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

In a series of papers by Hughes, 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 “first 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 are close. The corresponding value of the low bound is in a nanoscale range.