A new constitutive model to describe evolving elastoplastic behaviours of hexagonal close-packed sheet metals

Abstract

This study develops a new phenomenological constitutive model to capture the unique evolving cyclic elastoplastic behaviours of hexagonal close-packed (HCP) sheet metals. This new constitutive model is developed by adopting the concepts of multiple-yield surface approaches. Four phenomenological deformation modes, including Monotonic Compression (MC), Monotonic Tension (MT), Reverse Compression (RC), and Reverse Tension (RT), are considered to represent the hardening evolution of the materials, including the twining/untwining behaviours. Reference flow stress equations are introduced, and a Cazacu-Barlat 2004 (CB2004) type yield surface is employed to each deformation mode. In addition, the RT hardening parameters are defined as functions of plastic pre-strains to mitigate the interpolation error caused by parameter determination processes of existing models. For validation, the calculated stress–strain curves of AZ31B magnesium alloy are compared with experimental curves available from literature. Moreover, to show the accuracy of the proposed analytical model, the reproduced stress–strain curves are compared with those of an existing model—the modified homogeneous anisotropic hardening (HAH) model. The obtained results show that the new constitutive model can successfully reproduce experimental Tension–Compression-Tension (TCT) and Compression-Tension–Compression (CTC) stress–strain curves of HCP sheet metals with considerably less percentage errors.