On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

Abstract

The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated Keywords: piecewise homogeneous isotropic elastoplastic body, interfacial crack, process zone Introduction. In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].Most theoretical studies in the field of the mechanics of interfacial cracks supposed that the fracture process zone is a surface on which the normal or tangential displacements discontinue. This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].The present paper addresses a piecewise-homogeneous body consisting of elastic and elastoplastic half-spaces. There is a rectilinear crack in the interface between the half-spaces. The body is under the conditions of plane strain. We examine the asymmetric case where a thin fracture process zone modeled by a line of discontinuity of tangential displacements develops in the body. The condition at infinity is formulated so as to account for the influence of the external field on the stress-strain state of the body. The integral Mellin transform is used to derive the functional Wiener-Hopf equation. Its exact solution is expressed in terms of Cauchy integrals and gamma functions. This solution is used to derive an equation for the determination of the length of the zone and to analyze the dependences of its length and angle on the external load and other parameters of the problem.1. Problem Statement. Consider the following plane-strain problem for a piecewise-homogeneous isotropic body: Determine the direction of development of a thin fracture process zone at the tip of a crack located in the interface between two dissimilar homogeneous half-planes with Young's moduli E 1 and E 2 and Poisson's ratios ν 1 and ν 2 . The material of the upper half plane is assumed elastoplastic; therefore, the preferential strains in the process zone, which is a thin layer, follow the shear mechanism. Because of this, we will simulate the thin process zone by a straight line that emanates from the crack tip at an angle α to the interface and on which the tangential displacement discontinues and the tangential stress is equal to a predefined material constant τ. The constant τ is the tangential stress averaged over the length...

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