Finite size effects in a model for plasticity of amorphous composites

TL;DR

This paper investigates how the size of amorphous composites with reinforcing particles influences their plastic flow stress, revealing complex size-dependent behaviors and developing an analytical model that aligns well with numerical simulations.

Contribution

It introduces a mesoscopic depinning-like model incorporating elastic interactions and develops an analytical expression for size effects in amorphous composites.

Findings

Effective flow stress exhibits complex size dependence.

Departure from mixing law shows opposite trends due to matrix and particles.

Analytical model accurately predicts reinforcement size effects.

Abstract

We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size-dependence of the effective flow stress of the amorphous composite. In particular the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in $-(\log N/N)^{1/2}$ observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.