SUMMARY

The emergence of engineering components and material systems with microstructural features that have characteristic dimensions reaching into the submicron and nanometer regime has driven the need to develop advanced material models capable of describing their often unique and size-dependent behavior as compared to more conventional engineering systems/materials. Classical continuum models, being devoid of a length scale in the constitutive formulation, lack the ability to capture size-dependent mechanical behavior. In polycrystalline metals, the grain size has long been considered a critical microstructural dimension related to the strength of the material. For example, the Hall-Petch effect is an empirically derived relationship connecting the mean grain size of a polycrystal to its yield strength. Central to many of the physical explanations of this relationship is the role that grain boundaries (GBs) play in mediating plastic deformation via interaction with lattice dislocations. Likewise, explanations of the unique mechanical response of nanocrystalline materials have been rationalized in terms of GB-related micro-deformation processes. Accordingly, there is a need to develop physically-based models capable of predicting size-dependent mechanical behavior, and including enriched descriptions of GBs within a crystal plasticity framework. In this work, micropolar theory is pursued to achieve these goals as an alternative to the more common slip gradient-based approaches to generalized crystal plasticity. Existing models of micropolar single crystal plasticity are extended, and new formulations are proposed. Specifically, the role GBs play in slip obstruction, absorption, and transmission will be considered. The development of such models is necessary to accurately design and model polycrystals for advanced applications, as well as for corroborating results with simulations of higher spatial resolution.