Scaling Properties of Dislocation Simulations in the Similitude Regime

Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation patterns. Here we discuss the origin of these properties, which can be related to generic invariance properties of the equations of evolution of discrete dislocation systems, and their implications for a wide class of models of dislocation microstructure evolution. We demonstrate that under certain conditions dislocation simulations carried out at different stress, dislocation density, and strain rate can be considered as equivalent, and we study the range of deformation conditions ("similitude regime") over which this equivalence can be expected to hold. In addition, we discuss the restrictions imposed by the formulated invariance properties for density-based, nonlocal or stochastic models of dislocation microstructure evolution, and for dislocation patterns and size effects.