We obtain an approximate effective solution of the problem of nonstationary stress concentration near a spherical crack located inside a tapered shaft whose face is subjected to the action of impact tangential stresses. To solve the problem, we propose to use an approach based on the discretization of the problem in time with the help of a difference scheme. By the method of integral transformations, the problem is reduced to an integral equation for the unknown jump of displacements on the crack. This equation is solved by the method of orthogonal polynomials. The relation for the evaluation of the stress intensity factors is obtained.
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