About a stress deformation condition of a piecewise-uniform wedge with a system of collinear cracks at an antiplane deformation

Abstract

An antiplane problem of a stress deformation condition of a piecewise wedge consisting of two heterogeneous wedges with different opening angles and containing on the line of their attachment a system of arbitrary finite number of collinear cracks is investigated. With the help of Mellin's integral transformation the problem is brought to the solution of the singular integral equation relating to the density of the displacement dislocation on the cracks, which then is reduced to a system of singular integral equations with kernels being represented in the form of sums of Cauchy kernels and regular kernels. This system of equations is solved by the known numerical method. Stress intensity factors (SIF) are calculated and the behavior of characteristic geometric and physical parameters is revealed. Besides, the density of the displacement dislocation on the cracks, their evaluation, andJ-integrals are calculated.