On modeling the mechanical behavior and texture evolution of rolled AZ31 Mg for complex loadings involving strain path changes


  • Nitin Chandola
  • Crystal Pasiliao
  • Oana Cazacu
  • Benoit Revil-Baudard


AZ31 Mg, visco-plastic self consistent model, stress-path changes, texture evolution


An accurate description of the deformation response of AZ31 Mg under changing strain paths requires consideration of its strong anisotropy and its evolution with accumulated plastic deformation. In this paper, the viscoplastic self-consistent mean field crystal plasticity model, VPSC, is used for modeling the room-temperature deformation of rolled AZ31 Mg for a variety of loading paths. First, a step-by-step procedure, to calibrate the material parameters based on simple monotonic tensile and compressive mechanical test data is outlined. The good agreement between measured and predicted textures for these strain paths attest to the robustness of the identification. Next, it is investigated whether with the same set of parameters it is possible to predict the response of a thinner AZ31 Mg sheet. Specifically, it is shown that the model can predict with accuracy the macroscopic stress-strain response and texture evolution for loadings involving stress path changes. The interplay between slip and twinning and its influence on work hardening are well described.


KELLEY, E.W., HOSFORD, W., The deformation characteristics of textured magnesium, Trans Met Soc AIME, 242, 4, pp. 5–13, 1968.

KHAN, A., PANDEY, A., GNAUPEL-HEROLD, T., MISHRA, R.K., Mechanical response and texture evolution of AZ31 alloy at large strains for different strain rates and temperatures, Int. J. Plast., 27, 5, pp. 688–706, 2011.

LOU, X.Y., LI, M., BOGER, R.K., AGNEW, S.R., WAGONER, R.H., Hardening evolution of AZ31B Mg sheet, Int. J. Plast., 23, 1, pp. 44–86, 2007.

AGNEW, S.R., DUYGULU, O., Plastic Anisotropy and the role of non-basal slip in magnesium alloy AZ31B, Int. J. Plast., 21, 6, pp. 1161–1193, 2005.

MEKONEN, M.N., STEGLICH D., BOHLEN J., LETZIG D., MOSLER J., Mechanical characterization and constitutive modeling of Mg alloy sheets, Mat. Sci. Eng. A, 540, pp. 174–186, 2012.

BEAUSIR, B., TOTH, L.S., QODS, F., NEALE, K.W., Texture and mechanical behavior of Magnesium during free-end torsion, J. Eng. Mat. Technol., 131, 1, pp. 1–15, 2008.

BISWAS, S., BEAUSIR, B., TOTH, L. S., SUWAS, S., Evolution of texture and microstructure during hot torsion of a magnesium alloy, Acta Mat., 61, 14, pp. 5263–5277, 2013.

GUO, X.Q.,WU, W., WU, P.D., QIAO, H., AN K., LIAW P.K., On the Swift effect and twinning in a rolled magnesium alloy under free-end torsion, Scripta Mater., 69, 4, pp. 319–322, 2013.

SCUTTI, J. J., Flowformed titanium tubular products, Adv. Mat. Processes, 159, pp. 69–70, 2001.

HILL, R., A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London A: Math., Phy. and Eng. Sci., 193, 1033, pp. 281–297, 1948.

BARLAT, F., LEGE, D.J., BREM, J.C., A six-component yield function for anisotropic materials, Int. J. Plast., 7, 7, pp. 693–712, 1991.

BARLAT, F., MAEDA, Y., CHUNG, K., YANAGAWA, M., BREM, J.C., HAYASHIDA, Y., MAKOSEY, S., Yield function development for aluminum alloy sheets, J. Mech. Phy. of Solids, 45, 11–12, pp. 1727–1763, 1997.

BARLAT, F., YOON, J.W., CAZACU, O., On linear transformations of stress tensors for the description of plastic anisotropy, Int. J. Plast., 23, 5, pp. 876–896, 2007.

CAZACU, O., BARLAT, F., Generalization of Drucker's yield criterion to orthotropy, Math. Mech. of Solids, 6, 6, pp. 613–630, 2001.

CAZACU, O., BARLAT, F., A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals, Int. J. Plast., 20, 11, pp. 2027–2045, 2004.

CAZACU, O., PLUNKETT, B., BARLAT, F., Orthotropic yield criterion for hexagonal closed packed materials, Int. J. Plasticity, 22, 7, pp. 1171–1194, 2006.

NIXON, M.E., CAZACU, O., LEBENSOHN, R.A., Anisotropic response of high-purity a-titanium: Experimental characterization and constitutive modeling, Int. J. Plasticity, 26, 4, pp. 516–532, 2010.

GRAFF, S., BROCKS, W., STEGLICH, D., Yielding of magnesium: from single crystal to polycrystalline aggregates, Int. J. Plast., 23, 12, pp. 1957–1978, 2007.

CAZACU, O., REVIL-BAUDARD, B., BARLAT, F., New interpretation of monotonic Swift effects: Role of tension–compression asymmetry, Mech. of Materials, 57, pp. 42–52, 2013.

CAZACU, O., REVIL-BAUDARD, B., BARLAT, F., New interpretation of cyclic Swift effects, Euro. J. Mechanics-A/Solids, 44, pp. 82–90, 2014.

REVIL-BAUDARD, B., CHANDOLA, N., CAZACU, O., BARLAT, F., Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials, J. Mech. Phy. of Solids, 70, pp. 104–115, 2014.

CHANDOLA, N., LEBENSOHN, R.A., CAZACU, O., REVIL-BAUDARD, B., MISHRA, R.K., BARLAT, F., Combined effects of anisotropy and tension–compression asymmetry on the torsional response of AZ31 Mg, Int. J. of Solids and Struct., 58, 190–200, 2015.

LI, M., LOU, X.Y., KIM, J.H., WAGONER, R.H., An efficient constitutive model for room temperature, low-rate plasticity of annealed Mg AZ31B sheet, Int. J. Plast., 26, 6, pp. 820–858, 2010.

WANG, H., WU, P. D., WANG, J., TOMÉ, C.N., A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms, Int. J. of Plast., 49, 36–52, 2013.

HAMA, T., KARIYAZAKI, Y., HOSOKAWA, N., FUJIMOTO, H., TAKUDA, H., Work-hardening behaviors of magnesium alloy sheet during in-plane cyclic loading, Mat. Sci. Eng. A, 551, pp 209–217, 2012.

HAMA, T., NAGAO, H., KUCHINOMACHI, Y., TAKUDA, H., Effect of pre-strain on work-hardening behavior of magnesium alloy sheets upon cyclic loading, Mat. Sci. Eng. A, 591, pp. 69–77, 2014.

VAN HOUTTE, P., Simulation of the rolling and shear texture of brass by the Taylor theory adapted for mechanical twinning, Acta Metall., 26, 4, pp. 591–604, 1978.

TOME, C.N., LEBENSOHN, R., KOCKS, U.F., A model for texture development dominated by deformation twinning: application to Zirconium alloys, Acta Metall. et Mat., 39, 11, pp. 2667–2680, 1991.

WU, X., KALIDINDI, S.R., NECKER, C., SALEM, A.A., Prediction of crystallographic texture evolution and anisotropic stress-strain curves during large plastic strains in high purity a-Titanium using a Taylor-Type crystal plasticity model, Acta Mater., 55, 2, pp. 423–432, 2007.

PROUST, G., TOMÉ, C.N., JAIN, A., AGNEW, S.R., Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31, Int. J. Plast., 25, 5, pp. 861–880, 2009.

TAYLOR, G.I., Plastic strain in metals, J. of the Institute of Metals, 62, pp. 307–324, 1938.

TAYLOR, G.I., Analysis of plastic strain in a cubic crystal, in: Stephen Timoshenko 60thAnniversary, Mcmillan Co., New York, 1938, pp. 218–224.

LEBENSOHN, R.A., TOMÉ, C.N., A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys, Acta Metall. et Mater., 41, 9, pp. 2611–2624, 1993. Nitin Chandola, Crystal Pasiliao, Oana Cazacu, Benoit Revil-Baudard 2462

WANG, H., WU, P.D., TOMÉ, C.N., HUANG, Y., A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials, Journal of the Mechanics and Physics of Solids, 58, 4, pp. 594–612, 2010.

JAIN, A., AGNEW, S.R., Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet, Mat. Sci. Eng. A, 462, pp. 29–36, 2007.

CHOI, S.H., KIM, D.H., SEONG, B.S., Simulation of strain-softening behaviors in an AZ31 Mg alloy showing distinct twin-induced reorientation before a peak stress, Metals Mater. Int., 15, pp. 239–248, 2009.

WANG, H., RAEISINIA, B., WU, P.D., AGNEW S.R., TOMÉ, C.N., Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet, Int. J. of Solids and Struct., 47, 21, pp. 2905–2917, 2010.

WALDE, T., RIEDEL, H., Simulation of earring during deep drawing of magnesium alloy AZ31, Acta Mater., 55, 3, pp. 867–874, 2007.

CHANDOLA, N., MISHRA, R.K., CAZACU, O., Application of the VPSC model to the description of the stress-strain response and texture evolution in AZ31 Mg for various strain paths, Eng. Mater. Tech., In-press, 2015.

LEBENSOHN, R., Modelling the role of local correlations in polycrystal plasticity using viscoplastic self-consistent schemes, Model. Sim. Mat. Sci. Eng., 7, 5, pp. 739–746, 1999.

TOMÉ, C.N., KASCHNER, G.C., Modeling texture, twinning and hardening evolution during deformation of hexagonal materials, Materials Science Forum, 495, pp. 1001–1006, 2005.

PROUST, G., TOMÉ, C.N., KASCHNER, G.C., Modeling texture, twinning and hardening evolution during deformation of hexagonal materials, Acta Mat., 55, 6, pp. 2137–2148, 2007.

HAMA, T., KITAMURA, N., TAKUDA, H., Effect of twinning and detwinning on inelastic behavior during unloading in a magnesium alloy sheet, Mat. Sci. Eng. A, 583, pp. 232–241, 2013.

TOMÉ, C.N., LEBENSOHN, R.A., Self consistent homogenization methods for texture and anisotropy (Chap. 23)in: Continuum Scale Simulation of Engineering Materials: Fundamentals-Microstructures-Process Applications (eds. D. Raabe, F. Roters, F. Barlat, L.-Q. Chen), 2004, pp. 473–499.

TOMÉ, C.N., LEBENSOHN, R.A., Manual for code viscoplastic self-consistent (Version 7), Available at: http://public.lanl.gov/vpsc, 2008.

BEYERLEIN I.J, TOMÉ C.N, A dislocation-based constitutive law for pure Zr including temperature effects, Int. J. Plast., 24, 5, pp. 867–895, 2008.