Ph.D. Thesis Defense by John D. Clayton
Friday, October 4, 2002

(Dr. David L. McDowell, advisor)

"Homogenization and Incompatibility Fields in Finite Strain Elastoplasticity"

Abstract

A collection of multiscale models based upon explicit volume averaging methods describes the mechanical behavior of metallic single crystals and polycrystalline aggregates. A three-term multiplicative decomposition of the deformation gradient is derived for damage-free crystals. Included is an elastic term, related to the average applied stress and average lattice rotation in the polycrystalline aggregate, a plastic term, defined as the volume-averaged plastic deformation contribution from constituent grains, and a third “meso-incompatibility” term—absent in classical plasticity theories—correlating positively with residual elastic energy due to intergranular incompatibility. Finite element calculations invoking classical crystal elastoviscoplasticity theory within single crystals of the aggregate validate the model and demonstrate the reduction of intergranular incompatibility via specification of grain boundary misorientations.

Next, upon invocation of the generalized Gauss’s theorem, a hybrid multiplicative-additive decomposition for the deformation gradient is derived to simultaneously describe elasticity, heterogeneous plasticity, and anisotropic damage evolution within a polycrystalline aggregate. The kinematic description and multiscale framework enable formulation of novel failure criteria supplementing traditional damage measures such as porosity and crack density. Finite element calculations employing classical crystal elastoviscoplasticity theory in conjunction with a cohesive zone model of intergranular fracture accompany the theoretical framework.

Additionally, fundamental aspects of a constitutive model for single crystalline elastoviscoplasticity are developed following consideration of the finite deformation mechanics of discrete and continuously distributed dislocations. This model differs from classical crystal plasticity theories in three notable ways: inclusion of the meso-incompatibility deformation term in the kinematics, thermodynamics, and evolution laws; consideration of nonlocal effects stemming from the density of geometrically necessary dislocations couched in terms of the second gradient of the elastic deformation; and usage of the resolved Eshelby stress mapped to the plastic intermediate configuration as a driving force for shearing rates on individual glide systems.