Problems of Orthotropic Plastic Constitutive Models: Non-Associated Flow and Evolution of Anisotropy.

Two main topics are addressed in this thesis for anisotropic plastic behavior, e.g. textured polycrystals: (i) non-associated plastic flow and (ii) deformation-induced evolution of microstructure. We consider a class of elastic-plastic materials that possess local orthotropic symmetry which is represented in terms of second-order orientation tensors. In developing constitutive equations, significant use is made of representation theory for functions of tensors (Wang, 1969, 1970; Smith, 1969, 1970). Recent developments in multiscale modeling have unequivocally demonstrated that plastic flow in a wide range of crystalline materials is non-associative (i.e., distinct yield and flow functions) due to the effects of non-glide stresses on the motion of dislocations and slip. As a consequence, experimental observations of tension and compression asymmetries are widely approached. To describe orthotropic, non-associated behavior for polycrystals, yield and flow functions are developed based upon representation theory. Anisotropic plastic flow is commonplace for all materials possessing non-random microstructures. The second part of work focuses on the development of anisotropic elastic-plastic constitutive models to account microstructural evolution. Examples of material systems include polycrystals, whisker-reinforced composites, polymers, as well as complex viscoplastic fluids. For persistent orthotropic behavior, microstructural evolution is represented by the rotation of orthonormal vectors, which is governed by the constitutive relations for plastic spin. Representations for scalar- and tensor-valued functions of tensors are also utilized to develop phenomenological constitutive relations for plastic spin. Good agreement is demonstrated with experimental data for microstructural evolution in textured polycrystals. The effects of both non-associated flow and evolution of microstructure on strain localization are investigated. From the analyses of stress and load maxima and bifurcation from uniform state of deformation, significant effects are predicted. Furthermore, to investigate the full three-dimensional nature of necking instabilities in sheets, the constitutive model for non-associated flow with microstructural evolution has been implemented in a finite element program (Abaqus). The finite element simulations further demonstrate the strong effects of anisotropic non-associated flow and microstructural evolution on both the onset of localization and post-bifurcation deformation.