The objective of this study is the development of a theoretical framework for treating the flow stress response of two-phase alloys as emergent behaviour arising from fundamental dislocation interactions. To this end a field dislocation mechanics (FDM) formulation has been developed to model heterogeneous slip within a computational domain representative of a two-phase nickel-based superalloy crystal at elevated temperature. A transport equation for the statistically stored dislocation (SSD) field is presented and implemented within a plane strain finite element scheme. Elastic interactions between dislocations and the microstructure are explicitly accounted for in this formulation. The theory has been supplemented with constitutive rules for dislocation glide and climb, as well as local cutting conditions for the γ’ particles by the dislocation field. Numerical simulations show that γ’ precipitates reduced the effective dislocation mobility by both acting as discrete slip barriers and providing a drag effect through line tension. The effect of varying microstructural parameters on the crystal deformation behaviour is investigated for simple shear loading boundary conditions. It is demonstrated that slip band propagation can be simulated by the proposed FDM approach. Emergent behaviour is predicted and includes: domain size yield dependence (Hall-Petch relationship), γ’ volume fraction yield dependence (along with more complex γ’ dispersion-related yield and post-yield flow stress phenomena), and hardening related to dislocation source distribution at the grain boundary. From these simulations, scaling laws are derived. Also, the emergence of internal back stresses associated with non-homogeneous plastic deformation is predicted. Prediction of these back stresses, due to sub-grain stress partitioning across elastic/plastic zones, is an important result which can provide useful information for the calibration of phenomenological macroscale models. Validation for the presented model is provided through comparison to experimental micro-shear tests that can be found in published literature
