Subgrain size in view of the composite model of dislocation structure

The polygonized subgrain structure of plastically deformed metals is treated as a heterogeneous dislocation structure in terms of the composite model, and relations of the mean subgrain size to the total dislocation density and to the applied stress are investigated. The analysis supports the simple proportionality between the subgrain size d and the reciprocal applied stress σ, i.e., d = KGb/σ (K is a constant, G the shear modulus, and b the magnitude of the Burgers vector), corresponding to the principle of similitude. It suggests an interpretation of the highly dispersed values of K in different materials as a result of an influence of several parameters. The proportionality factor between d and ρ−1/2 (ρ is the total dislocation density) depends on the volume fraction of hard regions fH and takes into account that substructures with the same subgrain size can store different dislocation densities.