Abstract
A phenomenological crystal plasticity constitutive model for magnesium single crystal was presented. Four deformation mechanisms (including basal 〈a〉, prismatic 〈a〉, pyramidal 〈c + a〉 slip and tension twin) and their interactions were considered. Twin-induced lattice reorientation was also incorporated in the model. The proposed model was then applied to the simulation of plane-strain compression deformation for different orientations. Related material parameters were calibrated at first according to the classical channel-die tests. The predicted macro-and microscopic responses, along with the experimental results, show strong orientation-dependent properties. It is also found in the simulation that basal slip in the twinned region is active even before the saturation of twin activity in a twin-favored case. Furthermore, the effect of an initial deviation angle on the mechanical responses was evaluated, which is proved to be also orientation-dependent. Basal slip is found to be easily activated due to a slight deviation, while a slight deviation in the twin-favored case could result in a significant difference in the mechanical behavior after the reorientation. The effort on the study of magnesium single crystal in the present work contributes to further polycrystalline analysis.
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References
Kulekci MK. Magnesium and its alloys applications in automotive industry. Int J Adv Manuf Technol. 2008;39(9–10):851.
Staiger MP, Pietak AM, Huadmai J, Dias G. Magnesium and its alloys as orthopedic biomaterials: a review. Biomaterials. 2006;27(9):1728.
Herrera-Solaz V, Hidalgo-Manrique P, Pérez-Prado MT, Letzig D, Llorca J, Segurado J. Effect of rare earth additions on the critical resolved shear stresses of magnesium alloys. Mater Lett. 2014;128:199.
Kelley E, Hosford W. Plane-strain compression of magnesium and magnesium alloy crystals. Trans Met Soc AIME. 1968;242(1):5.
Wonsiewicz BC. Plasticity of magnesium crystals. Cambridge: Massachusetts Institute of Technology; 1966. 6.
Sułkowski B. Analysis of crystallographic orientation changes during deformation of magnesium single crystals. Acta Phys Pol A. 2014;126(3):768.
Drozdenko D, Bohlen J, Chmelík F, Lukáč P, Dobroň P. Acoustic emission study on the activity of slip and twin mechanisms during compression testing of magnesium single crystals. Mater Sci Eng A. 2016;650:20.
Catoor D, Gao YF, Geng J, Prasad MJ, Herbert EG, Kumar KS, Pharr GM, George EP. Incipient plasticity and deformation mechanisms in single-crystal Mg during spherical nanoindentation. Acta Mater. 2013;61(8):2953.
Kitahara H, Mayama T, Okumura K, Tadano Y, Tsushida M, Ando S. Anisotropic deformation induced by spherical indentation of pure Mg single crystals. Acta Mater. 2014;78:290.
Selvarajou B, Shin JH, Ha TK, Choi IS, Joshi SP, Han HN. Orientation-dependent indentation response of magnesium single crystals: modeling and experiments. Acta Mater. 2014;81:358.
Taylor GI. Analysis of plastic strain in a cubic crystal. In: Stephen Timoshenko 60th Anniversary Volume. New York; 1938, 218.
Hill R, Rice J. Constitutive analysis of elastic–plastic crystals at arbitrary strain. J Mech Phys Solids. 1972;20(6):401.
Peirce D, Asaro RJ, Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metall. 1983;31(12):1951.
Kalidindi SR. Polycrystal plasticity: constitutive modeling and deformation processing. Cambridge: Massachusetts Institute of Technology; 1992. 7.
Van Houtte P. Simulation of the rolling and shear texture of brass by the Taylor theory adapted for mechanical twinning. Acta Metall. 1978;26(4):591.
Kalidindi SR. Incorporation of deformation twinning in crystal plasticity models. J Mech Phys Solids. 1998;46(2):267.
Kraska M, Doig M, Tikhomirov D, Raabe D, Roters F. Virtual material testing for stamping simulations based on polycrystal plasticity. Comput Mater Sci. 2009;46(2):383.
Deng G, Lu C, Su L, Tieu AK, Li J, Liu M, Zhu H, Liu X. Influence of outer corner angle (OCA) on the plastic deformation and texture evolution in equal channel angular pressing. Comput Mater Sci. 2014;81:79.
Deng GY, Tieu AK, Si LY, Su LH, Lu C, Wang H, Liu M, Zhu HT, Liu XH. Influence of cold rolling reduction on the deformation behaviour and crystallographic orientation development. Comput Mater Sci. 2014;81:2.
Kalidindi S, Schoenfeld S. On the prediction of yield surfaces by the crystal plasticity models for fcc polycrystals. Mater Sci Eng A. 2000;293(1):120.
Zhang KS, Shi YK, Xu LB, Yu DK. Anisotropy of yielding/hardening and microinhomogeneity of deforming/rotating for a polycrystalline metal under cyclic tension–compression. Acta Metall Sin. 2011;47(10):1292.
Kadkhodapour J, Butz A, Ziaei-Rad S, Schmauder S. A micro mechanical study on failure initiation of dual phase steels under tension using single crystal plasticity model. Int J Plast. 2011;27(7):1103.
Kupka D, Huber N, Lilleodden E. A combined experimental–numerical approach for elasto-plastic fracture of individual grain boundaries. J Mech Phys Solids. 2014;64:455.
Kim J-B, Yoon JW. Necking behavior of AA 6022-T4 based on the crystal plasticity and damage models. Int J Plast. 2015;73:3.
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(19):6230.
Wang H, Raeisinia B, Wu P, Agnew S, Tomé C. Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet. Int J Solids Struct. 2010;47(21):2905.
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.
Abdolvand H, Majkut M, Oddershede J, Schmidt S, Lienert U, Diak BJ, Withers PJ, Daymond MR. On the deformation twinning of Mg AZ31B: a three-dimensional synchrotron X-ray diffraction experiment and crystal plasticity finite element model. Int J Plast. 2015;70:77.
Graff S, Brocks W, Steglich D. Yielding of magnesium: from single crystal to polycrystalline aggregates. Int J Plast. 2007;23(12):1957.
Zhang J, Joshi SP. Phenomenological crystal plasticity modeling and detailed micromechanical investigations of pure magnesium. J Mech Phys Solids. 2012;60(5):945.
Gan Y, Song W, Ning J, Tang H, Mao X. An elastic–viscoplastic crystal plasticity modeling and strain hardening for plane strain deformation of pure magnesium. Mech Mater. 2016;92:185.
Muránsky O, Carr D, Barnett M, Oliver E, Šittner P. Investigation of deformation mechanisms involved in the plasticity of AZ31Mg alloy: in situ neutron diffraction and EPSC modelling. Mater Sci Eng A. 2008;496(1):14.
Barnett M. Twinning and the ductility of magnesium alloys: part II. “Contraction” twins. Mater Sci Eng A. 2007;464(1):8.
El Kadiri H, Oppedal A. A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects. J Mech Phys Solids. 2010;58(4):613.
Capolungo L, Beyerlein I, Tomé C. Slip-assisted twin growth in hexagonal close-packed metals. Scripta Mater. 2009;60(1):32.
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This study was financially supported by the National Natural Science Foundation of China (No. 51375256).
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Xi, BL., Fang, G. Crystal plasticity behavior of single-crystal pure magnesium under plane-strain compression. Rare Met. 36, 541–549 (2017). https://doi.org/10.1007/s12598-016-0856-7
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DOI: https://doi.org/10.1007/s12598-016-0856-7