Effect of Threshold Twin Volume Fraction in Crystal Plasticity Modeling

Document Type : Original Article


College of Materials Science and Engineering, Chongqing University, Chongqing, China


Modeling of metals deforming by twinning requires reorienting the matrix into twin orientation. In twinning models like the Predominant Twin Reorientation scheme (PTR), a threshold volume fraction is defined with an empiric equation to reorient the parent grain into the dominant twin variant. This equation contains two parameters which are first investigated in the present study, showing their effect on simulated flow stress and twin volume fraction evolution. Magnesium, with a tension and a compression twinning modes, is taken as an example to compare the expected experimental behavior and the modeled behavior. Complex deformations such as strain path change and multiple twinning are modeled with the PTR, and simulated stress, twin volume fraction and texture are correlated with the expected behavior. The PTR shows a good agreement with experiments when the twin volume fraction corresponds to the fraction of grains reoriented into twins, but limited predictability when the twinned grains are not reoriented.


Main Subjects

[1] P.G. Partridge, The crystallography and deformation modes of hexagonal close-packed metals, Metall. Reviews 12 (1967), 169-194.
[2] P.A. Turner, C.N. Tomé, A study of residual stresses in Zircaloy-2 with rod texture, Acta metall. mater. 42 (1994), 4143-4153.
[3] R.A. Lebensohn, C.N. Tomé, A self-consistent anisotropic approch for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys, Acta metall. Mater. 41 (1993), 2611-2624.
[4] C.N. Tomé, R. A. Lebensohn and U.F. Kocks, 1991, A model for texture development dominated by deformation twinning: application to zirconium alloys, Acta Metall. Mater. 39 (1991), 2667-2680.
[5] S.-H. Choi, E.J. Shin, B.S. Seong, Simulation of deformation twins and deformation texture in an AZ31 Mg alloy under uniaxial compression, Acta Mater. 55 (2007) 4181-4192. Doi: 10.1016/j.actamat.2007.03.015
[6] S.-H. Choi, D.H. Kim, H.W. Lee, E.J. Shin, Simulation of texture evolution and macroscopic properties in Mg alloys using the crystal plasticity finite element method, Mater. Sci. Eng. A 527 (2010), 1151-1159. Doi: 10.1016/j.msea.2009.09.055
[7] H. Abdolvand, M.R. Daymond, Internal strain and texture development during twinning: Comparing neutron diffraction measurements with crystal plasticity finite-element approaches, Acta Mater. 60 (2012), 2240-2248. Doi: 10.1016/j.actamat.2012.01.016
[8] H. Qiao, M. R. Barnett, P. D. Wu, Modeling of twin formation, propagation and growth in a Mg single crystal based on crystal plasticity finite element method, Int. J. plasticity 86 (2016), 70-92. Doi: 10.1016/j.ijplas.2016.08.002
[9] H. Qiao, P. D. Wu, X. Q. Guo, S. R. Agnew, A new empirical equation for termination of twinning in magnesium alloys, Scripta Mater. 120 (2016) 71-75. Doi: 10.1016/j.scriptamat.2016.04.015
[10] H. Wang, P.D. Wu, J. Wang, C.N. Tomé, A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms, Int. J. Plast. 49 (2013), 36-52. Doi: 10.1016/j.ijplas.2013.02.016
[11] L.Y. Zhao, X.Q. Guo, A. Chapuis, Y.C. Xin, Q. Liu, P.D. Wu, Strain-Path Dependence of {10-12} Twinning in a Rolled Mg–3Al–1Zn Alloy: Influence of Twinning Model, Metall. and Mater. Trans. A 50A (2019) 118-131. Doi: 10.1007/s11661-018-4955-y
[12] H. Qiao, X.Q. Guo, S.G. Hong, P.D. Wu, Modeling of {10-12}-{10-12} secondary twinning in pre-compressed Mg alloy AZ31, J. Alloys Compd. 725 (2017) 96-107. Doi: 10.1016/j.jallcom.2017.07.133
[13] D.W. Brown, S.R. Agnew, M.A. M. Bourke, T. M. Holden, S.C. Vogel, C.N. Tomé, Internal strain and texture evolution during deformation twinning in magnesium, Mater. Sci. Eng. A 399 (2005), 1-12. Doi: 10.1016/j.msea.2005.02.016
[14] Y. Pei, A. Godfrey, J. Jiang, Y.B. Zhang, W. Liu, Q. Liu, Extension twin variant selection during uniaxial compression of a magnesium alloy, Mater. Sci. Eng. A 550 (2012), 138-145. Doi: 10.1016/j.msea.2012.04.046
[15] B. Wang, R. Xin, G. Huang, Q. Liu, Effect of crystal orientation on the mechanical properties and strain hardening behavior of magnesium alloy AZ31 during uniaxial compression, Mater. Sci. Eng. A 534 (2012), 588-593. Doi: 10.1016/j.msea.2011.12.013
[16] C. Ma, A. Chapuis, X.Q. Guo, L.Y. Zhao, P.D. Wu, Q. Liu, Modeling the deformation behavior of a rolled Mg alloy with the EVPSC-TDT model, Materials Science & Engineering A 682 (2017) 332–340. Doi: 10.1016/j.msea.2016.11.027
[17] H. Wang, B. Raeisinia, P.D. Wu, S.R. Agnew, C.N. Tomé, Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet, Int. J. Solids Struct. 47 (2010), 2905-2917. Doi: 10.1016/j.ijsolstr.2010.06.016
[18] K. Hazeli, J. Cuadra, P.A. Vanniamparambil, and A. Kontsos, In situ identification of twin-related bands near yielding in a magnesium alloy, Scr. Mater. 68 (2013), 83-86. Doi: 10.1016/j.scriptamat.2012.09.009
[19] M. R. Barnett, M.D. Nave, A. Ghaderi, Yield point elongation due to twinning in a magnesium alloy,  Acta Mater. 60 (2012), 1433-1443. Doi: 10.1016/j.actamat.2011.11.022
[20] P.D. Wu, X.Q. Guo, H. Qiao, D.J. Lloyd, A constitutive model of twin nucleation, propagation and growth in magnesium crystals: Mater. Sci. Eng. A 625 (2015) 140-145. Doi: 10.1016/j.msea.2014.11.096
[21] M.R. Barnett, Twinning and the ductility of magnesium alloys Part I: “Tension” twins, Mater. Sci. Eng. A 464 (2007), 1-7. Doi: 10.1016/j.msea.2006.12.037
[22] S.-G. Hong, S.H. Park, and C.S. Lee, Role of {10–12} twinning characteristics in the deformation behavior of a polycrystalline magnesium alloy, Acta Mater. 58 (2010) 5873-5885. Doi: 10.1016/j.actamat.2010.07.002
[23] M. Knezevic, A. Levinson, R. Harris, R.K. Mishra, R.D. Doherty, and S.R. Kalidindi, Deformation twinning in AZ31: Influence on strain hardening and texture evolution: Acta Mater. 58 (2010) 6230-6242. Doi: 10.1016/j.actamat.2010.07.041
[24] Z.Q. Wang, A. Chapuis, Q. Liu, Simulation of mechanical behavior of AZ31 magnesium alloy during twin-dominated large plastic deformation, Trans. Nonferrous Met. Soc. China 25 (2015) 3595−3603. Doi: 10.1016/S1003-6326(15)64000-6
[25] X.Y. Lou, M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, Hardening evolution of AZ31B Mg sheet, Int. J. Plasticity 23 (2007) 44–86. Doi: 10.1016/j.ijplas.2006.03.005
[26] H. Wang, P.D. Wu, C.N. Tomé, J. Wang, A constitutive model of twinning and detwinning for hexagonal close packed polycrystals, Materials Science and Engineering A 555 (2012) 93– 98. Doi: 10.1016/j.msea.2012.06.038
[27] A. Chapuis, Q. Liu, Simulations of texture evolution for HCP metals: Influence of the main slip systems, Comp. Mater. Sci. 97 (2015) 121–126. Doi: 10.1016/j.commatsci.2014.10.017
[28] M.R. Barnett, Twinning and the ductility of magnesium alloys Part II. “contraction” twins, Mater. Sci. Eng. A 464 (2007) 8–16. Doi: 10.1016/j.msea.2007.02.109
[29] É. Martin, L. Capolungo, L. Jiang, J.J. Jonas, Variant selection during secondary twinning in Mg–3%Al, Acta Mater. 58 (2010) 3970–3983. Doi: 10.1016/j.actamat.2010.03.027
[30] S.J. Mu, J.J. Jonas, G. Gottstein, Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy, Acta Mater. 60 (2012) 2043–2053. Doi: 10.1016/j.actamat.2012.01.014