Derivation of the Johnson-Samwer $T^{(2/3)}$ Temperature Dependence of the Yield Strain in Metallic Glasses

TL;DR

This paper provides a theoretical derivation for the universal $-T^{2/3}$ temperature dependence of the yield strain in metallic glasses, supported by simulation data, explaining their shear-banding failure behavior.

Contribution

It introduces a theoretical formula that explains the universal temperature dependence of yield strain in metallic glasses, validated by simulation data.

Findings

The derived formula fits well with simulation data.

The $-T^{2/3}$ law explains shear-banding failure.

Universal behavior across different metallic glasses.

Abstract

Metallic Glasses are prone to fail mechanically via a shear-banding instability. In a remarkable paper Johnson and Samwer demonstrated that this failure enjoys a high degree of universality in the sense that a large group of metallic glasses appears to possess a yield-strain that decreases with temperature following a $-T^{2/3}$ law up to logarithmic corrections. In this Letter we offer a theoretical derivation of this law. We show that our formula fits very well simulational data on typical amorphous solids.