A coupled plane-bending problem is considered for an elastic Kirchhoff-Poisson plate containing a through-the-thickness or (part-through) surface crack under closure. The stress intensity factors at the ends of the crack are not zero. Asymptotic solutions are derived for cases in which the ratio of the crack length to its depth is large. As is shown, the width of the contact strip decreases as the crack length increases; the limiting contact force and moment distribution may be determined by considering an edge-cracked strip with zero stress intensity factor in the thickness direction. As is also shown, the crack surface interaction in-plane force and bending moment can be derived directly from the initial force and moment distribution acting in the intact plate on the prospective crack line. The same result is valid for a collinear system of cracks; this collinear system may include alternating open and closed crack segments. In addition, the closure stress distribution is determined. For the latter, the width of the contact strip asymptote is derived as a function of the crack length coordinate, and the asymptotic stress distribution is found as a product of the thickness averaged closure stress and a function of a normalized plate thickness coordinate. The latter stress distribution is unique and universal for any slowly curving crack or crack system under closure. [References: 15]
展开▼
