No abstract

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Introduction. It is well known that the strength of real bodies depends heavily on the presence of structural defects such as cracks and inclusions, which are often stress concentrators. In studies of the stress-strain state of bodies with defects, particular attention is paid to the inertia effects caused by dynamic loads. Thus, in the case of infinite and semi-infinite bodies with cracks under harmonic and impact loading, the stress concentrations arising near the defects can far exceed the static values [1-4]. The above-mentioned effects are also influenced by the presence of the outer surface of the body [5][6][7]. One of the effective methods for solving dynamic problems of threedimensional theory of elasticity is the method of boundary integral equations (BIE) [8][9][10][11][12][13]. In the present paper, the BIE method is used to study the inertia effects near the contours of circular cracks in a half-space subjected to harmonic loads with a clamped boundary condition.Formulation of the Problem. We consider an isotropic elastic half-space whose boundary surface S 0 is clamped. The half-space contains K plane circular cracks of radius a, which occupy regions S k (k = 1, K) and are at equal depths d = |O 0 O 1 | in a plane perpendicular to the boundary S 0 . The opposite faces of the cracks S ± k are loaded by self-equilibrated harmonic tearing forces

No abstract

No abstract