ASYMPTOTIC SOLUTIONS FOR CRACK CLOSURE IN AN ELASTIC PLATE UNDER COMBINED EXTENSION AND BENDING

A coupled plane-bending problem is considered for an elastic Kirchhoff -Poisson plate containing a through-the-thickness or (part-through) su rface 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 show n, the width of the contact strip decreases as the crack length increa ses; the limiting contact force and moment distribution may be determi ned by considering an edge-cracked strip with zero stress intensity fa ctor in the thickness direction. As is also shown, the crack surface i nteraction in-plane force and bending moment can be derived directly f rom the initial force and moment distribution acting in the intact pla te on the prospective crack line. The same result is valid for a colli near system of cracks; this collinear system may include alternating o pen and closed crack segments. In addition, the closure stress distrib ution is determined. For the latter, the width of the contact strip as ymptote is derived as a function of the crack length coordinate, and t he asymptotic stress distribution is found as a product of the thickne ss averaged closure stress and a function of a normalized plate thickn ess coordinate. The latter stress distribution is unique and universal for any slowly curving crack or crack system under closure.