# Thermal weakening of cracks and brittle-ductile transition: a phase model

## TL;DR

This paper introduces a phase model for crack propagation considering thermal effects, explaining the brittle-ductile transition and stick-slip behavior through a dual-phase thermal weakening mechanism.

## Contribution

It presents a novel phase model that incorporates thermal effects into crack propagation, elucidating the brittle-ductile transition and thermal weakening phenomena.

## Key findings

- Identification of two crack propagation phases: mechanical and thermally weakened.
- Numerical simulations demonstrating dual-phase crack behavior.
- Prediction of a critical temperature for the brittle-ductile transition.

## Abstract

We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which being described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a plastic process zone. We show that such a model leads to a two-phase crack propagation: a first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanical load and by the toughness of the medium, and a second phase in which the crack is thermally weakened and propagates at greater velocity. Such a dual behavior can potentially explain the usual stick-slip in brittle fracturing, and we illustrate how with numerical simulations of mode I cracks propagating in thin disordered media. In addition, we predict the existence of a limiting ambient temperature above which the weakened phase ceases to exist and we propose this critical phenomenon as a novel explanation for the brittle-ductile transition of solids.