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Abstract A method is given for finding the equilibrium positions of a set of like dislocations in a common slip-plane under the influence of a given applied stress. Their positions are given by the roots of a certain set of orthogonal polynomials. The case of a set of free dislocations piled up against a fixed dislocation by a constant applied stress is discussed in detail and the resulting stress-distribution is compared with that produced by a crack with freely slipping surfaces.
Eshelby et al. (Sun,) studied this question.
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