Geometrical disorder of the fronts of a tunnel-crack propagating in shear in some heterogeneous medium

A statistical analysis of the deformation of the fronts of a tensile tunnel-crack propagating in fatigue in some medium with spatially varying Paris constant was recently performed, with special emphasis on the evolution of the power spectra and correlation functions of the fluctuations of the fronts around reference straight lines. This study is extended here to coplanar propagation (along a weak plane) of a tunnel-crack loaded in mode 2+3. The results are rather similar to those previously obtained for mode 1. In particular, just like for tensile loadings, there is an effect of gradual selection in time of Fourier components of the fluctuations of the fronts of large wavelength. One novelty, however, is that for shear loadings, the fronts no longer tend to become symmetrical in time, so that correlations between crack front fluctuations at two points are higher for points located on the same front than for points located on distinct ones.