Creep-fatigue life assessment of high-temperature weldments using the linear matching methodYevgen Gorash & Haofeng Chen

Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, UKyevgen.gorash@strath.ac.uk haofeng.chen@strath.ac.uk, http://www.thelmm.co.uk&

1. Theoretical Background and the Linear Matching Method

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purelyelasticbehavior

elasticshakedown

max�

min�

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�r& low-cycle fatigueeverse plasticity

ratchettingfollowed byincrementalcollapse

instantaneouscollapse

100

1

2

lim/P P

tm y/� � �

�

�

�

variable von Mises thermo - mechanical stress

yield stress taken as 0.2% plastic strain offset

constant component of applied mechanical load

limit load, the maximum load that a structure

can s

tm

y

lim

P

P

�

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afely carry without instantaneous collapse

1.1 Bree diagram with responses to cyclic loading1

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1iE �

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2iE �

3iE �

3i� �

2i� �

1i� �

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1.2 Fundamentals of the Linear Matching Method2

• belongs to the group of modified elastic modulus methods;• has the character of a non-linear programming method;• with each step involves the solution of a linear problem;• each solution satisfies the condition of force equilibrium;• non-linear constitutive assumptions are imposed sequentially;• strain rate histories give rise to equilibrium residual stress fields;• solution is the minimum of a functional of the strain rate history;• generates inelastic solutions for the stabilized cyclic state;• compatible with standard finite element codes, e.g. ABAQUS.

• Life Assessment Methods and Design Codes – R5 Procedure, ASME N47 and RCC-MR(1980's – today) based on Neuber's Rule

• Conventional incremental (transient) FEA• Direct Cyclic Analysis (DCA) incorporated into ABAQUS• Direct Methods using Static or Kinematic Bounding Theorem (Koiter, 1960)

Alternatives to the LMM:

• Modified Modulus Method (MMM) for limit load analysis (Ponter, early 1990’s)• MMM modified for elastic shakedown analysis (Ponter & Carter, 1997)• MEM implemented as ABAQUS UMATs (Ponter & Engelhardt, 2000)• Linear Matching Method (LMM) implemented in ABAQUS for reverse plasticity

(global shakedown) & ratchet boundary evaluation (Ponter & Chen, 2001)• LMM further developed to evaluate R5 related parameters (Ponter & Chen, 2005)

Development of the LMM framework:

2. Testing & modelling of cruciform weldment

2.1 Experimental facility and specimen with typical failures3

620800

1500

Load points FurnanceWeld

Servo motor

Moving crosshead

Furnance

Deflectionmonitor

Load cell

Specimen

RollerBox

550 C°

1) fatigue failure at weld toe corresponding to1.0% of total strain range

2) fatigue failure remote from weldcorresponding to 0.4% of total strain range

Typical failure locations:

1

2

2.2 Dimensions (mm) of the cruciform weldment specimen3

2.3 Parameters of the FE-model

10

0

26

60°

72

200

3

3

3

26

3

592

R25

50

M

M

Temperature: 550 C°

P

parent material

heat-affected zone

weld metal

material without creep

totally elastic material

1) 977 CPE8R finite elements: 8-node biquadratic

plane strain quadrilaterals with reduced integration

2) 3 variants of dwell period - pure fatigue, 1 hour, 5 hours

3) 5 variants of reverse bending moment corresponding to

equal to 1.0%, 0.6%, 0.4%, 0.3% and 0.25% of total strain

M

εΔ

� � � �3200 26

Area Moment of Inertia: , 13...1312

X

X

M yI P y y

I

� � � �

X

Y

4. Creep-Fatigue Evaluation Procedure

4.1 Creep-fatigue evaluation procedure with time fraction rule4

�1

2

3

tot �

cr �

�

�

cr�

�

tota

l str

ain

range

number of cycles to failure

tot �

N �

Saturated hysteresis loop

S-N diagram forlow-cycle fatigue

f

1c

1

N ��

Fatigue damageaccumulated per

1 cycle:

stre

ss

time

� �1

0

1, ,

t

t Z dtt

�� � �

Stress relaxationbehaviour

t

1� Z

1�

2�

2�

stre

ss

time to rupture

t�Creep rupture

curve

cr

1c

t

t�

�

Creep damageaccumulated

1 cycle:per

fatig

ue d

am

age

creep damage

Creep-fatigueinteraction diagram

1

f�

cr�

1

f cr

f

f 1c

cr

cr 1c

1

N N

N

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�� �

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1

2

3

5

4

4.2 FEA/LMM results corresponding to Δ = 1% and Δ = 5hε ttot

01.287e-032.617e-033.947e-035.277e-036.607e-037.937e-039.268e-031.060e-021.193e-021.326e-021.459e-021.592e-02

01.782e-043.576e-045.370e-047.164e-048.958e-041.075e-031.255e-031.434e-031.613e-031.793e-031.972e-032.152e-03

028.80459.07989.354119.629149.904180.178210.453240.728271.003301.278331.553361.828

024.06949.60175.132100.664126.195151.727177.258202.790228.321253.853279.384304.916

totalstrainrange

Δεtot

equiv.creepstrain

εcr

equiv.vM

stress(MPa)

5 ht equiv.

vMstress(MPa)

eq

vM�eq

vM�

4.3 Creep-fatigue evaluation results of the cruciform weldment

0.2

1

tota

l str

ain

range (

%)

200 1000 10000 100000

number of cycles to failure

0.5

Resultsof FEA

with LMM:

X-weld fatigue

X-weld = 1h

X-weld = 5h

Δt

tΔ

AvailableLCF tests

fittings :5

parent R66 curve

weld R66 curve

X-weld LCF tests

Resultsof X-weldtesting :3

X-weld fatigue

X-weld = 1h

X-weld = 5h

Δt

tΔ

Δεtot,%

Δt = 0 h Δ = 1 ht Δ = 5 ht

FEA/LMM experiments3 FEA/LMM experiments3 FEA/LMM experiments3

N* failure N* failure N* failure N* failure N* failure N* failure

1.0 857 T 918 T 430 T 562 U 278 T 275 P

0.6 4062 T 2499 U 1673 T 1048 U 967 T 943 W

0.4 17025 T 15747 P 6270 T 6512 U 3168 T — —

0.3 45374 W 38127 P 19776 T 21488 W 9679 T — —

0.25 90056 W 66847 P 52221 T — — 26901 T — —

(U) Specimen failed at the undercut close to the weld toe in the parent plate(T) Specimen failed at the weld toe propagating through the HAZ(P) Specimen failed in parent plate remote from weld(W) Specimen failed in weld metal

5. Analysis of the Obtained Results

5.1 Analytical functions for cycles to failure and residual life

Δt, dwell time (hours)

0 0.5 1 2 5 10 100 1000 10000

1.470528 857 500 430 362 278 223 95 33 8

1.153799 4062 2037 1673 1339 967 746 307 122 42

0.925507 17025 7963 6270 4756 3168 2294 799 308 121

0.777426 45374 24952 19776 14931 9679 6755 1963 635 230

0.691045 90056 63964 52221 40511 26901 18869 5116 1415 434

var

sh

MM

M

�

norm

aliz

ed m

om

ent

a1 a2 b1 b2

−0.4921 3.708929 0.0255 0.754959

� � � �

� � � �� � � �

3

1 2

tot

tot 1 2 2

2

1 3

1

2 ( )log( ) ,

365·24 (365·24·60·60)

0.2817, 0.17649

log 1

l

, 3.110

og 1

( ) 51

b t

p

t

a t a t a

b t b

MtN a t M L N

M p M p M p p

t b

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where - dependent parameter

with

s :

5.2 Design contour plot for creep-fatigue durability

0.01 0.1 1 10 100 1000 10000

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

dwell time (hours)

no

rma

lise

d m

om

en

t

10205010020050010002000500010000200005000010000020000050000010000002000000

No. of cycles

life (years)tests

1000

300

100

30

10310.30.10.030.010.003

fatigue dominant creep dominant

5.3 Comparison of the observed and predicted *N

100

1000

10000

100000

100 1000 10000 100000

optimal match

factor of 2

factor of 1.6

LMM (fatigue)

LMM (Δt = 1h)

LMM (Δt = 5h)

analitic (fatigue)

analitic (Δt = 1h)

analitic (Δt = 5h)

Non-conservative

Conservative

experimental cycles to failure

pre

dic

ted c

ycle

s to

failu

re

5.4 Dependence of FSRF on duration of dwell period7 Δt

1

2

3

4

5

6

7

8

0.01 0.1 1 10 100 1000 10000

maximum

average

minimum

FSRF

dwell time (hours)

FS

RF

2 3

0 1 2 3

0 1 2 3

,FSRF( ) log( 1) log( 1) log( 1)

1.7685, 0.53422, 0.00574, 0.02509

t f f t f t f t

f f f f

� � � � � �

where

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� �� �

� � � �� �

� �3

2

tot 0 1 2

1

tot 1

p

2

0 1

arent

x-weld

2

log log log ,

,log log

2.2274, 0.94691 and 0.085943

p

b t b t

m m N m N

a t a tp p

N N

m m m

� �

� � � � � � � � �� � � �� �

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parent

tot

x-weld

tot

FSRF ,,

NN t

N t

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�

3. Properties of the steel AISI type 316N(L) at 550°

-0.01 -0.005 0 0.005 0.01-400

-300

-200

-100

0

100

200

300

400

-0.01 -0.005 0 0.005 0.01-400

-300

-200

-100

0

100

200

300

400

total straintotal strain

stre

ss

stre

ss

saturated (R-O)1st cycle (R-O)saturated (EPP)saturated (tests)1st cycle (tests)

parent material MMA weld metal

3.1 Rate-independent cyclic plasticity3

1

tot 3

2(,

2 2 2 1 )E B

EE

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Zone E (MPa) B (MPa) β σy (MPa)

Parent 160000 1741.96 0.29960 270.662

Weld 122000 578.99 0.10162 307.894

HAZ 154000 1632.31 0.25304 338.731

Deformation plasticity (Ramberg-Osgood model):

3.2 Creep strain and rupture3,6

0

0.01

0.02

0.03

0.04

0.05

0 500 1000 1500 2000 2500

time

creep s

train

100

1000

100 1000 10000 100000

parent tests

weld tests

parent model

weld model

stre

ss

time to rupture

parent material: 390, 349, 310 and 285 MPaMMA weld metal: 270, 250 and 215 MPa

3

6

parent test (285 MPa)

weld test (270 MPa)

parent model (285 MPa)

weld model (270 MPa)

3

3

cr

cr 1

1

n m

n m

A t

At

m

�

�

�� �

� �

� �

Time to creep rupture:

k

Bt� �

�

Time-hardening power-law: ZonePrimary creep strain Time to creep rupture

A (MPa /h )-n m+1 n m B (MPa h)k k

Parent 6.604E-19 5.769 -0.55 2.172E+26 8.927

Weld 6.597E-23 7.596 -0.5 5.993E+29 10.61

HAZ 6.600E-21 6.683 -0.525 1.291E+28 9.768

0.1

1

1000 10000 100000

parent material

MMA weld metal

R66 fatigue endurance curves5

number of cycles

tota

lstr

ain

ran

ge

(%

)

3.3 Low-cycle fatigue endurance5

tot 2

0 1 2

tot 2 3

0 1 2 3

log( ) log( ) log( )

log( ) log( ) log( ) log( )

m m N m N

m m N m N m N

� �

� � �

� �

� � �

and�

�

ZoneQuadratic Cubic

parent MMA weld parent MMA weld

m0 1.73339 1.85169 2.40906 1.93432

m1 -0.72959 -0.76094 -1.25128 -0.82500

m2 0.06170 0.05951 0.19399 0.07585

m3 -0.01102 -0.00137

References

[1] Bree J. Elastic-plastic behaviour of thin tubes subjected to internal pressure andintermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements.

, 1967; : 226-238// In:

[2] Chen H.F., Chen W. and Ure J. Linear matching method on the evaluation of cyclic behaviourwith creep effect. // In: . Toronto,Canada: ASME; 2012, July 15-19

[3] Bretherton I. Reports by AEA Technology plc. and Serco Assurance (Warrington, UK)for British Energy Generation Ltd.: no. (1998), no. (1999), no.

(2000), no. (2004)

[4] Wada Y., Aoto K. and Ueno F. Creep-fatigue evaluation method for type 304 and 316FR SS.// In: . Vienna, Austria: IAEA;1997, p. 75–86

[5] Bate S.K. Further analyses to validate the R5 volume 2/3 procedure for the assessmentof austenitic weldments. // Report for British Energy Generation Ltd. no.

; SercoAssurance (Warrington, UK); 2005

[6] Data sheets on the elevated-temperature properties for base metals, weld metals andwelded joints of 18Cr-12Ni-Mo-middle N-low C hot rolled stainless steel plates (SUS 316-HP). ; National Institute for Materials Science; Tsukuba,Japan; 2005

[7] Ainsworth R.A., editor. R5:British Energy Generation Ltd (Gloucester, UK); 2003

Journal of Strain Analysis 2(3)

Proc. ASME Pressure Vessels & Piping Conf.

et al.R/NE/432 AEAT-3406 AEAT-

3406 RJCB/RD01186/R01

Creep-fatigue damage rules for advanced fast reactor design

et al.

SA/EIG/11890/R002

NIMS Creep Data Sheet No. 45A

An Assessment Procedure for the High Temperature Responseof Structures. Procedure R5: Issue 3.

(PVP2012)

Acknowledgements

The authors deeply appreciate the EPSRC of the United Kingdomfor the financial support in the frames of research grant no.EP/G038880/1, the University of Strathclyde for hosting during thecourse of this work, and EDF Energy for the experimental data.

Engineering and Physical

Sciences Research Council

6. Conclusions

1)

2)

3)≤

4)cases

cases

5)

6)

The series of have been implemented with LMM using:and corresponding constants to describe plastic strains under

saturated cyclic conditions;and corresponding constants to describe creep strains

during primary creep stage.The amount of damage per cycle caused by is estimated using:

experimentally defined dependent on numericallydefined total strain range for the fatigue damage ( );experimentally defined dependent on the average stress duringdwell period for the creep damage ;the during dwell period is defined as a mean value of analytical function for stressduring relaxation dependent on elastic follow-up factor ( ), initial stress and time.

A non-linear is used to define the caused by both creep andfatigue, which can’t exceed one ( + 1). Basing upon this interaction, the number of cycles tocreep-fatigue failure ( � ) is defined.Comparison of the observed and predicted cycles to failure with creep-fatigue FEA/LMM for 3 typesof experiments shows, that simulation of 9 of total available 11 is very close to .Simulation of other 2 produces results with factor of difference equal to ,which is even better than the factor acceptable for engineering analysis equal to .Sets of creep-fatigue FEA/LMM results analysis corresponding to 0, 0.5, 1, 2, 5 and 10 hours arefitted by and used for of cycles to failure ( *) depending on dwellperiod and normalized moment intended for design application.Further research will be devoted to parametric studies of the influence of variation of weldmentgeometrical parameters on the number of cycles to failure ( *) and formulation of a

to describe the corresponding dependence.

creep-fatigue analyses

creep-fatigue interaction

creep-fatigue diagram

1.62

• Ramberg-Osgood material model

power-law model in “time hardening” form

relation for number of cycles to fatigue failure ( *)

relation for time to creep rupture ( *)

average stress

total damage

optimal matchnon-conservative

analytical function contour plot

mathematicalrelation

•

•

•

•

N

tω

Z

ω ωN

N

N

f

f cr

( )ωcr