On the stress fields of crystal dislocations with fractal geometry

The elastic stress fields of single irregularly tangled dislocations were simulated numerically. The dislocations had fractal dimensions within the range 1.0 < D < 1.5. The results were compared with the stress fields associated with straight dislocations (D = 1). To calculate the stress fields with a high spatial resolution the dislocation lines were subdivided into small segments. The results confirm that the stress fields of tangled dislocations depend considerably on their fractal dimension. The maximum shear stress generated per unit length of a single dislocation decreases with an increase in fractal dimension of its dislocation line.