Dynamic phase diagram of plastically deformed amorphous solids at finite temperature

TL;DR

This paper investigates how finite temperature and shear rate influence the yielding transition in amorphous solids, revealing new scaling laws and phase diagram features through theoretical analysis and simulations.

Contribution

It extends the understanding of amorphous solid deformation by incorporating thermal effects into the phase diagram and avalanche dynamics.

Findings

Identifies a new temperature-dependent softening scaling at low strain rates.

Discovers a temperature-dependent Herschel-Bulkley exponent at high strain rates.

Develops a nonequilibrium phase diagram integrating temperature and strain rate effects.

Abstract

The yielding transition that occurs in amorphous solids under athermal quasistatic deformation has been the subject of many theoretical and computational studies. Here, we extend this analysis to include thermal effects at finite shear rate, focusing on how temperature alters avalanches. We derive a nonequilibrium phase diagram capturing how temperature and strain rate effects compete, when avalanches overlap, and whether finite-size effects dominate over temperature effects. The predictions are tested through simulations of an elastoplastic model in two dimensions and in a mean-field approximation. We find a new scaling for temperature-dependent softening in the low-strain rate regime when avalanches do not overlap, and a temperature-dependent Herschel-Bulkley exponent in the high strain rate regime when avalanches do overlap.