A 3-D model of wing crack growth and interaction

Abstract

A simple model of a 3-D wing crack growing in compression from a disk-like initial crack has been developed. At the initial stage of growth the wings are modeled in vertical cross sections as 2-D cracks wedged at one end by the displacement produced by the contact area (former initial crack). This displacement is evaluated by replacing the contact area with a Mode III crack of the length equal to the wing width. It is shown that the contribution of the contact area into the crack-generated stress field is at least comparable with that of the wings. To analyze the possibility of extensive growth, the crack is modeled by a vertical disk-like crack where the opening (wedging) action of the sliding contact area is simulated by the uniform pressure distributed over a central circular area of the same radius as the initial crack. It is shown that the continuation of the wing crack growth in such a mode would require a considerable increase in the load, which probably explains why extensive (few times the initial flaw size) growth of a single 3-D crack has never been observed in experiments. The mechanism of producing really large tensile fractures by pairs of 3-D wing cracks has also been investigated. On the basis of the dipole (far field) asymptotics, it has been shown that it is the total tensile stresses induced by the wing cracks in the direction perpendicular to the compression direction that could be responsible for the appearance of the tensile fractures. The magnitude of these stresses is affected by the crack locations and spacings.