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Stress intensity factors for three cracks at the interfaces of a graded layer bonding two different materials. (English) Zbl 1349.74151

Summary: We consider two dissimilar elastic half-planes bonded by a nonhomogeneous elastic layer in which there is one crack at the lower interface between the elastic layer and the lower half-plane and two cracks at the upper interface between the elastic layer and the upper half-plane. The stress intensity factors for these three cracks are solved for when tension is applied perpendicular to the interface cracks. The material properties of the bonding layer vary continuously between those of the lower half-plane and those of the upper half-plane. The differences in the crack surface displacements are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in the series are solved by the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors are calculated numerically for selected crack configurations.

MSC:

74G70 Stress concentrations, singularities in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74A40 Random materials and composite materials
74A50 Structured surfaces and interfaces, coexistent phases
74R10 Brittle fracture
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