On the Application of Lewis’s Law to Grain Sections of Polycrystalline Metallic Materials

The aim of the present study was to verify the Lewis law for microstructures of a wide range of metallic polycrystals subjected to various degrees of plastic deformation and heat treatment. The differences in the technological history of the specimens resulted in various grain shapes (quantified in terms of the ratio of dmax/d2, where dmax stands for maximum cell chord and d2 is the equivalent circle diameter). The cell structures also differed in their mean values of grain-section area, E(A), and the diversity/spread in grain-section size [quantified by using the grain-section area coefficient of variation, CV(A)]. An analysis of the data points has led to the conclusion that the they can be best approximated by two linear relations with different values of Lewis slopes, α. The first approximates the data for grains with a number of edges from 2 to 5 and the second one from 6 upward. It is suggested here that the existence of thee two regions can be rationalized by the distinct geometry/physical properties of the large grains, which are expected to have a number of edges larger than 6.