Two Analytical Solutions for Dynamic Crack Bifurcation in Antiplane Strain

Abstract

A semi-infinite crack is subjected to constant magnitude, dynamic antiplane loading at time t = 0. At the same instant the crack is assumed to bifurcate and propagate normal to its original plane or to propagate without branching. For constant crack-tip velocities the stresses and particle velocity are functions of r/t and θ only, which allows Chaplygin’s transformaton and conformal mapping to be used to obtain two Riemann-Hilbert problems which can be solved analytically. Expressions for the elastodynamic Mode III stress-intensity factors are then computed as functions of the crack-tip velocity and some conclusions concerning crack initiation are drawn.