Effect of yield surface distortion on the failure prediction of Mg alloy sheets
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O R I G I NA L
Kai Zhang
· Hao Li · Jianlin Liu
Effect of yield surface distortion on the failure prediction of Mg alloy sheets
Received: 31 March 2020 / Accepted: 19 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Strong initial and induced anisotropies, observed in the deformation of Mg alloys, have restricted their industrial applications. The initial anisotropic behavior is caused by the initial texture of Mg sheets which are fabricated by successive rolling operations. This behavior could be well described by appropriate yield criteria. However, the texture evolution inside the material induces the distortion of the yield surface, which has strong effects on the hardening and damage evolution. Classical isotropic and kinematic hardening could not precisely describe the induced anisotropic hardening. Therefore, distortional hardening, describing the shape alteration of the yield surface, should be considered in modeling the mechanical behaviors of Mg alloy sheets. In this study, a plasticity model fully coupled with isotropic damage for Mg alloys is proposed, and the constitutive equations are formulated within the thermodynamic framework using state variables. The current constitutive model could accurately reproduce the stress–strain evolution under tension, shear and compression for Mg alloy AZ31. In addition, both of the initial anisotropic yield surface and the subsequent distorted yield surface are captured correctly, and the failure under combined loading path is well predicted by the proposed model. Keywords Mg alloys · Anisotropy · Yield surface · Distortional hardening · Damage 1 Introduction Magnesium alloy, with a high ratio of strength versus density, is an excellent candidate for application in automotive industry aiming to enable lightweight design and improve fuel economy. This property also makes them good alternatives to traditional steels and aluminum alloys. Accordingly, lightweight design concept has become a popular term in new industrial development. However, the complex mechanical behaviors of Mg alloys bring difficulties in large-scale industrial applications. Since the Mg alloy sheets are obtained by successive rolling operations, a clear initial anisotropy is conferred to these sheets, which has a strong effect on their formability [1,2]. Mg alloys (e.g., AZ31) often exhibit tension– compression asymmetry or strength differential effect [3], where the yield stress in tension is much higher than that in compression [4]. This special feature of Mg alloys results from the activation of twinning under a K. Zhang (B) · J. Liu (B) Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China E-mail: [email protected] J. Liu E-mail: [email protected] H. Li School of Material Science and Engineering, Shandong University of Science and Technology, Qingdao 266580, China
K. Zhang et al.
Fig. 1 Yield surface evolution according to different hardening models
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