Topological transformation of grains in superplasticity-like deformation

Abstract

The maintenance of the equiaxed shape of grains after a large deformation is a common feature of superplasticity in polycrystalline solids. This feature is similar to that seen in the deformation of soap froth. The topological transformation of the grains was analyzed by using the Surface Evolver which simulated the three-dimensional simple shearing flow of soap froth. In this model the equiaxed shape of the grains could be maintained in a disordered system of N grains when both face-creation switching and face-elimination switching occurred αγN times in shear strain γ. The simulation gave α-values from 4.9 to 4.5 in the monodispersed structure and α=4.7 in the polydispersed structure. The strain, which is associated with grain switching, is represented by γ″=Δ F/ αN, where Δ F is the mean cumulative number of grain switchings. The intragranular strain, which is related to the aspect ratio of the grains, is represented by γ′= γ− γ″. The back stress by boundary tension was proportional to γ′. It can act to restore the equiaxed shape, and is one of the origins of anelasticity.