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Abstract
The basic theory for athermal dislocation storage and work hardening is revisited. The mean free slip length is redefined enabling a straightforward geometrical interpretation that can be directly compared to the grain size. It is realized that this geometrical mean free slip length is larger than the typical grain size of commercial alloys, i.e. linear stage II work hardening is predicted only for single crystals or very coarse-grained pure metals, in the athermal limit at sufficiently low temperatures. The new theory suggests that the distribution of obstacles in the slip plane can be represented by two parameters, a fractal dimension D and the density of obstacles n per area. For a given geometrical mean free slip length it is derived that the athermal storage rate of dislocations is proportional to
and to
. A new natural definition of a fractal dimension is proposed, enabling its calculation directly from discrete dislocation simulations. An estimate of D is given, based on line-tension simulations of a dislocation loop expanding through an array of obstacles of random cutting strengths.
Disclosure statement
No potential conflict of interest was reported by the author.