The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity

TL;DR

This paper introduces a method to determine yield stress distributions for stochastic plasticity models using discrete dislocation dynamics and weakest link arguments, demonstrating scale-linking and statistical equivalence between models.

Contribution

It presents a novel approach to connect microscopic dislocation simulations with mesoscopic stochastic models through a weakest link scaling method.

Findings

Stress-strain curves from mesoscopic and dislocation models are statistically equivalent.

Models behave identically in the thermodynamic limit.

Method applicable to various microstructures and amorphous materials.

Abstract

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.