Volume 34 Issue 3
Jun 2020
Turn off MathJax
Article Contents
LIU Jingnan, YE Changqing, LIU Guisen, SHEN Yao. Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process[J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874
Citation: LIU Jingnan, YE Changqing, LIU Guisen, SHEN Yao. Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process[J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874

Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process

doi: 10.11858/gywlxb.20190874
  • Received Date: 31 Dec 2019
  • Rev Recd Date: 17 Jan 2020
  • For shock deformation behavior of materials under high temperature, high pressure and high strain-rate loading conditions, dynamic crystal plasticity models can directly reflect the anisotropy of plastic slip and its dependence of temperature, pressure and microstructure in crystals. In consequence, dynamic crystal plasticity models are widely used in simulations of material impact dynamic response, microstructure evolution and dynamic damage. Theoretical models of dynamic crystal plasticity under high pressure shock loading conditions were reviewed in this paper, mainly including: deformation kinetics, hyperelastic constitutive models incorporating equations of state, and crystal plasticity constitutive models. This paper also covers plastic deformation mechanisms, including dislocation slip, phase transition and twinning; as well as dynamic damage, including spalling and adiabatic shear band.

     

  • loading
  • [1]
    BODNER S R, PARTOM Y. Constitutive equations for elastic-viscoplastic strain-hardening materials [J]. Journal of Applied Mechanics, 1975, 42(2): 385–389. doi: 10.1115/1.3423586
    [2]
    JOHNSON G R. A constitutive model and data for materials subjected to large strains, high strain rates, and high temperatures [J]. Proceeding of the 7th International Symposium on Ballistics, 1983: 541–547.
    [3]
    ZERILLI F J, ARMSTRONG R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations [J]. Journal of Applied Physics, 1987, 61(5): 1816–1825. doi: 10.1063/1.338024
    [4]
    STEINBERG D J, COCHRAN S G, GUINAN M W. A constitutive model for metals applicable at high-strain rate [J]. Journal of Applied Physics, 1980, 51(3): 1498–1504. doi: 10.1063/1.327799
    [5]
    GUPTA Y M, DUVALL G E, FOWLES G R. Dislocation mechanisms for stress relaxation in shocked LiF [J]. Journal of Applied Physics, 1975, 46(2): 532–546. doi: 10.1063/1.321678
    [6]
    ASAY J R, FOWLES G R, DURALL G E, et al. Effects of point defects on elastic precursor decay in LiF [J]. Journal of Applied Physics, 1972, 43(5): 2132–2145. doi: 10.1063/1.1661464
    [7]
    WOLFER W G. Phonon drag on dislocations at high pressures: UCRL-ID-136221 [R]. Office of Scientific and Technical Information (OSTI), 1999.
    [8]
    CAWKWELL M J, RAMOS K J, HOOKS D E, et al. Homogeneous dislocation nucleation in cyclotrimethylene trinitramine under shock loading [J]. Journal of Applied Physics, 2010, 107(6): 063512. doi: 10.1063/1.3305630
    [9]
    SHEHADEH M A, BRINGA E M, ZBIB H M, et al. Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations [J]. Applied Physics Letters, 2006, 89(17): 171918. doi: 10.1063/1.2364853
    [10]
    CERRETA E K, ESCOBEDO J P, RIGG P A, et al. The influence of phase and substructural evolution during dynamic loading on subsequent mechanical properties of zirconium [J]. Acta Materialia, 2013, 61(20): 7712–7719. doi: 10.1016/j.actamat.2013.09.009
    [11]
    BOURNE N K, MILLETT J C F, CHEN M, et al. On the Hugoniot elastic limit in polycrystalline alumina [J]. Journal of Applied Physics, 2007, 102(7): 073514. doi: 10.1063/1.2787154
    [12]
    MEYERS M A, GREGORI F, KAD B K, et al. Laser-induced shock compression of monocrystalline copper: characterization and analysis [J]. Acta Materialia, 2003, 51(5): 1211–1228. doi: 10.1016/S1359-6454(02)00420-2
    [13]
    RAHUL, DE S. A phase-field model for shock-induced α-γ phase transition of RDX [J]. International Journal of Plasticity, 2017, 88: 140–158. doi: 10.1016/j.ijplas.2016.10.006
    [14]
    ADDESSIO F L, LUSCHER D J, CAWKWELL M J, et al. A single-crystal model for the high-strain rate deformation of cyclotrimethylene trinitramine including phase transformations and plastic slip [J]. Journal of Applied Physics, 2017, 121(18): 185902. doi: 10.1063/1.4983009
    [15]
    WINEY J M, GUPTA Y M. Shock wave compression of hexagonal-close-packed metal single crystals: time-dependent, anisotropic elastic-plastic response of beryllium [J]. Journal of Applied Physics, 2014, 116(3): 033505. doi: 10.1063/1.4889886
    [16]
    KADAU K, GERMANN T C, LOMDAHL P S, et al. Shock waves in polycrystalline iron [J]. Physical Review Letters, 2007, 98(13): 135701. doi: 10.1103/PhysRevLett.98.135701
    [17]
    KANEL G I. Spall fracture: methodological aspects, mechanisms and governing factors [J]. International Journal of Fracture, 2010, 163(1/2): 173–191.
    [18]
    CHEN X, ASAY J R, DWIVEDI S K, et al. Spall behavior of aluminum with varying microstructures [J]. Journal of Applied Physics, 2006, 99(2): 023528. doi: 10.1063/1.2165409
    [19]
    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
    [20]
    郑松林. 晶体塑性有限元在材料动态响应研究中的应用进展 [J]. 高压物理学报, 2019, 33(3): 030108. doi: 10.11858/gywlxb.20190725

    ZHENG S L. Advances in the study of dynamic response of crystalline materials by crystal plasticity finite element modeling [J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030108. doi: 10.11858/gywlxb.20190725
    [21]
    HILL R, RICE J R. Constitutive analysis of elastic-plastic crystals at arbitrary strain [J]. Journal of the Mechanics and Physics of Solids, 1972, 20(6): 401–413. doi: 10.1016/0022-5096(72)90017-8
    [22]
    ASARO R J. Micromechanics of crystals and polycrystals [M]//Advances in Applied Mechanics. Elsevier, 1983: 1–115.
    [23]
    CLAYTON J D. Dynamic plasticity and fracture in high density polycrystals: constitutive modeling and numerical simulation [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(2): 261–301. doi: 10.1016/j.jmps.2004.06.009
    [24]
    VOGLER T, CLAYTON J. Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling [J]. Journal of the Mechanics and Physics of Solids, 2008, 56(2): 297–335. doi: 10.1016/j.jmps.2007.06.013
    [25]
    HANSEN B L, BEYERLEIN I J, BRONKHORST C A, et al. A dislocation-based multi-rate single crystal plasticity model [J]. International Journal of Plasticity, 2013, 44: 129–146. doi: 10.1016/j.ijplas.2012.12.006
    [26]
    DE S, ZAMIRI A R, RAHUL. A fully anisotropic single crystal model for high strain rate loading conditions with an application to α-RDX [J]. Journal of the Mechanics and Physics of Solids, 2014, 64: 287–301. doi: 10.1016/j.jmps.2013.10.012
    [27]
    SHAHBA A, GHOSH S. Crystal plasticity FE modeling of Ti alloys for a range of strain-rates. Part Ⅰ: a unified constitutive model and flow rule [J]. International Journal of Plasticity, 2016, 87: 48–68. doi: 10.1016/j.ijplas.2016.09.002
    [28]
    BELYTSCHKO T, LIU W K, MORAN B, et al. Nonlinear finite elements for continua and structures [M]. John Wiley & Sons, 2013.
    [29]
    BECKER R. Effects of crystal plasticity on materials loaded at high pressures and strain rates [J]. International Journal of Plasticity, 2004, 20(11): 1983–2006. doi: 10.1016/j.ijplas.2003.09.002
    [30]
    PI A G, HUANG F L, WU Y Q, et al. Anisotropic constitutive model and numerical simulations for crystalline energetic material under shock loading [J]. Mathematics and Mechanics of Solids, 2014, 19(6): 640–658. doi: 10.1177/1081286513482322
    [31]
    LUSCHER D J, BRONKHORST C A, ALLEMAN C N, et al. A model for finite-deformation nonlinear thermomechanical response of single crystal copper under shock conditions [J]. Journal of the Mechanics and Physics of Solids, 2013, 61(9): 1877–1894. doi: 10.1016/j.jmps.2013.05.002
    [32]
    LUSCHER D J, MAYEUR J R, MOURAD H M, et al. Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions [J]. International Journal of Plasticity, 2016, 76: 111–129. doi: 10.1016/j.ijplas.2015.07.007
    [33]
    DOS SANTOS T, ROSA P A R, MAGHOUS S, et al. A simplified approach to high strain rate effects in cold deformation of polycrystalline FCC metals: constitutive formulation and model calibration [J]. International Journal of Plasticity, 2016, 82: 76–96. doi: 10.1016/j.ijplas.2016.02.003
    [34]
    STAINIER L, ORTIZ M. Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity [J]. International Journal of Solids and Structures, 2010, 47(5): 705–715. doi: 10.1016/j.ijsolstr.2009.11.012
    [35]
    VON NEUMANN J, RICHTMYER R D. A method for the numerical calculation of hydrodynamic shocks [J]. Journal of Applied Physics, 1950, 21(3): 232–237. doi: 10.1063/1.1699639
    [36]
    VINET P, SMITH J R, FERRANTE J, et al. Temperature effects on the universal equation of state of solids [J]. Physical Review B, 1987, 35(4): 1945. doi: 10.1103/PhysRevB.35.1945
    [37]
    李欣竹. 金属物态方程的讨论 [D]. 绵阳: 中国工程物理研究院, 2003.

    LI X Z. Discussion for the semi-empiric equation of state of metals [D]. Mianyang: China Academy of Engineering Physics, 2003.
    [38]
    CAWKWELL M J, LUSCHER D J, ADDESSIO F L, et al. Equations of state for the α and γ polymorphs of cyclotrimethylene trinitramine [J]. Journal of Applied Physics, 2016, 119(18): 185106. doi: 10.1063/1.4948673
    [39]
    LUSCHER D J, ADDESSIO F L, CAWKWELL M J, et al. A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine [J]. Journal of the Mechanics and Physics of Solids, 2017, 98: 63–86. doi: 10.1016/j.jmps.2016.09.005
    [40]
    尚福林, 王子昆. 塑性力学基础 [M]. 西安: 西安交通大学出版社, 2011.

    SHANG F L, WANG Z K. Fundamentals of of plasticity [M]. Xi’an: Xi’an Jiaotong University Press, 2011.
    [41]
    HUTCHINSON J W. Bounds and self-consistent estimates for creep of polycrystalline materials [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1976, 348(1652): 101–127.
    [42]
    LI H W, YANG H, SUN Z C. A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method [J]. International Journal of Plasticity, 2008, 24(2): 267–288. doi: 10.1016/j.ijplas.2007.03.014
    [43]
    KHAN A S, LIU J, YOON J W, et al. Strain rate effect of high purity aluminum single crystals: experiments and simulations [J]. International Journal of Plasticity, 2015, 67: 39–52. doi: 10.1016/j.ijplas.2014.10.002
    [44]
    ZHANG K, HOPPERSTAD O, HOLMEDAL B, et al. A robust and efficient substepping scheme for the explicit numerical integration of a rate-dependent crystal plasticity model [J]. International Journal for Numerical Methods in Engineering, 2014, 99(4): 239–262. doi: 10.1002/nme.4671
    [45]
    LIM H, JONG BONG H, CHEN S R, et al. Developing anisotropic yield models of polycrystalline tantalum using crystal plasticity finite element simulations [J]. Materials Science and Engineering A, 2018, 730: 50–56. doi: 10.1016/j.msea.2018.05.096
    [46]
    BOBBILI R, MADHU V. Crystal plasticity modeling of a near alpha titanium alloy under dynamic compression [J]. Journal of Alloys and Compounds, 2018, 759: 85–92. doi: 10.1016/j.jallcom.2018.05.167
    [47]
    KOCKS U F, ARGON A S, ASHBY M F. Thermodynamics and kinetics of slip [J]. Progress in Materials Science, 1975, 19: 141–145.
    [48]
    LI J F, ROMERO I, SEGURADO J. Development of a thermo-mechanically coupled crystal plasticity modeling framework: application to polycrystalline homogenization [J]. International Journal of Plasticity, 2019, 119: 313–330. doi: 10.1016/j.ijplas.2019.04.008
    [49]
    BRONKHORST C A, GRAY G T III, ADDESSIO F L, et al. Publisher's note: “Response and representation of ductile damage under varying shock loading conditions in tantalum”[J. Appl. Phys. 119, 085103(2016)] [J]. Journal of Applied Physics, 2016, 119(10): 109901.
    [50]
    CHANDRA S, SAMAL M K, KAPOOR R, et al. Deformation behavior of Nickel-based superalloy Su-263: experimental characterization and crystal plasticity finite element modeling [J]. Materials Science and Engineering A, 2018, 735: 19–30. doi: 10.1016/j.msea.2018.08.022
    [51]
    王礼立, 胡时胜, 杨黎明. 材料动力学 [M]. 合肥: 中国科学技术大学出版社, 2017.

    WANG L L, HU S S, YANG L M. Thermodynamics and kinetics of materials [M]. Hefei: Press of University of Science and Technology of China, 2017.
    [52]
    MEYERS M A. 材料的动力学行为 [M]. 张庆明, 译. 北京: 国防工业出版社, 2006.

    MEYERS M A. Dynamic behavior of materials [M]. Translated by ZHANG Q M. Beijing: National Defense Industry Press, 2006.
    [53]
    黄克智, 肖纪美. 材料的损伤断裂机理和宏微观力学理论 [M]. 北京: 清华大学出版社, 1999.

    HUANG K Z, XIAO J M. Damage and fracture mechanisms of materials and macro-micro-mechanics [M]. Beijing: Tsinghua University Press, 1999.
    [54]
    BITTENCOURT E. Dynamic explicit solution for higher-order crystal plasticity theories [J]. International Journal of Plasticity, 2014, 53: 1–16. doi: 10.1016/j.ijplas.2013.06.010
    [55]
    PEIRCE D, ASARO R J, NEEDLEMAN A. An analysis of nonuniform and localized deformation in ductile single crystals [J]. Acta Metallurgica, 1982, 30(6): 1087–1119. doi: 10.1016/0001-6160(82)90005-0
    [56]
    ACHARYA A, BEAUDOIN A J. Grain-size effect in viscoplastic polycrystals at moderate strains [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(10): 2213–2230. doi: 10.1016/S0022-5096(00)00013-2
    [57]
    CLAYTON J D. Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys [J]. International Journal of Solids and Structures, 2005, 42(16/17): 4613–4640.
    [58]
    CLAYTON J D. Plasticity and spall in high density polycrystals: modeling and simulation [C]//AIP Conference Proceedings, Baltimore, Maryland (USA). AIP, 2006.
    [59]
    TAJALLI S A, MOVAHHEDY M R, AKBARI J. Simulation of orthogonal micro-cutting of FCC materials based on rate-dependent crystal plasticity finite element model [J]. Computational Materials Science, 2014, 86: 79–87. doi: 10.1016/j.commatsci.2014.01.016
    [60]
    LI J G, LI Y L, HUANG C X, et al. On adiabatic shear localization in nanostructured face-centered cubic alloys with different stacking fault energies [J]. Acta Materialia, 2017, 141: 163–182. doi: 10.1016/j.actamat.2017.09.022
    [61]
    LI J G, LI Y L, SUO T, et al. Numerical simulations of adiabatic shear localization in textured FCC metal based on crystal plasticity finite element method [J]. Materials Science and Engineering A, 2018, 737: 348–363. doi: 10.1016/j.msea.2018.08.105
    [62]
    JOHNSTON W G, GILMAN J J. Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals [J]. Journal of Applied Physics, 1959, 30(2): 129–144. doi: 10.1063/1.1735121
    [63]
    GILMAN J J. The plastic resistance of crystals [J]. Australian Journal of Physics, 1960, 13(2): 327. doi: 10.1071/PH600327a
    [64]
    GILMAN J J. Micromechanics of flow in solids [M]. McGraw-Hill, 1969.
    [65]
    JOHNSON J N, BARKER L M. Dislocation dynamics and steady plastic wave profiles in 6061-T6 aluminum [J]. Journal of Applied Physics, 1969, 40(11): 4321–4334. doi: 10.1063/1.1657194
    [66]
    ALANKAR A, EISENLOHR P, RAABE D. A dislocation density-based crystal plasticity constitutive model for prismatic slip in α-titanium [J]. Acta Materialia, 2011, 59(18): 7003–7009. doi: 10.1016/j.actamat.2011.07.053
    [67]
    ZHANG H M, DONG X H, DU D P, et al. A unified physically based crystal plasticity model for FCC metals over a wide range of temperatures and strain rates [J]. Materials Science and Engineering A, 2013, 564: 431–441. doi: 10.1016/j.msea.2012.12.001
    [68]
    MONNET G, VINCENT L, DEVINCRE B. Dislocation-dynamics based crystal plasticity law for the low- and high-temperature deformation regimes of bcc crystal [J]. Acta Materialia, 2013, 61(16): 6178–6190. doi: 10.1016/j.actamat.2013.07.002
    [69]
    NGUYEN T, LUSCHER D J, WILKERSON J W. A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals [J]. Journal of the Mechanics and Physics of Solids, 2017, 108: 1–29. doi: 10.1016/j.jmps.2017.07.020
    [70]
    GRILLI N, JANSSENS K G F, NELLESSEN J, et al. Multiple slip dislocation patterning in a dislocation-based crystal plasticity finite element method [J]. International Journal of Plasticity, 2018, 100: 104–121. doi: 10.1016/j.ijplas.2017.09.015
    [71]
    FROST H J, ASHBY M F. Motion of a dislocation acted on by a viscous drag through an array of discrete obstacles [J]. Journal of Applied Physics, 1971, 42(13): 5273–5279. doi: 10.1063/1.1659936
    [72]
    LIM H, BATTAILE C C, CARROLL J D, et al. A physically based model of temperature and strain rate dependent yield in BCC metals: implementation into crystal plasticity [J]. Journal of the Mechanics and Physics of Solids, 2015, 74: 80–96. doi: 10.1016/j.jmps.2014.10.003
    [73]
    KOCKS W. Thermodynamics and kinetics of slip [J]. Progress in Materials Science, 1975, 19: 1–281. doi: 10.1016/0079-6425(75)90005-5
    [74]
    AUSTIN R A. Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature [J]. Journal of Applied Physics, 2018, 123(3): 035103. doi: 10.1063/1.5008280
    [75]
    AUSTIN R A, MCDOWELL D L. A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates [J]. International Journal of Plasticity, 2011, 27(1): 1–24. doi: 10.1016/j.ijplas.2010.03.002
    [76]
    AUSTIN R A, MCDOWELL D L. Parameterization of a rate-dependent model of shock-induced plasticity for copper, nickel, and aluminum [J]. International Journal of Plasticity, 2012, 32/33: 134–154. doi: 10.1016/j.ijplas.2011.11.002
    [77]
    GAO C Y, ZHANG L C. Constitutive modelling of plasticity of fcc metals under extremely high strain rates [J]. International Journal of Plasticity, 2012, 32/33: 121–133. doi: 10.1016/j.ijplas.2011.12.001
    [78]
    WANG Z Q, BEYERLEIN I J, LESAR R. Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals [J]. Philosophical Magazine, 2008, 88(9): 1321–1343. doi: 10.1080/14786430802129833
    [79]
    TSCHOPP M A, MCDOWELL D L. Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading [J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 1806–1830. doi: 10.1016/j.jmps.2007.11.012
    [80]
    SHEHADEH M A, ZBIB H M. On the homogeneous nucleation and propagation of dislocations under shock compression [J]. Philosophical Magazine, 2016, 96(26): 2752–2778. doi: 10.1080/14786435.2016.1213444
    [81]
    MA A, ROTERS F, RAABE D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations [J]. Acta Materialia, 2006, 54(8): 2169–2179. doi: 10.1016/j.actamat.2006.01.005
    [82]
    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
    [83]
    LLOYD J T, CLAYTON J D, AUSTIN R A, et al. Plane wave simulation of elastic-viscoplastic single crystals [J]. Journal of the Mechanics and Physics of Solids, 2014, 69: 14–32. doi: 10.1016/j.jmps.2014.04.009
    [84]
    ALANKAR A, FIELD D P, ZBIB H M. Explicit incorporation of cross-slip in a dislocation density-based crystal plasticity model [J]. Philosophical Magazine, 2012, 92(24): 3084–3100. doi: 10.1080/14786435.2012.685964
    [85]
    KESHAVARZ S, GHOSH S. Multi-scale crystal plasticity finite element model approach to modeling nickel-based superalloys [J]. Acta Materialia, 2013, 61(17): 6549–6561. doi: 10.1016/j.actamat.2013.07.038
    [86]
    LIANG H, DUNNE F P E. GND accumulation in bi-crystal deformation: crystal plasticity analysis and comparison with experiments [J]. International Journal of Mechanical Sciences, 2009, 51(4): 326–333. doi: 10.1016/j.ijmecsci.2009.03.005
    [87]
    GÜVENÇ O, BAMBACH M, HIRT G. Coupling of crystal plasticity finite element and phase field methods for the prediction of SRX kinetics after hot working [J]. Steel Research International, 2014, 85(6): 999–1009. doi: 10.1002/srin.201300191
    [88]
    KONDO R, TADANO Y, SHIZAWA K. A phase-field model of twinning and detwinning coupled with dislocation-based crystal plasticity for HCP metals [J]. Computational Materials Science, 2014, 95: 672–683. doi: 10.1016/j.commatsci.2014.08.034
    [89]
    CHEN L, CHEN J, LEBENSOHN R A, et al. An integrated fast Fourier transform-based phase-field and crystal plasticity approach to model recrystallization of three dimensional polycrystals [J]. Computer Methods in Applied Mechanics and Engineering, 2015, 285: 829–848. doi: 10.1016/j.cma.2014.12.007
    [90]
    COTTURA M, APPOLAIRE B, FINEL A, et al. Coupling the phase field method for diffusive transformations with dislocation density-based crystal plasticity: application to Ni-based superalloys [J]. Journal of the Mechanics and Physics of Solids, 2016, 94: 473–489. doi: 10.1016/j.jmps.2016.05.016
    [91]
    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
    [92]
    IDESMAN A V, LEVITAS V I, STEIN E. Elastoplastic materials with martensitic phase transition and twinning at finite strains: numerical solution with the finite element method [J]. Computer Methods in Applied Mechanics and Engineering, 1999, 173(1/2): 71–98.
    [93]
    HUANG M, BRINSON L C. A Multivariant model for single crystal shape memory alloy behavior [J]. Journal of the Mechanics and Physics of Solids, 1998, 46(8): 1379–1409. doi: 10.1016/S0022-5096(97)00080-X
    [94]
    BHATTACHARYYA A, WENG G J. An energy criterion for the stress-induced martensitic transformation in a ductile system [J]. Journal of the Mechanics and Physics of Solids, 1994, 42(11): 1699–1724. doi: 10.1016/0022-5096(94)90068-X
    [95]
    STRINGFELLOW R G, PARKS D M, OLSON G B. A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels [J]. Acta Metallurgica et Materialia, 1992, 40(7): 1703–1716. doi: 10.1016/0956-7151(92)90114-T
    [96]
    LEBLOND J B, MOTTET G, DEVAUX J C. A theoretical and numerical approach to the plastic behaviour of steels during phase transformations: Ⅰ. derivation of general relations [J]. Journal of the Mechanics and Physics of Solids, 1986, 34(4): 395–409. doi: 10.1016/0022-5096(86)90009-8
    [97]
    THAMBURAJA P, ANAND L. Polycrystalline shape-memory materials: effect of crystallographic texture [J]. Journal of the Mechanics and Physics of Solids, 2001, 49(4): 709–737. doi: 10.1016/S0022-5096(00)00061-2
    [98]
    MA A X, HARTMAIER A. A study of deformation and phase transformation coupling for TRIP-assisted steels [J]. International Journal of Plasticity, 2015, 64: 40–55. doi: 10.1016/j.ijplas.2014.07.008
    [99]
    SUN C Y, GUO N, FU M W, et al. Modeling of slip, twinning and transformation induced plastic deformation for TWIP steel based on crystal plasticity [J]. International Journal of Plasticity, 2016, 76: 186–212. doi: 10.1016/j.ijplas.2015.08.003
    [100]
    LEE M G, KIM S J, HAN H N. Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite [J]. International Journal of Plasticity, 2010, 26(5): 688–710. doi: 10.1016/j.ijplas.2009.10.001
    [101]
    TURTELTAUB S, SUIKER A S J. Transformation-induced plasticity in ferrous alloys [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(8): 1747–1788. doi: 10.1016/j.jmps.2005.03.004
    [102]
    TURTELTAUB S, SUIKER A S J. A multiscale thermomechanical model for cubic to tetragonal martensitic phase transformations [J]. International Journal of Solids and Structures, 2006, 43(14/15): 4509–4545.
    [103]
    SUIKER A S J, TURTELTAUB S. Computational modelling of plasticity induced by martensitic phase transformations [J]. International Journal for Numerical Methods in Engineering, 2005, 63(12): 1655–1693. doi: 10.1002/nme.1327
    [104]
    MANCHIRAJU S, ANDERSON P M. Coupling between martensitic phase transformations and plasticity: a microstructure-based finite element model [J]. International Journal of Plasticity, 2010, 26(10): 1508–1526. doi: 10.1016/j.ijplas.2010.01.009
    [105]
    FENG B, BRONKHORST C A, ADDESSIO F L, et al. Coupled elasticity, plastic slip, and twinning in single crystal titanium loaded by split-Hopkinson pressure bar [J]. Journal of the Mechanics and Physics of Solids, 2018, 119: 274–297. doi: 10.1016/j.jmps.2018.06.018
    [106]
    GREEFF C W. Alpha-omega transition in Ti: equation of state and kinetics [C]//AIP Conference Proceedings. Atlanta, Georgia (USA). AIP, 2002: 225–228.
    [107]
    TJAHJANTO D D, TURTELTAUB S, SUIKER A S J. Crystallographically based model for transformation-induced plasticity in multiphase carbon steels [J]. Continuum Mechanics and Thermodynamics, 2008, 19(7): 399–422. doi: 10.1007/s00161-007-0061-x
    [108]
    THAMBURAJA P. A finite-deformation-based phenomenological theory for shape-memory alloys [J]. International Journal of Plasticity, 2010, 26(8): 1195–1219. doi: 10.1016/j.ijplas.2009.12.004
    [109]
    THAMBURAJA P, PAN H, CHAU F S. Martensitic reorientation and shape-memory effect in initially textured polycrystalline Ti-Ni sheet [J]. Acta Materialia, 2005, 53(14): 3821–3831. doi: 10.1016/j.actamat.2005.03.054
    [110]
    THAMBURAJA P. Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(4): 825–856. doi: 10.1016/j.jmps.2004.11.004
    [111]
    BARTON N R, BENSON D J, BECKER R. Crystal level continuum modelling of phase transformations: the αε transformation in iron [J]. Modelling and Simulation in Materials Science and Engineering, 2005, 13(5): 707–731. doi: 10.1088/0965-0393/13/5/006
    [112]
    AMOUZOU K E K, RICHETON T, ROTH A, et al. Micromechanical modeling of hardening mechanisms in commercially pure α-titanium in tensile condition [J]. International Journal of Plasticity, 2016, 80: 222–240. doi: 10.1016/j.ijplas.2015.09.008
    [113]
    GURAO N P, KAPOOR R, SUWAS S. Deformation behaviour of commercially pure titanium at extreme strain rates [J]. Acta Materialia, 2011, 59(9): 3431–3446. doi: 10.1016/j.actamat.2011.02.018
    [114]
    MEREDITH C S, LLOYD J T, SANO T. The quasi-static and dynamic response of fine-grained Mg alloy AMX602: an experimental and computational study [J]. Materials Science and Engineering A, 2016, 673: 73–82. doi: 10.1016/j.msea.2016.07.035
    [115]
    ROHATGI A, VECCHIO K S. The variation of dislocation density as a function of the stacking fault energy in shock-deformed FCC materials [J]. Materials Science and Engineering A, 2002, 328(1/2): 256–266.
    [116]
    KALIDINDI S R. Incorporation of deformation twinning in crystal plasticity models [J]. Journal of the Mechanics and Physics of Solids, 1998, 46(2): 267–290. doi: 10.1016/S0022-5096(97)00051-3
    [117]
    CLAYTON J D. Nonlinear elastic and inelastic models for shock compression of crystalline solids [M]. Cham: Springer International Publishing, 2019.
    [118]
    CLAYTON J. A continuum description of nonlinear elasticity, slip and twinning, with application to sapphire [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 465(2101): 307–334. doi: 10.1098/rspa.2008.0281
    [119]
    SALEM A A, KALIDINDI S R, DOHERTY R D, et al. Strain hardening due to deformation twinning in α-titanium: mechanisms [J]. Metallurgical and Materials Transactions A, 2006, 37(1): 259–268. doi: 10.1007/s11661-006-0171-2
    [120]
    SALEM A A, KALIDINDI S R, SEMIATIN S L. Strain hardening due to deformation twinning in α-titanium: constitutive relations and crystal-plasticity modeling [J]. Acta Materialia, 2005, 53(12): 3495–3502. doi: 10.1016/j.actamat.2005.04.014
    [121]
    KALIDINDI S R. A crystal plasticity framework for deformation twinning [M]//Continuum Scale Simulation of Engineering Materials. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005: 543–560.
    [122]
    ARDELJAN M, BEYERLEIN I J, MCWILLIAMS B A, et al. Strain rate and temperature sensitive multi-level crystal plasticity model for large plastic deformation behavior: application to AZ31 magnesium alloy [J]. International Journal of Plasticity, 2016, 83: 90–109. doi: 10.1016/j.ijplas.2016.04.005
    [123]
    ARDELJAN M, MCCABE R J, BEYERLEIN I J, et al. Explicit incorporation of deformation twins into crystal plasticity finite element models [J]. Computer Methods in Applied Mechanics and Engineering, 2015, 295: 396–413. doi: 10.1016/j.cma.2015.07.003
    [124]
    BEYERLEIN I J, TOMÉ C N. A dislocation-based constitutive law for pure Zr including temperature effects [J]. International Journal of Plasticity, 2008, 24(5): 867–895. doi: 10.1016/j.ijplas.2007.07.017
    [125]
    MADEC R, DEVINCRE B, KUBIN L P. From dislocation junctions to forest hardening [J]. Physical Review Letters, 2002, 89(25): 255508. doi: 10.1103/PhysRevLett.89.255508
    [126]
    SONG S G, GRAY G T III. Structural interpretation of the nucleation and growth of deformation twins in Zr and Ti: Ⅰ. application of the coincidence site lattice (CSL) theory to twinning problems in hcp structures [J]. Acta Metallurgica et Materialia, 1995, 43(6): 2325–2337. doi: 10.1016/0956-7151(94)00433-1
    [127]
    SONG S G, GRAY G T III. Structural interpretation of the nucleation and growth of deformation twins in Zr and Ti: Ⅱ. TEM study of twin morphology and defect reactions during twinning [J]. Acta Metallurgica et Materialia, 1995, 43(6): 2339–2350. doi: 10.1016/0956-7151(94)00434-X
    [128]
    SONG S G, GRAY G T. Influence of temperature and strain rate on slip and twinning behavior of Zr [J]. Metallurgical and Materials Transactions A, 1995, 26(10): 2665–2675. doi: 10.1007/BF02669423
    [129]
    朱兆祥, 李永池, 王肖钧. 爆炸作用下钢板层裂的数值分析 [J]. 应用数学和力学, 1981, 2(4): 353–368.

    ZHU Z X, LI Y C, WANG X J. Numerical analysis of the spallation of steel target under the explosive loading [J]. Applied Mathematics and Mechanics, 1981, 2(4): 353–368.
    [130]
    RINEHART J S. Some quantitative data bearing on the scabbing of metals under explosive attack [J]. Journal of Applied Physics, 1951, 22(5): 555–560. doi: 10.1063/1.1700005
    [131]
    ZHANG K S, ZHANG D, FENG R, et al. Microdamage in polycrystalline ceramics under dynamic compression and tension [J]. Journal of Applied Physics, 2005, 98(2): 023505. doi: 10.1063/1.1944908
    [132]
    LLOYD J T, MATEJUNAS A J, BECKER R, et al. Dynamic tensile failure of rolled magnesium: simulations and experiments quantifying the role of texture and second-phase particles [J]. International Journal of Plasticity, 2019, 114: 174–195. doi: 10.1016/j.ijplas.2018.11.002
    [133]
    LING C, BESSON J, FOREST S, et al. An elastoviscoplastic model for porous single crystals at finite strains and its assessment based on unit cell simulations [J]. International Journal of Plasticity, 2016, 84: 58–87. doi: 10.1016/j.ijplas.2016.05.001
    [134]
    NGUYEN T, LUSCHER D J, WILKERSON J W. A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals [J]. Journal of the Mechanics and Physics of Solids, 2017, 108: 1–29. doi: 10.1016/j.jmps.2017.07.020
    [135]
    NGUYEN T, LUSCHER D J, WILKERSON J W. The role of elastic and plastic anisotropy in intergranular spall failure [J]. Acta Materialia, 2019, 168: 1–12. doi: 10.1016/j.actamat.2019.01.033
    [136]
    BAI Y L, DODD B. Adiabatic shear localization: occurrence, theories, and applications [M]. Oxford: Pergamon Press, 1992.
    [137]
    DODD B, BAI Y L. Adiabatic shear localization: frontiers and advances [M]. Elsevier, 2012.
    [138]
    ZENER C, HOLLOMON J H. Effect of strain rate upon plastic flow of steel [J]. Journal of Applied Physics, 1944, 15(1): 22–32. doi: 10.1063/1.1707363
    [139]
    HINES J A, VECCHIO K S, AHZI S. A model for microstructure evolution in adiabatic shear bands [J]. Metallurgical and Materials Transactions A, 1998, 29(1): 191–203. doi: 10.1007/s11661-998-0172-4
    [140]
    LEE W B, WANG H, CHAN C Y, et al. Finite element modelling of shear angle and cutting force variation induced by material anisotropy in ultra-precision diamond turning [J]. International Journal of Machine Tools and Manufacture, 2013, 75: 82–86. doi: 10.1016/j.ijmachtools.2013.09.007
    [141]
    BRONKHORST C A, HANSEN B L, CERRETA E K, et al. Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions [J]. Journal of the Mechanics and Physics of Solids, 2007, 55(11): 2351–2383. doi: 10.1016/j.jmps.2007.03.019
    [142]
    WRIGHT T W. 绝热剪切带的数理分析 [M]. 李云凯, 孙川, 王云飞, 译. 北京: 北京理工大学出版社, 2013.

    WRIGHT T W. The physics and mathematics of adiabatic shear bands [M]. Translated by LI Y K, SUN C, WANG Y F. Beijing: Beijing Institute of Technology Press, 2003.
    [143]
    BARGMANN S, EKH M. Microscopic temperature field prediction during adiabatic loading using gradient extended crystal plasticity [J]. International Journal of Solids and Structures, 2013, 50(6): 899–906. doi: 10.1016/j.ijsolstr.2012.11.010
    [144]
    CULVER R S. Thermal instability strain in dynamic plastic deformation [M]//Metallurgical Effects at High Strain Rates. Boston: Springer, 1973: 519–530.
    [145]
    BAI Y L. A criterion for thermo-plastic shear instability [M]//Shock Waves and High-Strain-Rate Phenomena in Metals. Boston: Springer, 1981: 277–284.
    [146]
    SCHOENFELD S E, WRIGHT T W. A failure criterion based on material instability [J]. International Journal of Solids and Structures, 2003, 40(12): 3021–3037. doi: 10.1016/S0020-7683(03)00059-3
    [147]
    ZHANG Z, EAKINS D E, DUNNE F P E. On the formation of adiabatic shear bands in textured HCP polycrystals [J]. International Journal of Plasticity, 2016, 79: 196–216. doi: 10.1016/j.ijplas.2015.12.004
    [148]
    RECHT R F. Catastrophic thermoplastic shear [J]. Journal of Applied Mechanics, 1964, 31(2): 189–193. doi: 10.1115/1.3629585
    [149]
    DUSZEK-PERZYNA M K, PERZYNA P. Analysis of the influence of non-schmid and thermal effects on adiabatic shear band localization in elastic-plastic single crystals [M]//Finite Inelastic Deformations: Theory and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992: 155–165.
    [150]
    DUSZEK-PERZYNA M K, PERZYNA P. Adiabatic shear band localization in elastic-plastic single crystals [J]. International Journal of Solids and Structures, 1993, 30(1): 61–89. doi: 10.1016/0020-7683(93)90132-Q
    [151]
    DUSZEK-PERZYNA M K, PERZYNA P. Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process [J]. Archive of Applied Mechanics, 1996, 66(6): 369. doi: 10.1007/s004190050076
    [152]
    RITTEL D, WANG Z G, MERZER M. Adiabatic shear failure and dynamic stored energy of cold work [J]. Physical Review Letters, 2006, 96(7): 075502. doi: 10.1103/PhysRevLett.96.075502
    [153]
    BOUBAKER H B, MAREAU C, AYED Y, et al. Development of a hyperelastic constitutive model based on the crystal plasticity theory for the simulation of machining operations [J]. Procedia CIRP, 2019, 82: 20–25. doi: 10.1016/j.procir.2019.04.336
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(18)  / Tables(5)

    Article Metrics

    Article views(7032) PDF downloads(172) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return