Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

Abstract

In this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion [10] which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation [37]. From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. [32] –which investigated materials with yielding described by the orthotropic criterion of Hill [19]– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s−1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations