Statistical Physics of the Yielding Transition in Amorphous Solids

TL;DR

This paper investigates the statistical physics underlying the yielding transition in amorphous solids, revealing a fundamental change in energy barrier distributions that affects mechanical stability and deriving scaling laws for plastic events.

Contribution

It introduces a new understanding of the energy barrier distribution change at yielding and provides exact scaling exponents for energy and stress drops in plastic events.

Findings

Energy barrier distribution changes from zero to finite at zero energy.

A fundamental transition in mechanical stability properties occurs at yielding.

Exact scaling exponents for plastic event magnitudes are derived.

Abstract

The art of making structural, polymeric and metallic glasses is rapidly developing with many applications. A limitation to their use is their mechanical stability: under increasing external strain all amorphous solids respond elastically to small strains but have a finite yield stress which cannot be exceeded without effecting a plastic response which typically leads to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under mechanical loads. Here we show that the statistics of the energy barriers \Delta E that need to be surmounted changes from a probability distribution function (pdf) that goes smoothly to zero to a pdf which is finite at \Delta E=0. This fundamental change implies a dramatic transition in the mechanical stability properties with respect to external strain. We derive exact results for the scaling exponents that characterize the magnitudes of average energy and stress drops in plastic events as a function of system size.