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Materials Science and Engineering A 438–440 (2006) 48–54

Advances in theory: Martensite by design

G.B. Olson ∗Northwestern University, QuesTek Innovations LLC, Evanston, IL 60208, USA

Received 29 July 2005; received in revised form 5 January 2006; accepted 7 February 2006

bstract

The depth of scientific understanding of martensitic transformations provides a strong foundation for the predictive design of materials exploitingartensitic phenomena. Recent theoretical advances supporting this capability include two- and three-dimensional applications of Landau–Ginzburg

heory to martensitic nucleation, and important refinements of multiscale kinetic theory. Accurate control of transformation kinetics in ferrouslloys has provided both (a) commercial stainless maraging steels exploiting isothermal martensitic transformation in processing and (b) designedecondary-hardening martensitic steels exploiting optimized dispersed-phase transformation toughening in service. Predictive design of low-misfitoherent nanodispersion-strengthened shape memory alloys offer significant advances in actuation power density and cyclic life.

2006 Elsevier B.V. All rights reserved.

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eywords: Martensite theory; Materials design

. Introduction

This overview of recent advances in martensite theory willake the focused perspective of the evolving legacy of the late

orris Cohen. Morris Cohen’s pervasive contributions to thengineering science of materials, with special emphasis on theechanistic and kinetic basis of martensitic phenomena, has

rovided the foundation for a new scientific engineering of mate-ials. The predictive control of martensitic phenomena buildingn Cohen’s contributions has played a central role in the emerg-ng field of materials design.

. Martensitic nucleation

At ICOMAT ’02, Hsu [1] reviewed the application of one-imensional (1D) Landau–Ginzburg models to martensitic phe-omena. The extension of this approach to rigorous two-imensional (2D) and three-dimensional (3D) solutions for thetructure of a martensitic nucleus has recently clarified long-tanding issues in the theory of martensitic nucleation. Olson

nd Roitburd [2] reviewed the full range of possible theoreticalechanisms of martensitic nucleation set forth in the pioneeringork of Morris Cohen. A central issue has been whether nucle-

tion operates in the “classical” limit where a critical nucleus has

∗ Tel.: +1 847 491 2847; fax: +1 847 491 7820.E-mail address: g-olson@northwestern.edu.

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921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.02.168

he full strain amplitude corresponding to fully formed marten-ite, or exhibits “nonclassical” behavior with a significantlyeduced strain amplitude, resembling a local lattice instability.s first described by Olson and Cohen [3] the Landau–Ginzburg

heoretical framework allows a rigorous description of the com-etition between these modes of nucleation, when adapted tohe 2D and 3D variational solutions describing critical nuclei.ompared to the application of variational “phase field” meth-ds to other solid-state transformations, martensitic transfor-ations benefit from a more rigorous foundation, both in the

alculation of homogenous lattice deformation energetics fromrst-principles density functional theory (DFT) calculations,nd the determination of strain gradient energy coefficientsrom both phonon dispersion curve measurements and directeasurements of interfacial core width by high resolution elec-

ron microscopy (HREM). Using the case of a simple coher-nt shear transformation, Reid et al. [3–6] have applied suchandau–Ginzburg descriptions to obtain rigorous 2D varia-

ional solutions for heterogeneous nucleation at linear defectssing an element-free Galerkin (EFG) numerical method. Forhe case of a group of dislocations of sufficient potency toccount for nucleation at the Ms temperature, Fig. 1a showshe computed strain field (right) when the material is describeds linear elastic (left). The defect provides a significant volume

f highly distorted material. Representing conditions far abovehe To equilibrium temperature, Fig. 1b shows the computedeld (right) under conditions corresponding to the first appear-nce of a second energy well (left) representing the martensite

G.B. Olson / Materials Science and Engineering A 438–440 (2006) 48–54 49

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ig. 1. Heterogeneous nucleation at strong defects; 2D variational solutions tonset of martensite mechanical stability. Length scale in units of lattice dislocat

tructure. The variational solution shows that such a defect fieldecomes unstable with respect to the formation of a locally stabi-ized classical (fully formed) martensitic embryo well above theransformation temperature. This solution constitutes rigorousonfirmation of the “pre-existing embryo” hypothesis of Kauf-an and Cohen in 1958 [7]. “Operational nucleation” at the Ms

emperature then corresponds to the growth startup of such clas-ical embryos with kinetic control by processes of interfacialotion.A central concept of quantitative martensite kinetic theory

8] is a potency distribution of nucleation sites as originallyroposed by Machlin and Cohen [9]. For low potency heteroge-eous nucleation, Fig. 2 [6] shows the computed fields (right) atemperatures below To (left) for the case of a single lattice dis-ocation which would contribute to nucleation at temperaturesell below Ms. For the smaller distorted volume in this class ofefect, gradient energy suppresses the formation of a local clas-ical embryo, so that nucleation abruptly transforms the crystaln Fig. 2c without a pre-existing classical embryo. The defecteld in this case resembles the “strain embryo” concept of theon-classical reaction path model first proposed by Cohen et al.n 1949 [10]. The variational solutions of Fig. 2 confirm that thetrain amplitude of the critical nucleus in this weak defect limithows some departure from the classical limit.

Stronger departures from classical behavior can be expectedn the limit of homogeneous martensitic nucleation whichequires high driving forces approaching the critical drivingorce for lattice instability. The data points in Fig. 3 representhe measured critical driving force for homogeneous face cen-

ered cubic (FCC) → body centered cubic (BCC) martensiticucleation in defect-free 10 nm Fe–Co particles coherently pre-ipitated in a Cu matrix, as studied by Lin et al. [11]. The drivingorce is normalized to the critical driving force for FCC lattice

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u–Ginzburg model for (a) linear elastic material, and (b) nonlinear material aturgers vector, b [4].

nstability determined from DFT calculations. The solid curvehows the theoretical prediction of a 3D model of a single-omain fully coherent BCC nucleus based on a rigorous 1Dandau–Ginzburg description using the gradient energy coef-cient as a fitting parameter [12]. Significant departure of theritical nucleus strain amplitude from the classical limit is pre-icted. With the model parameters fixed, the upper dashed curvehows the predicted critical driving force for nucleation at fulltrain amplitude. The model predicts that in this limit of homo-eneous coherent FCC → BCC nucleation, nonclassical effectseduce the critical driving force for nucleation by 15–20%.

These examples of the incorporation of rigorous nonlinearhysics in 2D and 3D variational solutions of critical nucleustructure provide important guidelines for appropriate approxi-ations in the engineering application of martensite kinetic the-

ry. For the case of finely dispersed metastable particles, trans-ormation controlled by weak defect or homogeneous nucleationt high driving forces can require significant nonclassical correc-ions. For bulk polycrystals where transformation is dominatedy strong defects at relatively low driving forces, classical het-rogeneous nucleation theory [13] can be applied with highonfidence.

. Isothermal martensitic kinetics

A central theme of Morris Cohen’s exploration of the mech-nism and kinetics of martensitic transformations has been theetailed analysis of thermally activated behavior to constrainossible nucleation mechanisms. Beginning with the classic

ork of Shih et al. [14], this has centered on the isothermalode of martensitic nucleation, leading to a kinetic theoreti-

al framework that extends beyond the predictive control of Msemperatures [15] to describe the full course of transformation,

50 G.B. Olson / Materials Science and Engineering A 438–440 (2006) 48–54

F andau( in (c).

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ig. 2. Heterogeneous nucleation at weak defects; 2D variational solutions to La and b), leading to transformed crystal at critical driving force for nucleation

ltimately including the very practical problem of controllingetained austenite in martensitic steels.

Reproducible control of isothermal martensite kinetics hasaken on new practical significance with the commercial appli-ation of isothermally processed high-alloy stainless maragingteels such as Sandvik’s “Nanoflex” steel, with the measured

sothermal C-curve kinetics [16] shown in Fig. 4. An unusualeature of this isothermally transforming high Mo stainless com-osition is its formation of a lath martensite microstructure atryogenic temperatures [17] as also shown in Fig. 4.

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–Ginzburg model for single lattice dislocation with increasing driving force inLength scale in units of lattice dislocation Burgers vector, b [6].

In support of predictive process control in such alloys, theeneral martensite kinetic theory of Lin et al. [8], based onistributed heterogeneous classical nucleation with interfaceontrolled kinetics, has been numerically implemented [18] anddapted to lath microstructures using recent electron microscopyeasurements [19] of the evolution of average particle volume

¯ with transformed fraction f in lath martensites. An intrigu-ng prediction of the numerical model is that the temperature of

aximum transformation rate can change with increasing phaseraction as the potency distribution of autocatalytic nucleation

G.B. Olson / Materials Science and Engineering A 438–440 (2006) 48–54 51

Fig. 3. Normalized critical driving force for homogenous coherent FCC → BCCnucleation in defect-free Fe–Co particles comparing 3D Landau–Ginzburg vari-ational solution for nucleus (solid curve) with experimental data (open points).Horizontal dashed line denotes elastic energy threshold for coherent nucleation.Upper dashed curve represents classical nucleus of full strain amplitude [12].

Fig. 4. Isothermal martensite in commercial Sandvik “Nanoflex” steel. (a)Isothermal “C-curve” kinetics [16], (b) lath microstructure formed by 30 minhold at liquid nitrogen temperature [17].

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ig. 5. Simulated martensite kinetics in experimental stainless steel comparingptimal nonisothermal treatment with isothermal treatments [18].

volves. This opens the possibility that a theoretically predictedonisothermal cryogenic treatment can achieve a lower retainedustenite content for a given total process time, compared to anysothermal cycle. An example of such a model prediction forn experimental stainless steel is shown in Fig. 5. Although thedditional increment demonstrated here is modest, it illustrateshe scientific principle. Ongoing applications of the model arexploring more practical applications.

While such theory-based process optimization shows highuture promise, accurate predictions will require significantmprovements in low temperature alloy thermodynamics.

. Transformation toughened steels

Morris Cohen advocated a “reciprocity” between the deduc-ive and inductive logics of science and engineering for thefficient generation of useful knowledge [20]. Recent applica-ions of this philosophy have centered on exploitation of marten-itic transformation plasticity. Incorporating the thermodynamicffect of applied stress and the kinetic effect of strain-induceducleation sites, Olson and Cohen [21,22] extended the the-ry of the mechanism and kinetics of martensitic transforma-ions to mechanically induced transformations and developedransformation kinetics based constitutive laws applied to theransformation enhancement of uniform ductility and tough-ess in high-strength austenitic transformation-induced plas-icity (TRIP) steels. Exploiting the higher stability of smallarticles predicted by nucleation theory, designed multistep tem-ering treatments have been used to demonstrate transformationoughening in higher strength martensitic steels by the controlledrecipitation of an optimal stability austenite dispersion [23].

These principles were recently integrated in the systems-ased computational design of an ultratough, high-strength

eldable martensitic plate steel [24] summarized by the system

hart of Fig. 6. Specifically designed to meet demanding per-ormance requirements of naval hull applications, C content isimited to 0.05 wt.% for weldability, M2C alloy carbide compo-

52 G.B. Olson / Materials Science and Engineering A 438–440 (2006) 48–54

F of weldable, secondary-hardening, transformation-toughened martensitic plate steelf

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ig. 6. System chart representing process/structure/property relations for designor advanced naval hull applications [24].

ition is optimized for maximum carbide strengthening, and thealance of required strengthening is achieved by precipitationf 2 nm scale BCC Cu. Optimal dispersed austenite stability forransformation toughening is simultaneously achieved throughontrol of both particle size and composition, employing a two-tep tempering treatment where a first high temperature stepucleates austenite on the coherent Cu particles and a secondower temperature step enriches the austenite Ni content to theequired level. Evaluation of the design in a single 15 kg slab-ast hot-rolled plate demonstrated the desired properties afterptimization of the prescribed two-step tempering treatments,howing a remarkable Cv impact toughness of 180 J (130 ft lb)t a yield strength of 1100 MPa (160 ksi). The measured tem-

erature dependence of impact toughness in Fig. 7 indicatesroom temperature transformation toughening peak superim-

osed on the ductile “shelf” toughness, consistent with theesigned austenite stability optimization. Fig. 8 presents 3D

ig. 7. Temperature dependence of Charpy impact toughness showing room-emperature transformation toughening peak associated with optimal stabilityrecipitated austenite [25].

Fig. 8. 3D atom-probe microanalytical validation of Ni enriched austenite parti-cle nucleated on 2 nm coherent Cu particle; dark atoms Cu, light atoms Ni, shadedarea Ni enriched. Linear analysis profiles below are taken through top portion ofupper image showing austenite to right of Cu particle contains designed 30 at.%Ni [24].

Engineering A 438–440 (2006) 48–54 53

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tom-probe tomographic microanalysis verifying the formationn a 2 nm Cu particle of an austenite particle enriched in Nio the designed level of 30 at.%. The steel represents an impor-ant milestone achieving its property objectives and designed

icrostructure in a single iteration of computational design. Aarger scale heat of the alloy is undergoing testing for commer-ial applications.

. High-performance shape memory alloys

In seeking to clarify the defining attributes underlyingll martensitic transformations [25,26], Morris Cohen soughto establish a general mechanistic and kinetic theoreticalramework embracing both thermoelastic and nonthermoelasticartensites [22]. Important scientific contributions of thermoe-

astic systems to this framework include (a) the direct transmis-ion electron microscopy (TEM) observation of heterogeneouslassical nucleation at interfacial dislocations in TiNi [27], andb) the direct measurement of thermal and athermal interfacialobility via single interface transformations in Cu–Al–Ni crys-

als [28]. Quantitative stereological measurements in thermoe-astic systems support the same distributed-nucleation kineticheory originally applied to nonthermoelastic systems [5].

Building on these general principles, systems-based compu-ational materials design has been applied to a new class of high-erformance thermoelastic shape memory alloys [29] repre-ented by the system chart of Fig. 9. To increase the output stressnd cyclic life of TiNi-based alloys for high power density mem-ry and superelastic devices, the slip resistance of the B2 parenthase is efficiently increased by a nanoscale dispersion of coher-nt low-misfit multicomponent L21 Heusler phase aluminiderecipitates, while controlling the transformation temperatures

f the B2 matrix. For the Ti–Zr–Hf–Ni–Pd–Pt–Al system, ahermodynamic and molar volume database was developed toccurately describe the temperature-dependent partitioning andisfit between the desired B2 and L21 phases, the relative sta-

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ig. 9. System chart representing process/structure/property relations for design ofhape memory alloy for enhanced output stress and cyclic life [29].

ig. 10. Low-misfit coherent aluminide dispersion in B2 matrix of Ti–Zr–Ni–Allloy [29].

ility of undesirable embrittling phases and the thermodynamicsf the B2–B19′ martensitic transformation. The dark field TEMicrograph of Fig. 10 demonstrates a designed low-misfit coher-

nt L21 dispersion in the B2 matrix of a Ti–Zr–Ni–Al alloy.Modeling of the B2 phase Af reversion temperature employs

he Af = To approximation demonstrated for thermoelastic alloysy Salzbrenner and Cohen [30]. Consistent with interfacialobility theory [28], the nanoscale L21 dispersion optimized

or B2 slip strengthening causes no significant increase in trans-ormation hysteresis. However, a discrepancy between the mea-ured To and the calculated chemical To of the matrix B2 compo-ition is used to determine a very significant stored elastic energyn the martensite associated with the nontransforming coherent

21 dispersion. An elastic energy per volume of L21 thus defined

s then used to predictively control alloy To temperatures.Alloy design prototypes have demonstrated a B2 yield

trength of 2 GPa with controlled To temperatures providing

low-misfit coherent aluminide precipitation-strengthened controlled stability

54 G.B. Olson / Materials Science and Eng

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ig. 11. Toughness/strength combination demonstrated in Ferrium S53 stainlessteel compared to other stainless steels (dark bands) and nonstainless steels (openoints).

xcellent shape memory and superelastic properties. Continu-ng design and development addresses fabricability and cyclicerformance.

. Green steel

As chair of the Committee on the Survey of Materials Sciencend Engineering (COSMAT) study defining the field of materi-ls science and engineering [31], Morris Cohen called attentiono the “total materials cycle” and the central role of materials inechnology sustainability, identifying a major new opportunityor materials design with high societal impact. Responding tohis challenge, the multiagency Strategic Environmental R&Drogram (SERDP) has supported an ambitious computationalaterials design project at QuesTek aimed at the creation of a

ew class of martensitic stainless steel matching the mechani-al performance of the nonstainless steels currently employedn aircraft landing gear, motivated by the goal of eliminating theeed for carcinogenic Cd plating. Following a systems designpproach similar to that of Figs. 6 and 9, combining predictiveontrol of transformation temperatures, cryogenic treatment andultistep tempering to enable an optimal balance of corrosion

esistance and mechanical performance, the new “Ferrium S53”tainless steel achieved the desired strength/toughness combina-ion represented in Fig. 11. The successful design received theERDP Pollution Prevention Project of the Year Award and aight certification testing program is now well underway, withomponents scheduled to fly in 2007.

A science-based designed martensite, it will be a fitting tributeo the legacy of Morris Cohen when this “green steel” takes tohe sky.

. Conclusions

Advances in the theory of the mechanism and kinetics ofartensitic transformations have strengthened many important

oncepts first put forward in the pioneering work of Morris

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ineering A 438–440 (2006) 48–54

ohen. Consonant with his vision of a “reciprocity” of sciencend engineering philosophies, these scientific advances haverovided better engineering approximations and new simula-ion tools enabling predictive process optimization and design ofew materials responding efficiently to societal needs. Buildingn Morris Cohen’s legacy, martensitic materials today define therontier of the emerging field of computational materials design.

cknowledgments

Research at Northwestern and QuesTek reported here haseen supported by the National Science Foundation, the Office ofaval Research and the Strategic Environmental R&D Programith industry matching funds. The author is deeply grateful forany years of inspiring interactions with the late Morris Cohen

f MIT.

eferences

[1] T.Y. Hsu, in: Proc. ICOMAT’02, J. Phys. IV 112 (2003) 29.[2] G.B. Olson, A.L. Roitburd, in: G.B. Olson, W.S. Owen (Eds.), Martensite,

ASM, 1992, p. 149.[3] G.B. Olson, M. Cohen, J. Phys. 43 (1982) C4–C75.[4] A.C.E. Reid, G.B. Olson, B. Moran, Phase Trans. 69 (1999) 309.[5] G.B. Olson, Mater. Sci. Eng. A273–275 (1999) 11–20.[6] A.C.E. Reid, G.B. Olson, Mater. Sci. Eng. A309–310 (2001) 370.[7] L. Kaufman, M. Cohen, Prog. Met. Phys. 1 (1958) 165.[8] M. Lin, G.B. Olson, M. Cohen, Metall. Trans. 23A (1992) 2987.[9] E.S. Machlin, M. Cohen, Trans. AIME 194 (1952) 489.10] M. Cohen, E.S. Machlin, V.G. Paranjpe, Thermodynamics in Physical Met-

allurgy, ASM, 1949, p. 242.11] M. Lin, G.B. Olson, M. Cohen, Acta. Metall. Mater. 41 (1993) 253.12] Y.A. Chu, B. Moran, G.B. Olson, Metall. Mater. Trans. 31A (2000) 1321.13] G.B. Olson, M. Cohen, Metall. Trans. 7A (1976) 1897.14] C.H. Shih, B.L. Averbach, M. Cohen, Trans. AIME 203 (1955) 183.15] G. Ghosh, G.B. Olson, Acta Metall. Mater. 42 (1994) 3371.16] M. Holmquist, J.-O. Nilsson, A. Hultin Stigenberg, Scripta Metall. Mater.

33 (1995) 1367.17] J.-W. Jung, G.B. Olson, unpublished research, Northwestern University,

2004.18] L. Li, H.-J. Jou, G.B. Olson, unpublished research, QuesTek Innovations

LLC, 2005.19] G. Ghosh, G.B. Olson, J. Phys. IV France 112 (2003) 139.20] M. Cohen, Mater. Sci. Eng. 25 (1976) 3.21] G.B. Olson, M. Cohen, in: S.D. Antalovich, R.O. Ritchie, W.W. Gerberich

(Eds.), Mechanical Properties and Phase Transformations in EngineeringMaterials, TMS-AIME, 1986, p. 367.

22] G.B. Olson, M. Cohen, in: F.R.N. Nabarro (Ed.), Dislocations in Solids,vol. 7, North-Holland, 1986, p. 295.

23] G.B. Olson, C.J. Kuehmann, in: E.B. Damm, M.J. Merwin (Eds.), AusteniteFormation and Decomposition, ISS/TMS, 2003, p. 493.

24] A. Saha, doctoral thesis, Northwestern University, 2004.25] M. Cohen, G.B. Olson, P.C. Clapp, Proc. ICOMAT-79, MIT, 1979, p. 1.26] J.W. Christian, G.B. Olson, M. Cohen, J. de Phys. III 5 (1995) 3 (Coll. C8).27] T. Saburi, S. Nenno, Proc. ICOMAT 86, Japan Institute of Metals, 1986, p.

671.

28] M. Grujicic, G.B. Olson, W.S. Owen, Metall. Trans. 16A (1985) 1713.29] J. Jung, G. Ghosh, G.B. Olson, Acta Mater. 51 (2003) 6341.30] R.J. Salzbrenner, M. Cohen, Acta Metall. 27 (1979) 739.31] M. Cohen (Ed.), Materials and Man’s Needs, COSMAT Summary Report,

National Academy of Sciences, Washington, DC, 1974.