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Modeling slip zones with triangular dislocation elements

DEPARTMENT OF CIVIL ENGINEERING NORTHWESTERN UNIVERSITY, EVANSTON, IL 60208

Abstract

We derive in algebraic form the displacement and stress fields produced by a triangular element of constant slip by superposing the solution of Comninou and Dundurs (1975) for an angular dislocation in an elastic half-space. Triangular elements are more flexible for simulating complex geometries than the rectangular elements widely used for modeling slip zones as a superposition of constant slip elements. As an example, we use triangular elements to determine the distribution of slip on a planar surface caused by a prescribed stress drop. Because the slip in elements is uniform, the slip does not taper to zero at the edges of the slipping zone. Consequently, the strain energy in volumes containing the slip zone edge and the stress drop averaged over the slip zone are unbounded. To investigate the effects of these features, we compare our results using uniform slip elements with those from the more elaborate procedure of Wu et al. (1991) that takes proper account of stress singularity at the edge of the slipping zone. The comparison indicates that, for a prescribed uniform stress drop, the uniform slip model slightly overestimates the free surface displacements. The predicted slip surface displacements are more severely overestimated, particularly near the edges of the slipping zone. Nevertheless, extrapolation of the slip surface displacements yields values for the stress intensity factors, the coefficients of the singular stresses near the edge of a crack. The values of stress intensity factors are within 10% of those results obtained by Wu et al. (1991) for the same number of elements.

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