Nonaxisymmetric problem of the stress-strain state of an elastic half-space with a near-surface circular crack under the action of loads along it

Abstract

The nonaxisymmetric problem of the influence of a free surface of an elastic semifinite body on the distribution of stresses in the vicinity of a near-surface disk-shaped crack is considered within the framework of linearized mechanics of deformable solids. A joint analysis of two nonclassic mechanisms of fracture, namely, fracture of a material with initial stresses that act parallel to the plane of the crack and fracture of a body in compression along a crack, is performed. Using representations of the general solutions of linearized equilibrium equations in terms of harmonic potential functions and the apparatus of integral Fourier–Hankel transformations, we reduce the problem separately for each harmonic in the angular coordinate to resolving systems of Fredholm integral equations of the second kind. Expressions for stress intensity factors in the vicinity of the crack contour are obtained, and their dependence on the initial stresses and geometrical parameters of the problem is analyzed. For some highly elastic materials, critical compression parameters that correspond to nonaxisymmetric forms of local loss of stability of a material in compression along a near-surface crack are determined.