The Neighbor Switching Mechanism of Superplastic Deformation

At one time the notion that crystal plasticity resulted from the simultaneous motion of lattice planes over one another was entertained. This idea was displaced by the concept that relative atomic motions occur sequentially when dislocations move through the crystal. Similarly, McLean suggested that grains switch neighbors sequentially in a polycrystalline material undergoing superplastic flow. Morral and Ashby observed that the neighbor switching reactions in a froth occurred at irregular cells, and that these irregularities were associated with dislocations in the cellular array. They introduced cellular dislocation glide as a model for superplastic flow, and suggested that if the concentration of these defects required to make the froth flow increased with the flow stress, then the froth would have a non-Newtonian viscosity, like many superplastic materials. Cahn and Padawer pointed out that cellular dislocation climb was used as a model for grain growth by Hillert; this process results in the elimination of cells from the froth. Sato, Kuribayashi and Horiuchi used cellular dislocation climb to model both grain motion and the deformation-enhanced grain growth which can accompany superplastic flow. Here, the neighbor switching mechanism of superplastic deformation is developed as a topic in dislocation theory. The compatibility theory of dislocations is developed at an introductory level with exterior calculus. "Compatibility" of a cellular array corresponds to statements, a la Rivier, about the distribution of edges amongst the cells. The theory of dislocation motion, or crystal plasticity, is also developed with exterior calculus. Morral and Ashby's constitutive relationship for superplastic flow is analyzed and two models for deformation-enhanced grain growth are developed. The constitutive relationship and grain growth kinetics for superplastic flow are illustrated by modelling the behavior exhibited by single phase (Sn-1% Bi) and quasi -single phase (7475 Al) materials. It is suggested that the grain growth kinetics are strain rate dependent: kinetics in one strain rate regime give way to different kinetics when the strain rate is changed.