  In the present work, we propose a novel model coupling phase-field,
dislocation density based plasticity and damage. The dislocation density
governing equations are constructed based on evolutions of mobile and immobile
dislocations. Mechanisms including dislocation multiplication, annihilation,
mobile-immobile transfer due to dislocation interactions and block of
interfaces are incorporated in the model. Especially, the "swallow-gap" problem
surrounding the coarsened second phase, which often appears in dislocation and
phase-field coupled simulations, is solved in the present model. Moreover, the
phenomenon of dislocation cutting into the second phase during tertiary creep,
which has rarely been considered in previous phase-field simulations of single
crystal superalloys, is successfully captured in the present model with the
coupling of damage. The long range stresses induced by external loading,
coherent interface misfit, plastic activity and damage, as well as the short
range stresses induced by antiphase boundary, dislocation line tension and
forest dislocation trapping are considered in the dynamics of the model. High
temperature $\langle 001 \rangle$ creep simulations of single crystal
superalloys under 200 MPa and 350 MPa are conducted using the coupled model and
compared with experiments. The results show that simulated phase
microstructures, dislocations and creep properties principally agree with
experiments during the whole creep stage, in terms of both microscopic and
macroscopic features.
