Stress fields around a crack lying parallel to a free surface

Abstract

A method of stress analysis for a two dimensional crack, which is subjected to internal gas pressure, and situated parallel to a free surface of a material, is presented. It is based on the concept of continuously distributed edge dislocations of two kinds, i.e. one with Burgers vector normal to the free surface and the other with Burgers vector parallel to it.Stress fields of individual dislocations are chosen so as to satisfy stress free boundary conditions at the free surface, by taking account of image dislocations. Distributions of both kinds of dislocations in the crack are derived so as to give the internal gas pressure and, at the same time, to satisfy shear stress free boundary conditions on the crack surface. Stress fields try, ~ryy and trxy in the sub-surface layer are then determined from them. They have square root singularities at the crack-up.

Stress intensity factors around a crack parallel to a free surface of a half-plane

“…Recently, Ladopoulos has proposed a new technique for the numerical solution of Cauchytype singular integral equations [4], and has applied this method to the above problem treated in [3] and [2]. The numerical results for the stress intensity factors given by Ladopoulos are identical with Erdogan's.…”

“…Higasida and Kamada have solved the stress field around a crack which is parallel to the plane surface of the half-plane. In their investigation, the crack is loaded by internal pressure [2]. The same problem had already been treated by Erdogan [3].…”

Elastic reciprocity and symmetry constraints on the stress field due to a surface-parallel distribution of dislocations

“…Examining the stress intensity factors, K I and K II , in the limit of a very shallow crack using a beam approximation, Dyskin et al (2000) note agreement with Higashida and Kamada (1982) over Erdogan et al (1973). Additionally, several other authors have presented consistent solutions (Thouless et al, 1987;Yang and Li, 1997; the latter claim a misprint in the solution of Head, 1953, although we find no such misprint when comparing their solutions).…”

“…These factors were first numerically calculated in the case of the equal relation by Erdogan (1969) and Erdogan et al (1973), and in that of the opposite relation by Ashbaugh (1975), who first suggested the solution in Erdogan et al (1973) required correction. Subsequently, Chen et al (1980) also suggested the same correction, and, in addition to Higashida and Kamada (1982), also calculated the intensity factors in agreement with those of Ashbaugh (1975). It is the results of Higashida and Kamada (1982) that feature ambiguously alongside and in contrast with those of Erdogan et al (1973) in a handbook of stress intensity solutions (Murakami, 1987, p. 167).…”

“…Subsequently, Chen et al (1980) also suggested the same correction, and, in addition to Higashida and Kamada (1982), also calculated the intensity factors in agreement with those of Ashbaugh (1975). It is the results of Higashida and Kamada (1982) that feature ambiguously alongside and in contrast with those of Erdogan et al (1973) in a handbook of stress intensity solutions (Murakami, 1987, p. 167).…”