Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion

TL;DR

This paper investigates how sheared disordered solids behave under different strain rates, revealing critical behavior in quasistatic conditions and deriving a scaling theory for particle diffusion, with implications for understanding material failure.

Contribution

It provides a comprehensive analysis of rate effects on stress, avalanches, and diffusion in sheared disordered solids, introducing a scaling theory validated by simulation data.

Findings

Avalanche sizes follow a power-law distribution with a diverging cutoff in the quasistatic limit.

Flow stress increases as a power law with strain rate, characterized by the Herschel-Bulkley exponent.

Particle diffusion diverges as strain rate decreases, with a derived scaling theory confirming key exponents.

Abstract

Rate-effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size $L$. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent $1/\beta$, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure $\beta$ as well as the exponent $\nu$ which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as $L^{-d/2}$. As the largest avalanche in a system scales as $L^\alpha$, this implies $\alpha < d/2$. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm $\beta/\nu$.