Nonlocal Continuum Theory for Dislocation and Fracture.
PRINCETON UNIV NJ DEPT OF CIVIL ENGINEERING
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By means of linear theory of nonlocal elasticity, solutions are given for some Voltera dislocations situated in an elastic solid. The stress fields are determined for screw and edge dislocations. The stresses and elastic energy are devoid of usual singularities predicted by the classical local elasticity. A theory is developed for continuous distributions of dislocations on the basis of nonlocal incompatible elasticity. Stress fields are given for volume, surface and line distributions of dislocations. Celebrated Peach-Koehler formula is modified to include nonlocal Greens functions. The stress fields for three- and two-dimensional cases and for the anti-plane strain are determined for line distributions. Calculations are carried out for the uniform distributions of edge and crew dislocations along a straight line segment. By means of the maximum stress hypothesis, a fracture criteria is introduced. Calculated theoretical strengths are in good agreement with those based on the atomic models. Reduction of material strength with the presence of dislocation line and the maximum number of dislocations are given. Author