Spontaneous thermal runaway as an ultimate failure mechanism of materials

TL;DR

This paper introduces a theoretical mechanism where thermal runaway causes catastrophic failure in materials at shear strengths below the classical ultimate limit, with implications across scales.

Contribution

It presents a new theoretical model for thermal runaway failure, predicting maximum shear strength and shear band formation in viscoelastic materials.

Findings

Thermal runaway can cause failure below Frenkel's shear strength limit.

Failure involves localized shear bands with high deformation and temperature.

The model applies across different material scales.

Abstract

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [Z. Phys. 37, 572 (1926)]. He assumed that as slip occurred, two rigid atomic rows in the crystal would move over each other along a slip plane. Based on this simple model, Frenkel derived the ultimate shear strength to be about one tenth of the shear modulus. Here we present a theoretical study showing that catastrophic material failure may occur below Frenkel's ultimate limit as a result of thermal runaway. We demonstrate that the condition for thermal runaway to occur is controlled by only two dimensionless variables and, based on the thermal runaway failure mechanism, we calculate the maximum shear strength $\sigma_c$ of viscoelastic materials. Moreover, during the thermal runaway process, the magnitude of strain and temperature progressively localize in space producing a narrow region of highly deformed material, i.e. a shear band. We then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.