Crack front stability for a tunnel-crack propagating along its plane in mode 2 + 3

The authors recently studied stability of the straight configuration of the front of a tunnel-crack propagating along its plane in mixed mode 2 + 3 conditions. Coincidence of the extrema of the supposedly sinusoidal crack front perturbation and the energy release rate was assumed, which imposed a certain phase difference between the perturbations of the two parts of the front. The aim of this paper is to relax this constraint. The system is time-dependent so that the stability issue is prone to problems of definition. It is notably shown that for some appropriate definition of stability, certain perturbations develop "unstably" if their wavelength is larger than some critical value depending on mean crack width, Poisson's ratio and mode mixity.