On the origin of microstructure self-similarity in severe plastic deformation

In a series of papers by D. Hughes, N. Hansen and their coauthors it was established that laminar microstructures developed in compression and rolling possess a surprising property: probability distribution of misorientations referred to the average misorientation is universal, i.e. slightly dependent on the material and the magnitude of plastic deformation. A similar fact was found for lamina spacings. This paper aims to derive these probability distributions from "…rst principles". As such two propositions are suggested: microstructures that are compatible with the prescribed physical and geometrical conditions are equiprobable, and the product misorientation spacing cannot be smaller than some number. It turns out that the low bound for misorientation spacing can be chosen in such a way that the experimental and theoretical curves coincide. The corresponding value of the low bound is in a nanoscale range.