Rate-and-State Theory of Plastic Deformation Near a Circular Hole

TL;DR

This paper demonstrates that a simple rate-and-state theory can effectively describe various plastic deformation behaviors around a circular hole, including viscoelasticity, strain hardening, and failure modes, relevant to fracture mechanics.

Contribution

It introduces a rate-and-state model that captures both static and dynamic plasticity features in inhomogeneous materials, extending understanding of failure mechanisms.

Findings

Predicts plastic zone existence near the hole under certain conditions

Accounts for transition from viscoelasticity to viscoplasticity at yield stress

Suggests relevance to fracture mechanics through dynamic failure modes

Abstract

We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate. Those features include linear viscoelastic flow at small applied stresses, strain hardening at larger stresses, and a dynamic transition to viscoplasticity at a yield stress. In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters. The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics.