Lognormal Distribution of Local Strain: A Universal Law of Plastic Deformation in Material.

Abstract

Given the infinite diversity of microstructural inhomogeneity, the variation in spatial distribution of local strain could be infinite. However, this study finds that the statistical distribution of local strain universally follows a lognormal distribution irrespective of phase content and deformation mechanism. Moreover, this universal law is proved conditional upon the macroscopic homogeneity of deformation on the statistical window scale, equivalent to the equality between the macrostrain calculated from the displacements at the window corners and the average of the local strain. The discovery of a lognormal distribution law suggests the existence of a minimum statistical representative window (MSRW) size that is characteristic for each material. Explorations on the dependence of MSRW size on the microstructure, deformation mechanism, and strain magnitude are expected to add new dimensions to understanding of the relationship between microstructure and mechanical properties.