Interpolation-based anisotropic yield and hardening models

Abstract

In this paper, an interpolation-based anisotropic yield model and a corresponding anisotropic hardening model are proposed. The proposed yield model is an improvement on Vegter and van den Boogaard (2006)'s yield model. By introducing shape parameters into Bézier basis function to control the curvature of the curve, the number of interpolation curve segments is effectively reduced. The proposed yield model has very good material applicability (suitable for BCC, FCC, HCP materials) and can directly generate the tricomponent yield surface without any numerical fitting. In addition to being applied to capture tension-compression asymmetry, the model can also be extended to describe non-orthotropy, which is usually not realized by existing yield criteria. Based on the proposed yield model, a hardening model based on characteristic yield points tracking is proposed. The so-called characteristic yield points correspond to the uniaxial loading and equi-biaxial loading yield points for constructing the yield surface. By tracking the evolution curve of yield data (stress and r-value) with specific variables (e.g. equivalent plastic strain), the yield surface at different variable levels can be continuously predicted. The proposed hardening model can not only predict the evolution of yield surface with equivalent plastic strain under proportional loading, but also predict the effects of different pre-strains and preloading paths on yield surface, and can also couple other variables (e.g. strain rate) to comprehensively consider the effects of multiple factors.