Thermal weakening of cracks and brittle-ductile transition of matter: a phase model
Tom Vincent-Dospital, Renaud Toussaint, Alain Cochard, Eirik G. Flekkøy, Knut Jørgen Måløy
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 is 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 zone surrounding the tip. We show that such a model leads to a two-phase crack propagation: the 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 the second phase in which the crack is thermally weakened and propagates at greater velocity. We illustrate, with numerical simulations of mode I cracks propagating in thin disordered media, how such a dual behavior can explain the usual stick-slip in brittle fracturing. 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.