Keywords
crystal plasticity
polycrystalline materials
plastic deformation
CPFEM
dislocation slip
polycrystalline materials
plastic deformation
CPFEM
dislocation slip
How to Cite
Wójcik, M., Skrzat, A., Stachowicz, F., & Spišák, E. (2023). Crystal Plasticity Elastic-Plastic Rate-Independent Numerical Analyses of Pollycrystalline Materials. Advances in Mechanical and Materials Engineering, 40(1), 63-78. https://doi.org/10.7862/rm.2023.8
Abstract
Macroscopic analyses of plastic forming processes give only the overall description of the problem without the consideration of mechanisms of plastic deformation and the microstructure evolution. For the consideration of these processes, numerical simulations within crystal plasticity include the change of texture, anisotropy, and strain hardening of the material are used. In this paper, a crystal plasticity rate-independent model proposed by Anand and Kothari is applied for numerical analyses of polycrystalline materials. The slip was considered as the main mechanism of the plastic deformation. Basic constitutive equations of crystal plasticity for large deformation theories are presented. The selected results of elastic-plastic problems obtained using both macro- and micro- scales software for the explicit and implicit integration are featured here. The heterogeneous distribution of strain and stress in different grains are obtained, which is associated with the various crystal orientation. The crystal plasticity modelling of materials subject to plastic deformation involves not only the information about the change of a material’s shape in a macro-scale, but also describes the phenomena occurring in material in a micro-scale.
References
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Alankar, A., Eisenlohr, P., & Raabe, D. (2011). A dislocation density-based crystal plasticity constitutive model for prismatic slip in α-titanium. Acta Mater., 59, 7003-7009. https://doi.org/10.1016/j.actamat.2011.07.053
Anand, L., & Kothari, M. (1996). A computational procedure for rate-independent crystal plasticity. J Mech Phys Solids, 44, 525-588. https://doi.org/10.1016/0022-5096(96)00001-4
Asaro, R.J., & Needleman, A. (1985). Texture development and strain hardening in rate dependent polycrystals. Acta Metall., 33, 923-953. https://doi.org/10.1016/0001-6160(85)90188-9
Bridier, F., McDowell, D.L., Villechaise, P., & Mendez, J. (2009). Crystal plasticity modeling of slip activity in Ti–6Al–4V under high cycle fatigue loading. Int. J. Plast., 25, 1066-1082. https://doi.org/10.1016/j.ijplas.2008.08.004
Buljak, V., Baivier-Romero, S., & Kallel, A. (2021). Calibration of Drucker–Prager Cap Constitutive Model for Ceramic Powder Compaction through Inverse Analysis. Materials, 14, 4044. https://doi.org/10.3390/ma14144044
Chen, X., Jiao, R., & Kim, K.S. (2005). On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel. Int. J. Plast., 21, 161-184. https://doi.org/10.1016/j.ijplas.2004.05.005
Dabiri, M., Lindroos, M., Andersson, T., Afkhami, S., Laukkanen, A., & Björk, T. (2018). Utilizing the theory of critical distances in conjunction with crystal plasticity for low-cycle notch fatigue analysis of S960 MC high-strength steel. Int J Fatigue, 117, 257-273. https://doi.org/10.1016/j.ijfatigue.2018.07.042
Deng, G. (2014). Crystal plasticity finite element method simulation of equal channel angular pressing. University of Wollongong Press.
Faul, U. (2021). Dislocation structure of deformed olivine single crystals from conventional EBSD maps. Phys Chem Minerals, 48, 35. https://doi.org/10.1007/s00269-021-01157-3
FEPX: Finite Element Polycrystal Plasticity (2008). https://fepx.info
Frydrych, K., & Kowalczyk-Gajewska, K. (2016). A three-scale crystal plasticity model accounting for grain refinement in fcc metals subjected to severe plastic deformations. Mater. Sci. Eng. A, 658, 490-502. https://doi.org/10.1016/j.msea.2016.01.101
Genna, F. (1993). Integration of plasticity equations for the case of Ziegler's kinematic hardening. Comput Methods Appl Mech Eng, 109, 111-130. https://doi.org/10.1016/0045-7825(93)90227-O
Ibragimova, O., Brahme, A., Muhammad, W., Lévesque, J., & Inal, K. (2021). A new ANN based crystal plasticity model for FCC materials and its application to non-monotonic strain paths. Int. J. Plast., 144, 103059. https://doi.org/10.1016/j.ijplas.2021.103059
Jeong, J., & Voyiadjis, G.Z. (2022). A physic-based crystal plasticity model for the prediction of the dislocation densities in micropillar compression. J. Mech. Phys. Solids., 167, 105006. https://doi.org/10.1016/j.jmps.2022.105006
Khan, R., & Alfozan, A. (2019). Modeling of twinning-induced plasticity using crystal plasticity and thermodynamic framework. Acta Mech., 230, 2687–2715. https://doi.org/10.1007/s00707-019-02419-6
Khan, R., Pervez, T., Alfozan, A., Qamar, S.Z., & Mohsin, S. (2022). Numerical Modeling and Simulations of Twinning-Induced Plasticity Using Crystal Plasticity Finite Element Method. Crystals, 12, 930. https://doi.org/10.3390/cryst12070930
Khan, R., Zahedi, F.I., & Siddiqui, A.K. (2016). Numerical Modeling of Twinning Induced Plasticity in Austenite Based Advanced High Strength Steels. Procedia Manuf., 5, 772-786. https://doi.org/10.1016/j.promfg.2016.08.063
Li, C., Cao, F., Chen, Y., Wang, H., & Dai, L. (2022). Crystal Plasticity Model Analysis of the Effect of Short-Range Order on Strength-Plasticity of Medium Entropy Alloys. Metals, 12, 1757. https://doi.org/10.3390/met12101757
Li, H., Larsson, F., Colliander, M.H., & Ekh, M. (2021). Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials. Mater Sci Eng. A., 799, 140325. https://doi.org/10.1016/j.msea.2020.140325
Li, Y.L., Kohar, C.P., Mishra, R.K., & Inal, K. (2020). A new crystal plasticity constitutive model for simulating precipitation-hardenable aluminum alloys. Int. J. Plast., 132, 102759. https://doi.org/10.1016/j.ijplas.2020.102759
Liu, G., Mo, H., Wang, J., & Shen, Y. (2021). Coupled crystal plasticity finite element-phase field model with kinetics-controlled twinning mechanism for hexagonal metals. Acta Mater., 202, 399-416. https://doi.org/10.1016/j.actamat.2020.11.002
Men, M., & Meng, B. (2022a). Crystal Plasticity Simulation of Yield Loci Evolution of SUS304 Foil. Materials, 15, 1140. https://doi.org/10.3390/ma15031140
Men, M., & Meng, B. (2022b). Crystal Plasticity Simulation of Yield Loci Evolution of SUS304 Foil. Materials, 15, 1140. https://doi.org/10.3390/ma15031140
Messner, M.C., Rhee, M., Arsenlis, A., & Barton, N.R. (2017). A crystal plasticity model for slip in hexagonal close packed metals based on discrete dislocation simulations. Modelling Simul. Mater. Sci. Eng., 25, 044001. DOI: 10.1088/1361-651X/aa687a
Mlikota, M., & Schmauder, S. (2018). On the Critical Resolved Shear Stress and Its Importance in the Fatigue Performance of Steels and Other Metals with Different Crystallographic Structures. Metals, 8, 883. https://doi.org/10.3390/met8110883
Nguyen, K., Zhang, M., Amores, V.J., Sanz, M.A., & Montáns, F.J. (2021). Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review. Crystals, 11, 42. https://doi.org/10.3390/cryst11010042
Nibur, K.A., & Bahr, D.F. (2003). Identifying slip systems around indentations in FCC metals. Comput. Mater. Sci., 49, 1055-1060. https://doi.org/10.1016/j.scriptamat.2003.08.021
Okereke, M., & Keates, S. (2018). Finite Element Applications. A Practical Guide to the FEM Process. Springer.
Paudel, Y., Giri, D., Priddy, M.W., Barrett, C.D., Inal, K., Tschopp, M.A., Rhee, H., & El Kadiri, H. (2021). A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals. Metals, 11, 1373. https://doi.org/10.3390/met11091373
Perez, N. (2017). Theory of Elasticity. Springer.
Pramanik, S., Tasche, L., Hoyer, K.P., & Schaper, M. (2021). Correlation between Taylor Model Prediction and Transmission Electron Microscopy-Based Microstructural Investigations of Quasi-In Situ Tensile Deformation of Additively Manufactured FeCo Alloy. J. of Materi Eng and Perform, 30, 8048–8056. https://doi.org/10.1007/s11665-021-06065-9
Ramos, P.M., Herranz, M., Foteinopoulou, K., Karayiannis, N.Ch., & Laso, M. (2020). Identification of Local Structure in 2-D and 3-D Atomic Systems through Crystallographic Analysis. Crystals, 10, 1008. https://doi.org/10.3390/cryst10111008
Remache, D., Semaan, M., Rossi, J.M., Pithioux, M., & Milan, J.L. (2020). Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone. J Mech Behav Biomed Mater, 101, 103426. https://doi.org/10.1016/j.jmbbm.2019.103426
Romanova, V., Balokhonov, R., Zinovieva, O., Lychagin, D., Emelianova, E., & Dymnich, E. (2022). Mechanical Aspects of Nonhomogeneous Deformation of Aluminum Single Crystals under Compression along [100] and [110] Directions. Metals, 12, 397. https://doi.org/10.3390/met12030397
Ryś, M., Stupkiewicz, S., & Petryk, H. (2022). Micropolar regularization of crystal plasticity with the gradient-enhanced incremental hardening law. Int. J. Plast., 156, 103355. https://doi.org/10.1016/j.ijplas.2022.103355
Sajjad, H.M., Hanke, S., Güler, S., ul Hassan, H., Fischer, A., & Hartmaier, A. (2019). Modelling Cyclic Behaviour of Martensitic Steel with J2 Plasticity and Crystal Plasticity. Materials, 12, 1767. https://doi.org/10.3390/ma12111767
Schäfer, B.J., Song, X., Sonnweber-Ribic, P., ul Hassan, H., & Hartmaier, A. (2019). Micromechanical Modelling of the Cyclic Deformation Behavior of Martensitic SAE 4150—A Comparison of Different Kinematic Hardening Models. Metals, 9, 368. https://doi.org/10.3390/met9030368
Sundararaghavan, V., & Zabaras, N. (2008). A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing. Int. J. Plast., 24, 1581–1605. https://doi.org/10.1016/j.ijplas.2007.12.005
Weinberger, C.R., Boyce, B.L., & Battaile, C.C. (2013). Slip planes in bcc transition metals. Int. Mater. Rev., 58, 296-314. https://doi.org/10.1179/1743280412Y.0000000015
Wójcik, M., & Skrzat, A. (2020). Fuzzy logic enhancement of material hardening parameters obtained from tension–compression test. Continuum Mech. Thermodyn., 32, 959-969. https://doi.org/10.1007/s00161-019-00805-y
Wójcik, M., & Skrzat, A. (2021). The Coupled Eulerian-Lagrangian Analysis of the KOBO Extrusion Process. ASTRJ, 15, 197-208. https://doi.org/10.12913/22998624/131663
Wójcik, M., & Skrzat, A. (2022a). An Elastic-Plastic Analysis of Polycrystalline Structure Using Crystal Plasticity Modelling – Theory and Benchmark Tests. ASTRJ, 16, 163-177. https://doi.org/10.12913/22998624/154025
Wójcik, M., & Skrzat, A. (2022b). Coupled Thermomechanical Eulerian-Lagrangian Analysis of the KOBO Extrusion Process. Arch. Metall. Mater., 67, 1185-1193. https://doi.org/10.24425/amm.2022.139719
Wójcik, M., & Skrzat, A. (2022c). Numerical modelling of the KOBO extrusion process using the Bodner–Partom material model. Meccanica, 57, 2213–2230. https://doi.org/10.1007/s11012-022-01569-7
Yaghoobi, M., Ganesan, G., Sundar, S., Lakshmanam, A., Rudraraju, S., Allison, J.E., & Sundararaghavan, V. (2019). PRISMS-Plasticity: An open-source crystal plasticity finite element software. Comput. Mater. Sci., 169, 109078. https://doi.org/10.1016/j.commatsci.2019.109078
Yang, G., & Park, S.-J. (2003). Deformation of Single Crystals, Polycrystalline Materials, and Thin Films: A Review. Materials, 12, 2003. DOI: 10.3390/ma12122003
Yang, G., Dayong, A., Fengbo, H., Liu, X., Guozheng, K., & Xu, Z. (2022). Multiple-mechanism and microstructure-based crystal plasticity modeling for cyclic shear deformation of TRIP steel. Int. J. Mech. Sci., 222, 107269. https://doi.org/10.1016/j.ijmecsci.2022.107269
Alankar, A., Eisenlohr, P., & Raabe, D. (2011). A dislocation density-based crystal plasticity constitutive model for prismatic slip in α-titanium. Acta Mater., 59, 7003-7009. https://doi.org/10.1016/j.actamat.2011.07.053
Anand, L., & Kothari, M. (1996). A computational procedure for rate-independent crystal plasticity. J Mech Phys Solids, 44, 525-588. https://doi.org/10.1016/0022-5096(96)00001-4
Asaro, R.J., & Needleman, A. (1985). Texture development and strain hardening in rate dependent polycrystals. Acta Metall., 33, 923-953. https://doi.org/10.1016/0001-6160(85)90188-9
Bridier, F., McDowell, D.L., Villechaise, P., & Mendez, J. (2009). Crystal plasticity modeling of slip activity in Ti–6Al–4V under high cycle fatigue loading. Int. J. Plast., 25, 1066-1082. https://doi.org/10.1016/j.ijplas.2008.08.004
Buljak, V., Baivier-Romero, S., & Kallel, A. (2021). Calibration of Drucker–Prager Cap Constitutive Model for Ceramic Powder Compaction through Inverse Analysis. Materials, 14, 4044. https://doi.org/10.3390/ma14144044
Chen, X., Jiao, R., & Kim, K.S. (2005). On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel. Int. J. Plast., 21, 161-184. https://doi.org/10.1016/j.ijplas.2004.05.005
Dabiri, M., Lindroos, M., Andersson, T., Afkhami, S., Laukkanen, A., & Björk, T. (2018). Utilizing the theory of critical distances in conjunction with crystal plasticity for low-cycle notch fatigue analysis of S960 MC high-strength steel. Int J Fatigue, 117, 257-273. https://doi.org/10.1016/j.ijfatigue.2018.07.042
Deng, G. (2014). Crystal plasticity finite element method simulation of equal channel angular pressing. University of Wollongong Press.
Faul, U. (2021). Dislocation structure of deformed olivine single crystals from conventional EBSD maps. Phys Chem Minerals, 48, 35. https://doi.org/10.1007/s00269-021-01157-3
FEPX: Finite Element Polycrystal Plasticity (2008). https://fepx.info
Frydrych, K., & Kowalczyk-Gajewska, K. (2016). A three-scale crystal plasticity model accounting for grain refinement in fcc metals subjected to severe plastic deformations. Mater. Sci. Eng. A, 658, 490-502. https://doi.org/10.1016/j.msea.2016.01.101
Genna, F. (1993). Integration of plasticity equations for the case of Ziegler's kinematic hardening. Comput Methods Appl Mech Eng, 109, 111-130. https://doi.org/10.1016/0045-7825(93)90227-O
Ibragimova, O., Brahme, A., Muhammad, W., Lévesque, J., & Inal, K. (2021). A new ANN based crystal plasticity model for FCC materials and its application to non-monotonic strain paths. Int. J. Plast., 144, 103059. https://doi.org/10.1016/j.ijplas.2021.103059
Jeong, J., & Voyiadjis, G.Z. (2022). A physic-based crystal plasticity model for the prediction of the dislocation densities in micropillar compression. J. Mech. Phys. Solids., 167, 105006. https://doi.org/10.1016/j.jmps.2022.105006
Khan, R., & Alfozan, A. (2019). Modeling of twinning-induced plasticity using crystal plasticity and thermodynamic framework. Acta Mech., 230, 2687–2715. https://doi.org/10.1007/s00707-019-02419-6
Khan, R., Pervez, T., Alfozan, A., Qamar, S.Z., & Mohsin, S. (2022). Numerical Modeling and Simulations of Twinning-Induced Plasticity Using Crystal Plasticity Finite Element Method. Crystals, 12, 930. https://doi.org/10.3390/cryst12070930
Khan, R., Zahedi, F.I., & Siddiqui, A.K. (2016). Numerical Modeling of Twinning Induced Plasticity in Austenite Based Advanced High Strength Steels. Procedia Manuf., 5, 772-786. https://doi.org/10.1016/j.promfg.2016.08.063
Li, C., Cao, F., Chen, Y., Wang, H., & Dai, L. (2022). Crystal Plasticity Model Analysis of the Effect of Short-Range Order on Strength-Plasticity of Medium Entropy Alloys. Metals, 12, 1757. https://doi.org/10.3390/met12101757
Li, H., Larsson, F., Colliander, M.H., & Ekh, M. (2021). Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials. Mater Sci Eng. A., 799, 140325. https://doi.org/10.1016/j.msea.2020.140325
Li, Y.L., Kohar, C.P., Mishra, R.K., & Inal, K. (2020). A new crystal plasticity constitutive model for simulating precipitation-hardenable aluminum alloys. Int. J. Plast., 132, 102759. https://doi.org/10.1016/j.ijplas.2020.102759
Liu, G., Mo, H., Wang, J., & Shen, Y. (2021). Coupled crystal plasticity finite element-phase field model with kinetics-controlled twinning mechanism for hexagonal metals. Acta Mater., 202, 399-416. https://doi.org/10.1016/j.actamat.2020.11.002
Men, M., & Meng, B. (2022a). Crystal Plasticity Simulation of Yield Loci Evolution of SUS304 Foil. Materials, 15, 1140. https://doi.org/10.3390/ma15031140
Men, M., & Meng, B. (2022b). Crystal Plasticity Simulation of Yield Loci Evolution of SUS304 Foil. Materials, 15, 1140. https://doi.org/10.3390/ma15031140
Messner, M.C., Rhee, M., Arsenlis, A., & Barton, N.R. (2017). A crystal plasticity model for slip in hexagonal close packed metals based on discrete dislocation simulations. Modelling Simul. Mater. Sci. Eng., 25, 044001. DOI: 10.1088/1361-651X/aa687a
Mlikota, M., & Schmauder, S. (2018). On the Critical Resolved Shear Stress and Its Importance in the Fatigue Performance of Steels and Other Metals with Different Crystallographic Structures. Metals, 8, 883. https://doi.org/10.3390/met8110883
Nguyen, K., Zhang, M., Amores, V.J., Sanz, M.A., & Montáns, F.J. (2021). Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review. Crystals, 11, 42. https://doi.org/10.3390/cryst11010042
Nibur, K.A., & Bahr, D.F. (2003). Identifying slip systems around indentations in FCC metals. Comput. Mater. Sci., 49, 1055-1060. https://doi.org/10.1016/j.scriptamat.2003.08.021
Okereke, M., & Keates, S. (2018). Finite Element Applications. A Practical Guide to the FEM Process. Springer.
Paudel, Y., Giri, D., Priddy, M.W., Barrett, C.D., Inal, K., Tschopp, M.A., Rhee, H., & El Kadiri, H. (2021). A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals. Metals, 11, 1373. https://doi.org/10.3390/met11091373
Perez, N. (2017). Theory of Elasticity. Springer.
Pramanik, S., Tasche, L., Hoyer, K.P., & Schaper, M. (2021). Correlation between Taylor Model Prediction and Transmission Electron Microscopy-Based Microstructural Investigations of Quasi-In Situ Tensile Deformation of Additively Manufactured FeCo Alloy. J. of Materi Eng and Perform, 30, 8048–8056. https://doi.org/10.1007/s11665-021-06065-9
Ramos, P.M., Herranz, M., Foteinopoulou, K., Karayiannis, N.Ch., & Laso, M. (2020). Identification of Local Structure in 2-D and 3-D Atomic Systems through Crystallographic Analysis. Crystals, 10, 1008. https://doi.org/10.3390/cryst10111008
Remache, D., Semaan, M., Rossi, J.M., Pithioux, M., & Milan, J.L. (2020). Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone. J Mech Behav Biomed Mater, 101, 103426. https://doi.org/10.1016/j.jmbbm.2019.103426
Romanova, V., Balokhonov, R., Zinovieva, O., Lychagin, D., Emelianova, E., & Dymnich, E. (2022). Mechanical Aspects of Nonhomogeneous Deformation of Aluminum Single Crystals under Compression along [100] and [110] Directions. Metals, 12, 397. https://doi.org/10.3390/met12030397
Ryś, M., Stupkiewicz, S., & Petryk, H. (2022). Micropolar regularization of crystal plasticity with the gradient-enhanced incremental hardening law. Int. J. Plast., 156, 103355. https://doi.org/10.1016/j.ijplas.2022.103355
Sajjad, H.M., Hanke, S., Güler, S., ul Hassan, H., Fischer, A., & Hartmaier, A. (2019). Modelling Cyclic Behaviour of Martensitic Steel with J2 Plasticity and Crystal Plasticity. Materials, 12, 1767. https://doi.org/10.3390/ma12111767
Schäfer, B.J., Song, X., Sonnweber-Ribic, P., ul Hassan, H., & Hartmaier, A. (2019). Micromechanical Modelling of the Cyclic Deformation Behavior of Martensitic SAE 4150—A Comparison of Different Kinematic Hardening Models. Metals, 9, 368. https://doi.org/10.3390/met9030368
Sundararaghavan, V., & Zabaras, N. (2008). A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing. Int. J. Plast., 24, 1581–1605. https://doi.org/10.1016/j.ijplas.2007.12.005
Weinberger, C.R., Boyce, B.L., & Battaile, C.C. (2013). Slip planes in bcc transition metals. Int. Mater. Rev., 58, 296-314. https://doi.org/10.1179/1743280412Y.0000000015
Wójcik, M., & Skrzat, A. (2020). Fuzzy logic enhancement of material hardening parameters obtained from tension–compression test. Continuum Mech. Thermodyn., 32, 959-969. https://doi.org/10.1007/s00161-019-00805-y
Wójcik, M., & Skrzat, A. (2021). The Coupled Eulerian-Lagrangian Analysis of the KOBO Extrusion Process. ASTRJ, 15, 197-208. https://doi.org/10.12913/22998624/131663
Wójcik, M., & Skrzat, A. (2022a). An Elastic-Plastic Analysis of Polycrystalline Structure Using Crystal Plasticity Modelling – Theory and Benchmark Tests. ASTRJ, 16, 163-177. https://doi.org/10.12913/22998624/154025
Wójcik, M., & Skrzat, A. (2022b). Coupled Thermomechanical Eulerian-Lagrangian Analysis of the KOBO Extrusion Process. Arch. Metall. Mater., 67, 1185-1193. https://doi.org/10.24425/amm.2022.139719
Wójcik, M., & Skrzat, A. (2022c). Numerical modelling of the KOBO extrusion process using the Bodner–Partom material model. Meccanica, 57, 2213–2230. https://doi.org/10.1007/s11012-022-01569-7
Yaghoobi, M., Ganesan, G., Sundar, S., Lakshmanam, A., Rudraraju, S., Allison, J.E., & Sundararaghavan, V. (2019). PRISMS-Plasticity: An open-source crystal plasticity finite element software. Comput. Mater. Sci., 169, 109078. https://doi.org/10.1016/j.commatsci.2019.109078
Yang, G., & Park, S.-J. (2003). Deformation of Single Crystals, Polycrystalline Materials, and Thin Films: A Review. Materials, 12, 2003. DOI: 10.3390/ma12122003
Yang, G., Dayong, A., Fengbo, H., Liu, X., Guozheng, K., & Xu, Z. (2022). Multiple-mechanism and microstructure-based crystal plasticity modeling for cyclic shear deformation of TRIP steel. Int. J. Mech. Sci., 222, 107269. https://doi.org/10.1016/j.ijmecsci.2022.107269