Stress State Near Arbitrarily Oriented Cracks on the Continuation of a Rigid Inclusion Under Action of Longitudinal Shear Wave

Abstract

The problem about determining of the dynamic stress intensity factors (SIF) for the cracks that are located at an angle from the ends of the inclusion is solved. The inclusion is located in an unbounded elastic body, in which the longitudinal shear harmonic waves are propagated. Unknown amplitude of inclusions are determined from the equations of motion. Boundary conditions are formed in the assumption that the inclusion is fully coupled with the medium (matrix), and the surface of cracks are not loaded. The method of the solution is based on the presentation of displacements in the body as a superposition of three discontinuous solutions which are built respectively to the cracks and the inclusion. As result the original problem is reduced to the system of the singular integral equations for unknown jumps of stresses and displacements to the defect. For the numerical solution of the system the method is developed. It takes into consider the real asymptotic of the unknown functions and uses the special quadrature formulas for singular integrals.