Dislocation Pile-Up in Half-Space

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Abstract
If an obstacle exists in the vicinity of the free surface of a half‐space and a stress field is applied in such a manner that dislocations are pushed towards the obstacle, an array of dislocations then piles up into an equilibrium distribution against the obstacle. The distributions of dislocations are obtained by the Wiener‐Hopf technique for the edge and screw dislocations. The total strength of dislocations (Burgers vector multiplied by the number of dislocations) distributed in the distance L is calculated as 0.92π(1−v)σAL/G for edge dislocations and 2σAL/G for screw dislocations, where G, v are the shear modulus and Poisson ratio respectively and σA is the applied stress. The result can be applied to crack problems. The above two numbers for the total strength of dislocations give the crack openings at the free surface for the extensional mode and the antiplane shear mode of fracture, respectively.

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