Abstract
The stress field is obtained in an isotropic elastic layer containing an edge dislocation. The dislocation solution is used to derive integral equations for a cracked layer. These are a set of Cauchy singular integral equations which are solved numerically for the density of dislocations on a crack surface. The density of dislocations is utilized to determine stress components in the vicinity of a crack tip. The stress field contains singular as well as non-singular terms. Assuming small scale yielding, the von-Mises yield criterion is adopted to define a plastic region around a crack tip under the plane-stress situation. Several examples are solved and the plastic region developed by a crack with different orientations and loadings is specified. Moreover, in another example, plastic regions around the tips of two interacting cracks are defined. The geometry of the plastic regions is utilized to obtain a crack propagation angle.
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