Thermal fracture as a framework for quasi-static crack propagation

TL;DR

This paper develops an analytical and numerical framework for predicting crack paths under thermal loading, explaining the transition from straight to wavy cracks using local symmetry and Griffith criteria, validated by phase field simulations.

Contribution

It introduces a combined analytical and numerical approach to predict thermal crack paths, elucidating the supercritical transition from straight to oscillatory cracks.

Findings

The instability from straight to wavy cracks can be explained by local symmetry and Griffith criterion.

The phase field model confirms the supercritical nature of the crack transition.

Theoretical predictions align with numerical simulations across various loading conditions.

Abstract

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.