure 3-49).

Figure 3-49 Coincidence Between SCC (in Term of Crack Growth Rate in BWR Environment) and DSA Susceptibility (in Term of Reduction of Area) [102]

DSA can enhance the localization of plastic deformation by favoring planar deformation, thus favoring brittle crack extension processes, but it may also affect oxide film rupture.

3-52


It is said that the most pronounced DSA effects on EAC are close to EAC crack growth thresholds. Strong effects are observed close to the transition from high to low sulfur crack growth thresholds (Figure 3-50 and Figure 3-51). Under specific conditions, they may even predominate over steel sulfur effects.

Figure 3-50 Schematic Synergistic Effect of Different Parameters (Including DSA) for SCC Crack Growth [102]

Figure 3-51 Schematic Synergistic Effect of Different Parameters (Including DSA) for Corrosion Fatigue Crack Growth [102]

Finally, Wu [103] has shown that the low cycle fatigue resistance of A533B in BWR environment is reduced when the cyclic strain rate decreases. Fatigue cracks initiate from surface pits caused by MnS dissolution in high-temperature water at high strain rate (hydrogen induced cracking). Fatigue cracks also initiate at surface pits with film rupture at low strain rate (film rupture/slip-dissolution mechanism) and Wu correlated this phenomenon to DSA.

3-53


3.4.2.2 Effect of Hydrogen

In LWR environments, protons are produced at the crack-tip by hydrolysis of dissolved metallic ions (Equation 3-27). Furthermore, in LAS, the dissolution of MnS inclusions also generates H+ (Equation 3-28). Hydrogen is absorbed in the metal because of the cathodic reaction (Equation 3-29), and is transported along stress gradients toward the regions of maximum hydrostatic tension (near the crack-tip).

Mn+ + p H2O → M(OH)p

(n–p)+ + p H+ Equation 3-27

MnS + 4 H2O → Mn+ + SO4

2– + 8 H+ + 8 e– Equation 3-28

H+ + e– → Habs Equation 3-29

Locally absorbed hydrogen enhances plastic strain localization by promoting multiplication and motion of dislocations [106]. Such enhanced strain localization will increase the stress concentration at internal interfaces, where localized strains are expected to develop, due to plastic incompatibilities and dislocation pile-ups.

A combined effect of hydrogen embrittlement and DSA has been observed by Wu: during cyclic strain, strain localization (such as Lüders bands) may be induced by DSA ahead of the fatigue crack-tip. Both the high density of dislocations and the localized strain structure are preferred sites for hydrogen to concentrate [103].

3.5 Conclusion

Evidence of suspected EAC/strain localization interactions is presented in Table 3-4 The main interactions result in crack tip localization, GBS and strain incompatibilities. DSA effect has been shown in the case of LAS and could be suspected for other materials. In nickel base alloys, ordering/disordering seems another source of strain incompatibilities that could promote EAC mechanisms. Experiments should be performed to evaluate the strain localization in weld materials, and to correlate with eventual EAC.

3-54


Table 3-4 EAC/Strain Localization Interactions in Nuclear Materials/Environments

Materials/ Environments

Evidence of Strain Localization/ EAC Correlations Main Issues

Alloy 600 in PWR

- KISCC necessary for rapid CGR

- Correlation between GBS and CGR

- Strain path effect on time to initiation

- Correlation between ctε and CGR

- Unloading-reloading effect on CGR

- Relevance of ctε and K in physical mechanisms of PWSCC?

- Correlation between internal oxidation mechanism with ctε and GB precipitation?

- Quantitative effect of strain localization (especially due to strain path) on chemical surface reactivity?

- Consequences for prediction of initiation?

Weld metal 182 in PWR

? ?

Alloy 690 in PWR

- Necessary high pre-strain hardening + high strain localization during CERT for initiation

- Explanation of good resistance to initiation?

- Effect of possible ordered phase on strain localization? Consequences on EAC?

Alloy X-750 in PWR

? - Effect of B on the nature and feature of precipitation?

- Possible correlation between precipitation induced strain localization and initiation?

Alloy 718 in PWR

- Effect of loading on SCC susceptibility (no SCC for CERT).

- DSA/PLC effect on SCC susceptibility?

- Explanation of the effect of loading on SCC susceptibility?

3-55


Table 3-4 EAC/Strain Localization Interactions in Nuclear Materials/Environments (Continued)

Materials/ Environments

Evidence of Strain Localization/EAC Correlations Main Issues

Austenitic stainless steels in PWR

- Strain incompatibilities promoting IGSCC

- Necessary strain hardening for initiation

- Necessary localized strain rate for initiation and propagation

- Relevance of ctε parameter in physical mechanisms of PWSCC?

- Contribution of GBS to IGSCC?

- Effect of strain localization (especially at grain boundaries) on the chemical surface reactivity?

Austenitic stainless steels in BWR

- Strain incompatibilities promoting IGSCC

- CGR- ctε correlation

- Relevant quantification of ctε ?

- Quantification of strain localization effect on initiation?

Irradiated austenitic stainless steels in LWR

- Low SFE promoting IGSCC

- Irradiation hardening increasing CGR

- Effect of ctε on SCC morphology

- Relative contribution of irradiation hardening, irradiation induced segregation and irradiation induced strain localization to EAC? Thresholds?

- Irradiation saturation effect?

- Relevant correlation between IASCC susceptibility and SFE?

LAS - DSA effect on EAC

- H effect on EAC

- Lüders effect at a crack tip?

- Interactions between DSA and H at a crack tip?

3-56

4 DISCUSSION OF EAC AND STRAIN LOCALIZATION INTERACTIONS

4.1 Approach

In the previous section, EAC was described for different material/environment combinations. Evidence of certain EAC/strain localization interactions was presented, while others were only suspected. All of the instabilities mentioned in Section 2 (see Table 2-2) are not necessarily associated with an increase in susceptibility to EAC. Increased strain localization can account for enhanced EAC, at least when considering crack growth rate, but such an effect is not guaranteed. Even if increased localization is not itself responsible for EAC growth, it can enhance EAC mechanisms in some circumstances. Thus, in order to determine for each stage of cracking how strain localization could interact with EAC, three questions are examined:

• Which oxidation and resulting transport mechanisms are operating at the interfaces, in the environment and in the material?

• How can plastic flow and strain localization be influenced by transported species in the metal and in the environment?

• How can the EAC criteria be influenced by strain localization and transported species?

Three stages of EAC are studied: incubation, slow propagation of short cracks and rapid propagation. Then the two transitions between these stages of EAC are examined. Depending on the stage considered, the effects of strain localization prior to exposure and during exposure are considered.

The objective of the discussion is to review possible interactions between oxidation and strain localization via transported species, in order to build a future numerical tool of investigation for physical and quantitative EAC prediction. The aim is not to discuss the validity of existing physical models. In contrast, the results obtained with such a numerical tool should allow selection of mechanisms for specific cases (material/environment/loading).

4.2 Incubation, Slow and Rapid Propagation

4.2.1 Incubation

Generally, the incubation period can correspond to setting up the cracking conditions (electrochemical, surface film quality…). In the case of the internal oxidation model, incubation involves a period of metal degradation before the first geometrical defect is created. The duration of the incubation period depends on temperature, surface state and loading conditions, as shown on Alloy 600 in PWR [34].

4-1

Discussion of EAC and Strain Localization Interactions

4.2.1.1 Oxidation Reactions: Case of Austenitic Ni-Base Alloys in PWR

For example, the oxide formed at the surface of Alloy 600 in PWR is composed of a “compact” internal layer at the interface with the metal, with a composition (Ni, Fe)(Cr, Fe)2O4 strongly dependent on dissolved hydrogen. Table 4-1 shows that Ni content decreases when the partial H overpressure increases. For low H overpressure, NiO is stable. Table 4-1 also shows that oxide thickness is not a monotonic function of H overpressure. PWSCC susceptibility is at a maximum when the thickness of the internal compact layer of oxide is highest.

Cr2O3 may be stable at all overpressures of interest, even in aerated conditions. NiO has never been observed in the protective part of the oxide layers on Alloy 600 or 690. Its presence in the external layer depends on the presence of dissolved iron ions in the environment. Accordingly, NiO cannot be responsible for the resistance to cracking. The transition near the Ni/NiO equilibrium may involve a transition in the composition of the inner oxide layer from a low to a higher Ni content.

Table 4-1 Chemical Composition and Thickness of the Internal Oxide Layer Formed on Alloy 600 Exposed to the PWR Primary Environment, as a Function of Dissolved Hydrogen. EDS Normalized Measurements

Partial H Overpressure

< 1kPa 30 kPa 2000 kPa

Thickness (nm) 19-24 62-94 21-27

Cr% 63 59 80

Ni% 16 21 2

Fe% 21 20 18

The external oxide layer formed on Alloy 600 in PWR is composed of disseminated crystallites of NiFe2O4.

The possible implied reactions are:

1. Anodic dissolution of the metal at the surface:

Ni → Ni2+ + 2 e– + v Equation 4-1

Cr → Cr3+ + 3 e– + v Equation 4-2

Fe → Fe2+ + 2 e– + v Equation 4-3

Fe → Fe3+ + 3 e– + v Equation 4-4

where v is a vacancy. According to the current view, an inner oxide layer could be formed by solid reactions, followed by the transport of Fe and Ni cations through this layer to become either dissolved in the environment or precipitated in the external Cr-free layer.

4-2


2. Oxide layer formation depends on the corrosion potential. For high potentials, NiO is stable (Equation 4-5). For a potential close to the Ni/NiO equilibrium potential, NiFe2O4 and NiCr2O4 are stable (Equation 4-6 and Equation 4-7), leading to a pronounced dissolution of Ni in the metal and a susceptibility to SCC, because NiFe2O4 and NiCr2O4 promote ionic conduction. For low potentials, Cr2O3 is stable (Equation 4-8) and protects the metal from SCC. Nickel chromite (NiCr2O4) is stable at much lower potentials than nickel ferrite (NiFe2O4). NiO structure oxides are associated with PWSCC immediately after cracks form and later apparently transform to spinels, as one might expect on thermodynamic grounds. Nickel chromite also forms at much lower potentials than Ni/NiO. Chromia forms at all the potentials of interest.

2 Ni + O2 → 2 NiO + v Equation 4-5

Ni2+ + 2 Fe3+ + 4 H2O→ NiFe2O4 + 8 H+ + v Equation 4-6

Ni2+ + 2 Cr3+ + 4 H2O → NiCr2O4 + 8 H+ + v Equation 4-7

4 Cr3+ + 6 H2O → 2 Cr2O3 + 12 H+ + v Equation 4-8

The redox potential depends on the partial pressure of hydrogen in the environment, according to the Nernst Law (Equation 4-10), and consequently the potential depends on the equilibrium between H2 and H+ (Equation 4-9).

H2 → 2 H+ + 2 e– Equation 4-9

( )pHpLnnFRTEE H ××+−=− 23.2)(

20 Equation 4-10

3. Hydrolysis of dissolved metallic cations:

Ni2+ + H2O → Ni(OH)+ + H+ Equation 4-11

Fe3+ + H2O → Fe(OH)2+ + H+ Equation 4-12

4. Cathodic reaction (hydrogen reduction) with hydrogen coming from the hydrolysis in reducing and basic environments:

H2O + e– → Habs + OH– Equation 4-13

5. Formation of Ni ferrite crystallites NiFe2O4 by:

• deposition of Fe(OH)2+ and Ni(OH)+ at the surface of the external oxide layer to form NiFe2O4. In such cases, formation of the spinel reduces the local acidification of the environment, consuming H+.

• oxidation of Ni by magnetite (Equation 4-14):

3 Ni + 2 Fe3O4 + 4 H2O → 3 NiFe2O4 + 4 H2 Equation 4-14

4-3


The thermodynamics of this reaction need looking at carefully and it could only occur over a very narrow band of redox potential.

In previous equations, production of H+ cations leads to a local acidification of the environment when anions apart from OH–, such as SO4

2– or Cl–, are present. If only OH– is present, the H+ cannot rise above neutral because it reacts with OH– (Equation 4-15). Indeed, in high purity water, the pH shifts alkaline because the metal ion solubility balances the extra OH–.

H+ + OH– → H2O Equation 4-15

Hydrogen, oxygen and vacancies diffuse then interact in the oxide and in the metal until a microcrack forms due to local stresses. In previous reactions, stress, strain and strain hardening are not required. Nevertheless, they could have a significant influence on the surface reactivity.

4.2.1.2 Mechanical Dependence of Surface Reactivity

The law (Equation 4-16) proposed by Lister [108] for oxide growth on austenitic stainless steels seems acceptable in the first stages of oxidation of Alloy 600, and for Alloy 718 [109, 110].

e = k tn Equation 4-16

where, e is the thickness, t is time, k and n are constants (n ≈ 0.5). But, when austenitic steels are under stress, Equation 4-16 is not sufficient to describe the oxidation of the materials. For example, Gardey [110] has observed that the internal oxide layer ( ) 26 is not fully present on electropolished Alloy 600 exposed to primary environment (Figure 4-1), while the internal layer is very compact on strain hardened metal (Figure 4-2). This effect is probably due to the dislocation structure providing short circuit diffusion pathways for Cr. Oriani [111] found that plastic deformation of nickel much enhances the cathodic reduction of hydrogen ion and the anodic dissolution of nickel in sulfuric acid, but impedes the passivation of nickel and reduces the passivation efficiency. Furthermore, the deformation-produced surface features responsible for these differences have a limited duration, controlled by surface diffusion in the cathodic range, and by surface diffusion and preferential dissolution in the anodic range.

Consequently, mechanical parameters such as stress, strain and strain hardening should be considered to predict initiation of EAC.

( )26 The oxide formed on Alloy 600 exposed to the PWR primary environment is usually composed of a porous outer

layer formed on an internal layer at the interface between the outer oxide layer and the metal.

4-4


Figure 4-1 Compact Oxide Formed at the Surface of Electropolished Alloy 600 (Inner Surface of a Tube) Exposed 1170 h to Primary Water at 325°C [110]

Figure 4-2 Compact Oxide Formed at the Surface of Cold-Worked Alloy 600 (Inner Surface of a Tube) Exposed 1170 h to Primary Water at 325°C [110]

The surface reactivity depends on stresses. At the surface, the increase of elastic stress, or elastoplastic stress, reduces the standard potential and increases the exchange current (and so the kinetics of reactions) [112]. Thus localized elastic stresses at a grain boundary triple point or at twin boundary intersections could affect the surface reactivity. Nevertheless, this would be difficult on a stainless steel or a nickel alloy, since the corrosion potential in PWR systems is almost the same as the redox potential. Moreover, strain cannot do more than thermodynamics allows. Heterogeneities resulting from pre-strain hardening lead to a distribution of preferential sites for the initiation of pits as demonstrated by Peguet [113]. This author studied the frequency of metastable initiation of corrosion pits in 304 in 0.1 M NaCl solution (Figure 4-3). Results have shown that:

4-5


• The number of metastable pits is a maximum for 20% cold rolling, with or without strain induced martensite, indicating that stress incompatibilities play an important role.

• The nucleation rate of pits is a maximum when the amount of dislocation pile-ups is highest.

• The more unstable the austenite, the larger the effect of cold work on nucleation rate.

• A lower SFE enhances hardening and pile-up stability by increasing the dissociation of dislocations and decreasing cross-slip activity, with a direct effect on the nucleation of pits according to the author.

• The increase of nucleation rate for 20% cold rolling (compared to 0% cold rolling), decreases globally when SFE increases. Nevertheless, SFE is not sufficient to explain the increase in nucleation rate.

Figure 4-3 Number of Metastable Pits Formed on 304 Austenitic Stainless Steel, Tested in 0.1 M NaCl at 25°C, for 0-70% of Pre-Straining [113]

Takeda [114] characterized oxide layers formed in a BWR environment (288°C, 2 ppm O2) on sensitized 304L and annealed 316L during CERT (5.10–7 s–1 for sensitized 304L and 3.10–7 s–1 for annealed 316L). In-situ Raman spectroscopy permited observation of the structure of the external oxide layer (50–150 nm). The electrical resistance of internal and external oxide layers has been measured, and interrupted CERT permitted evaluation of the chemical composition and the thickness of oxide layers by ESCA. Takeda observed:

• The presence of NiFe2O4, whatever the strain amplitude;

• The formation of α-Fe2O3, FeCr2O4 and NiCr2O4 spinels for ε > 0.001;

• An increase in electric resistance of the oxide layer until ε = 0.02, then a slow decrease;

• No variation of oxide thickness for ε > 0.25;

• A maximum concentration of Cr(III) in internal and external layers for ε = 0.013.

Thus, strain hardening can influence surface diffusion in the material and oxide, changing mechanical properties and kinetics of oxide growth.

4-6


Localized oxidation can result from the appearance of slip bands at the surface of a loaded specimen. Slip bands are likely to be preferential sites for anodic dissolution, while inter-slip regions probably act as preferential sites for cathodic reactions. At equilibrium, the total current I is zero (Equation 4-17):

I = ia Sa + ic Sc = 0 Equation 4-17

where ia and ic are the anodic and cathodic densities of current respectively, and Sa and Sc are

the anodic (slip lines) and cathodic (inter-slip regions) surfaces respectively. When c

a

SS

is low,

localized corrosion is high, because the high anodic current is localized on a small area ( )27 . Consequently, corrosion initiation can be delayed when the inter-slip region is strongly reduced as shown by de Curière [115] on 316L austenitic stainless steel tested in boiling MgCl2 at 117°C (Figure 4-4). Figure 4-5 and Figure 4-6 illustrate the initial surface states of pre-strained specimens used by de Curière in his study. When the material is pre-strain hardened by fatigue at saturation (50 cycles, ∆ε/2 = 10–3, ε = 10–3 s–1), the inter-slip area is strongly reduced (Figure 4-6), and the free potential during CERT remains below the corrosion potential (Figure 4-4) until the activation of new slip systems leads to new, strong and well-spaced slip bands at the surface of the specimen.

Inter-slip spaces ≈ 10 µm

Inter-slip spaces ≈ 1 µm

Figure 4-4 Free Potential at Initiation of SCC in 316L Tested in Boiling MgCl2 (117°C). CERT [115]

( )27 In BWR water there are additional issues associated with the very high resistivity of the water, so that the anodes

and cathodes must necessarily be very close together.

4-7


Several parameters can affect strain localization at the surface (slip bands), such as absorbed hydrogen and DSA:

• Slip bands (lamella spacing, slip distance h, inter-slip region) depending for small and large deformation on absorbed H, and on grain size [116] (h increases with Habs and with d)

• When DSA operates, planar dislocation slip can develop, leading to localized plastic strain on the slip bands (316L, 250-650°C). Emerging at the surface, these slip bands could enhance crack initiation. Localization results in solute locking of moving dislocations. So, during low cycle fatigue deformation, DSA can enhance the partitioning of strain.

In conclusion, stresses, and in particular stress concentrations due to strain localization, modify the surface reactivity, the structure and the nature of the oxides formed on austenitic stainless steels exposed to nuclear environments, at least for low and medium deformations.

Direction of slip lines

Figure 4-5 Surface State After Oligocyclic Fatigue (10 Cycles) in Air of 316L. Inter-Slip Spaces ≈ 10 µm [115]

Direction of slip lines

Figure 4-6 Surface State After Oligocyclic Fatigue (50 Cycles) in Air of 316L. Inter-Slip Spaces ≈ 1 µm [115]

4-8


4.2.1.3 Main Issues

Despite the fact that the incubation period is the most important period in EAC mechanism, relatively little knowledge is available. The main issues concern:

• The most favorable sites for EAC initiation.

• The quantitative probabilistic prediction (initiation rate per unit surface exposed to the environment), based on physical mechanisms.

• The effect of stress and strain hardening on electrochemical parameters at the interfaces with the environment.

• The effect of stress and strain hardening on oxide structure (porosity).

• The effect of stress and strain hardening on production and diffusion of species such as O, H and vacancies in the oxide, and therefore in the bulk material.

Accordingly, a better understanding of the incubation period with respect to mechanical parameters such as strain localization is required.

4.2.2 Slow Propagation of Short Cracks

4.2.2.1 Configuration

In this section, short cracks resulting from EAC are considered. The environment can be assumed to be not too different inside and outside of the crack, with low gradients of concentration and potential. Possible restricted confinement resulting from diffusion and convection in the crack depend on the loading (CERT, unloading/reloading…). The stress intensity factor is not strictly defined.

Experimental studies of EAC of austenitic alloys in the PWR primary environment have displayed common characteristics:

• In the presence of absorbed species, such as H and O, embrittlement is strongly increased;

• Cracking is brittle, as shown by sharp crack tips and smooth crack surfaces;

• Cracking is quasi static and depends on oxidation, diffusion and deformation processes.

Therefore, we can postulate that these embrittlement phenomena can be interpreted by the following mechanisms:

• Production of species due to oxidation. Oxidation can be promoted by stress at the crack tip or strain localization (slip lines at the crack tip), as previously discussed;

• Diffusion of species in the grain and at the grain boundaries. The size of the transport affected zone is important with respect to the local mechanical response of the material. Diffusion can be assisted by the stress field ahead of the crack, or by the strain (transport by dislocations);

• Reduction of the cohesive strength at the boundary, or on slip planes, due to the diffusion of species and strain localization.

4-9


4-10

Therefore, modeling EAC/strain localization interactions requires that three main issues be addressed simultaneously:

• Production and diffusion of species (see Section 4.2.2.2).

• Definition of the cohesive strength (see Section 4.2.2.3).

• Interactions between hydrogen or oxidation with plastic flow at the crack tip in order to reach the rupture criteria (see Section 4.2.2.3 and 4.2.2.4).

4.2.2.2 Production and Diffusion of Species at the Crack Tip

Oxidation leads to the production of soluble and insoluble species. Soluble species contribute to modify the electrochemical conditions at the crack tip (pH, electronic equilibrium…) and consequently to promote transport and additional reactions in the crack. Thus, some soluble species can contribute to form an oxide or deposit in the crack, or close to the mouth of the crack. Others can be adsorbed, then absorbed in the oxide and in the bulk alloy (oxygen, hydrogen). Insoluble species can directly form layers (oxide, hydroxide, oxyhydroxide…) at the interfaces, or result in particular reactions (formation of vacancies due to preferential anodic dissolution…).

First, it is necessary to identify the “products” resulting from oxidation. For example, mechanisms in LWR environments can be simplified as follow:

1. Anodic dissolution of the metal M at the crack-tip:

M → Mn+ + n e– + v Equation 4-18

The anodic dissolution produces chemical crack tip blunting, which can modify the geometry and the stress-strain state at the tip if repassivation does not occur, or is very slow with respect to dissolution kinetics. Crack blunting is often expressed as (potentially) occurring when the crack growth rate approaches (or falls below) the general corrosion rate of the crack walls.

2. Compact oxide layer formation:

p Mn+ + 2n

q O2 + np e– → n MpOq Equation 4-19

3. Hydrolysis of dissolved metallic cations:

Mn+ + p H2O → M(OH)p

(n–p)+ + p H+ Equation 4-20

4. Cathodic reaction (hydrogen-reduction) with hydrogen coming from hydrolysis in reducing and acid environments (Equation 4-21), then adsorption of mono-atomic hydrogen at the crack tip (Equation 4-22).

2 H+ + 2 e– → H2 Equation 4-21

H2 → 2Habs Equation 4-22


4-11

5. Cathodic reaction (oxygen reduction) at the mouth of the crack in oxidising and basic environments:

O2 + 2 H2O + 4 e– → 4 OH– Equation 4-23

6. Diffusion of M(OH)p

(n–p)+ and H+ to the mouth of the crack and of OH– to the crack-tip to establish electrical charge equilibrium. Convection of species due to periodic unloading and reloading of the crack.

2 M(OH)p

(n–p)+ + q O2 + 2(n–p) e– → 2 MOq+p/2 + p H2O Equation 4-24

H+ + OH– → H2O Equation 4-25

Accordingly, the main products of the previous reactions are:

• H+, leading to a local acidification of the environment when H+ does not react with OH– (see Section 4.2.1.1). Nevertheless, H+ does not generally lead to acidification, and if acidification does occur, the potential rises following the H2O/H2 line. Furthermore, the excess of positive charge due to H+ production is continuously balanced by maintaining the charge neutrality in the solution. In addition, H+ can result from neutron irradiation of the alloy. However, its rate of creation is microscopic compared to the flux of H available to flow through the metal from interactions with the coolant (even in water that contains only O2). Lastly, absorbed hydrogen can influence the localized plastic flow. Hydrogen-plasticity interactions has been widely studied, showing that hydrogen can locally strengthen or soften an alloy. For example, Brass [117] has shown that in AM3 Ni base superalloy, hydrogen strengthens the material when no γ’ precipitates are present, while hydrogen induces softening, promoting planar glide and thus strain localization, when γ’ precipitates are present. The hydrogen softening would result from the preferential hydrogen trapping to γ’ precipitates.

• Oxygen, resulting from NiO dissociation. No dissolved oxygen can be present at the crack tip. The equilibrium partial pressure of oxygen is below 10–15 bars in deaerated conditions and close to 10–28 bars in PWR water.

• Vacancies, resulting from irradiation, anodic dissolution and oxide formation. Many radiation-induced vacancies recombine with radiation-induced interstitials. But a small fraction of them diffuse and are absorbed by dislocations or grain boundaries.

These species are produced or adsorbed at the interfaces, then absorbed. Finally, they diffuse in the oxide and in the metal. For example, laws have been established to describe the absorption (Equation 4-26) and the diffusion of hydrogen in the bulk metal (Equation 4-27), even considering the presence of grain boundaries (Equation 4-28).

⎟⎠⎞

⎜⎝⎛ −=RTQPPH exp0 Equation 4-26

where PH is the hydrogen permeation and Q is the activation energy.


⎟⎠⎞

⎜⎝⎛ −

=RT

QDDH exp0 Equation 4-27

where DH is the diffusion coefficient of hydrogen.

⎟⎠⎞

⎜⎝⎛

−=

− RTH

CC

CC B

H

H

GB

GB exp11

Equation 4-28

where CH is the hydrogen concentration, CGB is the hydrogen concentration at grain boundaries, and HB is the boundary energy.

More generally, the diffusion of a species of concentration C can be formulated as a function of the stress tensor σ~ at the crack tip. In this case, the chemical potential µ of the species is defined by Sofronis [118]:

µ = µ0 + kT Ln ⎟⎟⎠

⎞⎜⎜⎝

⎛

0CC

–N

V *

3kkσ

Equation 4-29

where µ0 is the chemical potential of a solute atom in a “chemical reservoir”, C0 is the concentration this reservoir, C is the local concentration, N is the Avogadro constant, V* is the partial molar volume ( )28 , k is the Boltzmann constant, and σkk is the hydrostatic stress. Then, the gradient of chemical potential µ∇ leads to a diffusion of the species toward low energy regions,

with the flux J :

µ∇−=kT

CDJ H Equation 4-30

Therefore, the first Fickian Law can be expressed as:

3.*. kkH

H CRT

VDCDJ σ∇+∇−= Equation 4-31

Whipple [119] has considered the diffusion of oxygen at grain boundaries under stress (see Equation 4-32). But in his analysis, Whipple does not take the chemical reaction (oxidation) into consideration, which would significantly complicate the evaluation of diffusion. In the case of hydrogen, and considering a static crack, the increased concentration induced by the

hydrostatic stress at the crack tip is expressed by: σHC

⎟⎠⎞

⎜⎝⎛=

RTV

CC kkHH 3

*exp

σσ

Equation 4-32

( )28 Typically, in a FCC structure, 2

*3NbV = . For example, V* = 7.1 cm3.mol–1 for b = 2,55 Å.

4-12


where is the hydrogen concentration outside the crack tip stress field [HC 120].

There is pretty solid evidence that the H fugacity in the metal is controlled by the coolant fugacity. The high diffusivity of hydrogen in austenitic stainless steels and nickel base alloys further supports this. Measurements of high H content in the metal can be erroneously converted to huge H fugacities if it is assumed that H is not trapped or stored in voids. It is well known that highly deformed or irradiated stainless steels can have very high H content without any applied stress. Indeed H content can be under-estimated, because there is almost always plenty of time for the H to diffuse out of the metal during cooling, or at room temperature, in most experiments.

Similarly, the stress-assisted diffusion of vacancies is expressed by [121]:

xC

xRTVD

xCD

tC vvv

vv

∂∂

∂∂

−∂∂

=∂

∂ σ*2

2

Equation 4-33

Larché [122] has proposed a generalized diffusion law, coupling the mechanical stresses and bulk diffusion, based on the thermodynamics of self-stressed solids. The stress-free strain εchem, due to the diffusion species transport, results from the chemical reaction. εchem is associated with the mismatch between the metal and the oxide lattices, and with the movement of atomic defects such as vacancies and dislocations. Larché expresses J with a “Fickian” term, similar to the first term in the Equation 4-31, and corresponding to a diffusion dominated by vacancy mechanisms or at the grain boundaries. In this case, the chemical expansion remains small. The second term of J (“Nernstian” term) is quite different from the second term of the Equation 4-31, integrating the important effect of the chemical expansion εchem. The Nernstian term corresponds to diffusion dominated by an interstitial mechanism in the bulk. Montesin [123] coupled the generalized diffusion law of Larché with a finite element code to estimate the oxidation rate of Ni at 800°C under atmospheric pressure in air. The author showed that the oxidation rate for NiO on Ni depends on the Ni crystallographic plane at the interface with the environment. The oxidation rate was higher for (511) planes than for (111) planes, in agreement with previous observations performed by Li [124].

For steady-state cracking in the direction x at velocity , the Lagrange time derivative of the second Fickian Law can be expressed by:

a

JDxCa

tC

∇−∂∂

=∂∂

Equation 4-34

In the slow propagation regime, xCa

∂∂

is probably negligible, contrary to the rapid propagation

regime.

Usually, diffusion is expected to be confined to a very short distance ahead of the crack tip, as in the case of oxygen in Alloy 600 for instance. Moreover, the local formation of oxides could induce a local stress field, as in the case of NiO at the grain boundaries of Alloy 600 for example. In this case, an additional equation is needed to describe variations of concentration along the grain boundary.

4-13


4-14

4.2.2.3 Consequences of Oxidation on Brittle Rupture Criteria at a Crack-Tip

This paragraph is dedicated to local environmentally assisted fracture. The notion of local brittle rupture criteria cannot be associated with mechanically assisted corrosion, such as slip dissolution model. Contrary to the first case (EAF), the second case (MAC) corresponds to a dissolution of the bare metal (see definitions in Section 3.1.3.1).

A rupture mechanism can be quantitative only if a rupture criterion, expressed by a binary formulation of a non evolving phenomenon, is defined:

φ(xi) – φcritic > 0 Equation 4-35

This criterion can be local or global, empirical or physical, based on xi variables such as stress, strain or energy. For EAC, the rupture criteria must be a local criterion leading to a step- by-step failure. This local criterion must include the effect of chemistry on the conditions for propagation. This can be done in three ways: either by assuming a critical value for the incriminated transported species, or by reducing the value of the critical stress, or by modifying the value of the critical energy release for crack propagation. Since EAC fracture is always “brittle” in nature, it is not suitable to consider a criterion based on strain. The various options outlined above can be expressed in different formulations:

• A Kachanov-type damage function fD associated, for example, with a critical concentration C0 of hydrogen or oxygen on a critical diffusion length (grain boundary or slip plane):

κ

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

01CCfD Equation 4-36

Then, rupture happens when the local strength σ on the critical length reaches the reduced strength fD σ*, where σ* is the nominal strength, as described by Equation 4-37:

σ – fD σ∗ > 0 Equation 4-37

• A “maximum stress” criterion can be associated with a resistance to extension of an oxidized grain boundary, for example, or with a resistance to shearing on preferential slip planes.

• An energetic criterion can be based on the energy release J describing the strain and stress state at a crack tip (Equation 4-38), or on a symmetrical fragility tensor F whose properties are close to the symmetrical compliance tensor (Equation 4-39). In these cases, JIC and Fijkl should be expressed as a function of relevant physical parameters with respect to EAC mechanisms. The definition of JIC could be a “standard” approach, while F could be an efficient way to model anisotropic phenomena.

J – JIC > 0 Equation 4-38

Fijkl σij σkl ≤ 1 Equation 4-39


For instance, the effect of the tensile axis on grain boundary strength of a martensitic stainless steel has been studied at 320°C by Christien [125]. In this example, the brittleness depends on the intergranular phosphorus concentration. Christien proposed a relation between the intergranular phosphorus fraction xp and the angle α between the grain boundary and the tensile axis:

xp = 0.25 + 5.10–3 (α – π/4) Equation 4-40

The stress required for crack propagation is defined by:

⎟⎠⎞

⎜⎝⎛ −

=αππ

σ

2cosd

Ewj Equation 4-41

where wj is the work of decohesion of the grain boundary (see Equation 4-42), E is the Young modulus, d is the grain size, and α is the angle between the main stress axis and the grain boundary.

( jsp

j GGx

ww ∆−∆−=ω0 ) Equation 4-42

with w0 the work of decohesion of a grain boundary without phosphorus;

xp the phosphorus intergranular concentration;

∆Gs the Gibbs free energy of phosphorus segregation at the surface of the steel;

∆Gj the Gibbs free energy of phosphorus segregation at the grain boundaries;

ω the molar surface.

Considering these equations, Christien has shown that crack propagation is much easier when there is an enrichment of phosphorus in the grain boundaries lying perpendicular to the main axis of stress than when the phosphorus concentration is homogeneous. Such an analysis could be adapted in the case of oxygen penetration along the grain boundaries of nickel-base alloys, for example.

Coupling with strain instabilities could enter either via a multiplicative factor on stress accounting for stress concentration (such as singularities at PSB interfaces in fatigue), or via a modification of transport conditions for species: transport of dislocations, fracture of a protective layer, etc. The difficulty here is a difference, however, between temper embrittlement throughout the material and a small zone of material with a gradient of oxygen (or hydrogen) damage ahead of the crack tip.

4-15


4-16

4.2.2.4 Interactions Between Oxidation and Plastic Flow at a Crack-Tip

When the local fracture criteria are defined, interactions between hydrogen, oxidation and plastic flow at the crack tip must be described to establish how and when the criteria can be reached. Thus, it is necessary to analyze the interactions between oxidation and strain localization mechanisms with respect to the time-dependent crack-tip stress field and diffusion of species.

The effect of stress on surface reactivity has been presented earlier, while stress-assisted diffusion has been addressed in Section 4.2.2.2. For example, oxygen enhanced diffusion by the local stress at the crack tip and decohesion along grain boundaries [126] has been proposed to explain the oxidation process in nickel base superalloy 718 in air at high temperatures. Intergranular oxidation promoted by stress can also now be mentioned. For example, stress-assisted formation of a brittle niobium oxide at the grain boundary has also been proposed [127, 128] to explain the oxidation process in nickel base superalloy 718 in air at high temperatures. Stress is the driver for EAC mechanisms and the local stress is the superposition of the applied stress upon the stress resulting from strain localization.

We can now consider interactions in the alloy due to strain localization (Figure 4-7). Strain localization induces a partition of strains in the crack tip region and allows for the rupture criteria to be reached locally. Emerging slip bands at the crack tip blunt the tip and enhances the oxidation process described by Equation 4-18. A number of species produced by oxidation or irradiation, or initially present in the alloy, can interact with the localized plastic flow:

Strain localization

Partition of strain

Reach of the EAC local fracture criteria

Enhancement of oxidation

Absorption and diffusion of hydrogenvacancies

Figure 4-7 Example of Absorption and Diffusion Enhanced Strain Localization Process

• Vacancies: for example, nickel oxide formation at the crack tip, injecting vacancies, is suspected by some authors to be responsible for intergranular cracking in nickel base superalloy 718 [129]. Vacancies are homogeneously produced by irradiation in materials, except in the case of irradiation by ions. In such cases, production in limited to a superficial layer because of the reduced penetration of ions in the material.

• Hydrogen: comes from an external source (environment, oxidation) and an internal source (transmutation in irradiated material). Hydrogen can be transported by mobile dislocations. Strain concentration due to shear band formation at the crack tip can also affect hydrogen transport by stress-strain assisted diffusion. Finite element calculations performed by Toribio [130] have shown that strain localization in the form of shear bands appears for both monotonic and cyclic loading if kinematic hardening is considered.


• Interstitial carbon and nitrogen: The reasons for the increase of mass transport of interstitial atoms in strained materials are still not clear. Globally, however, it can be assumed that the acceleration results from the interaction between mobile dislocations and Cottrel type atmosphere formation with subsequent transfer under the influence of temperature and tension. The influence of a crack tip on interstitial atom concentrations could be investigated, mainly in the case of irradiated materials for which a lot of interstitial atoms are continuously created.

Different mechanisms could be assumed in order to understand the possible interactions between DSA and EAC (Figure 4-8):

– By continuous locking of dislocations, DSA reduces the blunting of the crack tip. Blunting results in cross-slip, which accommodates the curvature of the crack front. This mechanism should promote EAC, because DSA restricts plasticity at the crack-tip.

– DSA can induce Lüders bands and PLC bands in the areas ahead of fatigue crack tips. This mechanism should promote EAC.

– Fournier [49] has shown that, in Alloy 718, the transition between uniform deformation in air and the PLC domain is observed between 470°C and 500°C at 5.10–7 s–1 (Figure 4-9). From a fractographic point of view, the transition from serrated flow to continuous plastic flow is accompanied by a change from a ductile mode to a brittle intergranular mode. Assuming that the oxidation process does not drastically change from 470 to 500°C, this result indicates that oxidation-induced intergranular cracking is strongly influenced by the plastic deformation mode. The drop in the value of the strain rate sensitivity (SRS) of the flow stress associated with DSA increases the tendency for localized deformation, and the effect is more pronounced when SRS becomes negative (in the PLC domain). Crack initiation occurs in the vicinity of oxidized niobium carbides, suggesting that oxidation and swelling of the primary niobium carbides is responsible for crack initiation in air. The result of the CERT performed by Fournier with an abrupt transition in plastic flow seems to indicate that the cracking mechanism could be controlled by the local plastic flow instability at the crack tip.

Dynamic Strain Ageing

Reduction of cross slipping

Reduction of crack blunting

Reduction of accommodation of crack curvature

Strain localization

Lüders band PLC bands

Figure 4-8 Possible Strain Localization Enhanced by DSA at a Crack Tip

4-17


Figure 4-9 Stress-Elongation Curve from CERT (5×10• 7 s• 1) Conducted in Air, First at 500°C up to 0.04 Plastic Strain and then at 470°C Up to Rupture. At 500°C, the SRS of the Flow Stress is Slightly Positive and the Flow Stress is Continuous. At 470°C, the SRS of the Flow Stress Becomes Negative and the PLC Effect Occurs

Finally, we can consider the possible strain localization of SRO effects at a crack tip of aged Alloy 690, or at a crack tip of Alloy 718 containing γ’ precipitates. In the case of Alloy 718, the bad resistance to SCC propagation in the PWR primary environment could result from local strain softening induced by γ’ destruction or irradiation damage.

4.2.2.5 Main Issues

The main issue during slow propagation of EAC is to determine if strain localization is a limiting factor for EAC.

Secondly, considering that strain localization is a relevant parameter to predict slow crack growth rate, the consequences of strain localization on transport mechanisms and local rupture criteria should be investigated:

• Solid transport phenomena are strongly dependent on local stresses, which depend on microplasticity and thus on strain incompatibilities. Moreover, the possible spatial coupling of propagative plastic flow instabilities (PLC bands) with strain incompatibilities can be mentioned [131].

• Grain boundary character plays an important role in the EAC process. Usually, only twin Σ3 boundaries resist crack propagation ( )29 . Except for Σ3, the fractions of grain boundary types that crack correspond to their frequency of occurrence in the alloy [132]. Nevertheless, grain boundary crystallography is not sufficient to predict the crack growth path. Other grain

( )29 Their importance depends on the system and these comments refer to Alloy 600. For sensitization, there is a

progressive increase in the numbers of GBs affected, depending on the temperature and time at temperature, and this impacts directly on the probability of exceeding the percolation threshold.

4-18


4-19

boundary parameters controlling the crack growth path should be considered, such as the interface energy, the microchemistry, the cohesion energy or intergranular precipitation. Jacques [133] studied the contribution of localized stress and strain to initiation of SCC of Zr alloys in aggressive environments (30), analyzing the crystallographic orientation of grains. He observed that the major parameter controlling the nucleation of intergranular cracks is not related to strain incompatibilities, but to the orientation of the grain boundary planes with respect to the tensile stress. Such experiments should be performed on austenitic steels exposed to the PWR primary environment, with respect to hydrogen, vacancy and oxygen diffusion (especially for nickel-base alloys).

4.2.3 Rapid Propagation of Deep Cracks

4.2.3.1 Configuration

The rapid propagation of deep cracks is the ultimate stage of EAC. Consequently, the main issue in this situation is estimation of the remaining period before failure.

The main difference to slow propagation of a short crack is the contribution of crack growth itself to oxidation, transport, deformation and rupture mechanisms.

4.2.3.2 Consequences of Crack Growth for Transport Mechanisms within the Crack

Transport mechanisms include convection and diffusion in the crack, and diffusion in the material at the crack tip, depending on crack depth and length.

Because of the geometrical configuration, exchanges between the crack internal and bulk environments are limited. Thus, it is not obvious that the electrochemical environments are the same for short and long cracks (pH, potential…). TEM examinations provide critical information on the nature and structure of the oxides in both cases, and their differences can be interpreted as a consequence of differences in the local environment. For example, in the case of austenitic stainless steel 304L tested in the PWR primary environment, oxides are similar at the surfaces for short and long cracks (see Section 3.3.2), and the environments can be considered similar. On the contrary, in the case of Alloy 600 exposed to the PWR primary environment, short crack films are composed of hydroxides, while deep crack films are composed of an internal Cr-enriched oxide layer and an external layer of NiO oxide mixed with Ni fibers [134]. In this case, we could assume that the environments are different for short and deep cracks. Meanwhile, CERT have shown that the dependence of crack growth rate on crack tip strain rate is the same for short and long cracks, which is not consistent with a difference in the propagating process and local conditions.

Convection essentially plays a role in very short cracks. In long cracks, convection operates only a short distance into the crack, unless the crack is highly planar and flat (e.g., TGSCC in low-alloy steel) and the flow is aligned along the crack mouth (e.g. an axial crack in a pipe) and the crack has little oxide in it. This moves the “boundary” condition for bulk water into the crack, but rarely has a consequential effect on the chemistry or electrochemistry at the crack tip.

(30) 30 g of Zn chloride + 140 g Al Chloride + 50 ml of n-butyl alcohol + 600 ml of ethanol.


4-20

4.2.3.3 Consequences of Crack Growth on Oxidation Mechanisms

Differences in electrochemical environments at the crack tip lead to different equilibriums, then to different oxidation mechanisms and different kinetics of oxidations, and therefore to different amounts of oxygen, vacancies and hydrogen when compared with the case of slow propagation of short cracks. Thus, the equations presented in Section 4.2.2.2 should be reconsidered with possible new equilibriums and additional reactions.

4.2.3.4 Consequences of Crack Growth on Plastic Flow at the Crack Tip

Several authors have expressed the strain rate at the crack tip CTε as a function of the applied macroscopic strain rate mε and the strain rate resulting of the crack propagation a [1]:

akk mCT 21 += εε Equation 4-43

where k1 and k2 are constant. In the slow regime of propagation k2 a was negligible compared with k1 mε , but this is not the case during rapid propagation. Accordingly, each EAC mechanism (oxidation, transport, strain localization) controlled by the strain rate parameter can be strongly affected by the crack propagation rate.

4.2.3.5 Consequences of Crack Growth on Rupture Criteria

At the crack tip, a mechanical rupture happens when the local stress intensity kIC is reached. Furthermore, the rupture is strongly dependent on the dislocation structure. The emission of dislocations shields the tip and leads to an increase of the K applied to the crack. Hydrogen transport depends on the motion of dislocations, which depends on the crack advance. It also depends on blunting and on the density of the dislocation forest ahead of the crack tip. Moreover, for a critical dislocation velocity, there is transport of hydrogen by the dislocations. As a consequence, the rupture criteria associated with EAC could be totally modified by rapid crack propagation, depending on the kinetics of each mechanism. This could be the case for materials tested in the laboratory using CERT, or for unloading-reloading propagation tests.

4.2.3.6 Main Issues

The limiting factor for EAC mechanisms is usually not readily identified. For rapid propagation, it could be the oxidation reaction, the transport of species, or the extent of strain localization. Because of strong interactions between chemistry, transport, plasticity and rupture phenomena, it could be impossible to determine the relevant parameters for quantitative predictions without efficient modeling tools, such as numerical simulations which enable coupling of several physical phenomena.


4.3 Transitions in EAC Stages

4.3.1 True Initiation

Srolovitz [135] examined the stability of a flat solid surface subjected to stresses. He observed that, above a critical wavelength, the perturbation of the surface with sinusoidal waves amplifies the surface waviness by evaporation and condensation. Similarly, the dissolution rate at the surface of an alloy exposed to an aggressive environment depends on the surface stress. Thus, stress-assisted dissolution has long been suggested as a mechanism for crack nucleation [136].

Furthermore, stress concentration induced by plastic flow instabilities could play a significant role on crack initiation. Initiation of EAC could be enhanced after the propagation of Lüders bands to the surface, or through defects such as scratches or pits. Such propagative instabilities could result from localized loading due to impact. For example, Huang [137] has shown that duplex stainless steels used in the nuclear industry (SAF 2205 ( ) 31 and SAF 2507 ( )32 show strain softening and shear bands at the surface when impacted ( ε = 8.5.102 s–1 and ε = 5.103 s–1). He also demonstrated that austenitic stainless steel 254 SMO ( ) 33 exhibits diffuse Lüders bands at the surface when impacted.

True initiation happens when the necessary electrochemical (pH, potential) and loading conditions for EAC are attained at the surface of the material. Thus, several parameters are required to quantify initiation:

• the probability of reaching the critical electrochemical conditions,

• the probability of reaching the critical mechanical conditions, and

• the surface of material exposed to the environment where these conditions could be reached.

Plastic flow instabilities can affect both the second and third points:

• When materials are globally loaded above the critical value, plastic instabilities can lead to localized loading fluctuations which would allow the critical load to be reached locally.

• Surface defects (scratches…), confined areas and possible strain localization areas (including possible in-service strain localization) must be considered in order to estimate the total surface susceptible to nucleation.

Consequently, it is necessary to define a strain localization rate (SLR), depending on the material, the temperature and the loading, to estimate the probability of initiation in a given area.

( )31 22.16% Cr, 5.52% Ni, 3.13% Mo, 0.026% C. ( )32 24.55% Cr, 6.78% Ni, 3.7% Mo, 0.025% C. ( )33 20.01% Cr, 18.2% Ni, 5.72% Mo, 0.02% C.

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4.3.2 Slow/Rapid Propagation Transition

It seems doubtful that the slow → rapid propagation transition corresponds to a sudden change in the oxidation or transport mechanisms. Therefore, the origin of the transition could correspond to the crossing of a microstructural barrier (grain boundary), to the coalescence of isolated short cracks, or to a threshold in the localized mechanical loading. But it could also be due to a change in plastic flow at the crack tip, or of the rupture criteria. The origin of the transition probably depends on the material, the EAC mechanism and the applied load. For industrial predictions, several authors have correlated the transition to a critical stress intensity. With such a hypothesis, the acceleration depends on both the depth of the crack and the applied load.

SCC of austenitic steels exposed in PWR is probably not a continuous mechanism of propagation, but a succession of crack arrests and crack advances. From a mechanical point of view, this fact has importance for strain localization at the crack tip. It is usually assumed that a stationary crack leads to a singularity proportional to 1/r, while it is Ln(1/r) for a propagative crack. Accordingly, the stress-strain state at the stress corrosion crack tip could probably be affected by the periodic succession of stationary and propagative situations, as well as by the resulting interactions between crack tip induced localization and other plastic flow instabilities such as DSA, Lüders bands, etc.

4.4 Main Issues

It is always difficult to demonstrate that mechanisms observed in the laboratory are representative of mechanisms implicated in the field behavior of nuclear components. Thus, mechanisms must be identified using various types of tests (several types of loading), and the relevance of stress corrosion tests is the first main issue.

Concerning the interactions between EAC and localized deformation:

• Interactions between electrochemical and mechanical mechanisms in LWR during the incubation period remain insufficiently understood for a relevant time to initiation prediction.

• Previous sections and discussion have demonstrated that strain localization can promote EAC. However, additional research, as previously mentioned, is required to determine if:

– Strain localization significantly influences the surface reactivity, with respect to EAC mechanisms?

– Strain localization significantly influences the transport of species (H, O, vacancies) in the material, with respect to quantitative EAC prediction?

– Propagation of EAC is driven by a strain localization network?

– Interactions exist between neighboring localization areas?

– The transition from slow to rapid propagation is correlated to plastic flow instabilities at the crack tip?

– Strain localization could be a relevant parameter for each stage of EAC (incubation, slow propagation and rapid propagation). Actually it has been shown that Alloy 718 has a good resistance to EAC initiation but a poor resistance to crack propagation in the PWR primary environment [138]. No interpretation with respect to DSA has been established in this case.

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Absorbed hydrogen has been mentioned as an important species for the different stages of EAC. Hydrogen/plasticity interactions have been widely studied, showing that hydrogen can locally strengthen or soften an alloy depending on the microstructure, for example. Consequently, quantitative prediction of EAC requires precise knowledge, at LWR relevant temperatures, of:

• the mechanical behavior of the material containing hydrogen,

• the possible activity of hydrogen in the materials in hot temperature water, and

• the possibly significant increase of hydrogen activity near a propagating crack tip.

Finally, investigations should be performed in order to determine if parameters related to plastic flow instabilities are relevant for modeling EAC/strain localization interactions. For example, stacking fault energy (SFE) has a strong influence on mechanical behavior. Low SFE (austenitic steels) reduces the ability for cross gliding of dislocations, and therefore promotes strain localization in restricted slip planes, as well as the formation of strong dislocation pile-ups at obstacles.

There are special issues when considering strain localization at smooth surfaces versus growing crack tips. Despite the variety of observations on the dislocation density near crack tips, there is almost invariably higher plasticity, triaxiality, and a larger number of active slip systems there. Thus, plastic flow contribution is a major issue to be clarified for initiation.

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5-1

5 RECOMMENDATIONS

Evidence of possible interactions between EAC and strain localization has been identified in Section 3. Because plastic deformation is always localized in metals (e.g. along slip planes), it seems appropriate to investigate the possible contribution of relevant plastic flow instabilities to EAC mechanisms. Furthermore, as a consequence of the absence of EDF experience in the BWR field, the present recommendations are dedicated to the PWR primary environment. Thus, in this last section, a program of possible research topics on the synergistic effect of pre-strain localization (outside the environment) with subsequent exposure to the PWR primary environment, or strain localization rate with simultaneous exposure to the PWR primary environment, is proposed.

Experiments should first establish whether strain localization occurs in the materials at the temperatures and strain rates of interest (for PWR), and clearly identify and quantify possible cause-and-effect relationships between localized deformation and EAC (ideally without any other change in factors such as bulk composition, Cr depletion, precipitation, etc., which could affect both EAC and localized deformation).

5.1 Strategy for Investigations

Recommendations here are focused on the key gaps in knowledge, identified in previous sections, with respect to actual field experience. Such gaps can be important challenges to the nuclear industry, as detailed in Table 5-1. They first concern the evolution of the electrochemical reactivity of interfaces (surface of metal and grain boundaries) during the incubation period for EAC. Secondly, the effect of strain localization (essentially due to substructure instabilities and grain boundary sliding) on the initiation period (as defined in Section 3.1.3.1 from an industrial point of view) is a main issue and a priority for future investigations (Table 5-3). Thirdly, the effect of plastic instabilities associated with strain localization induced by the presence of a crack tip itself is of great interest for further study.

Several tasks have been identified in order to:

• Define, and eventually develop, tools for investigation.

• Quantify strain localization effects on EAC. The objective of the investigation is to characterize the EAC response in the temperature/load range encountered in PWR. Low and high strain-rate tensile tests would be carried out in order to provide the parameters for implementation into equations. Quantification includes clear identification of possible necessary conditions for strain localization and threshold localization for EAC (especially for initiation).

• Evaluate possible EAC/strain localization synergy as it applies to plant components.

Recommendations

Table 5-1 Main Issues and Identified Key Gaps from the Present Study

Environment Material EAC Stage Key Gaps


Initiation Consequences of strain localization associated with cyclic loading on time to initiation of PWSCC. Austenitic

stainless steel


Effect of plastic flow instabilities due to solute atoms/dislocations interactions on the CGR.

Effect of strain incompatibilities due to localization on the crack growth path.


Initiation Consequences of strain localization (due to strain path and GBS) on time to initiation of PWSCC.

Relevance of ctε and low K as mechanical parameters for coupling with internal oxidation mechanism.

Correlation between precipitation and strain localization at grain boundaries.

Correlation between transport (oxygen) and strain localization at grain boundaries.


Identification of the local rupture criteria due to the internal oxidation process.

Wrought Alloy 600

Rapid propagationEffect of loading on strain localization at the crack tip.

Consequences of plastic flow instabilities for the CGR.


Initiation Effect of strain localization (due to material heterogeneity) on time to initiation.

HAZ in wrought Alloy 600

Propagation Effect of strain localization (due to material heterogeneity) on the CGR.


Initiation Consequences of strain localization (due to periodic reverse strain path) on time to initiation of PWSCC.

Weld metal 182


Correlation between transport (oxygen) and strain localization at grain boundary.

PWR

Wrought Alloy 690 Initiation

Consequences of high strain localization (due to complex or periodic reverse strain path) on time to initiation of PWSCC.

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Recommendations

Table 5-2 provides an evaluation of the different levels of difficulty and possible time scale for each task. Finally, Table 5-3 proposes a prioritization of the experiments proposed for tasks 2 and 3 in the following paragraphs.

Table 5-2 Difficulty and Time Scale for Identified Tasks

Task Description Difficulty Time Scale

Qualitative techniques for characterization of the cracks 1 1

SEM observation of in-situ deformation in corrosive environment 3 3

Quantitative characterization of strain localization 1 1

Development of specific tests to characterize EAC/strain localization interactions

2 2

– 1 –

Tools of investigation

Numerical simulation of propagation of EAC 3 3

Experimental quantification of the effect of strain localization rate on EAC propagation 2 3

Experimental quantification of the effect of strain localization rate on EAC initiation in austenitic stainless steels 1 2

Modeling the effect of strain localization on EAC in austenitic stainless steels 3 3

Experimental quantification of the effect of strain localization rate on EAC initiation in Ni base alloys 1 2

– 2 –

Quantification of the effect of

strain localization rate on EAC

Modeling the effect of strain localization on EAC in Ni base alloys 2 2

Substructure instabilities due to fabrication process 2 2 – 3 –

Experimental evaluation of

possible EAC/strain localization synergy for components

Material heterogeneities due to fabrication process 2 2

The top priority concerns improvement in prediction of the time to “industrial” initiation of EAC, taking into account the effects of strain localization due to:

• Initial structural discontinuities such as GBS or heterogeneities in HAZ;

• Strain softening due to substructure instabilities (resulting from a change in strain path);

• Fatigue instabilities as PSBs.

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Recommendations

Table 5-3 Prioritization of Investigations for the PWR Primary Environment

Priority Austenitic Stainless Steels

Wrought Ni Base Alloy Ni Base Weld Metals

1 Rate of appearance of PSBs and shear bands at the surface. Correlation with initiation of SCC. (Task 1-2)

Strain softening effect (due to complex strain paths) on time to initiation. (Task 1-2)

Strain localization in welds (due to cyclic loading) and correlation with initiation sites. (Task 1-2)

2 Range of T-ε promoting interactions between solute atoms and mobile dislocations (reducing intragranular creep). Correlation with initiation of SCC. (Task 1-2)

Strain softening effect (due to complex strain paths) on the CGR. (Task 2)

Strain localization in welds (due to cyclic loading) and correlation with the crack growth path. (Task 2)

3 Range of T-ε promoting GBS. Correlation with initiation of SCC. (Task 1)

Strain localization in HAZ and correlation with initiation sites. (Task 3)

Rate of appearance of PSBs and shear bands at the surface. Correlation with time to initiation of IGSCC. (Task 1)

4 Evolution of surface reactivity during the incubation period as a function of pre-strain hardening. (Task 1)

Strain localization in HAZ and correlation with the crack growth path. (Task 3)

Rate of appearance of PSBs and shear bands at a crack tip. Correlation with the CGR of IGSCC. (Task 2)

5 Modeling of SCC. (Task 1) Modeling of IGSCC. (Task 1) Modeling of IGSCC. (Task 1)

At each step, experimental and modeling work is recommended in two simultaneous directions:

• To advance understanding of the physical mechanisms. In particular, it is essential to identify the contribution of local mechanics (plastic flow and/or brittle fracture) and thereby better understand the process of crack initiation and advance. Physical parameters controlling crack initiation and propagation are not the same in the case, for example, of local brittle fracture and in the case of disruption of the protective layer leading to dissolution.

• To develop quantitative models of initiation and propagation phenomena, based on physical mechanisms. Firstly, empirical modeling should permit experimental results to be integrated more directly into industrial applications. Then, equations predicting the material behavior should be implemented into large-scale computational codes so as to model the structural response for environmentally assisted rupture.

5.2 Task 1: Tools of Investigation

The study of strain localization requires the use of specific tools for both macroscopic tests and quantitative microstructural characterization. Some of these are used in other areas and need to be adapted for this purpose.

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Recommendations

5.2.1 Qualitative Techniques for the Characterization of Cracking

• In-situ Raman spectroscopy: in order to directly analyze the structure of oxide films on metals in high temperature water: an in-situ Raman spectroscopic system has been developed and applied for the characterization of the surface oxide films on Alloy 600 under PWR primary water conditions up to 350°C [139]. This in-situ technique allows observation of phases such as NiO, Cr2O3, and NiCr2O4 during stress corrosion tests.

• Etch pitting: EAC/strain localization interactions are faced with the need to explain the kinetics of processes required to continuously produce periodic active dislocation fluxes that result in localized plastic strain. Rate of dislocation generation is vital in relaxation problems, especially in the vicinity of the crack tip. Etch pitting of the flank region of an arrested crack front could reveal the slip activity emanating from the arrested crack front (Figure 5-1). Etch pitting reflects the points of exit of the dislocations created by the arrested crack, but it gives no information on the distribution of the dislocations in depth [140]. Etch pitting could be used to investigate the location of dislocation emission at the crack tip.

• Analytical Transmission Electron Microscopy (ATEM): the use of high resolution ATEM methods and sub-nanometer electron-probe analysis is necessary to characterize the cracks, crack tips, corrosion products and adjacent matrix alloy.

• Electron Back Scattering Diffraction (EBSD): EBSD, associated with polycrystalline finite element modeling, is a useful tool allowing characterization of microplasticity around crack tips and possible strain localization along the crack growth path, for example.

• SEM or TEM in-situ deformation observations in corrosive environment. Given that mechanisms change radically as a function of temperature, this point will present a challenge for electron microscopy!

Figure 5-1 Etch Pit Patterns of Dislocations Emitted from Crack-Tip Sources Roughly a Distance of 5 µm Apart. The Sources are Envisioned to be Associated with Cleavage Ledges [140]

5-5

Recommendations

5.2.2 Quantitative Characterization of Strain Localization

• Grid deposits or Digital Imagery Correlation (DIC): these techniques allow precise measurement of the localization field. Deposit techniques could be developed for applications in high temperature environment.

• Quantification of post-deformation slip bands: channel spacing, lamella spacing, slip distance, and inter-slip region can all be characterized by atomic force microscopy (AFM), for example.

5.2.3 Development of Specific Tests to Characterize EAC/Strain Localization Interactions

• Use of critical strain samples (trapezoidal gauge section) in inert and corrosive media to investigate the whole range of strain with a reduced number of specimens.

• Develop or adapt specific tests for studying and measuring grain boundary sliding (bamboo structures [18]).

• Use of Jominy-type samples ( )34 under stress in a corrosive medium to investigate pre-strain hardening thresholds.

• Use of plane-strain specimens (wide gauge section) for pre-strain hardening in an inert environment and change of strain path in the PWR primary environment.

5.2.4 Numerical Simulation of Environmentally Assisted Rupture

Numerical simulation is a powerful tool allowing testing of both assumed hypotheses and physical, but qualitative models (such as the corrosion enhanced plasticity model for stainless steels and the internal oxidation model for nickel-base alloys). Furthermore, the development of a numerical simulation tool would efficiently guide experiments and the strategy of investigation of EAC. The objectives of numerical simulation should be:

1. To simulate interactions between oxidation and plasticity, leading to the propagation of a crack, as a function of mechanical and electrochemical boundary conditions introduced in a FEM code.

2. To evaluate crack growth rates in several material-environment systems as a function of these boundary conditions.

The envisaged approach would involve performing the following tasks (Figure 5-2):

1. Synthesis of actual fundamental mechanisms and identification of the phenomena (or physical parameters) for quantification: choice of oxidation, diffusion, deformation and rupture laws.

( ) 34 The Jominy Test involves heating a steel test piece to an austenitising temperature and quenching. After

quenching the hardness profile is measured at intervals from the quenched end. The hardness variation along the test surface is a result of microstructural variations which arise since the cooling rate decreases with distance from the quenched end.

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Recommendations

2. Definition of the strategy of simulation and validation. Two strategies for coupling are possible. The first one (weak coupling) consists of a chaining of FEM and oxidation codes. The second one (strong coupling) consists of the development of new finite element codes which include the integration of oxidation, transport and mechanical behaviors.

3. Specific experiments or calculations: mechanical, metallurgical and electrochemical characterizations of metal/oxide/environment interfaces, in order to describe local physical mechanisms of oxidation, deformation, diffusion and rupture. For example, 2.5D discrete dislocation dynamics could be used to treat localization in a monocrystal and possible stress concentrations at grain boundaries.

4. Development and validation of the simulation tool: chaining of routines describing each elementary physical mechanism (oxidation, diffusion, rupture), then comparison of modeling results with experimental databases.

Local electrochemistry

• Input: Environment, T, t, active area

• Output: oxide properties, [H], [O], [ν]

Local transport

• Input: T, t, [H], [O], [ν]

• Output: species maps

Local mechanics

• Input: loading, T, t, species maps

• Output: σ, ε, strain localizationEAR propagation Output: additional active area

EAR Test based on a local fracture

No

Yes

Physics of EAR based on existing

mechanisms

Figure 5-2 Coupling Mechanisms for Environmentally Assisted Rupture (EAR) Simulation

5.3 Task 2: Quantification of the Effect of Strain Localization Rate on EAC

For the different types of strain localization identified in section 2 that are relevant to the SCC examples in nuclear materials (identified in section 3), a careful, comparative approach seems necessary to quantify the strain localization, both in and out of the environment, and to identify the possible conditions for synergy between corrosion and localization. In particular, it should be determined if the environment is capable of changing the mode of strain localization (for instance by the introduction of vacancies via oxidation…).

Quantification of the effect of strain localization on EAC in the PWR primary environment should be first focused on austenitic stainless steels 304L and 316L, nickel base Alloys 600 and 690, and weld metal 182. Furthermore, plastic flow instability effects could be restricted to:

5-7

Recommendations

• Grain boundary sliding (spatial material heterogeneity)

• Substructure instabilities due to complex strain paths (strain softening)

• Persistent slip bands (fatigue instabilities)

• DSA (strain rate softening)

Quantification should include both local effects of plastic instabilities on EAC, and macroscopic correlations between local phenomena with applied conditions (load) and results (CGR).

5.3.1 Strain Localization Maps in an Inert Environment

Objective: The first step should consist of investigating the susceptibility of Alloy 600, Alloy 690, weld metal 182 and austenitic stainless steel to plastic flow instabilities (GBS, DSA, PBS) as a function of temperature and strain rate. After a review of the literature, tests should be performed in order to build maps for strain localization in an inert environment, and possibly for hydrogenated materials (see Test # 1). In the case of weld metal 182, the orientation of dendrites versus the loading axis should also be considered (see Test # 2).

Expected end-products: strain localization maps (GBS, DSA, PSB) for several material parameters (grain boundary precipitation, interstitial atom concentration, cold work, hydrogen). Investigations should start from reference values of parameters (Figure 5-3). Then, the evolution of the critical boundaries of the reference map should be investigated. For example, an effect of intergranular grain boundary precipitation on GBS is expected (Figure 5-4). An effect of temperature and strain rate is also expected on the density of PSB in the material (Figure 5-5).

Temperature

Strain rate

DSA

GBS

Figure 5-3 Reference Map for Strain Localization due to DSA and GBS in Inert Environment

5-8

Recommendations

Temperature

Strain rate

DSA

GBS

Low IG precipitation

High IG precipitation

Figure 5-4 Evolution of Reference Map with Intergranular Precipitation

Temperature

Strain rate d1

d2

d3

Figure 5-5 Evolution of the Density of PSB Under Cyclic Loading with Strain Rate and Temperature

Test # 1

• Test: CERT and CLT in an inert environment, using “Jominy-type” samples with gradient of cold work for the determination of strain hardening thresholds for DSA.

• Parameters: temperature T, macroscopic strain rate ε , frequency of possible cyclic loading, grain boundary precipitation, interstitial atom concentration (C+N), cold work (possibly the gradient thereof), hydrogen.

• Measurements:

– GBS susceptibility

– PSB intensity

– DSA susceptibility

5-9

Recommendations

Test # 2

• Test: CERT and CLT in an inert environment

• Parameters: temperature T, macroscopic strain rate ε , grain boundary precipitation, interstitial atom concentration (C+N), dendrite orientation, hydrogen

• Measurements:

– GBS susceptibility

– PSB intensity

– DSA susceptibility

5.3.2 SCC of Alloy 600 in the PWR Primary Environment

5.3.2.1 Incubation and Initiation of IGSCC

• Effect of GBS on surface reactivity and on the time to initiation

Objectives: the contribution of GBS to SCC initiation should be investigated and quantified with respect to grain boundary misorientation (Test # 3).

Expected end-products

– At the local scale: ta = f (T, , A) S

– Correlation between local and macroscopic scales: = f(S ε , T)

– Identification of detrimental grain boundary misorientation with respect to IGSCC for future investigations on bamboo structures (see section on identification of fracture criteria). Specific tests on bamboo structures were initially developed by Raj and Ashby [18] to study GBS and recently readapted by Lehockey [141] for microplasticity study of Alloy 600, by Skidmore [142] for the study of the evolution of grain boundary energy in Alloy 600, and Scivastava [143] for the study of creep and surface profiles of thin copper wires.

Test # 3

• Test: interrupted CERT on flat specimens (use of grid deposit or DIC)

• Parameters: extension rate, temperature (290–360°C)

• Measurements:

– Time to initiation ta on the exposed area A

– Slide rate S

– Misorientation θ of grain boundaries (EBSD)

– Macroscopic strain rate ε

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Recommendations

• Effect of strain softening due to substructure instabilities on surface reactivity and on the time to initiation

Objectives: the effect of strain softening due to substructure instabilities on SCC initiation should be investigated and quantified with respect to oxide characteristics (see Test # 4). Substructure instabilities could be introduced via change of strain path. Oxide characteristics should include structure, thickness, porosity and oxygen penetration at grain boundaries.



– Correlation between local and macroscopic scales: = f(εS 1, ε2, β, T) where ε1 is the pre-strain hardening in an inert environment and ε2 is the strain hardening in the PWR primary environment.

Test # 4

• Test: interrupted CERT on flat specimens

• Parameters: time, temperature (290–360°C), strain path β (+1,0,–1), stability of dislocation organization for β = –1

• Measurements:

– Location of initiation after different durations of test at T

– Thickness of the oxide layer

– Structure of the oxide layer

– Maximum penetration of oxygen at grain boundaries

• FEM calculations:

– Local strain at the location of initiation at T

• Effect of the substructure of dislocations developed during pre-strain hardening, with or without DSA, on surface reactivity and on the time to initiation

Objectives: the consequences for SCC initiation of strain rate softening due to dynamic strain aging during pre-strain hardening should be investigated and quantified with respect to oxide characteristics and grain boundary sliding (see Test # 5). DSA enhances planar dislocation structures, while cells are usually observed in materials strained outside the range of DSA. Pre-strain hardening in and out of the range of DSA would allow investigation of the possible effect of dislocation organization on the time to initiation for equivalent hardening.


– At the local scale:

o = f(T, dislocation structure) S

o Oxide properties = f(T, t, dislocation structure)

– Correlation between local and macroscopic scales: ta = f (T, dislocation structure)

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Recommendations

Test # 5

• Test: interrupted CLT on flat specimens removed from pre-strain hardened materials

• Parameters: time, temperature (290–360°C), dislocation organization (planar, cells)

• Measurements:

– Time to initiation at T




• Effect of fatigue instabilities on surface reactivity and on time to initiation

Objectives: the consequences for SCC initiation of fatigue instabilities, such as persistent slip bands, should be investigated and quantified with respect to the oxide characteristics (Test # 6).


– At the local scale: ta = f (T, ) PSBd

– Correlation between local and macroscopic scales: = f(T, ∆σ, σPSBd m, F)

Test # 6

• Test: interrupted tests under cyclic loading on axisymetric notched specimens

• Parameters: time, temperature (290–360°C), strain rate ε , stress deflection ∆σ, mean stress σm, frequency F

• Measurements:

– Time to initiation at T

– Location of initiation, after different durations of test at T, versus PSB

– Density dPSB of PSB (SEM/TEM)




5.3.2.2 Slow Propagation of Short Cracks

• Identification of local fracture criteria

Objectives: the identification of local fracture criteria is required to simulate interactions between the environment and plasticity, and then to validate mechanisms of EAC proposed in the literature. The first step could consist of identifying a simple criteria based on stress, strain or energy release, for example (see Test # 7). Then, additional experiments would be necessary to improve simulation, including specific effects of transport (vacancies, hydrogen, oxygen), oxidation and plastic flow instabilities.

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Recommendations


– At the local scale: first local fracture criteria for IGSCC propagation

– Correlation between local and macroscopic scales: use of the identified fracture criteria to simulate slow crack propagation in a polycrystalline wire and comparison with experiment.

Test # 7

• Test: CLT on bamboo structure

• Parameters: load, temperature (290–360°C), “texture” of the bamboo structure

• Measurements:

– EBSD characterization before testing

– Polycrystalline FEM calculation before testing

– Required duration of exposure to the environment to complete the oxidation of a grain boundary as a function of grain boundary misorientation (or energy)

– Quantitative effect of applied load on this required duration

– Quantitative evaluation of the local stress and strain (via FEM calculations) necessary to fracture a completely oxidized grain boundary

• Effect of GBS on slow crack growth rate in the PWR primary environment

Objectives: correlation between slow crack growth rate and grain boundary sliding (Test # 8)


– At the local scale: = f (T, ) Op S

– Correlation between local and macroscopic scales: = f( , T) a Op

Test # 8

• Test: interrupted CERT or CLT on bamboo structure

• Parameters: extension rate or load, “texture” of the bamboo structure

• Measurements

– Oxygen penetration pO

– Crack depth a

– Slide rate S

5.3.2.3 Rapid Propagation

• Effect of strain localization induced by the crack tip itself on plastic flow instabilities at the crack tip

Objectives: possible enhancement of plastic flow instabilities such as GBS, PSB and DSA at a crack tip, in and out of the PWR primary environment.

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Recommendations

Expected end-products: local amplification of plastic flow instabilities versus loading and crack length.

• Effect of strain rate softening due to DSA on the crack growth rate

Objectives: possible contribution of DSA to slow crack growth rate (see Test # 9)


– At the local scale: = f (T, DSA susceptibility) Op

– Correlation between local and macroscopic scales: = f(DSA susceptibility, T) a

Test # 9

• Test: interrupted CERT or CLT on a bamboo structure

• Parameters: extension rate, “texture” of the bamboo structure, T, solute atoms (C+N)

• Measurements:

– Oxygen penetration pO

– Crack depth a

– Slide rate S– Activated slip systems and then strain incompatibilities

5.3.3 IGSCC of Weld Metal 182 in the PWR Primary Environment

5.3.3.1 Incubation and Initiation of IGSCC

• Effect of GBS on the surface reactivity and time to initiation

Objectives: the objectives are similar to those presented previously, with an additional consideration concerning orientation of the dendrites (see Test # 10)



– Correlation between local and macroscopic scales: = f(S ε ,ζ, T)

Test # 10

• Test: interrupted CERT on flat specimens (use of grid deposit or DIC)

• Parameters: extension rate, temperature (290–360°C), dendrite orientation versus axis of loading ζ

• Measurements:

– Time to initiation ta on the exposed area A

– Slide rate S– Misorientation θ of grain boundaries (EBSD)

– Macroscopic strain rate ε

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Recommendations

• Effect of strain softening due to substructure instabilities on surface reactivity and the time to initiation

Objectives: the consequence for SCC susceptibility of strain softening due to substructure instabilities could be limited to the case of reverse strain path with respect to possible in-service loading of weld metals (see Test # 11).


– At the local scale: ta = f (T , A) , S

– Correlation between local and macroscopic scales:

o = f(εS 1, ε2, ζ, T)

o Oxide properties = f(ε1, ε2, ζ, T)

Test # 11

• Test: interrupted CERT on flat specimens

• Parameters: time, temperature (290–360°C), stability of dislocation organization for reverse strain path (β = –1)

• Measurements:

– Location of initiation after different durations of test at T




• Effect of fatigue instabilities on surface reactivity and the time to initiation

Objectives: the consequence of PSB for stress and strain thresholds for SCC should be investigated under cyclic loading (see Test # 12).




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Recommendations

Test # 12

• Test: interrupted tests under cyclic loading on axisymetric notched specimens

• Parameters: time, temperature (290–360°C), strain rate ε , stress deflection ∆σ, mean stress σm, frequency F

• Measurements:

– Location of initiation after different durations of test at T, with respect to PSB

– Density dPSB of PSB (SEM/TEM)




5.3.4 Incubation and Initiation of IGSCC for Alloy 690 in the PWR Primary Environment

• Effect of strain softening due to substructure instabilities on surface reactivity and the time to initiation

Objectives: the effect of strain softening due to substructure instabilities on SCC initiation should be investigated and quantified with respect to oxide characteristics (see Test # 4). Substructure instabilities could be introduced via a change of strain path. Oxide characteristics should include structure, thickness, porosity and oxygen penetration at grain boundaries.





Objectives: the consequences for SCC initiation of fatigue instabilities such as persistent slip bands should be investigated and quantified with respect to the oxide characteristics (Test # 6).




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Recommendations

5.3.5 SCC of Austenitic Stainless Steels 304L and 316L in the PWR Primary Environment

5.3.5.1 Incubation and Initiation of SCC

• Effect of GBS on the time to initiation

Objectives: the contribution of GBS to SCC initiation should be investigated and quantified as a function of grain boundary misorientation (Test # 3).



– Correlation between local and macroscopic scales: = f(S ε , T)

– Identification of detrimental grain boundary misorientation versus SCC for future investigations on bamboo structures.


Objectives: the consequences for SCC initiation of fatigue instabilities such as persistent slip bands should be investigated and quantified with respect to the oxide characteristics (Test # 6).


– At the local scale: ta = f (T, , A) PSBd


• Effect of substructure instabilities associated with fatigue instabilities on surface reactivity and the time to initiation

Objectives: the effect of strain softening due to substructure instabilities on SCC initiation should be investigated and quantified with respect to oxide characteristics (Test # 4). Substructure instabilities could be introduced via a change of strain path. Oxide characteristics should include structure, thickness, porosity and oxygen penetration at grain boundaries.


– At the local scale: ta = f (T, , , A) S PSBd


5-17

Recommendations

• Effect of the substructure of dislocations developed during pre-strain hardening, with or without DSA, on surface reactivity and the time to initiation

Objectives: the consequences for SCC initiation of strain rate softening due to dynamic strain aging during pre-strain hardening should be investigated and quantified with respect to oxide characteristics and grain boundary sliding (see Test # 5).


– At the local scale:

o = f(T, dislocation structure) S

o Oxide properties = f(T, t, dislocation structure)

– Correlation between local and macroscopic scales: ta = f (T, dislocation structure)

5.3.5.2 Slow Propagation of Short Cracks

• Identification of local fracture criteria

Objectives: the identification of local fracture criteria is required to simulate interactions between the environment and plasticity, and then to validate mechanisms of EAC proposed in the literature (CEPM).


– At the local scale: first local fracture criteria for SCC propagation

– Correlation between local and macroscopic scales: use of the identified fracture criteria to simulate a slow crack propagation in a polycrystalline wire and comparison with experiment.

• Effect of GBS on slow crack growth rate in the PWR primary environment

Objectives: correlation between slow crack growth rate and grain boundary sliding (Test # 8)


– At the local scale: = f (T, ) Op S

– Correlation between local and macroscopic scales: = f( , T) a Op

5.3.5.3 Rapid Propagation

• Effect of the strain localization induced by the crack tip itself on plastic flow instabilities at the crack tip

Objectives: possible enhancement of plastic flow instabilities such as GBS, PSB and DSA at a crack tip in and out of the PWR primary environment.

Expected end-products: local amplification of plastic flow instabilities versus loading and crack length.

5-18

Recommendations

• Effect of strain rate softening due to DSA on slow crack growth rate

Objectives: possible contribution of DSA to slow crack growth rate (see Test # 9)


– At the local scale: = f (T, DSA susceptibility) Op

– Correlation between local and macroscopic scales: = f(DSA susceptibility, T) a

5.4 Task 3: Experimental Evaluation of Possible EAC/Strain Localization Synergy for Components

For an evaluation of possible EAC/strain localization interactions in components, two main aspects must be considered:

• Strain localization resulting from the manufacturing process. In this case, substructure instabilities (due to complex strain paths for example) and material heterogeneities (HAZ for example) should first be investigated, with particular attention being paid to the stability of dislocation structures due to the manufacturing process.

• Strain localization resulting from in-service loading, including nominal and transient regimes. In this case, recovery, relaxation and creep could be considered via appropriate loading. The evolution of the stability of the dislocation structure could be a key parameter, especially under cyclic loading.

5.4.1 Substructure Instabilities Due to the Manufacturing Process

As shown in Section 3, a change in strain path could be at the origin of significant changes in the SCC behavior for cold-worked stainless steels and nickel-base alloys exposed to the PWR primary environment. This could be an issue resulting from the manufacturing process (forming), or for comparing results obtained from different types of laboratory tests (for instance strain paths are significantly different for RUB or constant load specimens).

Substructure instabilities should be investigated considering different forming processes, possibly in combination. Then, their evolution under constant, transient or cyclic loading should be studied.

5.4.2 Material Heterogeneities Resulting from the Manufacturing Process

Failure initiation is frequently found in the heat-affected and welded zones of HSLA 100 steels ( )35 , and is mainly caused by tensile stresses [144]. The heat-affected zone, which is cooled at different rates and includes different regions of microstructure, could be the source of failure in a welded joint. During the welding thermal cycle, base metal close to the fusion zone can transform depending on the cooling rate and steel composition. These different phase microstructures correspond to different mechanical properties (Figure 5-6 and Figure 5-7). ( )35 High Strength Low-alloy 100 steels (YS = 690 MPa) are used in naval vessels subject to dynamic loading from

impact or explosion.

5-19

Recommendations

The SCC behavior of Heat Affected Zones is a potential issue for all the materials constitutive of components used in nuclear power plants. The relevant issue concerns the influence of macroscopic heterogeneities in the plastic behavior (such as welds and HAZ) and possible effect on SCC.

First, the source and mechanisms of failure for a weld joint with or without pre-defects under different “in-service-type” loading still need to be investigated with respect to a possible strain rate sensitivity of EAC mechanisms. So, strain localization could be examined versus distribution of hardness or failure configuration for example.

Second, the effect of parameters such as precipitation should be studied, because of their implication in strengthening mechanisms.

Figure 5-6 Distribution of Vickers Micro-Hardness Along the HAZ. HSLA 100 Steel [144]

Figure 5-7 Mechanical Responses of Base Metal, Weld Metal and Boundary with the HAZ in the Center of the Specimen. HSLA 100 Steel [144]

5-20

6 CONCLUSIONS

Evidence of strain localization/EAC interactions have been identified in the laboratory for various environments, materials, and loads. These interactions occur at different stages of EAC. Sometimes, strain localization seems to be a necessary condition for EAC, but more usually, plastic flow instabilities simply promote EAC. The contribution of strain localization to EAC is often not quantified.

The understanding and prevention of EAC/strain localization interactions is an essential issue to maintain the integrity of PWR and BWR components throughout their service lives. Consequently, efforts should be focused on better understanding and modeling of such phenomena.

If experimental studies allow identification of the global processes for these mechanisms, their association to theoretical models still remains particularly complex, because of the variety of scientific disciplines with which they are connected. The main difficulty in EAC modeling is due to the fact that interactions between oxidation and strain localization are confined to a narrow region ahead of the crack tip. An analytical solution seems inadequate to describe EAC/strain localization interactions. The resulting coupled equations described in the discussion should be solved numerically for steady-state cracking. Development of numerical simulations would allow hypotheses to be tested on physical models, and should provide insight into the interplay between local oxidation, diffusion, plastic flow and rupture. It would also provide guidance on better design of experiments, better understanding and, ultimately, better design of components in LWR.

Future investigations on austenitic stainless steels and Ni-based alloys (including wrought Alloy 600, weld metals 182/82 and corresponding heat affected zones) exposed to the PWR primary environment should be dedicated to both quantitative modeling and understanding of the physical phenomena. The prioritization of investigations should focus on improved prediction of the “industrial” initiation time for EAC, including the effects of strain localization due to:

• Initial structural discontinuities, such as GBS or heterogeneities in HAZ;

• Strain softening due to substructure instabilities (resulting in a change of strain path);

• Fatigue instabilities such as persistent slip bands.

The development of a quantitative model for EAC/strain localization interactions will require additional experiments in order to define local and individual processes of oxidation, transport, deformation and rupture, as well as to deal with their coupling.

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A DIFFUSION OF OXYGEN IN ALLOYS

+⎟⎟

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πη d

tDx

DDDD

erfvj DD

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with tDD

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β = Equation A-2

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Equation A-4

A-1

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Printed on recycled paper in the United States of America

Program:Nuclear Power

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Relationship Deformation Cracking

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