Crystal plasticity models: dislocation based

This chapter is devoted to the class of constitutive models for single-crystal nickel-base superalloys that are motivated by dislocation mechanics. The focus lies on alloys with cuboidal precipitates of the γ′ phase with a large volume fraction (>40%) and on models that are amenable to conventional structural analysis by finite elements. It starts with a short summary of the most important results in dislocation mechanics and presents the different ingredients required to formulate physically-based constitutive laws for these alloys. In particular, the formulation of evolution laws for the dislocation densities, the mathematical modeling of the known deformation mechanisms, and the computation of the internal stresses at the microstructure level are discussed.