Crack front instability in mixed-mode I+III: The influence of non-singular stresses

Abstract

In a previous paper (Leblond et al., 2011), a theoretical instability threshold was derived for the currently observed phenomenon of crack front fragmentation under mixed-mode I+III loading conditions. Instability modes were shown to emerge when the mode mixity ratio KIII0/KI0 exceeds some critical value [KIII0/KI0] that only depends on Poisson’s ratio. Unfortunately, the predicted threshold was found to be much larger than that observed in general. Numerical simulations of crack front fragmentation (Chen et al., 2015), based on a phase-field model, subsequently evidenced an important role of the specimen size on the non-coplanar instability. Here, we explore theoretically the influence of existence of some finite characteristic length(s), arising from the loading, by accounting for the presence of non-singular stresses Tij0 in the unperturbed configuration of the crack. By re-examining the linear stability analysis of Leblond et al. (2011) with these more general assumptions, we show that a negative non-singular stress Txx0 in the direction of propagation does not affect crack front fragmentation, while a negative non-singular Tzz0 in the direction of the crack front strongly hampers it. On the contrary, positive non-singular stresses Txx0 and Tzz0, or non-zero non-singular (antiplane shear) stresses Txz0, promote the fragmentation process, sometimes through the formation of facets that drift along the front as propagation proceeds. Large values of all three of these non-singular stresses may result in a significant lowering of the threshold value [KIII0/KI0] of the mode mixity ratio for instability, even possibly down to zero; which stresses out the potential existence of the fragmentation instability even in pure mode I. Yet, our results cannot explain the often observed formation of non-coplanar facets at extremely low mode mixity ratios; indeed the wavelength of the instability modes predicted are comparable to the finite characteristic length(s) introduced, of at least centimetric order of magnitude, while the formation of facets has been observed experimentally at scales as low as some tens of microns.