A texture-dependent yield criterion based on Support Vector Classification

Abstract

Conventional yield criteria for anisotropic plasticity rely on linear transformations of the stress tensor to map the directional dependence of critical stress tensors at yield onset onto a unit sphere in stress space. These linear transformations are made material specific by a number of anisotropic parameters, which need to be determined by experimental procedures for each material. One drawback of this approach is that these anisotropic parameters cannot be explicitly expressed as functions of the crystallographic texture. Hence, any change in the texture of a material, as it occurs during cold deformation, requires a complete re-parametrization of the yield function. In this work, we present a data-oriented yield criterion based on Support Vector Classification (SVC) that is an explicit function of the crystallographic texture. This texture-dependency is achieved by including the coefficients of the general spherical harmonics (GSH) series expansion of the orientation distribution function (ODF) to the feature space of the machine learning model. The capabilities of the proposed yield criterion are demonstrated by training the model on a dataset containing micromechanical data from over 8000 distinct cubic-orthorhombic textures. The trained SVC combines the efficiency of classical phenomenological models with the flexibility of elaborate CP models. It provides a path to efficient hierarchical materials modeling as the anisotropy of the macroscopic yield onset is explicitly linked to the crystallographic texture.