A method for predicting the state of stress in a body consisting of two isotropic materials including the intersection of the interface with a stress-free boundary is presented. The prediction of the so-called 'free edge stress' is accomplished using a stress intensity parameter. The solution, which addresses arbitrary two-dimensional geometries with mechanical and thermal loading and plane strain or plane stress behavior, couples the finite element method to a singular integral representation of a dislocation. The finite element solution of the two layers, which allows for independent displacement of the two layers based on the applied loading, is added to the solution of distributed dislocations along the interface of two semi-infinite layers. Coupling of the two solutions occurs along the interface and at the finite boundary. At the interface, the two solutions add together to provide for no relative displacement between the two layers. At the finite boundary, correction forces equal to the opposite of the tractions that are produced by the semi-infinite dislocation solution must be added to the finite element model. The unknowns in the problem are the finite element displacements and the dislocation density along the interface. The stress intensity factors at the free edge interface are found directly from the singular integral solution, i.e. the unknown amplitude of the dislocation density at the edge.
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