Analysis of a crack-tip dual zone model

Abstract

An analytic model is proposed for an opening mode of crack face displacement with crack-tip dual zones, i.e. an elastic core zone plus a plastic strip zone. A presence of such dual zones in the vicinity of the crack tip was experimentally observed in a recent study based on the generation of dislocations. A Papkovich-Neuber formulation of the resulting four-part mixed boundary value problem leads to a set of quadruple integral equations which are solved with an application of finite Hilbert transform technique. With conditions of boundedness on the stresses in the plastic strip zone, the results show an inverse square root of the distance type singularity at the base of the crack tip and a relaxation of stresses in the crack-tip elastic core zone is realized. The stress intensity factors and the crack-tip opening displacements are presented in exact forms involving elliptic integrals and Heuman's lambda function and are shown to depend upon the crack size, the applied loading and the crack-tip dual zone lengths. The analytic and graphical solutions are compared with the Dugdale model to which they reduce as a limiting case of vanishing elastic core zone.

Résumé

On propose un modèle analytique pour décrire la déformation d'ouverture selon le mode I, en utilisant une approche de mécanique des milieux continus pour décrire la double zone-élastique et plastique-située à la pointe d'une fissure.