  Creep in single crystal Nickel-based superalloys has been a topic of interest
since decades, and nowadays simulations are more and more able to complement
experiments. In these alloys, the $\gamma/\gamma'$ phase microstructure
co-evolves with the system of dislocations under load, and understanding the
mutual interactions is essential for understanding the resulting creep
properties. Predictive modeling thus requires multiphysics frameworks capable
of modeling and simulating both the phase and defect microstructures. To do so,
we formulate a coupled model of phase-field evolution and continuum dislocation
dynamics which adequately accounts for both statistically stored and
geometrically necessary dislocations. The simulated $\gamma/\gamma'$ phase
microstructure with four $\gamma'$ variants and co-evolving dislocation
microstructure is found to be in good agreement with experimental observations.
The creep strain curve is obtained as a natural by-product of the
microstructure evolution equations without the need for additional parameter
fitting. We perform simulations of $\gamma/\gamma'$ evolution for different
dislocation densities and establish the driving forces for microstructure
evolution by analyzing in detail the changes in different contributions to the
elastic and chemical energy density. Together with comparisons between
simulated and experimental creep curves this investigation reveals the
mechanisms controlling the process of directional coarsening (rafting) and
demonstrates that the kinetics of rafting significantly depends on
characteristics of the dislocation microstructure. In addition to rafting under
constant load, we investigate the effect of changes in loading conditions and
explore the possibility of improving creep properties by pre-rafting along a
different loading path.
