Asymmetric yield effect evolving with internal variables during continuous large deformations and its FEM validation

Abstract

In hexagonal close-packed (HCP) metals and alloys, the asymmetric yield effect that strongly evolves with the internal variables during continuous large deformations is clearly evident and significantly influences their formability. This limits their engineering applications and significant scientific issues regarding the macro performance corresponding to microstructural and texture evolution arise. In this study, a powerful stress-invariant-asymmetric-yield function capable of accurately describing the hydrostatic pressure sensitivity (HPS), tension-compression strength differential effect (SDE), and anisotropy is applied. An analytical interpolation approach based on the hardening effect with the function of the internal variable and the Lode parameter of the stress state is developed to build the continuous evolution between two adjacent yield surfaces. A rate-independent large deformation hypoelasto-plastic constitutive relationship adequately considering the asymmetric yield evolution is built. A plastic potential for the non-associated flow rule is introduced to eliminate the plastic dilatancy. The plastic modulus, corrected with the partial derivative of the continuously interpolated yield function with respect to the internal variable that is capable of capturing the evolution effect, is analytically deduced and straightforwardly expressed. The evolving asymmetric yield effect and its constitutive description are then numerically validated, with insignificant errors and high efficiency, by the explicit integration algorithm of finite element simulations of continuous large deformations of the through-thickness and in-plane compressed Zr. The results indicate that (1) for the different levels of pre-strain, the continuously interpolated asymmetric yield function, together with the proposed constitutive relationship, can precisely describe the non-evolving asymmetric yield of HCP-structured Zr as the traditional ones (Yoon et al., 2014; Plunkett et al., 2007) without considering the evolution effect; (2) for continuous large deformation loading, the continuous yield surfaces built by the continuous interpolation of the stress-invariant-asymmetric-yield function and the proposed constitutive relationship, considering the evolution effect, jointly and clearly corrects the strain hardening rates for all loading routes except the X uniaxial tension without the evolution, and the corrected simulations are in better agreement with the theoretical stress-strain data than uncorrected simulations, in particular for the routes along which the yield surfaces clearly evolve; (3) although the in-plane compressed Zr presents a significantly stronger asymmetric yield effect evolving with the accumulative plastic strain compared to the through-thickness compressed Zr during continuous large deformations, the continuously interpolated yield function and the constitutive relationship considering the evolution effect can still precisely describe the strain hardening processes and stress-strain relationships, and accurately capture the strain-softening effect along the equibiaxial tensile route of the in-plane compressed Zr that cannot be captured by the combinations of the traditional yield functions without considering the HPS, SDE, anisotropy, and their evolution and the general constitutive relationships unsuitable for the large deformation asymmetric yield. It is anticipated that the proposed asymmetric yield evolution and its large deformation constitutive description with the high accuracy and extensive applicability on various asymmetric yield functions, single or multiple internal variables, and complicated loading routes of nonlinear plastic behaviors will be used in precise engineering simulations of HCP metals and alloys and the corresponding scientific studies of microscopic mechanisms.