Generalized Disclination Mechanics with Couple Stress

The objective of this work is to develop and implement a computational algorithm for calculating stress and moment-stress fields induced by line and planar defects, such as dislocations and phase/grain boundaries, represented as g.disclinations, as well as their evolution. This results in coupled plasticity and interface motion, fully coupled to stress, couple stress and applied boundary conditions. To achieve this the continuum approach for small deformations will be considered, following the formulation outlined in [AF15] extended herein in the thermodynamics to accommodate physically necessary ingredients that arose in the modeling in [ZA18, ZAP18]. Constitutive relations will be derived from kinematics, balance laws and from the use of the second law of thermodynamics in global form. Kinematic

relations will also inform the evolution of fields, among them the defect fields themselves and the plastic deformation field. One of the challenges presented by this approach is the inclusion of couple stresses [Tou64], and the consequent

treatment of 4th order systems arising from the equations of balance of linear momentum and angular momentum. In order to deal with these equations the classic FEM approach is replaced by iso-geometric analysis (IGA), as proposed

by [HCB05]. The motivation to use couple stresses in the model is twofold. First, based on [Her51, Mul56] and subsequent work, there is a widely used and successful framework for grain-boundary evolution based on misorientation dependent energy density without any consideration of stresses or elastic deformation. This approach indicates that grain boundary evolution is dependent not on stresses on the boundary, but on the couples/torques acting on it. Second, motivated by the analysis of shear-coupled grain boundary migration performed by [TCH+17] and the work done by [TCF14], the inclusion of couple stresses have been shown to model the

experimentally observed phenomenon of shear-coupled grain boundary migration attributable to disclination defects. Complementary to these couple-stress driven approaches to interface migration, it is shown in this thesis that the new thermodynamic dependencies allow for the evolution of eigenwall-modeled boundaries to migrate driven simply by applied stress, which also permits the treatment of

shear-coupled grain boundary migration. The coupling of the dislocation density with the eigenwall allows for the capturing of the shear parallel to the grain boundary

that is concomitant with the grain boundary migration, as has been observed experimentally and through molecular dynamics.