A method for the simultaneous identification of anisotropic yield and hardening constitutive parameters for sheet metal forming

Abstract

Sheet metal forming processes and their simulations often require knowledge of both anisotropic yield and hardening constitutive parameters. The identification of these properties, however, involves a large number of homogeneous tests as well as various expensive testing machines. In this paper, a novel method is proposed to enable a simultaneous identification of the multiple anisotropic yield and hardening constitutive parameters from a single test and using the simplest uniaxial testing machine, which significantly simplifies the conventional complex constitutive identification procedures. In particular, the test configuration is elaborately designed to exhibit both heterogeneous stress states and insignificant buckling under compressive loadings based on the plate buckling theory. The virtual fields method is adopted as the inverse problem solution for the selected anisotropic yield and hardening laws, namely, Hill1948 and the nonlinear kinematic hardening models. The proposed identification scheme is first validated through the simulated full-field strain and load data of the designed bridge-like test configuration. Its identification sensitivity is analyzed with respect to the influences of measurement noise, type and combination of virtual fields. The results show that using the designed test configuration it is possible to identify all the target anisotropic parameters from a single test despite a noticeable level of error. This however can be markedly improved by combining the two tests performed in the rolling and transverse directions, and with the multiple virtual fields constraints, from which accurate and robust identification results are obtained for the selected models. The validity of this method is then illustrated experimentally with the application on the wrought magnesium alloy AZ31B sheet specimens. Finally, potential improvements and applications of this method are suggested.