Thermal weakening of cracks and brittle-ductile transition of matter: A phase model

How heat controls fracture: the thermodynamics of creeping and avalanching cracks

“…We have here also written T as T 0 + DT, where T 0 is the absolute room temperature (B296 K) and DT is any deviation from this background value, as we will proceed to propose that the tip temperature can vary. Eqn (4) differs from that of Vincent-Dospital et al 28 by the introduction of the healing term and the consideration of the over-critical regime (G 4 G c ). These features are necessary to fit some experimental crack dynamics (as discussed in Section 3.1).…”

“…We here consider a refinement of the propagation model already introduced by Vincent-Dospital et al, 28 that did not compare it to any actual, experimental, crack propagation. Let us start by restating the various components of this model.…”

“…(i.e., eqn (3)), although it was discussed by Vanel et al, 14 was also absent of this previous work. 28 Note finally that one could also write eqn (4) as a function of the mechanical stress s that is applied at the crack tip, using…”

“…We have now derived the two constitutive equations of our fracture dynamics model: eqn (4), that gives the velocity of a crack as a function of its tip temperature, and eqn (5), that governs the thermal state around a progressing front. In a previous work, 28 we have simultaneously solved these two equations and, focusing on their steady state, showed that they predict two stable phases for the propagation of cracks. These two behaviors are shown by the plain curve in Fig.…”

“…Indeed, in a previous experimental and theoretical study of the tearing-induced heating in paper sheets, 27 we were able to relate the temperature field around moving cracks to a certain percentage of the mechanical energy which gets converted into heat as the tip advances. More recently, this rise in temperature was fed back into a sub-critical growth law and showed 28 that one can thus obtain a dynamics model holding numerous qualitative similarities with the observed behavior of cracks, namely, two stable phases of propagation and a critical point that is similar to a brittle-ductile transition (e.g., ref. 29).…”