Two unequal cracks with coalesced plastic zones - the generalised Dugdale model approach

The problem of two collinear hairline unequal cracks weakening an infinite thin elastic plate is considered. The faces of the cracks open in mode I ty pe deformation on account of the uniform constant uniaxial tension applied at infinity. The tension is increased to the limit such that the plastic zo nes developed at two interior tips of the unequal cracks get coalesced. Eac h of the plastic zones developed is closed by distributing a normal cohesiv e stress distribution over its rim. The problem reduces to dual Hilbert pro blems, the solution of which gives a set of non-linear simultaneous equatio ns to determine the length of the plastic zones. Expressions are derived to obtain crack opening displacement at the rips of the cracks, An illustrati ve numerical example is considered to study the variation of load ratio req uired for the closure of the prescribed plastic zone. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.