On the phenomenological modelling of yield surface distortion

TL;DR

This paper presents a flexible phenomenological model for metal plasticity that smoothly interpolates between different yield surfaces, capturing complex distortions and anisotropies during hardening.

Contribution

It introduces a novel interpolation approach between key yield surfaces, allowing for realistic modeling of yield surface evolution with preserved convexity.

Findings

The model can represent arbitrary yield surface distortions.

It ensures smooth evolution and convexity of the yield surface.

The approach is exemplified through a rheological analogy.

Abstract

A simple phenomenological approach to metal plasticity, including the description of the strain-induced plastic anisotropy, is considered. The advocated approach is exemplified by a two-dimensional rheological analogy. This analogy provides insight into modelling of nonlinear kinematic hardening of Armstrong-Frederick type combined with a nonlinear distortional hardening. In the previous publications of the authors, an interpolation rule between the undistorted yield surface of a virgin material and the saturated yield surface of a pre-deformed material was considered. In the current publication, a somewhat more flexible approach is considered. Given a set of convex symmetric key surfaces which correspond to different hardening stages, the form of the yield surface is smoothly interpolated between these key surfaces. Thus, any experimentally observed sequence of symmetric convex yield surfaces can be rendered. In particular, an arbitrary sharpening of the yield locus in the loading direction combined with a flattening on the opposite side can be taken into account. Moreover, the yield locus evolves smoothly and its convexity is ensured at each hardening stage.