Stress distribution near the edge of a crack in a prestressed elastic body (Q1821615)

The effect of preliminary loading in the plane of a crack on the stress distribution around the crack edge is investigated for normal fracture, as well as transverse and longitudinal shear. Unlike in the work of (*) \textit{A. N. Guz}' [Brittle fracture mechanics of initially stressed materials (1983; Zbl 0535.73076)], where complex potentials of the linearized theory of elasticity were used, a different method is employed to solve the problem and the following questions are discussed: the effect of initial deformation on the stress intensity coefficients and the connection between the conditions of solvability of the problem of a crack and the Hadamard inequality. In the case of an isotropic incompressible material of general type it is shown that the initial deformation does not affect the order of the stress singularity at the crack edge. Asymptotic representations of displacements and stresses near the crack edge are obtained in more explicit form than those in (*). It is established that the initial deformation does not influence the stress intensity coefficients of the normal fracture and longitudinal shear, but increases the stress intensity coefficient in the case of transverse shear.