Modeling Slip Gradients and Internal Stresses in Crystalline Microstructures with Distributed Defects

Abstract

This thesis addresses a formulation and investigation of length-scale effects in the presence of heterogeneities and internal stresses in continuum crystal plasticity. A three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses is developed. The resulting internal stress is discussed in terms of the long-range dislocation-dislocation and dislocation-boundaries elastic interactions and physical and mathematical origins of corresponding length scales are argued. It will show that internal stress is a function of spatial variation of GND density in absence of finite boundaries where internal stress arises from GND ?GND long range elastic interactions. However in presence of finite boundaries such as free surfaces or interfaces, additional source of internal stress is present due to long range interaction between GND and boundaries. Using these approaches, we investigate several important examples that mimic real problems where internal stresses play an important role in mediating the overall response under monotonic and cyclic loading.