Plane Cracks in a Transversely Isotropic Layer

• Published in: Mechanics of solids Vol. 55; no. 8; pp. 1406 - 1414
• Main Authors: Artamonova, E. A., Pozharskii, D. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-12-2020; Springer Nature B.V
• Subjects: Anisotropy; Asymptotic methods; Classical Mechanics; Cracks; Differential equations; Eigenvalues; Eigenvectors; Elastic layers; Integral equations; Integral transforms; Isotropic material; Mathematical analysis; Physics; Physics and Astronomy; crack; theory of elasticity; transversal isotropy; layer
• ISSN: 0025-6544; 1934-7936
• DOI: 10.3103/S002565442008004X

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Problems of plane cracks of normal fracture (mathematical cuts) in the middle plane of a transversely isotropic elastic layer, the outer faces of which are under conditions of a sliding support, are considered. Isotropic planes are parallel or perpendicular to layer faces. Using the Fourier integral transform, the problems are reduced to integro-differential equations for crack opening, from which one can obtain the known equations of the corresponding problems for a transversely isotropic space and an isotropic layer by passing to the limit. A regular asymptotic method is applied for elliptical cracks; this method is effective for a relatively thick layer. It is shown the applicability domain of the method narrows with increasing anisotropy that is characterized by the roots of the characteristic equation (for an isotropic material, all roots are equal to unity). For strip-like cracks, closed solutions are obtained based on special approximations of the kernel symbols of integral equations, the relative errors of which decrease with increasing anisotropy. Calculations are made for known transversely isotropic materials.