Dynamic ductile to brittle transition in a one-dimensional model of viscoplasticity

TL;DR

This paper investigates a one-dimensional viscoplastic model revealing a ductile to brittle transition, where decohesion behavior becomes unstable at certain speeds due to non-monotonic energy dependence, informing fracture stability theories.

Contribution

It introduces a viscoplastic model capturing strain relaxation and flow, and explores its implications for fracture phenomena and ductile-brittle transition in a novel way.

Findings

Energy for decohesion is non-monotonic at low yield stress.

Steady decohesion becomes unstable at certain speeds.

Results relate to ductile to brittle transition understanding.

Abstract

We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. In this paper, we describe a first step in exploring the implications of these models for theories of fracture and related phenomena. We consider a one dimensional problem of decohesion from a substrate of a membrane that obeys the viscoplastic constitutive equations that we have constructed. We find that, quite generally, when the yield stress becomes smaller than some threshold value, the energy required for steady decohesion becomes a non-monotonic function of the decohesion speed. As a consequence, steady state decohesion at certain speeds becomes unstable. We believe that these results are relevant to understanding the ductile to brittle transition as well as fracture stability.