The elastic stress fields of dislocations in such a lattice were investigated by treating the dislocations as line defects which were embedded in an otherwise linear isotropic elastic medium. The dislocation lines were decomposed into piece-wise straight segments which had a length of a/2(110) or a/2(112). The dislocations had a dimension that ranged from 1.0 to 1.26. The stress fields of dislocations with a non-Euclidean geometry (dimension greater than 1) were compared with the stress fields of straight dislocations (with a dimension of 1). The simulations revealed that both the maximum and minimum principal stresses, and the maximum shearing stress, of irregularly tangled dislocations depended upon their fractal dimension. The increase in dimension was achieved by randomly adding screw-type or edge-type segments to the initially straight dislocation. Although this led to an increase in the dislocation density, the maximum stresses remained constant with increasing dimension. When scaled by the length of the dislocation line, the maximum stresses even decreased with increasing dimension. Thus, increasing the dimension from 1 to 1.1 led to a 50% degradation of the maximum shearing stress.

Numerical Three-Dimensional Simulations of the Stress Fields of Dislocations in Face-Centered Cubic Crystals. D.Raabe: Modelling and Simulation in Materials Science and Engineering, 1995, 3[5], 655-64