TRIP-150 Blast Protection Alloy

TRIP-150 Blast Protection Alloy

Completed in Concordance with the MSE 390 Capstone Design Course

Team Members:Ruilong Ma

Wisaruth MaethasithBen RichardsonEric Schwenker

Zhibo Zhao

Advisors:Dr. Zack FeinbergDr. Greg Olson

Northwestern UniversityDepartment of Materials Science and Engineering

2220 Campus DriveEvanston, Illinois 60208

June 15, 2012

Contents

1 Executive Summary 3

2 The Need for Better Blast Protection 42.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Anatomy of a Blast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Theoretical Background 53.1 TRIP Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Mechanical Transformation Start Temperature . . . . . . . . . . . . . . . . . 73.3 Austenite Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Precipitation Strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5 Warm Work and Cellular Reaction . . . . . . . . . . . . . . . . . . . . . . . 133.6 Modeling and Computational Tools . . . . . . . . . . . . . . . . . . . . . . . 13

4 Team Organization 144.1 Technical Background and Role Assignment . . . . . . . . . . . . . . . . . . 14

5 Role Assignment 16

6 Property Objectives 176.1 Primary Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.2 Secondary Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7 System Structure 18

8 Previous Work 198.1 Blast Alloy 160 (BA-160) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198.2 Experimental Alloy 425 (EX425) . . . . . . . . . . . . . . . . . . . . . . . . 198.3 TRIP-120 Steel Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

9 Design Approach 20

10 TRIP-120 Prototype 2110.1 Grain Boundary Cellular Reaction . . . . . . . . . . . . . . . . . . . . . . . . 2110.2 Elimination of the Cellular Reaction through Warm Working . . . . . . . . . 22

11 Optimizing TRIP-120 2311.1 Determination of Tempering Temperature and Time . . . . . . . . . . . . . . 2311.2 Characterization of Precipitation (γ’) . . . . . . . . . . . . . . . . . . . . . . 2511.3 Ham Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2611.4 Validating the Effect of Austenite Stability on Uniform Ductility . . . . . . . 27

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12 Re-evaluating the Strength Objective 2812.1 Determining Amount of Warm Work Reduction . . . . . . . . . . . . . . . . 2912.2 Meeting the Strength Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2912.3 Achieving the Austenite Stability Goal . . . . . . . . . . . . . . . . . . . . . 3312.4 Iteration to Meet Both Strength and Stability Goals . . . . . . . . . . . . . . 3512.5 Predicting Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . 3612.6 Aluminum Content Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 37

13 Conclusion 38

14 Acknowledgements 40

15 References 41

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1 Executive Summary

The recent upward trend of indiscriminate terrorist attacks worldwide underscores theincreasing need for blast-mitigation materials designed for civilian applications. However,current blast mitigation trash cans either do not have adequate blast mitigation propertiesor are excessively expensive. There exists strong civilian and military need for new materialsthat are both cheap and have adequate materials properties to resist bomb blasts. This reportdemonstrates how a systems-based computational materials approach can be employed inthe design of a better blast-resistant steel: TRIP-150.

Blast resistant materials need to meet two primary design objectives: (1) resistance tolocalized shear stresses and (2) uniform tensile ductility. Existing work on blast-resistantsteels has produced TRIP-120, which exploits the Transformation-Induced Plasticity (TRIP)phenomenon to meet the performance requirements under blast-related stresses. However,TRIP-120 suffers from an embrittling cellular reaction during tempering that severely limitsits blast-resistant properties.

In the design of our TRIP-150 alloy, we improve upon TRIP-120 by reducing embrittlingcellular reactions via warm working. Additionally, we have further increased the materialyield strength to 150ksi via introducing the precipitation of an intermetallic Ni3(Ti,Al) γ’phase. That impedes dislocation shearing through antiphase boundary (APB). Our designintegrates calculated values from the Ham strength model and the Olson-Cohen model intocomputational phase and precipitation modeling tools to develop a novel alloy, TRIP-150,for use in blast-mitigation applications.

TRIP-150 Al Ti Cr Ni Mo V C B Fe Phase Fraction γ’Overall Composition 0.159 2.946 3.986 18.044 1.245 0.319 0.010 0.0125 Balance –Matrix Phase Composition 0.114 2.256 1.357 12.879 0.805 0.389 – – Balance 0.0961

Table 1: Summary of TRIP-150 Composition

Property TRIP-120 TRIP-150Stress-assisted Martensitic transformation temperature, M σ

s 36◦C 24.7◦CYield strength, σy 120 ksi 150 ksiTempering Conditions 750◦C, 10 hours 700◦C, 1 hourFerromagnetic transition temperature, TCurie -125◦C -254.3◦C% Warm Working ∼36% ∼5%

Table 2: Summary of Design Improvements

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2 The Need for Better Blast Protection

2.1 Motivation

In efforts to protect military personnel, engineers have long designed structures to with-stand all manners of forces under all sorts of conditions. Increased enemy use of improvisedexplosive devices (IEDs), however, has recently driven demand for new and improved blast-resistant materials and structures for military applications. For example, on October 12,2000, 17 soldiers were killed when a small boat carrying explosives crashed into the U.S.S.Cole.[1] From the period of 2001-2012, IED attacks have caused an average of 290 casual-ties per month on Coalition Forces in Iraq and Afghanistan and 1,116 casualties per monthworldwide.[2] The vulnerability of U.S. military transport vehicles to such comparativelyunsophisticated weaponry highlights the critical need for new blast protection technologies.

Moreover, recent increases in indiscriminate terrorist attacks worldwide underscore a grow-ing need for blast-mitigation materials designed for civilian applications as well. The firsthalf of 2012 in particular saw several high-profile bombings in major urban centers, demon-strating that current designs for outdoor trash receptacles in politically sensitive locationspose a real threat to public safety.[3],[4] Although trash receptacles are an essential part ofwaste management, they are often located in crowded public areas, and by their very na-ture allow for the easy concealment of hazardous devices. During explosions, the materialwhich comprises the trash receptacles itself becomes transformed into shrapnel that cansignificantly increase the number of casualties.

In light of these threats, groups and governments are increasing their demand for blastmitigation products. In preparation for the 2012 G8 and NATO summits, the City ofChicago Office of Emergency Management has ordered more than 50 bomb-resistant trashcans that can resist 6-pound TNT equivalent explosions.[5],[6] However, these purchases werenot made due to the high cost and limited blast protection capabilities of trash cans madefrom currently available steels. In preparation for the 2012 Summer Olympic Games, the Cityof London Corporation ordered bomb-proof trash cans from Renew capable of containing9-pound TNT equivalent explosions.[7]

The protection of both military personnel and civilians against intentional or acciden-tal explosive blasts necessitates the development of next-generation materials designed andoptimized for protection against blasts and resulting shrapnel. Thus, for our project, co-denamed Design TRIP-150, we utilized a systems-based approach to the design processonethat used a suite of predictive computational tools to assist us in development of a class ofblast-resistant high performance steels that would fulfill the property objectives required foruse in high-bomb-risk civilian structures. Our ultimate goal was to deploy this coordinatedand computationally assisted design process to streamline development of the material andthus translate the complex material system into a fully functional prototype alloy in a muchshorter time period and at much lower cost than traditional trial and error methods wouldtypically allow.

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2.2 Anatomy of a Blast

A blast explosion is the sudden expansion and outward projection of matter, typicallycharacterized by an abrupt rise in pressure, temperature and flow density. Blast damage,which must be accounted for in the design process, arises primarily from two classes of dam-age: (1) damage caused by the high-impact explosion-generated pressure wave, (2) damagecaused by collision with high velocity fragments ejected by detonation. These two classes ofdamage affect steel structures in different manners (see Figure 1).

Figure 1: Stress states present in a blast. Fragments cause a state of local shear while the pressure wavecauses bulging.

Primary explosion damage causes steel sheet bulging, introducing tensile loading. Finiteelement analysis (FEA) shows that at the point of maximum explosion deflection, there existsa state of balanced biaxial tensile stress. Therefore maximizing material uniform ductilityat sufficient strength and fracture toughness levels to avoid shattering likewise maximizesthe materials blast energy absorption properties and best enables a material so designed towithstand a blast.

Secondary explosion damage creates localized regions of penetration via a plugging modeat locations of fragment impact. This is a common failure mode in ultra-high strength steels,since shear deformation at the area of impact leads to nucleation of microvoids, which thenleads to material shear failure.

3 Theoretical Background

This section reviews the prerequisite materials science background necessary for the designof our material.

3.1 TRIP Steels

Our project builds upon existing research on TRIP-120, a high-performance steel designedto maximize uniform ductility. Transformation-induced plasticity (TRIP) is the phenomenon

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in which a material exhibits significantly increased plasticity during a phase change. Com-pared to typical high strength steels, fully austenitic TRIP steels can be designed to ex-hibit high strength, ductility, shear resistance, and toughness. These favorable propertiesarise from mechanically-induced martensitic transformation, which stabilizes plastic flowby providing an exponential strain hardening effect. Conventionally, martensitic phases areachieved via quenching austenitic phases to room temperature. In TRIP steels, however, me-chanical strain-induced or stress-assisted martensitic transformation dominates and providesideal strain hardening behavior, thus maximizing uniform ductility for energy absorption.A simple derivation illustrates how strain hardening effects that come from the martensitictransformation can be optimized to stabilize plastic flow during necking and improve bothuniform and fracture ductility.

The necking point in tensile deformation corresponds to the point on the force-deflectioncurve at which the slope is zero (dF/dl = 0). This in turn corresponds to the condition wherethe geometric softening associated with area reduction in tensile deformation is balanced bythe intrinsic true strain hardening of the material. In terms of true stress and true strain,this is expressed by the well-known condition:

dσ

dε= σ (1)

Thus, to optimally maintain stable plastic flow and avoid necking, the stress-strain conditiondσdε

= σ should be maintained throughout deformation. Solving this as a differential equationfor stress yields the ideal exponential strain hardening equation required to maintain stableplastic flow indefinitely:

σ = σoeε (2)

This behavior is compared with the conventional downward curving behavior of dislocation-based strain hardening in Figure 2.

Figure 2: A schematic stress-strain curve for a typical power law metal in comparison to the ideal expo-nential strain hardening behavior exhibited by TRIP steels.

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Thorough studies of transformation plasticity have shown that an optimal rate of strain-induced transformation can achieve the ideal exponential behavior (see Figure 3) througha combination of the “static” hardening of martensite at high strains and the “dynamic”softening of the transformation as a deformation mechanism at low strains.[8-11] Our approachhere will focus on fully austenitic TRIP steels to maximize these transformation plasticitybenefits.

Figure 3: True stress-strain curves of an austenitic TRIP steel over a range of temperatures. Necking strainis shown by the arrows.[8]

3.2 Mechanical Transformation Start Temperature

The two TRIP martensitic transformation nucleation mechanismsstrain-induced and stress-assistedare dependent on the operating temperature, T, and the stability of the austen-ite phase, which is quantitatively described by the M σ

s temperature. The M σs tempera-

ture is defined by the maximum temperature at which an elastic stress causes martensitictransformation.[34] Below the M σ

s temperature (T < M σs ), stress-assisted nucleation is domi-

nant. Above the M σs temperature (T > M σ

s ) but below the transformation limit temperature,Md , strain-induced is dominant. This temperature dependent stress behavior is shown inFigure 4. In the strain-induced nucleation regime, plastic strains create shear bands in theparent austenitic phase. Martensite with fine morphology nucleates preferentially at shearband interactions and provides the characteristic ideal exponential strain hardening behav-iorthe desired regime in which our TRIP-150 alloy should operate.

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Figure 4: Schematic plot of yield stress against temperature for TRIP steels. Stress-assisted transformationcurves show examples for both isothermal and athermal kinetic barriers

Figure 5 demonstrates that maximum uniform ductility is achieved at an operating tem-perature approximately 30◦C above the M σ

s temperature.

Figure 5: Plot of uniform ductility against temperature for a TRIP steel. The maximum uniform ductilityoccurs at approximately 30◦C above M σ

s .[12]

In a diffusionless martensitic transformation, martensite and its parent phase (austenite)have the same homogenous chemical composition. Each individual phase has a chemical freeenergy that is temperature and composition dependent. For a given alloy, T0 defines thetemperature at which these two free energies (GBCC and GFCC) are equal. However, for anyother given temperature, the difference in free energy is expressed as:

∆Gch = GBCC −GFCC (3)

The sign and magnitude of this difference is a quantitative measure of the chemical drivingforce for a martensitic transformation (a larger negative quantity representing a greaterdriving force).

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In the cooling of any alloy from the austenitic range, the Ms (martensite start temperature)lies below the T0 temperature. This results because a critical driving force is required forheterogeneous nucleation at characteristic defects. Martensitic transformation by the samenucleation mechanism can be assisted by an applied stress at temperatures above Ms. Here,the total driving force of martensitic transformation is described by:

∆Gtot = ∆Gch −∆Gσ (4)

which combines both the chemical and mechanical contributions. The mechanical drivingforce is a function of the applied stress and the stress state. There is a characteristic n(defect potency) for nucleation at a given thermodynamic driving force per unit volume∆Gch, where n describes the thickness of the nucleus stabilized by defect interaction. Thisvalue is summarized in an energy term Gn, and when considered alongside the frictional workof martensite interface motion in the solid solution, Wsol

f , forms a critical energy criterion.

∆Gcrit = −∆Gn −W solf (5)

This is the form of the critical driving force given by the Olson-Cohen heterogeneous nucle-ation method.[13]

The Olson-Cohen model relates ∆Gσ, W solf , ∆Gch, Gn with the following equation. At

the M σs temperature, the sum of these four terms is equal to zero.

∆Gch + ∆Gσ = −∆Gn −W solf (6)

These terms can be individually defined as follows.

∆Gσ:

∆Gσ = −[0.7183σ + 6.85

(∆V

V

)σh − 185.31− e−0.003043σ

](7)

•(

∆VV

): volume change associated with transformation (0.04)

• σ: yield stress at M σs

• σh: the hydrostatic stress (σh = σ/3 for uniaxial tension and σh = 0 for pure shear)By changing the hydrostatic stress state, it is possible to find the value of M σ

s fordifferent stress states.

In order to find the yield stress, σ, the following equation is used.

σ − σ0 = −1.425(T − 298.15) (8)

• T: Temperature in Kelvin

• σ0: the yield stress at 25◦C (298.15 K) in MPa. This value can be determined using thePrecipicalc model discussed in the later section Modeling and Computational Tools.

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W solf : A frictional work term, which is the sum of three primary components:

W solf = Wµ + Wth + Wρ (9)

• Wµ: Athermal component of interfacial frictional work term. It can be calculated usingthe following equation discussed in theoretical background.[32]

Wµ =

√∑i

k2i Xi +

√∑j

k2j Xj +

√∑k

k2kXk (10)

• Wth: Thermal component of interfacial frictional work term. It can be calculated usingthe following equation discussed in theoretical background.

Wth(T ) = W0

[1−

(T

Tµ

) 1q

] 1p

(11)

• Wρ: The forest hardening contribution to interfacial frictional work term. It can becalculated using the following equation.

Wρ = Aε0.5 (12)

A needed to be determined for the TRIP-120 system. It was calculated by the pre-vious group which used two samples whose M σ

s temperature and yield stress wereexperimentally determined(25◦C and 184.5 ksi, -13◦C and 180 ksi), and whose matrixcompositions were determined using the LEAP-calibrated PrecipiCalc model. A wasfound to be 710.4 J/mol.ε is prior plastic strain and is defined as ε = ln

(1

1−ww

), where ww is the fraction of

warm-working reduction. i.e. For 36% warm-working, ww is 0.36.

∆Gch: The chemical driving force calculated by plugging composition (which can be deter-mined by PrecipiCalc) into ThermoCalc.

∆Gn: Constant derived from the defect potency n. According to the experimental M σs

temperature, Gn is found to be 1,654 J/mol.

3.3 Austenite Stability

Rearranging this expression to group the composition dependent terms and the microstruc-ture dependent terms yields:

∆Gch + W solf = −∆Gn −∆Gσ (13)

The composition dependence of the left-hand side defines what is called the Austenite Sta-bility Parameter (ASP).

ASP = ∆Gch + W solf (

J

mol) (14)

The ASP is a quantitative description of the critical energy required to drive a martensitictransformation at the M σ

s temperature at an applied stress equal to the yield stress[14]. Thusthe ideal ASP value is fixed when the yield strength objective is determined.

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In order to reflect the ASP parameter in computational modeling, it is important tounderstand the origin of each component. ∆Gch is the chemical driving force outlined above,and W sol

f is the frictional work term, which is the sum of three primary components:

W solf = Wµ + Wth + Wρ (15)

where Wµ represents athermal work, Wth represents thermal work (both from solid solu-tion hardening), and Wρ represents frictional work caused by forest dislocations from priordeformation.

The athermal solution frictional work of interfacial motion Wµ, is strictly a function ofchemical composition, thus to estimate its value in a multicomponent alloys containing dif-ferent kinds of solute atoms of different strengths, Ghosh and Olson consider the followingsuperposition law.[15]

Wµ =

√∑i

k2i Xi +

√∑j

k2j Xj +

√∑k

k2kXk (16)

where X is the mole fraction of each component and k represents the athermal coefficients,shown in Table 1. The i summation represents C and N, j represents Cr, Mo, Ti, and V,and k represents Al, B, and Ni.

Al Ti Cr Ni Mo V C N Bk (athermal) J/mol 280 1473 1868 172 1418 1618 3807 3048 0

Table 3: Athermal coefficients, k, for solutes used in TRIP-120.[15]

At low temperatures thermal activation plays an important role in determining the criticaldriving force for martensitic nucleation. The thermal component of the interfacial frictionwork term can be described as:

Wth(T ) = W0

[1−

(T

Tµ

) 1q

] 1p

(17)

where Tµ, (taken to be 510 K) is interfacial rate dependent (although the calculated behaviorof Wth is not all that sensitive to Tµ)[16] and p and q are 1/2 and 3/2 respectively, asdetermined by the thermally-activated deformation theory of Kocks, Argon, and Ashby.[17]

The molar quantity W0 is evaluated according to the equation:

W0 = W Fe0 +

√∑i

(ki0X

0i .5)2 +

√∑j

(kj0X

0j .5)2 +

√∑k

(kk0X

0k .5)2 (18)

which demonstrates the same X0.5 behavior as the athermal contribution Wµ given above.[16]

The quantity W Fe0 , defined as the level of W0 for pure Fe, is found to be 836 J/mol.[16] The

table below shows the k0 values for solutes used in TRIP-120.

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Al Ti Cr Ni Mo V C N Bk0 (thermal) J/mol 576 3031 3923 345 2918 3330 21216 16986 0

Table 4: Thermal coefficients, k0, for solutes used in TRIP-120.

Finally, Wρ represents the contribution of the forest dislocations to the frictional workterm, in a prestrained material, which can be modeled by a power law of plastic strain, whereWρ shows a ε0.5 strain dependence

Wρ = Aε0.5 (19)

Here A is an experimentally determined constant, and ε is the plastic strain, in this caseproportional to the area reduction caused by warm working TRIP-120.

3.4 Precipitation Strengthening

The precipitation of the intermetallic Ni3(Ti,Al) γ’ phase with ageing, is known to efficientlystrengthen austenitic steels. The Ni3(Ti,Al) γ’ phase has an L12 crystal structure, is coherentwith the austenite matrix, and impedes dislocation shearing through antiphase boundary(APB) formation.[18] The strengthening contribution associated with precipitation of the γ’phase in austenite is defined quantitatively by the Ham model, which is as follows[19],[20]:

τ = τ0 + ∆τ (20)

∆τ =γ0

2b[(

8γ0rsf

πGb2)1/2 − f ] (21)

Where:

• f : volume fraction of γ’

• b: matrix dislocation Burger’s vector = 2.5 angstroms

• γ0: anti-phase boundary (APB) energy of γ’ phase

• rs: average radius of the precipitates

• G : matrix shear modulus = 76.54 ∗ 109 N/m2

• τ0: strength without precipitates (fully austenitic material) = 341 MN/m2

Optimal aging of austenitic steels gives rise to the γ’ phase with the critical particle radiusthat represents the transition from single dislocation cutting to paired dislocation cuttingfor the most effective strengthening increment.[15] A schematic of the relationship betweenprecipitate radius and the provided strengthening contribution is shown below:

This optimized particle size delivers the most efficient strengthening contribution that theγ’ phase can offer.[17]

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Figure 6: Strengthening contribution vs. γ’ particle radius at fixed phase fraction

3.5 Warm Work and Cellular Reaction

The γ’ phase is only metastable, and thus at elevated temperatures the discontinuousprecipitation of the equilibrium η phase (Ni3Ti) has a tendency to occur at grain boundariespromoting intergranular fracture. Since cellular reaction requires coupled precipitation andgrain boundary migration, it is possible to eliminate the cellular reaction by pinning thegrain boundary which can be done through warm working. Warm working is a procedureadded to the processing of the TRIP steels that intentionally introduces dislocations into thematrix, which provide preferential nucleation sites for the heterogeneous precipitation of theγ’ phase at lower aging temperatures. During warm working, serrated grain boundaries alsoappear, which help inhibit intergranular fracture. In previous research[14], warm working ofthe TRIP-120 steel proved successful in eliminating cellular reaction and increasing fractureductility. As shown in Figure 7 on the following page, warm working allows the steel topreserve fracture ductility at significantly higher yield strengths than the non-warm-workedsteel.

3.6 Modeling and Computational Tools

The TRIP-150 design team performed its calculations using a variety of specialized soft-ware packages. ThermoCalc, developed by the Royal Institute of Technology in Sweden, usesthe CALPHAD method to perform equilibrium and metastable thermodynamic and phasediagram calculations. We used ThermoCalc to calculate the matrix composition and thegamma prime phase fraction. The MAterials DEsign (MADE) software suite, developed byQuestek Innovations LLC, is a helpful interface with ThermoCalc that simplifies thermody-namic and kinetic calculations. We used MADE to calculate the Curie temperature and theaustenite stability parameter. Another useful tool developed by Questek is the PrecipiCalc

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Figure 7: Plot showing the increase in yield strength and fracture strain from increased levels of warmworking. Numbers indicate number aging time in hours to achieve peak hardness.

(PpC) software. Using the DIffusion Controlled TRAnsformation (DICTRA) software andThermoCalc, PrecipiCalc models precipitate nucleation, growth, and coarsening. PrecipiCalcis used specifically to find the tempering temperature and time combinations that achievethe strength and M σ

s goals.

4 Team Organization

Our TRIP-150 design team is composed of five Materials Science and Engineering un-dergraduates enrolled in a Materials Design class at Northwestern University, advised byDr. Zack Feinberg, a materials design engineer at QuesTek Innovations LLC. Dr. Feinbergadvised the team on computations and modeling, and other technical facets of the project.

4.1 Technical Background and Role Assignment

Ruilong Ma had previously worked with the Carnegie-Mellon Institute of Science to de-velop atomically precise large aspect ratio nanoclusters. He is currently a member of theOdom Research Group at Northwestern University, where he is studying higher-order chro-mosome organization using gold nanoparticles. Ma is interested in the real-world applicationsof the TRIP-150 design project and the mechanisms of austenite stability and thus led theresearch into the context and application areas for the project as well as modeling austenitestability and M σ

s temperature.

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Wisaruth Maethasith is currently a member of the Joester Research Group at Northwest-ern University, where he is studying bone scaffolding for regenerative medicine applications.Maethasith is also interested in the real-world applications of blast-resistant steels and mech-anisms of austenite stability, so he worked with Ma to investigate the project context andmodel austenite stability and M σ

s temperature.

Benjamin Richardson is currently researching solid-state lasers based on yttrium aluminumgarnet doped with rare earth elements. Richardson is interested in computational modelingof mechanical properties; thus he worked primarily on calculations to predict yield strength asa function of warm working using the Ham strength model. Richardson was also responsiblefor analyzing the uniform ductility as a function of transformation stability to ensure ductilityobjectives can be achieved.

Eric Schwenkers first exposure to blast-related physics was from previous internship inthe Engineering Physics Department of the Air Force Institute of Technology (AFIT) wherehe focused specifically on nuclear forensics. In addition to that earlier experience, he hasworked with classical molecular dynamics codes on tuning coarse-grained water systems forthe Keten Research Group at Northwestern. This background in computation made him agood leader for some of the computational portions of the TRIP-150 design project.

Zhibo Zhao previously investigated the effects of iron nanoparticles on biological systems atAuburn University. He is currently a member of the Huang Research Group at NorthwesternUniversity, where he is studying graphene- and conducting polymer-based materials. Zhaois interested in precipitate evolution and the application of computational models to designfuture materials. Thus, Zhao worked with Schwenker on PrecipiCalc modeling and oversawthe integration of the team members findings into a single system that determined the finalcomposition of a material that would meet all necessary property objectives.

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5 Role Assignment

16

6 Property Objectives

6.1 Primary Objectives

• Uniform tensile ductility: εu ≥ 0.30

• Shear ductility: γi ≥ 0.50

• Yield strength: σy ≥ 150ksi

• Fracture toughness: KIC ≥ 100 MPa√

m

• Optimal austenite stability: M σs (shear)= 25◦ C

6.2 Secondary Objectives

• Nonmagnetic: Tcurie < 0◦ C

• Weldability: Low Cr and Mn content

• Resistant to stress corrosion cracking: KISCC/KIC > 0.5

• Hydrogen resistant: KISCC/KIC > 0.5

• Light-weight: ρ ∼ 7750 kg/m3

• Cost: Suitable for use in a variety of municipal and military applications

In the event of an explosion, the final TRIP steel will need to resist both fragment pen-etration and the blast pressure wave. To optimize for these dual conditions, we need toconsider two primary design objectives in two independent stress states: (1) resistance to lo-calized shear stresses from fragmentation and (2) uniform tensile ductility to mitigate biaxialstresses generated by the pressure wave.

During fragment ballistic penetration, deformation is highly localized into thin shearbands. This strain localization causes the formation of microvoids, while subsequent mi-crovoid coalescence can produce plastic shear instability that leads to a shear plugging modeof failure. In this failure mode, the steel offers little energy absorption, and as a consequencethe material ahead of the fragment is ejected at high velocity.

Thus to improve upon existing steels for blast resistance, a new material would have tomeet several requirements. In order to resist this shear localization, the shear ductility underadiabatic conditions would have to be higher than 50% so as to improve upon the baselinematerial used currently in naval ship hulls. To resist the pressure wave from the blast, theuniform tensile ductility would need to be greater than 30%. The material would also needsufficient tensile strength for high energy absorption; thus we targeted a tensile yield strengthof 150 ksi(∼1030 MPa), an improvement over the TRIP-120 steel with a yield strength of120 ksi(∼827 MPa). In order to ensure that the material could sustain large strains withoutpremature failure, the fracture toughness had to be at least 100 MPa

√m.

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Finally, it was necessary to determine the material’s M σs (sh) temperature. It has been

experimentally shown that uniform ductility is maximized at about 30◦C above the M σs

temperature at isothermal conditions. Adiabatic heating during an explosion, however, willeffectively raise the operating temperature at large plastic strains, making lower austenitestability (higher M σ

s temperature) more desirable. Yet a M σs temperature too far above

room temperature will severely compromise the room temperature tensile yield strength.These considerations had to be balanced with practical concerns that the material shouldbe able to operate in different weather conditions, including large seasonal temperaturevariations. Given these factors, it was determined that the material needed to have anM σ

s (sh) temperature of 25◦C, though this value may vary across different applications.

In addition to those primary mechanical requirements, the material ideally would meetseveral secondary constraints to optimize performance. For naval applications, it is idealfor the material to be nonmagnetic to avoid mines, meaning the Curie temperature shouldbe below 0◦C. Stress corrosion cracking and hydrogen embrittlement resistance are alsonecessary to protect against unexpected catastrophic failure over the lifetime of the material.This constrains the composition to low P and S impurity levels, and the addition of Bto enhance grain boundary cohesion.[21] The material should also be relatively lightweightin order to reduce fuel-related costs in naval ships and transportation costs in municipalapplications. Most steels have densities falling in the range from 7750-8050kg/m3, so the finalTRIP-150 alloy should fall toward the low end of this range. From a processing standpoint,the material must be weldable for ease of fabrication into weight efficient “sandwich panel”structures.[22] So that workers can avoid hazardous fumes during welding, the Cr and Mncontent should be held low. Finally, the material should be sufficiently low cost to produce inlarge quantities for everyday civilian applications, especially considering the strained financialbudgets of many local and state level governments today.

7 System Structure

In our design, we use a systems approach that emphasizes the interlocking relationshipsamong processing, structure, properties, and performance. In Figure 8 on the following page,we depict how processing, structure, and properties impact performance for precipitation-strengthened TRIP steels.

In such alloys, the TRIP effect and the final matrix grain size are controlled by thetempering and warm working conditions. These processing parameters will affect the ASPand thus allow us to design the composition for the optimal austenite phase stability and γ’phase fraction.

In this project, we focus on the effects of warm working. As we can see from the sys-tem chart above, the objective of warm working is to increase the dislocation density of thealloy to precipitate the γ’ phase at lower aging temperature while simultaneously avoidingthe stress-induced martensitic transformation during processing and the embrittling cellular

18

reaction associated with high aging temperatures. The increase in dislocation density cre-ates additional heterogeneous nucleation sites for γ’ precipitates to form for precipitationstrengthening.

Figure 8: System chart for austenitic TRIP alloy

8 Previous Work

8.1 Blast Alloy 160 (BA-160)

The martensitic BA-160 was previously designed according to simplistic blast models thatfocused on achieving maximum impact toughness to optimize energy absorption proper-ties. The resultant BA-160 steel was a weldable dual precipitation-strengthened martensiticsteel.[23] However, it has been demonstrated from finite element analysis that high uniformductility, not impact toughness, must be the key property for blast resistance.

8.2 Experimental Alloy 425 (EX425)

Re-evaluation of design criteria for blast-resistant steels led to the development of fullyaustenitic Transformation Induced Plasticity (TRIP) steels with a renewed focus on op-timizing uniform ductility through a strain-induced martensitic transformation. EX425,

19

developed by Frode Stavehaug,[24] was based on the commercial alloy A-286, which usedhigh Ni and Cr content to stabilize the austenite phase. The EX425 was a fully austeniticalloy strengthened by γ’ Ni3(Ti,Al) precipitates.[23] EX425 exhibited the TRIP effect wheredeformation can induce a transformation from the γ-austenite to the α-martensite phase,thereby increasing the strain hardening and delaying necking instability. However, the M σ

s

temperature of the EX425 was 70◦C, which was too low for effective blast protection at 25◦C.

8.3 TRIP-120 Steel Prototype

In the spirit of EX425, the fully austenitic and γ’ precipitate-strengthened TRIP-120steel addressed the focus on optimizing uniform ductility. The composition, microstructure,and processing of the alloy were optimized to raise the M σ

s temperature closer to roomtemperature to allow the strain-induced martensitic transformation to occur under blastconditions in naval applications. At the same time, the alloy was also designed to maintainsufficient shear and tensile ductility, yield strength, and impact fracture toughness.

TRIP-120 steel, however, still face one major problem: limited fracture ductility causedby a cellular reaction resulting in the precipitation of equilibrium Ni3Al η phase at grainboundaries. Warm working was found to prevent the embrittling cellular reaction with ef-fects on ductility and austenite stability that were modeled using the Ham strength model,Olson-Cohen austenite stability model, and PrecipiCalc simulations calibrated with LEAPcompositional data. The models developed by previous design projects were able to simulatethe evolution of precipitate size with good accuracy, but overestimated the γ’ phase fraction.Deviations in phase fraction drastically impact the matrix composition, which in turn leadsto inaccurate predictions of the M σ

s temperature. Previous models have also yielded unre-alistically low γ’ phase fractions for reaching the requisite strength goals, and thus shouldbe reevaluated.

9 Design Approach

We will begin the computational design process by creating and calibrating a computa-tional model to experimental data for the warm-worked TRIP-120 alloy. The precipitationstrengthening due to γ’ precipitates can be well described by the Ham strength model,summarized in the following two equations:

τ = τ0 + ∆τ (22)

∆τ =γ0

2b[(

8γ0rsf

πGb2)1/2 − f ] (23)

Where:

• f : volume fraction of γ’

• b: matrix dislocation Burger’s vector = 2.5 angstroms

• γ0: anti-phase boundary (APB) energy of γ’ phase

20

• rs: average radius of the precipitates

• G : matrix shear modulus = 76.54 ∗ 109 N/m2

• τ0: strength without precipitates (fully austenitic material) = 341 MN/m2

We used ThermoCalc to calibrate the Ham strength model to LEAP compositional datafor TRIP-120 steels and fit a value for the anti-phase boundary energy.

Next, we determined the warm work contribution to the yield strength by modeling thestrength increase as a function of warm work reduction of area. By setting a desired amountof warm work, we were able to compute the amount of additional precipitation strengtheningneeded to achieve the overall strength goal of 150 ksi. Using the Ham strength model, wecan calculate the volume fraction of γ’ needed for this level of additional strengthening. Wesubsequently tuned the Al/Ti content to attain this volume fraction.

The M σs temperature was determined by calculating the Austenite Stability Parameter

(ASP) as a function of temperature. Recall that the ASP is defined by the equation:

ASP = ∆Gch + W solf (24)

The chemical driving force is a function of temperature and pressure, and the temperaturedependence of this term can be determined by ThermoCalc equilibrium calculations. Thefrictional work term has three separate components, but only the dislocation density termvaries with warm work. The dislocation density term has the form:

Wρ = Aε0.5 (25)

The constant A can be calibrated using experimental data from samples whose yield stressand M σ

s temperature have already been determined. Then, we determined a critical ASPto target in the new design, which we expect to achieve the desired austenite stability(M σ

s (shear)=25◦C). The critical ASP will be achieved by designing the Ni content.

Varying the Ni content,however, affects the equilibrium γ’ volume fraction, which in turnaffects the overall yield strength. Thus, we had to iterate through the Ni content and theAl/Ti content until we can obtain a yield strength and M σ

s temperature. These models werethen applied to the computationally designed TRIP-150 to determine appropriate temperingtemperatures to achieve the strength and austenite stability goals.

10 TRIP-120 Prototype

10.1 Grain Boundary Cellular Reaction

The designed heat treatment of TRIP-120 at 750◦C for 10 hours has been previously ob-served to induce a grain boundary cellular reaction. In the cellular reaction, the equilibrium

21

η (Ni3Ti) phase precipitates from the grain boundaries of the parent γ phase.[27] η phase pre-cipitates grow along a reaction front perpendicular to the grain boundary forming a lamellarmicrostructure shown in Figure 9.

Figure 9: Optical micrograph of the γ and η phase in a lamellar structure due to the cellular reaction inTRIP-120. GB refers to the grain boundary; RF refers to the reaction front.

The presence of η significantly weakens grain boundaries and has been shown to decreaseductility of the alloy.[25],[26] For the purposes of this project, tempering of the steel must beconducted at a temperature below which η forms (T < 775◦C), but high enough to allow forsufficiently fast γ’ kinetics to occur (T ≥ 700◦C).

10.2 Elimination of the Cellular Reaction through Warm Working

In order to eliminate the cellular reaction and the commensurate formation of the η phase,warm working was employed on the steel at 450◦C following solution treatment. This warmworking occurs above the Md temperature, thus introducing dislocations into the steel matrixwithout having the austenitic matrix undergo a martensitic transformation under strain.These dislocations act as sites for heterogeneous nucleation, which reduces the barrier energyto nucleation. Because the γ’ to η transformation occurs at higher temperatures (T >∼750◦C), warm working helps bring about the precipitation of γ’ without precipitating

22

η. Optical microscopy confirms that warm working in conjunction with lower temperingtemperature (700◦C) and time (1h) significantly reduces η phase formation (see Figure 10).

Figure 10: Optical micrograph of TRIP-120 A) tempered at 750◦C for 10hr without prior warm working andB) tempered at 700◦C for 1hr with 36% warm working. The dark areas on the image indicate η formation.

11 Optimizing TRIP-120

11.1 Determination of Tempering Temperature and Time

The magnitude of tempering temperature can affect the microhardness of TRIP-120. InFigure 11, samples at different warm-working reduction amounts and different temperingtimes are subjected to Vickers microhardness testing.[28]

23

Figure 11: Microhardness measurement vs. tempering temperature for different warm-working amountsand different warm-working times.

As shown in Figure 11, samples with a tempering time of 8 hours reach peak hardnessat 700◦C. It was found that tempering at 700◦C prevents formation of undesired η (Ni3Ti)phase at the grain boundaries, while permitting γ’ precipitation kinetics.[28]

By setting tempering temperature at 700◦C, one can estimate the optimal tempering timeby measuring microhardness as a function of time. The result is shown below in Figure 12.

Figure 12: Microhardness measurement vs. tempering time for 23% and 36% warm-working at 700◦C.

According to Figure 12, both 23% and 36% warm working samples reach peak hardnessat 8 hours. Thus for those conditions, the optimal tempering temperature is 700◦C with atempering time of 8 hours.

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11.2 Characterization of Precipitation (γ’)

Characterization of γ’ phase fraction and precipitate particle radius was required for cal-culating the yield strength through the Ham strength model, a necessary component forcalculation of the austenite stability parameter. Previous work on the TRIP-120 alloy hasused LEAP tomography to demonstrate that the average γ’ particle radius at peak hard-ness is 6.9 nm. The same techniques have been used to reconstruct the TRIP-120 36%warm-worked alloy as shown in Figure 13 below.

Figure 13: Three-dimensional atom probe reconstruction of TRIP-120 36% WW 700◦C 5 hour specimen.γ’ precipitates are shown in green. Fe is shown in pink.

From the LEAP data, a proximity histogram of the particle-matrix interface has beengenerated below in Figure 14.

Figure 14: Proximity histogram of TRIP-120 36% WW 700◦C 5 hour specimen. The dashed line showsthe interface between the matrix and precipitate, defined as the location with the same concentration of Niand Ti.

For the TRIP-120 36% WW alloy, the M σs temperature is at the desired value of 25◦C.

However, the LEAP data above have been used to demonstrate that the average γ’ particle

25

radius for the alloy is 2.92 nm (Table 5). This radius is well below the average particle radiusfor TRIP-120 at peak hardness. Thus, we seek to design a new TRIP steel with processingconditions such that M σ

s =25◦C at the peak hardness condition corresponding to a particlesize of 6.9 nm.

Fe Ni Ti Cr Al V Mo Phase Fraction Average RadiusBulk 69.8 22.4 2.3 4.5 0.16 0.36 0.46 – –Matrix 75.1 18.3 1.5 4.4 0.09 0.36 0.25 – –γ’ 3.9 73.4 19.3 1.6 0.87 0.16 0.81 7.22% 2.92 nm

Table 5: Compositions (atomic %), phase fraction, and average precipitate size determined from LEAPtomography for TRIP-120 36% WW 700◦C 5 hour sample.

11.3 Ham Model Calibration

The strength contribution of the precipitate γ’ phase fraction can be calculated using aHam Strength model. Because Ham model calculates for single dislocations cutting throughprecipitates, this model is only applicable for systems where temperature is less than M σ

s .The Ham model term ∆τ is the shear stress contributed by precipitates and can be calculatedusing the equation below.

∆τ =γ0

2b

[(8γ0rsf

πGb2

) 12

− f

](26)

The total shear stress of the material can be found by adding the shear stress contributedby the precipitate phase to the fully austenitic material, which can be calculated using thefollowing equation.

τ = τ0 + ∆τ (27)

The shear stress, τ , is related to the yield strength by the average FCC Taylor polycrys-talline factor, M=3.06.[30] The base yield strength of the TRIP-120, τ0, warmed worked to23% and 36% area reductions have been measured to be 104.1 ksi and 121.6 ksi respec-tively. Although increasing the amount of dislocations into TRIP-120 was shown to increasebase yield strength, warm working also impacts the precipitate strengthening contributionby changing the γ’ phase fraction and γ’ precipitate radii. Therefore, higher yield strengthdoes not mean a commensurate increase in total material shear stress. The Ham model canbe used to summarize the strength and γ’ phase fraction at different percent warm workvalues (see Figure 15). The Ham strength model was calibrated using LEAP tomographydata. Now, material strength can be successfully modeled as a function of percentage warmworking and γ’ phase fraction.

26

Figure 15: Ham strength model curves calibrated by experimental and theoretical values as a function ofphase fraction and percentage warm work.

11.4 Validating the Effect of Austenite Stability on Uniform Duc-tility

One of the primary objectives for the designers of TRIP-120 was that the alloy have avery high uniform ductility while retaining high yield strength. Figure 16 below shows bothfracture and uniform ductility as a function of T-M σ

s , where T=25◦C (tensile tests were con-ducted at room temperature). Zero on the x-axis represents a sample whose M σ

s temperatureis 25◦C. Our trends correlate with previous work on austenitic steels, where a maximum inductility occurs when M σ

s is approximately 20-30◦C below the testing temperature. Thus,if our M σ

s temperature is 25◦C, we expect the alloy to exhibit sufficiently high levels ofductility across a range of reasonable operating temperatures.

Figure 16: Plots of Ductility vs. Temperature for (a) TRIP-120, (b) an austenitic steel. Legend: ∆−23%warm work, X−36% warm work. Blue symbols and trend line correspond to fracture ductility. Red symbolsand trend line correspond to uniform ductility. Error bars indicate an estimate of the inaccuracy of the M σ

s

predictions, approximately ±12◦C.

27

12 Re-evaluating the Strength Objective

The TRIP-120 alloy focused on avoiding the grain boundary embrittling cellular reaction.Warm working at 450◦C followed by aging at 700-800◦C was found to make a significantcontribution in preventing the formation of the brittle γ+η lamellar phase structure. Samplescreated with different levels of warm working and subsequently tempered at 700◦C did notexhibit any signs of the embrittling η phase and showed promising tensile ductility and yieldstrength.

Recent impact velocity experiments on military steels, however, have led to a re-evaluationof the yield strength objective. V50 is the impact velocity of blast fragments at whichpenetration occurs with 50% probability for a given alloy. Alloys with high yield strengthsabove 100 ksi have been shown to have reduced V50 as high strength steels often fail in aplugging mode and demonstrate poor ballistic penetration resistance. The TRIP-120 alloycan achieve high yield strengths around 180 ksi, but only with large amounts of warm workthat significantly adds to processing time and costs. Our new alloy design, named TRIP-150,was designed to have high yield strength around 150 ksi while reducing the amount of warmwork required and preserving high uniform tensile and shear ductility.

The quantitative property objectives for TRIP-150 are as follows:

• σy=150 ksi

• M σs (shear)=25◦C

• Reduced warm working: 5-10% area reduction

Figure 17: Plot of V50 vs. ultimate tensile strength for Baseline 3 Ni versus 10 Ni and QuesTek 6 Nimartensitic steels. Due to the classified nature of military steels, V50 values are presented relative to abaseline in lieu of the exact values.

28

12.1 Determining Amount of Warm Work Reduction

The amount of warm work was selected based on balancing 2 criteria: (1) the positive cor-relation between warm work and fracture ductility and (2) the trade-off between warm workand amount of γ’ precipitates. In general, higher amounts of warm work will provide higherlevels of fracture ductility (see Figure 18), but higher warm work will also reduce the phasefraction of γ’ precipitates, thereby compromising the robustness of the design by increasingthe sensitivity to Al content as will be discussed shortly. With these two counterbalancingscenarios in mind, we estimate a warm work reduction of 5% should successfully maintainsufficient fracture toughness and precipitation strengthening.

Figure 18: Strain at Fracture vs. Warm Work Reduction. Note that 5% WW reduction still results in atrue strain at failure of 0.43 which is within acceptable limits.

12.2 Meeting the Strength Goal

As a starting point, it is useful to predict the base strength of the alloy (in the solutiontreated condition) as a function of warm work. Warm working increases the base strength ofthe alloy by increasing the density of dislocations, and increases the ductility by eliminatingcellular reaction at the grain boundary. This dislocation-based strain hardening is usuallyquantified by a power law, in the form:

∆σ⊥ = Cεn (28)

where σ⊥ is the increase in strength due to dislocations.

29

This equation was fitted to experimental strength data for the warm-worked TRIP-120alloy in the pre-aged condition. A least-squares fit yields the following parameter values:C=136.1 ksi and n=0.62. At this point, we are interested in predicting the base strengthand thus we must use the following relationship to rewrite the power law in terms of basestrength.

σb = σ0 + ∆τ⊥ (29)

where σ0 is yield stress in zero warm work conditions.

The results of the fitting are summarized in Figure 19 below.

Figure 19: Strength Increase as a Function of Warm Work.

The three experimental results, (0%, 23%, 36%), are denoted by the large data points,and the base strength in the 5-10% warm working reduction window is highlighted becausethese are the optimal warm working conditions for design of TRIP-150.

To achieve the desired yield strength of 150 ksi from the base strength dictated by warm-working, the fraction of γ’ precipitates, f, must be determined using the Ham strength model.To solve for f in the Ham strength model, we must first calculate using the expression:

τ = τ0 + ∆τ (30)

30

Where:

• τ=shear strength goal corresponding to σy=150 ksi

• τ0=the base shear strength corresponding the case of 5/

The yield strength can be related to the shear strength τ via the Taylor Factor M:

∆σ⊥ = Mτ (31)

where M=3.06 for slip in an FCC polycrystal.[30]

Combining the above equations, we obtain the expression:

∆τ =1

M(σy − σb) (32)

where σb is is the base strength at a given amount of warm work reduction, and σy is thetarget yield strength (150 ksi for TRIP-150). This demonstrates the practicality of predictingbase strength as a function of warm-working. Using this ∆τ , we can solve for the necessaryγ’ phase fraction f using the Ham model. The results of the phase fraction calculations aresummarized below.

Warm Work Reduction ∆σ⊥ [ksi] σb [ksi] ∆τ 140 [ksi] (σy=140 ksi) ∆τ 150 [ksi] (σy=150 ksi) f (∆τ 140) f (∆τ 150)0 0.00 49.5 29.58 32.84 – –0.05 21.15 701.7 22.66 25.93 6.43E-2 9.61E-20.1 32.54 82.0 18.94 22.21 3.99E-2 6.08E-20.15 41.86 91.4 15.89 19.16 2.59E-2 4.11E-20.2 50.06 99.6 13.22 16.48 1.68E-2 2.83E-20.23 54.60 104.1 11.73 15.00 1.28E-2 2.26E-20.36 72.13 121.6 6.00 9.27 3.00E-3 7.62E-3

Table 6: Warm work reduction, additional strengthening desired, and necessary γ’ phase fractions

For the case of 5% warm work, ∆τ 150 is 25.9 ksi, and the necessary γ’ phase fraction fromthe Ham strength model is f =0.096. A plot of target yield strength versus γ’ volume fractioncorresponding to peak hardness for the case of a 5% warm worked alloy is shown in Figure20 on the following page.

31

Figure 20: Ham Model Strength vs. Volume Fraction as predicted for various warm working conditions.

In order to obtain an alloy with the desired γ’ phase fraction, the Al and Ti content ofthe alloy can be varied to obtain f =0.096. However, the ratio between the two must be keptconstant (Al/Ti=0.054) to maintain a constant anti-phase boundary energy.[33] Figure 21 onthe following page summarizes the results of our preliminary runs.

The two composition axes show the Al/Ti dependence, and the shaded boxes illustratethe composition and phase fraction ranges that meet the 5% and 10% warm-working criteriagiven the two strength goals. A capillary energy of 208 J/mol was added to the calculation toobtain a more accurate γ’ phase fraction. This corresponds to the peak hardness conditionas opposed to equilibrium. For the first iteration, the proper Al composition (weight %) is0.143, and thus the Ti compostion (weight %) is 2.656. The first iteration of the initial overallcomposition and the resulting matrix composition output from ThermoCalc is included inTable 7 below.

TRIP-150 Al Ti Cr Ni Mo V C B Fe γ’ phase fractionOverall Composition (wt %) 0.143 2.656 3.986 23.542 1.245 0.319 0.01 0.0125 Balance –Matrix Composition (mol %) 0.0958 0.9256 4.7663 18.3545 0.8080 0.3898 7.3340E-05 n/a 74.6442 0.096155

Table 7: Composition at intermediate iteration.

Again, this composition is only the γ’ phase fraction optimization for the first iteration.The austenite stability must also be taken into account to ensure the alloy has the proper

32

Figure 21: Gamma prime phase fraction as a function of Al/Ti content.

M σs temperature and uniform ductility required to withstand blast stresses.

12.3 Achieving the Austenite Stability Goal

Given that the target yield strength of the alloy is 150 ksi at an M σs temperature of 25◦C,

we can calculate a critical Austenite Stability Parameter (ASP). The critical driving forcecan be defined as is:

∆Gcri = −Gn −W solf (33)

Gn is a constant defined by defect potency (n). According to the experimental M σs tem-

perature from TRIP-120, is found to be 1,654 J/mol and W solf is the frictional work of the

system.

Since the critical driving force is equal to total driving force M σs at temperature (which

for our goal is room temperature of 300K) at an applied stress equal to the yield stress, theequation can be redefined as:

∆Gch + ∆Gσ = −Gn −W solf when σ = σy and T = M σ

s (34)

Rearranging the equation above, we derive the composition dependent Austenite StabilityParameter (ASP) which is the summation of chemical driving force (∆Gch) and frictional

33

work (W solf ).

∆Gch + W solf = −Gn −∆Gσ (35)

ASP = −Gn −∆Gσ (36)

The right hand side of the equation is a function of stress-state and yield strength.

As mentioned above, Gn is defined as a constant with a value of 1,654 J/mol. ∆Gσ isdefined to be mechanical driving force and the equation dictating the mechanical drivingforce can be determined using the Olson-Tsuzaki-Cohen[22] integration of the Patel-Cohenwork relation over a random orientation distribution of embryos. The resulting equation isshown below.

∆Gσ = −[0.7183σ + 6.85

(∆V

V

)σh − 185.3(1− e−0.003043σ)

](37)

In which σh = σ/3 for uniaxial tension and σh = 0 for pure shear; σ is defined as the goalstrength in MPa (which is 150 ksi=1034.2 MPa).

In order to find the critical ASP, we use hydrostatic stress σh for shear conditions (σh=0)since we want M σ

s for shear at room temperature. Thus the calculation will be as follows:

ASP = −Gn −∆Gσ (38)

ASP = −1654 +

[0.7183(1034.2) + 6.85

(∆V

V

)(0)− 185.3(1− e−0.003043∗1034.2)

](39)

ASP = −1088.5 J/mol (40)

Since the ASP dictates the yield strength at the desired M σs temperature, the TRIP-150 steel

must be designed to achieve the ASP of -1088.5 J/mol at 25◦C. MADEs calculation of theASP does not include the dislocation density work term, however, so when we are consideringa target output ASP, the value must reflect our critical value minus the dislocation densitywork term, Wρ. As described earlier, Wρ only depends on warm-work and is given by:

Wρ = Aε0.5 = 160.89 J/mol (41)

where A = 710.4 J/mol and ε = ln 10.95

, representing a 5% warm work reduction. The newmodified target ASP value, ASP∗, becomes:

ASP ∗ = ASP −Wρ = −1249.5 J/mol (42)

ASP∗ is quite sensitive to the Ni content, thus we must vary the Ni content of the matrixuntil we achieve this critical value. Figure 22 on the following page shows the dependenceof ASP∗ on matrix Ni content. Figure 22 shows that the necessary Ni matrix compositionto achieve the critical ASP is 12.91 mol%. Therefore, the overall alloy composition must bedesigned such that the equilibrium Ni matrix composition after γ’ precipitation matches thedesired value.

34

Figure 22: ASP∗ vs. matrix Ni content computed with MADE

12.4 Iteration to Meet Both Strength and Stability Goals

Adjusting the overall composition to meet the ASP goal yields the following composition:


Table 8: Composition at intermediate iteration.

At this composition, however, the volume fraction of γ’ precipitate, as calculated usingThermoCalc equilibrium thermodynamics, is too low. Thus, the Al/Ti content was variedagain to adjust the volume fraction of γ’ precipitates. At this point, the material was re-evaluated to ensure the critical ASP criterion was still met. In this manner, iterations varyingNi, Ti, and Al content (while maintaining a constant Al/Ti ratio of 0.054) were repeateduntil we obtained γ’ volume fraction and ASP∗ values that converged to our desired values.The final alloy composition that meets both the strength and stability criteria is reportedon the following page in Table 9:

35


Tolerances (+/− wt%) 0.15 0.3 0.3 0.5 0.2 0.15 n/a n/a n/a –

Table 9: Final TRIP-150 Composition.

As a method of checking that our proposed final overall alloy composition satisfies theinitial property objectives (σy = 150 ksi,M σ

s = 25◦C), −Gn −∆Gσ was plotted against theMADE output ASP values from the final matrix composition (see Figure 23). The critical

Figure 23: Austenite stability plot to verify M σs temperature

ASP value becomes the point of intersection of these two lines. Because the critical ASP isdefined by:

σ = σy and T = M σs (43)

it is clear that the alloy’s predicted M σs temperature is 24.7◦C, and the predicted yield

strength is 150 ksi, which achieves the primary design goals of TRIP-150.

12.5 Predicting Magnetic Properties

Finally, since the TRIP-150 steel should also be suitable for military applications, the alloyshould be paramagnetic at operating temperatures in order to reduce the magnetic footprintof any vehicles employing the steel. This reduces the radar detectability of our material andprovides protection against magnetic land mines often used against naval vessels. The Niand Cr content of the TRIP-150 alloy were expected to provide the largest contributions tothe final magnetic properties, so a cross-plot of the variation of Curie temperature versusmatrix Ni and Cr content was generated.

36

Figure 24: Curie Temperature Contours vs. matrix Ni and Cr contents.

As indicated in Figure 24, the Ni and Cr matrix composition in the TRIP-150 alloy yieldsa Curie temperature of 18.7 K, which is well below expected operating temperatures. TheCurie/Neel transition region marks the region over which the Curie temperature becomes aNeel temperature. The Neel temperature is analogous to the Curie temperature, in that itrepresents a value above which spontaneous magnetization ceases; however the Neel temper-ature applies to antiferromagnetic materials.

12.6 Aluminum Content Sensitivity

For manufacturing purposes, it is important that the element compositions specified forthe final overall TRIP-150 are followed as closely as possible. For a requirement like yieldstrength, which is highly dependent on the phase fraction of the gamma prime precipitates,we see that error in manufacturing the specified Al values in our designed TRIP-150 alloy(5% WW) is substantial, especially in cases where the Al content is deficient. Figure 25 onthe following page illustrates this dependence. The data points were obtained by varyingthe Al and the associated Ti values in the ThermoCalc model (final alloy composition) tooutput gamma prime phase fraction values. These gamma prime phase fraction values wereused in the Ham model to obtain yield strength values. The final results show that evensmall variations from the designed Al content of 0.159 weight percent will result in dramaticchanges in yield strength. For example, a change from 0.159 to 0.155 weight percent willproduce a nearly 20 ksi drop in the overall yield strength of the final alloy. Typical industrial

37

tolerances for Al content specify a minimum of 0.14 weight percent with an error of ±0.15weight percent. Though the final Al content meets the 0.14 minimum, we recognize thaterrors of ±0.15 weight percent could be catastrophic given the final composition of 0.159weight percent. In this case, the error is nearly equal in magnitude to the total Al contentof the final alloy. We note that at higher Al content, the yield strength seems to becomeless sensitive to small changes in Al content. Thus, we propose that introducing a higherAl content would improve the robustness of the design. At this point, the robustness of thedesign is certainly questionable, and future iterations of this design project should look toincrease the Al content and incorporate robustness as a primary design objective.

Figure 25: Yield strength vs. Al content (5% WW).

13 Conclusion

The design of TRIP steels presents a complex, multifaceted challenge with tangible real-world consequences. Though the sheer breadth and depth of the relevant models and designparameters that need to be taken into account may seem overwhelming at first glance, acoordinated and focused design process can streamline the process many-fold. By fullyemploying the power of available computational tools, the complex system structure canbe translated into a fully functional prototype alloy in a much shorter time period thantraditional trial and error methods.

The primary problem facing the TRIP-120 alloy was the embrittling cellular reactionarising from precipitation of the Ni3Al η phase. Warm working was found to prevent η phase

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precipitation, but had unknown effects on the ductility and austenite stability because TRIP-120 was not originally designed for warm working. When LEAP compositional analysis wasused to calibrate the Ham strength model and the PrecipiCalc model, and Olson-Cohenmodel used for austenite stability, however, it was possible to improve model predictions andapply a physics-based framework to computational materials design.

These calibrated models were used to predict the precipitation of the Ni3(Ti,Al) γ’ phaseand the corresponding change to the matrix composition. With this information, we em-barked on a fully computational design of the TRIP-150 alloy, whose goal was to achievea yield strength of 150 ksi while maintaining the high uniform ductility required for blastresistance and controlling the austenite stability to optimize for adiabatic conditions. Theyield strength criterion was addressed by establishing a 5% warm worked baseline and com-puting the required precipitation strengthening for final yield strength of 150 ksi. The highuniform ductility was addressed by redesigning the composition around a characteristic M σ

s

temperature of 25◦C while employing 5% warm work. The final results of our modeling workare summarized below.

Overall Composition of TRIP-150


Tolerances (+/− wt%) 0.15 0.3 0.3 0.5 0.2 0.15 n/a n/a n/a –

Property TRIP-120 TRIP-150Stress-assisted Martensitic transformation temperature, M σ

s 36◦C 24.7◦CYield strength, σy 120 ksi 150 ksiTempering Conditions 750◦C, 10 hours 700◦C, 1 hourFerromagnetic transition temperature, TCurie -125◦C -254.3◦C

Future work should aim to apply the calibrated PrecipiCalc model to the TRIP-150 alloyto model the γ’ precipitate phase evolution as a function of processing conditions (agingtemperature, aging time, warm working reduction of area). For our TRIP-150 design, wehave designed around an aging temperature of 700◦C. Modeling should be performed todetermine the aging time to reach optimal precipitate size at 700◦C. The application of thePrecipiCalc model will allow us to determine whether such tempering conditions are feasiblein real-world processing applications.

Future iterations of this design should also aim to increase the robustness of the design,particularly by exploring variations in the Al/Ti content. In our design, even small changesin the Al/Ti content will have a disproportionately large effect on the final yield strength.This sensitivity can be attributed to relatively low levels of Al resulting in low fractions of γ’precipitates prone to variability. Perhaps designing the TRIP-150 alloy around higher Al/Ticontent would result in more robust final compositions.

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Though the final design leaves several issues unresolved, this project has nonetheless re-sulted in the successful computational design of a blast-resistant TRIP steel with predictedproperties that meet the primary design objectives and show promise for improved perfor-mance under adiabatic conditions. We believe this design can mark a promising startingpoint for the journey toward next-generation blast-resistant steels that can ultimately beused to save thousands of civilian and military lives.

14 Acknowledgements

The TRIP-150 design team would like to thank Professor Greg Olson for his continuedsupport of design-based education. The systems approach to materials design has proven aninvaluable contribution to the rational and high-throughput design of ultra high-performancematerials.

The TRIP-150 design team builds upon the work previously done to characterize TRIP-120. Without the countless hours of painstaking effort put forth by previous researchers, wecould not have begun to aspire to what humble heights we may have reached. We representonly the most recent iteration of a design process that remains far from complete.

We would also like to thank our advisor, Dr. Zack Feinberg, for his superb guidanceand patient teaching. This project would be nowhere without Zack and his dedication andexcellent metallurgical acumen.

Finally, the TRIP-150 design team would like to acknowledge the contributions of previousMSE 390, Design 398, and Engineering Design and Communication teams in the developmentof blast-resistant alloys. Their contributions make an excellent body of literature and helplessen the steep learning curve associated with TRIP steels.

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15 References

1: Defense.gov News Release: USS COLE CASUALTY UPDATE. at<http://www.defense.gov/releases/release.aspx?releaseid=2721>

2: Brook, T. Use of Humvees restricted in Afghanistan. USA Today (2010).

3: V. Hurst, “Teen Arrested after Explosive Device Found at Salem Middle School.”KATU.com. Fisher Communications, 3 May 2012. Web. 10 May 2012.<http://www.katu.com/news/local/Boy-14-arrested-after-explosive-device-found-at-Salem-middle-school-150100895.html>.

4: O. Rudenko, “Mysterious Dnipropetrovsk Bombings Remain Unsolved.” Kyiv Post.Independence. Community. Trust. Public Media, 10 May 2012. Web. 10 May 2012.<http://www.kyivpost.com/news/nation/detail/127403/>.

5: F. Spielman, “City Looking to Buy ’blast Resistant’ Trash Cans to Guard againstTerrorism.” Chicago Sun-Times. Sun-Times Media, 2 Apr. 2012. Web. 10 May 2012.<http://www.suntimes.com/news/crime/10966744-418/city-looking-to-buy-blast-resistant-trash-cans.html>.

6: City of Chicago, Office of Procurement Services, Blast Resistant Trash Receptacle Quo-tation. By Jamie L. Rhee. 29 Nov. 2011. Web. 10 May 2012.<http://www.cityofchicago.org/content/dam/city/depts/dps/ContractAdministration/Specs 2012/101360BlastResistantTrashReceptacle.pdf>.

7: Renew America, “Market Engagement Overview” January 2008

8: Olson, G.B. Transformation Plasticity and the Stability of Plastic Flow. in Defor-mation, Processing and Structure, Chapter 9, 1982 ASM Materials Science Seminar.1984.

9: Olson, G.B. and M. Azrin, Transformation Behavior of TRIP Steels. Met. Trans. A,1978. 9A: p. 713-720.

10: Fiedler, H.C., B.L. Averbach, and M. Cohen, Trans. ASM, 1955. 47: p. 267.

11: Zackay, V.F., Parker, E. R., Fahr, D., and Busch, R. Enhancement of Ductility inHigh-Strength Steels. Asm Transactions Quarterly, 1967. 60(2): p. 252-.

12: Young, C.C. Transformation toughening in phosphocarbide-strengthened austeniticsteels. (1988).

13: G. Olson and M. Cohen, “A general mechanism of martensitic nucleation: Part I.General concepts and the FCC → HCP transformation,” Metallurgical and MaterialsTransactions A, vol. 7, pp. 1897-1904, 1976.

14: Z. Feinberg, “Design Optimization of an Austenitic TRIP Steel for Blast and Frag-ment Protection,” Ph.D., Materials Science and Engineering, Northwestern University,Evanston, 2012.

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15: G. Ghosh and G. B. Olson, “Kinetics of F.C.C. → B.C.C. heterogeneous martensiticnucleationI. The critical driving force for athermal nucleation,” Acta Metallurgica etMaterialia, vol. 42, pp. 3361-3370, 1994.

16: G. Ghosh and G. B. Olson, “Kinetics of F.C.C. → B.C.C. heterogeneous martensiticnucleationII. Thermal activation,” Acta Metallurgica et Materialia, vol. 42, pp. 3371-3379, 1994.

17: U. F. Kocks, A.S. Argon, M. F. Ashby, Thermodynamics and Kinetics of Slip vol. 19:Pergamon Press, 1975.

18: S. Asgari, “Structure and strain hardening of superalloy AEREX350,” Journal of Ma-terials Processing Technology, vol. 118, pp. 246-250, 2001.

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20: R. K. Ham, Ordered Alloys: Structrual Applications and Physical Metallugy. BatonRouge, LA: Claitors, 1970.

21: http://www.ncemt.ctc.com/useruploads/file/publications/Laser-Welded%20Metallic%20Sandwich%20Panels.pdf

22: Olson G.B., Tsuzaki K., and Cohen M., “Statistical Aspects of Martensitic Nucle-ation”, Turnbull Symposium: Phase Transitions in Condensed Systems, G.S. Cargill,F. Spaepen, and K.N. Tu Eds. (MRS,1987) pp. 129-148.

23: A. Saha and G.B. Olson, Computer-aided design of transformation toughened blastresistant naval hull steels: Part I. J Computer-Aided Mater Des, 14, 177-200, 2007.

24: F. Stavehaug, Transformation Toughening of γ’ Strengthened Metastable AusteniticSteels, Ph.D., MIT, 1990.

25: Kotval, P.S. and H. Hatwell, Trans. AIME, 1969. 245: p. 1821-1824.

26: Manna, I.P., S.K., Gust, W., Discontinuous reactions in solids. International MaterialsReviews, 2001. 46(2): p. 53-90.

27: Speich, G.R., Cellular Precipitation in Austenitic Fe-30 Ni-6 Ti Alloy. Transactionsof the Metallurgical Society of AIME, 1963. 227: p. 754-762.

28: Feinberg, Zechariah D. “Steel Design for Blast and Fragment Protection. October(2009) : n. pag. Print.

29: Sadhukhan, P., Z. Feinberg, and R. Glamm Experimental Characterization of γ’Ni3(TixAl1−x) Precipitation: Evolution and Coarsening of Strengthening Precipitatesin Non-Stainless Austenitic TRIP Steels. unpublished, 2009.

30: Taylor, G.I.J. Inst. Metals 62, (1938)

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31: Olson, G.B. and M. Cohen, A General Mechanism of Martensitic Nucleation: Part I.General Concepts and the FCC-HCP Transformation. Metall. Trans., 1976. 7A: p.1897-1904.

32: Ghosh, G. and G.B. Olson, Kinetics of F.C.C. → B.C.C. Heterogeneous Marten-sitic Nucleation–I. The Critical Driving Force for Athermal Nucleation. Acta Metall.mater., 1994. 42(10): p. 3361-3370.

33: Padmanava, S. Computational Design and Analysis of High-Strength Austenitic TRIPSteels for Blast-Protection Applications. (2008)

34: Richman, R.H. and G.F. Bolling, Stress, Deformation and Martensitic Transformation.Met. Trans., 1971:pp. 2451-2463

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TRIP-150 Blast Protection Alloy

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