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Some Limitations of Dislocation Walls as Models for Plastic Boundary Layers

It has recently become popular to analyze the behavior of excess dislocations in plastic deformation under the assumption that such dislocations are arranged into walls with periodic dislocation spacing along the wall direction. This assumption is made plausible by the fact that periodic walls represent minimum energy arrangements for dislocations of the same sign, and it allows to use the analytically known short-ranged stress fields of such walls for analyzing the structure of plastic boundary layers. Here we show that unfortunately both the idea that dislocation walls are low-energy configurations and the properties of their interactions depend critically on the assumption of a periodic arrangement of dislocations within the walls. Once this assumption is replaced by a random arrangement, the properties of dislocation walls change completely.