The formation and growth of echelon cracks in brittle materials

Cracks subjected to mode III shear loading fragment into numerous daughter cracks. The formation of such patterns—called echelon cracks—is explored in this work through a phase-field model of fracture. It is shown that the phase field method predicts that a crack subjected to mixed-mode I +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document} III grows along the extension of the parent crack plane, contrary to experimental observations. In order to replicate the experimentally observed fragmentation of crack fronts, defects are introduced in the vicinity of the crack front to trigger fragmentation of the front; examples of successful formation and growth of these echelon cracks is demonstrated in this paper. It is also shown that the intrinsic scale parameter in the phase field model must be very small in comparison to the scale of formation of the echelon cracks.