马氏体相变的相场模型研究进展

于继东 姚松林 吴强

于继东, 姚松林, 吴强. 马氏体相变的相场模型研究进展[J]. 高压物理学报, 2021, 35(4): 040109. doi: 10.11858/gywlxb.20210772
引用本文: 于继东, 姚松林, 吴强. 马氏体相变的相场模型研究进展[J]. 高压物理学报, 2021, 35(4): 040109. doi: 10.11858/gywlxb.20210772
YU Jidong, YAO Songlin, WU Qiang. Advances of Phase Field Modeling of Martensitic Phase Transformation[J]. Chinese Journal of High Pressure Physics, 2021, 35(4): 040109. doi: 10.11858/gywlxb.20210772
Citation: YU Jidong, YAO Songlin, WU Qiang. Advances of Phase Field Modeling of Martensitic Phase Transformation[J]. Chinese Journal of High Pressure Physics, 2021, 35(4): 040109. doi: 10.11858/gywlxb.20210772

马氏体相变的相场模型研究进展

doi: 10.11858/gywlxb.20210772
基金项目: 冲击波物理与爆轰物理重点实验室基金(6142A03191001);国家自然科学基金(11602249)
详细信息
    作者简介:

    于继东(1981-),男,博士,副研究员,主要从事高压物理力学研究. E-mail:yujidong@caep.cn

  • 中图分类号: O521.2

Advances of Phase Field Modeling of Martensitic Phase Transformation

  • 摘要: 马氏体相变是一种无扩散位移型一阶相变,会形成针状、表面浮凸等复杂的特征微结构。马氏体相变的特征微结构会显著影响材料的宏观物理力学特性,相关研究具有重要的科学和工程价值。相场模型具有可处理复杂界面演化问题的独特优势,已成为模拟马氏体相变的有力的理论与计算工具。概述了马氏体相变相场模型的研究进展,并分析了相场模型应用于弱马氏体相变和重构型马氏体相变的特点。

     

  • 图  TiNi合金降温-升温过程中的原位SEM图像:(a) 290 K,(b)降温至222 K,(c)再升温至265 K,(d)再升温至290 K[54]

    Figure  1.  Series of in situ SEM images of TiNi alloy at (a) 290 K and (b) 222 K upon cooling, and (c) 265 K and (d) 290 K upon heating[54]

    图  冲击加载下金属铁回收样品的TEM图像[55]

    Figure  2.  TEM image showing the microstructure of shock-compressed iron[55]

    图  铁的$\alpha $$\varepsilon $正相变过程(红线)及$\varepsilon $$\alpha $′逆相变过程(蓝线)中对称性相关的变体示意图[70]

    Figure  3.  Schematic illustration of the multiple symmetry-related variants for the forward $\alpha $$\varepsilon $ (red) and the reverse $\varepsilon $$\alpha $′ (blue) phase transitions in iron[70]

    图  塑性变形对双晶结构在压剪作用下高压相成核生长的影响[50]

    Figure  4.  Effect of dislocation band on nucleation and evolution of the high pressure phase of bicrystal under compression and shear[50]

  • [1] CHEN L Q. Phase-field models for microstructure evolution [J]. Annual Review of Materials Research, 2002, 32: 113–140. doi: 10.1146/annurev.matsci.32.112001.132041
    [2] LOGINOVA I S, SINGER H M. The phase field technique for modeling multiphase materials [J]. Reports on Progress in Physics, 2008, 71(10): 106501. doi: 10.1088/0034-4885/71/10/106501
    [3] EMMERICH H. Advances of and by phase-field modelling in condensed-matter physics [J]. Advances in Physics, 2008, 57(1): 1–87. doi: 10.1080/00018730701822522
    [4] STEINBACH I. Phase-field models in materials science [J]. Modelling and Simulation in Materials Science and Engineering, 2009, 17(7): 073001. doi: 10.1088/0965-0393/17/7/073001
    [5] WANG Y Z, LI J. Phase field modeling of defects and deformation [J]. Acta Materialia, 2010, 58(4): 1212–1235. doi: 10.1016/j.actamat.2009.10.041
    [6] BOETTINGER W J, WARREN J A, BECKERMANN C, et al. Phase-field simulation of solidification [J]. Annual Review of Materials Research, 2002, 32: 163–194. doi: 10.1146/annurev.matsci.32.101901.155803
    [7] WANG Y, KHACHATURYAN A G. Three-dimensional field model and computer modeling of martensitic transformations [J]. Acta Materialia, 1997, 45(2): 759–773. doi: 10.1016/S1359-6454(96)00180-2
    [8] WANG Y Z, KHACHATURYAN A G. Multi-scale phase field approach to martensitic transformations [J]. Materials Science and Engineering: A, 2006, 438/439/440: 55–63. doi: 10.1016/j.msea.2006.04.123
    [9] MAMIVAND M, ZAEEM M A, KADIRI H E. A review on phase field modeling of martensitic phase transformation [J]. Computational Materials Science, 2013, 77: 304–311. doi: 10.1016/j.commatsci.2013.04.059
    [10] DENG Y, GAMMER C, CISTON J, et al. Hierarchically-structured large superelastic deformation in ferroelastic-ferroelectrics [J]. Acta Materialia, 2019, 181: 501–509. doi: 10.1016/j.actamat.2019.10.018
    [11] CLAYTON J D, KNAP J. A phase field model of deformation twinning: nonlinear theory and numerical simulations [J]. Physica D: Nonlinear Phenomena, 2011, 240(9/10): 841–858. doi: 10.1016/j.physd.2010.12.012
    [12] LIU G S, MO H X, WANG J, et al. Coupled crystal plasticity finite element-phase field model with kinetics-controlled twinning mechanism for hexagonal metals [J]. Acta Materialia, 2021, 202: 399–416. doi: 10.1016/j.actamat.2020.11.002
    [13] WANG L Y, LIU Z L, ZHUANG Z. Developing micro-scale crystal plasticity model based on phase field theory for modeling dislocations in heteroepitaxial structures [J]. International Journal of Plasticity, 2016, 81: 267–283. doi: 10.1016/j.ijplas.2016.01.010
    [14] ALBRECHT C, HUNTER A, KUMAR A, et al. A phase field model for dislocations in hexagonal close packed crystals [J]. Journal of the Mechanics and Physics of Solids, 2020, 137: 103823. doi: 10.1016/j.jmps.2019.103823
    [15] BOURDIN B, FRANCFORT G A, MARIGO J J. The variational approach to fracture [M]. Berlin: Springer Verlag, 2008.
    [16] MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits [J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45/46/47/48): 2765–2778. doi: 10.1016/j.cma.2010.04.011
    [17] REZAEI S, MIANROODI J R, BREPOLS T, et al. Direction-dependent fracture in solids: atomistically calibrated phase-field and cohesive zone model [J]. Journal of the Mechanics and Physics of Solids, 2021, 147: 104253. doi: 10.1016/j.jmps.2020.104253
    [18] WANG T, YE X, LIU Z L, et al. Modeling the dynamic and quasi-static compression-shear failure of brittle materials by explicit phase field method [J]. Computational Mechanics, 2019, 64(6): 1537–1556. doi: 10.1007/s00466-019-01733-z
    [19] WANG T, YE X, LIU Z L, et al. A phase-field model of thermo-elastic coupled brittle fracture with explicit time integration [J]. Computational Mechanics, 2020, 65(5): 1305–1321. doi: 10.1007/s00466-020-01820-6
    [20] BALL J M, JAMES R D. Fine phase mixtures as minimizers of energy [J]. Archive for Rational Mechanics and Analysis, 1987, 100(1): 13–52. doi: 10.1007/BF00281246
    [21] BALL J M, JAMES R D. Proposed experimental tests of a theory of fine microstructure and the two-well problem [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1992, 338(1650): 389–450. doi: 10.1098/rsta.1992.0013
    [22] KOHN R V. The relaxation of a double-well energy [J]. Continuum Mechanics and Thermodynamics, 1991, 3(3): 193–236. doi: 10.1007/BF01135336
    [23] BHATTACHARYA K. Microstructure of martensite [M]. Oxford: Oxford University Press, 2004.
    [24] 唐志平. 冲击相变[M]. 北京: 科学出版社, 2008: 87.
    [25] WEN Y H, WANG Y, BENDERSKY L A, et al. Microstructural evolution during the α2α2 + O transformation in Ti-Al-Nb alloys: phase-field simulation and experimental validation [J]. Acta Materialia, 2000, 48(16): 4125–4135. doi: 10.1016/S1359-6454(00)00186-5
    [26] ARTEMEV A, JIN Y, KHACHATURYAN A G. Three-dimensional phase field model of proper martensitic transformation [J]. Acta Materialia, 2001, 49(7): 1165–1177. doi: 10.1016/S1359-6454(01)00021-0
    [27] RAO W F, KHACHATURYAN A G. Phase field theory of proper displacive phase transformations: structural anisotropy and directional flexibility, a vector model, and the transformation kinetics [J]. Acta Materialia, 2011, 59(11): 4494–4503. doi: 10.1016/j.actamat.2011.03.072
    [28] JAVANBAKHT M, ADAEI M. Investigating the effect of elastic anisotropy on martensitic phase transformations at the nanoscale [J]. Computational Materials Science, 2019, 167: 168–182. doi: 10.1016/j.commatsci.2019.05.047
    [29] XIE X, KANG G Z, KAN Q H, et al. Phase-field theory based finite element simulation on thermo-mechanical cyclic deformation of polycrystalline super-elastic NiTi shape memory alloy [J]. Computational Materials Science, 2020, 184: 109899. doi: 10.1016/j.commatsci.2020.109899
    [30] WANG D, LIANG Q L, ZHAO S S, et al. Phase field simulation of martensitic transformation in pre-strained nanocomposite shape memory alloys [J]. Acta Materialia, 2019, 164: 99–109. doi: 10.1016/j.actamat.2018.10.030
    [31] LEVITAS V I, LEVIN V A, ZINGERMAN K M, et al. Displacive phase transitions at large strains: phase-field theory and simulations [J]. Physical Review Letters, 2009, 103(2): 025702. doi: 10.1103/PhysRevLett.103.025702
    [32] VAN DER WAALS J D. The thermodynamic theory capillarity under the hypothesis of a continuous variation of density [J]. Verhandelingen van de Koninklijke Academie voor Wetenschappen, 1893, 1: 1–56.
    [33] GIBBS J W. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces [J]. Transactions of the Connecticut Academy, 1873, 2: 382–404.
    [34] CAHN J W, HILLIARD J E. Free energy of a nonuniform system. I. interfacial free energy [J]. The Journal of Chemical Physics, 1957, 28(2): 258. doi: 10.1063/1.1744102
    [35] ALLEN S M, CAHN J W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening [J]. Acta Metallurgica, 1979, 27(6): 1085–1095. doi: 10.1016/0001-6160(79)90196-2
    [36] KOBAYASHI H, ODE M, KIM S G, et al. Phase-field model for solidification of ternary alloys coupled with thermodynamic database [J]. Scripta Materialia, 2003, 48(6): 689–694. doi: 10.1016/S1359-6462(02)00557-2
    [37] SEOL D J, HU S Y, LI Y L, et al. Computer simulation of spinodal decomposition in constrained films [J]. Acta Materialia, 2003, 51(17): 5173–5185. doi: 10.1016/S1359-6454(03)00378-1
    [38] WANG Y, JIN Y M, CUITIÑO A M, et al. Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations [J]. Acta Materialia, 2001, 49(10): 1847–1857. doi: 10.1016/S1359-6454(01)00075-1
    [39] CAHN J W, HAN S C, MCFADDEN G B. Anisotropy of interfaces in an ordered hcp binary alloy [J]. Journal of Statistical Physics, 1999, 95(5/6): 1337–1360. doi: 10.1023/A:1004583324097
    [40] OGATA S, LI J, YIP S. Ideal pure shear strength of aluminum and copper [J]. Science, 2002, 298(5594): 807–811. doi: 10.1126/science.1076652
    [41] OGATA S, LI J, YIP S. Energy landscape of deformation twinning in bcc and fcc metals [J]. Physical Review B, 2005, 71(22): 224102. doi: 10.1103/PhysRevB.71.224102
    [42] SHEN C, LI J, WANG Y Z. Finding critical nucleus in solid-state transformations [J]. Metallurgical and Materials Transactions A, 2008, 39(5): 976–983. doi: 10.1007/s11661-007-9302-7
    [43] KARMA A, RAPPEL W J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics [J]. Physical Review E, 1996, 53(4): R3017. doi: 10.1103/PhysRevE.53.R3017
    [44] KARMA A, RAPPEL W J. Quantitative phase-field modeling of dendritic growth in two and three dimensions [J]. Physical Review E, 1998, 57(4): 4323–4349. doi: 10.1103/PhysRevE.57.4323
    [45] FINEL A, BOUAR Y L, DABAS B, et al. Sharp phase field method [J]. Physical Review Letters, 2018, 121(2): 025501. doi: 10.1103/PhysRevLett.121.025501
    [46] PROVATAS N, GOLDENFELD N, DANTZIG J. Efficient computation of dendritic microstructures using adaptive mesh refinement [J]. Physical Review Letters, 1998, 80(15): 3308–3311. doi: 10.1103/PhysRevLett.80.3308
    [47] JEONG D, KIM J. Fast and accurate adaptive finite difference method for dendritic growth [J]. Computer Physics Communications, 2019, 236: 95–103. doi: 10.1016/j.cpc.2018.10.020
    [48] LEVITAS V I, IDESMAN A V, PRESTON D L. Microscale simulation of martensitic microstructure evolution [J]. Physical Review Letters, 2004, 93(10): 105701. doi: 10.1103/PhysRevLett.93.105701
    [49] STEINBACH I, APEL M. Multi phase field model for solid state transformation with elastic strain [J]. Physica D: Nonlinear Phenomena, 2006, 217(2): 153–160. doi: 10.1016/j.physd.2006.04.001
    [50] LEVITAS V I, ESFAHANI S E, GHAMARIAN I. Scale-free modeling of coupled evolution of discrete dislocation bands and multivariant martensitic microstructure [J]. Physical Review Letters, 2018, 121(20): 205701. doi: 10.1103/PhysRevLett.121.205701
    [51] ABBOUD H, KOSSEIFI C A, CHEHAB J P. A stabilized bi-grid method for Allen-Cahn equation in finite elements [J]. Computational and Applied Mathematics, 2019, 38(2): 35. doi: 10.1007/S40314-019-0781-0
    [52] 徐祖耀. 材料相变[M]. 北京: 高等教育出版社, 2013: 352.
    [53] BHATTACHARYA K, CONTI S, ZANZOTTO G, et al. Crystal symmetry and the reversibility of martensitic transformations [J]. Nature, 2004, 428(6978): 55–59. doi: 10.1038/nature02378
    [54] SOEJIMA Y, MOTOMURA S, MITSUHARA M, et al. In situ scanning electron microscopy study of the thermoelastic martensitic transformation in Ti-Ni shape memory alloy [J]. Acta Materialia, 2016, 103: 352–360. doi: 10.1016/j.actamat.2015.10.017
    [55] WANG S J, SUI M L, CHEN Y T, et al. Microstructural fingerprints of phase transitions in shock-loaded iron [J]. Scientific Reports, 2013, 3: 1086. doi: 10.1038/srep01086
    [56] FALK F. One-dimensional model of shape memory alloys [J]. Archives of Mechanics, 1983, 35(1): 63–84.
    [57] FALK F, KONOPKA P. Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys [J]. Journal of Physics: Condensed Matter, 1990, 2(1): 61–77. doi: 10.1088/0953-8984/2/1/005
    [58] JACOBS A E, CURNOE S H, DESAI R C. Simulations of cubic-tetragonal ferroelastics [J]. Physical Review B, 2003, 68(22): 224104. doi: 10.1103/PhysRevB.68.224104
    [59] CAHN J W, KALONJI G. Symmetry in solid state transformation morphology [M]. Warrendale, USA, 1981.
    [60] VEDANTAM S, ABEYARATNE R. A Helmholtz free-energy function for a Cu-Al-Ni shape memory alloy [J]. International Journal of Non-Linear Mechanics, 2005, 40(2/3): 177–193. doi: 10.1016/j.ijnonlinmec.2004.05.005
    [61] SHCHYGLO O, SALMAN U, FINEL A. Martensitic phase transformations in Ni-Ti-based shape memory alloys: the Landau theory [J]. Acta Materialia, 2012, 60(19): 6784–6792. doi: 10.1016/j.actamat.2012.08.056
    [62] LEVITAS V I, PRESTON D L. Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. austenite ↔ martensite [J]. Physical Review B, 2002, 66(13): 134206. doi: 10.1103/PhysRevB.66.134206
    [63] LEVITAS V I, PRESTON D L. Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. multivariant phase transformations and stress space analysis [J]. Physical Review B, 2002, 66(13): 134207. doi: 10.1103/PhysRevB.66.134207
    [64] SHE H, LIU Y L, WANG B. Phase field simulation of heterogeneous cubic→tetragonal martensite nucleation [J]. International Journal of Solids and Structures, 2013, 50(7/8): 1187–1191. doi: 10.1016/j.ijsolstr.2012.12.020
    [65] GOMEZ H, BURES M, MOURE A. A review on computational modelling of phase-transition problems [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 377(2143): 20180203. doi: 10.1098/RSTA.2018.0203
    [66] WEN Y H, WANG Y, CHEN L Q. Effect of elastic interaction on the formation of a complex multi-domain microstructural pattern during a coherent hexagonal to orthorhombic transformation [J]. Acta Materialia, 1999, 47(17): 4375–4386. doi: 10.1016/S1359-6454(99)00247-5
    [67] WEN Y H, WANG Y, CHEN L Q. Phase-field simulation of domain structure evolution during a coherent hexagonal-to-orthorhombic transformation [J]. Philosophical Magazine A, 2000, 80(9): 1967–1982. doi: 10.1080/01418610008212146
    [68] DEVILLE S, GUÉNIN G, CHEVALIER J. Martensitic transformation in zirconia: Part I. nanometer scale prediction and measurement of transformation induced relief [J]. Acta Materialia, 2004, 52(19): 5697–5707. doi: 10.1016/j.actamat.2004.08.034
    [69] BAIN E C. The nature of martensite [J]. Trans. AIME, 1924, 70: 25–46.
    [70] VATTRÉ A, DENOUAL C. Polymorphism of iron at high pressure: a 3D phase-field model for displacive transitions with finite elastoplastic deformations [J]. Journal of the Mechanics and Physics of Solids, 2016, 92: 1–27. doi: 10.1016/J.JMPS.2016.01.016
    [71] DENOUAL C, CAUCCI A M, SOULARD L, et al. Phase-field reaction-pathway kinetics of martensitic transformations in a model Fe3Ni alloy [J]. Physical Review Letters, 2010, 105(3): 035703. doi: 10.1103/PhysRevLett.105.035703
    [72] DENOUAL C, VATTRÉ A. A phase field approach with a reaction pathways-based potential to model reconstructive martensitic transformations with a large number of variants [J]. Journal of the Mechanics and Physics of Solids, 2016, 90: 91–107. doi: 10.1016/j.jmps.2016.02.022
    [73] VATTRÉ A, DENOUAL C. Continuum nonlinear dynamics of unstable shock waves induced by structural phase transformations in iron [J]. Journal of the Mechanics and Physics of Solids, 2019, 131: 387–403. doi: 10.1016/j.jmps.2019.07.012
    [74] HOMAYONIFAR M, MOSLER J. Efficient modeling of microstructure evolution in magnesium by energy minimization [J]. International Journal of Plasticity, 2012, 28(1): 1–20. doi: 10.1016/j.ijplas.2011.05.011
    [75] CLAYTON J D. Nonlinear Eulerian thermoelasticity for anisotropic crystals [J]. Journal of the Mechanics and Physics of Solids, 2013, 61(10): 1983–2014. doi: 10.1016/j.jmps.2013.05.009
    [76] OLSON G B, ROITBURD A L. Martensitic nucleation [M]//OLSON G B, OWEN W S. Martensite. Materials Park, Ohio: ASM International, 1992: 149.
    [77] HENNIG R G, TRINKLE D R, BOUCHET J, et al. Impurities block the α to ω martensitic transformation in titanium [J]. Nature Materials, 2005, 4(2): 129–133. doi: 10.1038/nmat1292
    [78] CASPERSEN K J, CARTER E A. Finding transition states for crystalline solid-solid phase transformations [J]. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(19): 6738–6743. doi: 10.1073/pnas.0408127102
    [79] DUPÉ B, AMADON B, PELLEGRINI Y P, et al. Mechanism for the αε phase transition in iron [J]. Physical Review B, 2013, 87(2): 024103. doi: 10.1103/PhysRevB.87.024103
    [80] BAKHTIARI S, LIU J Z, LIU Y N, et al. Monoclinic angle, shear response, and minimum energy pathways of NiTiCu martensite phases from ab initio calculations [J]. Acta Materialia, 2019, 178: 59–67. doi: 10.1016/j.actamat.2019.07.050
    [81] GAO Y P, SHI R P, NIE J F, et al. Group theory description of transformation pathway degeneracy in structural phase transformations [J]. Acta Materialia, 2016, 109: 353–363. doi: 10.1016/j.actamat.2016.01.027
    [82] GAO Y P, WANG Y Z. Hidden pathway during fcc to bcc/bct transformations: crystallographic origin of slip martensite in steels [J]. Physical Review Materials, 2018, 2(9): 093611. doi: 10.1103/PhysRevMaterials.2.093611
    [83] ZHANG T L, WANG D, WANG Y Z. Novel transformation pathway and heterogeneous precipitate microstructure in Ti-alloys [J]. Acta Materialia, 2020, 196: 409–417. doi: 10.1016/j.actamat.2020.06.048
    [84] GAO Y P. Symmetry and pathway analyses of the twinning modes in Ni-Ti shape memory alloys [J]. Materialia, 2019, 6: 100320. doi: 10.1016/j.mtla.2019.100320
    [85] GAO Y P, ZHENG Y F, FRASER H, et al. Intrinsic coupling between twinning plasticity and transformation plasticity in metastable β Ti-alloys: a symmetry and pathway analysis [J]. Acta Materialia, 2020, 196: 488–504. doi: 10.1016/j.actamat.2020.07.020
    [86] OLSON G B. Computational design of hierarchically structured materials [J]. Science, 1997, 277(5330): 1237–1242. doi: 10.1126/science.277.5330.1237
    [87] CISSÉ C, ZAEEM M A. A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia [J]. Acta Materialia, 2020, 191: 111–123. doi: 10.1016/j.actamat.2020.03.025
    [88] WEI S L, KIM J W, CANN J L, et al. Plastic strain-induced sequential martensitic transformation [J]. Scripta Materialia, 2020, 185: 36–41. doi: 10.1016/j.scriptamat.2020.03.060
    [89] LEVITAS V I. High pressure phase transformations revisited [J]. Journal of Physics: Condensed Matter, 2018, 30(16): 163001. doi: 10.1088/1361-648X/aab4b0
    [90] XU Y, MING P B, CHEN J. A phase field framework for dynamic adiabatic shear banding [J]. Journal of the Mechanics and Physics of Solids, 2020, 135: 103810. doi: 10.1016/j.jmps.2019.103810
    [91] JAVANBAKHT M, LEVITAS V I. Phase field simulations of plastic strain-induced phase transformations under high pressure and large shear [J]. Physical Review B, 2016, 94(21): 214104. doi: 10.1103/PhysRevB.94.214104
    [92] GUO X H, SHI S Q, MA X Q. Elastoplastic phase field model for microstructure evolution [J]. Applied Physics Letters, 2005, 87(22): 221910. doi: 10.1063/1.2138358
    [93] PARANJAPE H M, MANCHIRAJU S, ANDERSON P M. A phase field-finite element approach to model the interaction between phase transformations and plasticity in shape memory alloys [J]. International Journal of Plasticity, 2016, 80: 1–18. doi: 10.1016/j.ijplas.2015.12.007
    [94] KUNDIN J, RAABE D, EMMERICH H. A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite [J]. Journal of the Mechanics and Physics of Solids, 2011, 59(10): 2082–2102. doi: 10.1016/j.jmps.2011.07.001
    [95] ESFAHANI S E, GHAMARIAN I, LEVITAS V I. Strain-induced multivariant martensitic transformations: a scale-independent simulation of interaction between localized shear bands and microstructure [J]. Acta Materialia, 2020, 196: 430–443. doi: 10.1016/j.actamat.2020.06.059
    [96] SCHMITT R, KUHN C, MÜLLER R, et al. Crystal plasticity and martensitic transformations: a phase field approach [J]. Technische Mechanik, 2014, 34(1): 23–38. doi: 10.24352/UB.OVGU-2017-051
    [97] ROTERS F, EISENLOHR P, HANTCHERLI L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications [J]. Acta Materialia, 2010, 58(4): 1152–1211. doi: 10.1016/j.actamat.2009.10.058
    [98] RICE J R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity [J]. Journal of the Mechanics and Physics of Solids, 1971, 19(6): 433–455. doi: 10.1016/0022-5096(71)90010-X
    [99] MA A, ROTERS F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals [J]. Acta Materialia, 2004, 52(12): 3603–3612. doi: 10.1016/j.actamat.2004.04.012
    [100] YAO S L, YU J D, CUI Y N, et al. Revisiting the power law characteristics of the plastic shock front under shock loading [J]. Physical Review Letters, 2021, 126(8): 085503. doi: 10.1103/PhysRevLett.126.085503
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