An Internal Variable Approach to Inelastic Deformation Including Structural Superplasticity

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Abstract
An internal variable theory has been proposed to account for the essential microstructures during inelastic deformation. The framework of the theory is built on the basis of well known dislocation dynamics to provide the concept of an internal strain tensor as the most fundamental deformation state variable. The plastic and inelastic strain rate tensors are then naturally defined and also a kinematics relation among them can further be derived from the time rate of change of this internal strain tensor, which in fact accounts for the evolution of microstructures during inelastic deformation. To complete the theory, the constitutive relations between the various stress variables and their conjugate deformation rate variables are then derived based on the dislocation kinetics. The theory is then further extended to describe the structural superplasticity, taking this slip zone model with dislocation pile-ups as the major accommodation mechanism for grain boundary sliding. The experimental results obtained from the various crystalline materials are then presented and compared with each other in relation to the internal variable theory for inelastic deformation.