Abstract
We propose a method for the explicit determination of singular solutions of arbitrary systems of Cauchy-type singular integral equations of the second kind. The method is based on the numerical-analytic computer-assisted solution of the indicated problem. We obtain asymptotic expansions for stresses in the vicinity of the ends of a thin interlayer of any physical nature formed at the interface of the materials, generalize the definition of the stress intensity factors, numerically analyze the cases of an interphase crack and an absolutely rigid interphase interlayer under biaxial tension-compression, and compare one-term and two-term asymptotics of stresses with the well-known exact solution for a crack.
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