A Strain Rate Sensitive Formulation to Account for the Effect of \(\gamma ^{\prime }\) Rafting on the High Temperature Mechanical Properties of Ni-Based Single Crystal Superalloys

The **Polystar** model was recently developed to fulfill the effects of possible fast microstructure evolutions occurring upon high temperature non-isothermal loadings. New internal variables were introduced in a crystal plasticity framework to take into account microstructure evolutions such as \(\gamma ^{\prime }\) dissolution/precipitation and dislocation recovery processes, and their effects on the creep behavior and creep life. Nevertheless, this model does not take into account one of the main microstructural evolutions occurring specifically at high temperature, the \(\gamma ^{\prime }\) directional coarsening. Fedelich and Tinga have already proposed models respectively based on a modification of the kinematic hardening and on the level of the von Mises stress. Nevertheless, if the Fedelich’s model is implicitly strain rate sensitive, improvements have to be performed for strain controlled tests under fast conditions for which such a model may overestimates the \(\gamma \) channel width evolutions. A new formulation has been proposed to explicitly account for such a strain rate sensitivity and was successfully implemented in the **Polystar** model. The effect of \(\gamma ^{\prime }\) rafting on the mechanical behavior is well reproduced for both cyclic and monotonic tension tests.