A phase field model incorporating strain gradient viscoplasticity: Application to rafting in Ni-base superalloys

The first formulation of a phase field model accounting for size-dependent viscoplasticity is developed to study materials in which microstructure evolution and viscoplastic behavior are strongly coupled. Plasticity is introduced using a continuum strain gradient formalism which captures the size effect of the viscoplastic behavior. First, the influence of this size effect on the mechanical behavior of the material is discussed in static microstructures. Then, the dynamic coupling between microstructure evolution and viscoplastic activity is addressed and illustrated by the rafting of the microstructure observed in Ni-base superalloys under creep conditions. It is found that the plastic size effect has only a moderate impact on the shape of the rafts but is crucial to reproduce the macroscopic mechanical behavior of that particular material.