Insights on kinked cracks under mode III

Abstract

A parent flat crack under pure mode III kinks in subsequent crack nucleation. It fragments leaving a complex crack nucleation pattern of facets on the fracture surface. However, the energy release rate (ERR), erroneously predicts a crack nucleation path along the original flat surface (similarly to mode I loading) (Mittelman and Yosibash, 2015), contradicting experimental observations.

We consider here a surrogate simplified problem for a possible reconciliation of the ERR prediction leading to the fragmented surface: the Laplace equation in a circular 2D domain with a crack. This problem represents the cross-section of a 3D circular bar with a longitudinal crack under mode III. An asymptotic analysis demonstrated a maximum ERR resulting from a small crack segment that kinks from the tip of a parent crack when the first non-singular small term in mode III loading is non-zero (Oleaga, 2004, 2006).

Here we present the asymptotic mathematical analysis and investigate it further by a finite element analysis. We thereafter generalize the mathematical analysis to a small crack nucleating at a V-notched tip and interpret the outcome concerning the elasticity system under pure mode III loading.