Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

Abstract

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Introduction. It is well known that the strength of real bodies depends heavily on the presence of structural defects such as cracks and inclusions, which are often stress concentrators. In studies of the stress-strain state of bodies with defects, particular attention is paid to the inertia effects caused by dynamic loads. Thus, in the case of infinite and semi-infinite bodies with cracks under harmonic and impact loading, the stress concentrations arising near the defects can far exceed the static values [1-4]. The above-mentioned effects are also influenced by the presence of the outer surface of the body [5][6][7]. One of the effective methods for solving dynamic problems of threedimensional theory of elasticity is the method of boundary integral equations (BIE) [8][9][10][11][12][13]. In the present paper, the BIE method is used to study the inertia effects near the contours of circular cracks in a half-space subjected to harmonic loads with a clamped boundary condition.Formulation of the Problem. We consider an isotropic elastic half-space whose boundary surface S 0 is clamped. The half-space contains K plane circular cracks of radius a, which occupy regions S k (k = 1, K) and are at equal depths d = |O 0 O 1 | in a plane perpendicular to the boundary S 0 . The opposite faces of the cracks S ± k are loaded by self-equilibrated harmonic tearing forces

Effect of the compliant interlayer on the dynamic stress intensity factor in a piecewise-homogeneous solid with a circular crack

“…In the three-dimensional case, the most convenient configuration for the theoretical analysis is a solid consisting of connected elastic half-spaces with a single crack. Problems of dynamic loading of the defect in such a bimaterial were solved in [1][2][3][4][5] under the assumption of an ideal mechanical contact; dynamic stress intensity factors in the vicinity of the crack were demonstrated to differ substantially from quasi-static coefficients [6-8] because of inertial effects of crack interaction with the interface. The present paper deals with these effects in the case of a nonideal connection of the half-spaces, modeling the presence of a thin (as compared with the length of the exciting wave) and compliant (having a low shear modulus, as compared with the shear modulus of matrix materials) interlayer.…”