Stress intensity factors for transversely loaded elastic plates and their application to predictions of crack arrest

Abstract

Running cracks in elastic plates have been observed to be arrested as they pass under a zone of externally applied transverse compression. The compression is applied over circular zones on each face of the plate, directly opposite one another. This phenomenon has been observed in a variety of materials, and the purpose of this paper is to examine the mechanics of this crack arrest from a theoretical standpoint. The analysis was conducted for two cases: (1) a very thin plate, in which rigorous closed form solutions are obtained for the stress intensity factors. K, and (2) a thick plate, for which an approximate technique was devised to obtain an expression for the stress intensity factor. This expression was in terms of triple integrals, which required excessive computer time for their evaluation. Attention was therefore focused on the average stress intensity through the plate thickness, which can be evaluated economically. A comparison of the average K for the thick plate with the corresponding thin plate results showed a good agreement, which indicated that the approximations and numerical calculations provided reasonable results. The average K results were then applied in conjunction with fracture initiation and arrest criteria to the prediction of the conditions under which crack arrest could be achieved in an edge-cracked half-plane in tension, which is felt to be representative of an actual structure. The results predicted that a compression zone diameter of about one plate thickness was optimum for crack arrest, and that this technique is most suitable for high-strength, low-toughness materials with a high Poisson's ratio.