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.


Google Scholar


Main Subjects

[1]     Partridge PG. The crystallography and deformation modes of hexagonal close-packed metals. Metall Rev 1967;12:169–94. doi:10.1179/mtlr.1967.12.1.169.
[2]     Turner PA, Tomé CN. A study of residual stresses in Zircaloy-2 with rod texture. Acta Metall Mater 1994;42:4143–53. doi:10.1016/0956-7151(94)90191-0.
[3]     Lebensohn RA, Tomé CN. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metall Mater 1993;41:2611–24. doi:10.1016/0956-7151(93)90130-K.
[4]     Tomé CN, Lebensohn RA, Kocks UF. A model for texture development dominated by deformation twinning: Application to zirconium alloys. Acta Metall Mater 1991;39:2667–80. doi:10.1016/0956-7151(91)90083-D.
[5]     CHOI S, SHIN E, SEONG B. Simulation of deformation twins and deformation texture in an AZ31 Mg alloy under uniaxial compression. Acta Mater 2007;55:4181–92. doi:10.1016/j.actamat.2007.03.015.
[6]     Choi S-H, Kim DH, Lee HW, Shin EJ. Simulation of texture evolution and macroscopic properties in Mg alloys using the crystal plasticity finite element method. Mater Sci Eng A 2010;527:1151–9. doi:10.1016/j.msea.2009.09.055.
[7]     Abdolvand H, Daymond MR. Internal strain and texture development during twinning: Comparing neutron diffraction measurements with crystal plasticity finite-element approaches. Acta Mater 2012;60:2240–8. doi:10.1016/j.actamat.2012.01.016.
[8]     Qiao H, Barnett MR, Wu PD. Modeling of twin formation, propagation and growth in a Mg single crystal based on crystal plasticity finite element method. Int J Plast 2016;86:70–92. doi:10.1016/j.ijplas.2016.08.002.
[9]     Qiao H, Wu PD, Guo XQ, Agnew SR. A new empirical equation for termination of twinning in magnesium alloys. Scr Mater 2016;120:71–5. doi:10.1016/j.scriptamat.2016.04.015.
[10]   Wang H, Wu PD, Wang J, Tomé CN. A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms. Int J Plast 2013;49:36–52. doi:10.1016/j.ijplas.2013.02.016.
[11]   Zhao L, Guo X, Chapuis A, Xin Y, Liu Q, Wu P. Strain-Path Dependence of $$ { 10bar{1}2} $$ { 10 1 ¯ 2 } Twinning in a Rolled Mg–3Al–1Zn Alloy: Influence of Twinning Model. Metall Mater Trans A 2019;50:118–31. doi:10.1007/s11661-018-4955-y.
[12]   Qiao H, Guo XQ, Hong SG, Wu PD. Modeling of {10-12}-{10-12} secondary twinning in pre-compressed Mg alloy AZ31. J Alloys Compd 2017;725:96–107. doi:10.1016/j.jallcom.2017.07.133.
[13]   Brown DW, Agnew SR, Bourke MAM, Holden TM, Vogel SC, Tomé CN. Internal strain and texture evolution during deformation twinning in magnesium. Mater Sci Eng A 2005;399:1–12. doi:10.1016/j.msea.2005.02.016.
[14]   Pei Y, Godfrey A, Jiang J, Zhang YB, Liu W, Liu Q. Extension twin variant selection during uniaxial compression of a magnesium alloy. Mater Sci Eng A 2012;550:138–45. doi:10.1016/j.msea.2012.04.046.
[15]   Wang B, Xin R, Huang G, Liu Q. Effect of crystal orientation on the mechanical properties and strain hardening behavior of magnesium alloy AZ31 during uniaxial compression. Mater Sci Eng A 2012;534:588–93. doi:10.1016/j.msea.2011.12.013.
[16]   Ma C, Chapuis A, Guo X, Zhao L, Wu P, Liu Q, et al. Modeling the deformation behavior of a rolled Mg alloy with the EVPSC-TDT model. Mater Sci Eng A 2017;682:332–40. doi:10.1016/j.msea.2016.11.027.
[17]   Wang H, Raeisinia B, Wu PD, Agnew SR, Tomé CN. Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet. Int J Solids Struct 2010;47:2905–17. doi:10.1016/j.ijsolstr.2010.06.016.
[18]   Hazeli K, Cuadra J, Vanniamparambil PA, Kontsos A. In situ identification of twin-related bands near yielding in a magnesium alloy. Scr Mater 2013;68:83–6. doi:10.1016/j.scriptamat.2012.09.009.
[19]   Barnett MR, Nave MD, Ghaderi A. Yield point elongation due to twinning in a magnesium alloy. Acta Mater 2012;60:1433–43. doi:10.1016/j.actamat.2011.11.022.
[20]   Wu PD, Guo XQ, Qiao H, Lloyd DJ. A constitutive model of twin nucleation, propagation and growth in magnesium crystals. Mater Sci Eng A 2015;625:140–5. doi:10.1016/j.msea.2014.11.096.
[21]   Barnett MR. Twinning and the ductility of magnesium alloys. Mater Sci Eng A 2007;464:1–7. doi:10.1016/j.msea.2006.12.037.
[22]   Hong S-G, Park SH, Lee CS. Role of {10–12} twinning characteristics in the deformation behavior of a polycrystalline magnesium alloy. Acta Mater 2010;58:5873–85. doi:10.1016/j.actamat.2010.07.002.
[23]   Knezevic M, Levinson A, Harris R, Mishra RK, Doherty RD, Kalidindi SR. Deformation twinning in AZ31: Influence on strain hardening and texture evolution. Acta Mater 2010;58:6230–42. doi:10.1016/j.actamat.2010.07.041.
[24]   WANG Z, CHAPUIS A, LIU Q. Simulation of mechanical behavior of AZ31 magnesium alloy during twin-dominated large plastic deformation. Trans Nonferrous Met Soc China 2015;25:3595–603. doi:10.1016/S1003-6326(15)64000-6.
[25]   LOU X, LI M, BOGER R, AGNEW S, WAGONER R. Hardening evolution of AZ31B Mg sheet. Int J Plast 2007;23:44–86. doi:10.1016/j.ijplas.2006.03.005.
[26]   Wang H, Wu PD, Tomé CN, Wang J. A constitutive model of twinning and detwinning for hexagonal close packed polycrystals. Mater Sci Eng A 2012;555:93–8. doi:10.1016/j.msea.2012.06.038.
[27]   Chapuis A, Liu Q. Simulations of texture evolution for HCP metals: Influence of the main slip systems. Comput Mater Sci 2015;97:121–6. doi:10.1016/j.commatsci.2014.10.017.
[28]   Barnett MR. Twinning and the ductility of magnesium alloys. Mater Sci Eng A 2007;464:8–16. doi:10.1016/j.msea.2007.02.109.
[29]   Martin É, Capolungo L, Jiang L, Jonas JJ. Variant selection during secondary twinning in Mg–3%Al. Acta Mater 2010;58:3970–83. doi:10.1016/j.actamat.2010.03.027.
[30]   Mu S, Jonas JJ, Gottstein G. Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy. Acta Mater 2012;60:2043–53. doi:10.1016/j.actamat.2012.01.014.