Wave field of displacement in layered structures with internal cracks

Layered structural materials are widely used across many sectors. Under external loads and long-term operation, internal and interfacial cracks, delaminations, and other defects may develop within these materials, reducing structural durability and potentially leading to premature failure. The acoustic emission (AE) method enables the detection of such defects during their formation and growth by recording elastic waves that propagate through the material and cause surface oscillations. For the AE method, evaluating the displacement field on the solid surface is of primary importance. This paper presents the analytical solution to the 3D dynamic problem of determining the displacement field on the surface of an elastic three-layered composite under steady oscillations of internal penny-shaped Mode III cracks. The problem is reduced to a system of boundary integral equations. Displacements in the body are represented through Helmholtz potentials. An integral presentation of displacements for a special case of a three-layer composite is obtained – on the surface of a layer placed in a half-space with a crack (two layers have the same properties). The paper analyzes numerical results based on the analytical solution in detail. The dependence of displacement on the elastic characteristics of the components, the frequency of crack-surface displacement, the distance between the observation point and the fracture epicenter, and the crack depth in the two-component body has been established.