A new combined analytical and finite-element solution method for stability analysis of the growth of interacting tension cracks in brittle solids

Abstract

The analysis of stable and unstable growth regimes of a system of tension cracks in brittle solids, requires accurate estimates of the values of the stress intensity factors at various crack tips, and their derivatives with respect to the crack lengths. A new combined analytical and finite-element solution method is developed which is specially suited to problems of this kind. For illustration the method is applied to estimate the results corresponding to: (1) a single Griffith crack in an infinite space; and (2) possible unstable growth regimes corresponding to a system of edge cracks in a strip of finite width. Comparison of the results with those obtained by other methods, reveals that the present method is indeed very effective and efficient, and therefore provides a useful tool for the stability analysis of interacting cracks.