Modeling inelasticity in materials with application to superplasticity

The focus of this dissertation is on developing a continuum model of the superplastic response of fine grained materials. Inelasticity in fine structured materials occurs in part due to grain boundary sliding between adjacent grains or between grain groups. In addition, the grain boundary migrates in a direction normal to itself. Superplasticity is accompanied by static grain growth and deformation induced grain growth. Most of the specimen deformation can be attributed to the grain boundary shear. In this dissertation, the broad focus is to develop a continuum framework based on the notion of natural configurations of a material. The idea of natural configurations is embodied by evolving internal variables that are mathematically represented as tensor fields.; The present framework has provisions for an explicit treatment of material microstructure and seeks to augment continuum models with information about the changing microstructure. The model is based on the classical crystal plasticity approach and the viscoplasticity approach based on overstress. The attendant effects of grain growth and hardening are included. A finite strain finite element model is developed to perform numerical studies. The tangent stiffness is derived explicitly. The numerical approach is a combination of the total Lagrangian and updated Lagrangian techniques. This mixed approach is facilitated by the underlying theory of evolving configurations. One of the central aims of the research is to develop an effective multiaxial model based on the kinematics of deformation that is special to superplasticity. It is expected that the present study will aid further studies into the phenomenon of superplasticity of composite media, and to develop accurate multiaxial models that derive from simple uniaxial experimental data. The framework has been applied successfully in crystal plasticity studies previously and has potential applications in areas such as granular media and powder compaction.