Modeling of Yield Surface Evolution in Uniaxial and Biaxial Loading conditions using a Pre-strained Large-scale Specimen

Abstract

The present study discusses the influence of the sheet metal’s prior loading history on the flow curves, r-values and yield surfaces for several non-proportional loadings to the initial strain path. All the effects of the measured data are captured via a distortion-based hardening model.

Large-scale steel specimens were deformed using a novel grip system mounted on a 500-kN MTS servo-hydraulic tension machine. The large gauge-section, after pre-strain, was able to procure a strain distribution, which was reasonably homogeneous. It was then used as a pre strained material to examine the plastic behavior in biaxial tension tests of cruciform specimens with various load ratios. The large pre-strained gauge was also used to conduct orthogonal and cross-tension tests of the pre-strained uniaxial specimens with respect to the pre-loading. The flow curves and the r-values of the pre-strained steel in each of the aforementioned uniaxial testing conditions were measured and compared to that of the undeformed sheet sample. Furthermore, an exhaustive analysis of the yield loci, delimited to the first quadrant of a 2D-plane stress space was also conducted and the results, prior and post-prestrain are represented as a function of the plastic work. In this study, DP600 (1.4t) was used for two levels of prestrains whereas DP780 (1t) and CHSP45R (1.2t) sheet were used for one.

The homogeneous anisotropic hardening (HAH) model was employed to predict the behavior of the pre-strained material. The material coefficients were identified sequentially, starting with the anisotropic yield function, isotropic hardening law and finally with the HAH distortional hardening plasticity framework. In the present study, the Yld2000-2d plane stress anisotropic yield function was selected to represent the yield surface of the sheet sample and the Swift law was incorporated to capture the monotonic uniaxial flow curve. A set of distortional hardening coefficients was manually determined to best fit all the experimental responses, i.e. flow curves and r-value fluctuations at reloading in cross- and orthogonal-tension after 45 and 90 strain path changes, respectively. Moreover, the same set of coefficients was also used to model the yield surface in uniaxial and biaxial non-proportional loading conditions. In this study, sets of distortional hardening coefficients were manually acquired for DP600, DP780 and CHSP45R sheet samples. Each set of the parameters was then used to characterize all the experimental results of a material.

It was found that the HAH-predicted stress-strain curves after a non-linear strain path change and the distortions of the yield surface shape were in good agreement with the experiments, while the nature of the r-value evolution was qualitatively well predicted.