Numerical three-dimensional simulations of the stress fields of dislocations in face-centred cubic crystals

Abstract

The elastic stress fields of crystal dislocations in a face-centred cubic lattice are investigated using numerical three-dimensional simulations. The dislocations are treated as line defects embedded in an otherwise linear isotropic elastic medium. The dislocation lines are decomposed into piecewise straight segments having a length of (a/2)(110) or (a/2)(112). The dislocations have dimensions within the range 1.0<or=D<or=1.26. The stress fields of dislocations with non-Euclidean geometry (D>1) are compared to the stress fields of straight dislocations (D=1). The simulations substantiate that both the maximum and the minimum principal stresses and the maximum shearing stress of irregularly tangled dislocations depend on their fractal dimension. The increase in dimension is achieved by randomly adding screw- or edge-type segments to the initially straight dislocation. Although this procedure leads to an increase in the dislocation density, the maximum stresses remain constant with increasing dimension. If expressed per unit length of the dislocation line the maximum stresses even decrease with increase in the dimension. Increasing D=1 to D=1.1 leads to a degradation of the maximum shearing stress by 50%.