The yielding of amorphous solids at finite temperatures

TL;DR

This paper investigates how finite temperature affects the yielding transition in amorphous solids, showing it becomes a smooth crossover explained by a simple stochastic model, and relates to experimental observations in metallic glasses.

Contribution

It introduces a unified scaling framework for thermally smoothed yielding transitions using simple models, extending phenomenological laws to generic amorphous solids.

Findings

Temperature converts the sharp athermal transition into a smooth crossover.

The crossover follows a universal scaling form explained by a stochastic one-particle model.

Results support interpreting the yielding transition as an effective mean-field phenomenon.

Abstract

We analyze the effect of temperature on the yielding transition of amorphous solids using different coarse-grained model approaches. On one hand we use an elasto-plastic model, with temperature introduced in the form of an Arrhenius activation law over energy barriers. On the other hand, we implement a Hamiltonian model with a relaxational dynamics, where temperature is introduced in the form of a Langevin stochastic force. In both cases, temperature transforms the sharp transition of the athermal case in a smooth crossover. We show that this thermally smoothed transition follows a simple scaling form that can be fully explained using a one-particle system driven in a potential under the combined action of a mechanical and a thermal noise, the stochastically-driven Prandtl-Tomlinson model. Our work harmonizes the results of simple models for amorphous solids with the phenomenological $\sim T^{2/3}$ law proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)] in the framework of experimental metallic glasses yield observations, and extend it to a generic case. Finally, our results strengthen the interpretation of the yielding transition as an effective mean-field phenomenon.