Numerical simulations were made of the 3-dimensional elastic stress fields which were associated with finite ordered and weakly disordered dislocation walls. The walls consisted of discrete dislocations which were regarded as being piece-wise linear defects that were embedded within an otherwise isotropic elastic medium. The dislocation line vectors and Burgers vectors made up a simple cubic lattice. The dislocations were sub-divided into small segments. Two basic types of dislocation wall were studied. These were a finite low-angle tilt boundary, and a finite dislocation cell which consisted of 45 edge dislocation dipoles. The tilt boundary consisted of 100 straight parallel dislocations. The dipole wall contained 100 alternating anti-parallel edge dislocations. The effect of weak spatial disorder on their stress fields was investigated for both wall types. For this purpose, non-straight dislocations with a fractal dimension of 1.05 were used instead of straight dislocations. The results confirmed that weak spatial disorder appreciably affected the stress field in the vicinity of the dislocation walls. However, the behavior of the long-range stress was not determined mainly by the spatial disorder of the dislocation lines but by the finite geometry of the walls. The maximum shearing stress which was associated with the finite tilt boundary revealed a strong non-exponential decay in the immediate vicinity of the wall. A local minimum occurred within a distance which exceeded the dislocation spacing in the wall by less than an order of magnitude. A local stress maximum appeared within a distance that exceeded the dislocation spacing by about 2 orders of magnitude. A long-range stress was predicted which corresponded to the solution that was obtained for a corresponding super-dislocation with a Burgers vector which was 100 times that of the dislocations in the walls. The stress field of the dipole wall was non-negligible, and exhibited short-range and intermediate-range stress components which decayed inversely as the distance from the wall.

D.Raabe: Physica Status Solidi B, 1995, 192[1], 23-36