A microstructure-sensitive constitutive modeling of the inelastic behavior of single crystal nickel-based superalloys at very high temperature

The prediction of the viscoplastic behavior of nickel-based single crystal superalloys remains a challenging issue due to the complex loadings encountered in aeronautical engine components such as high pressure turbine blades. Under particular in-service conditions, these materials may experience temperature cycles which promote the dissolution of the strengthening γ′ phase of the material on (over)heating, and subsequent precipitation on cooling, leading to a transient viscoplastic behavior. Within this context, a model was recently developed by Cormier and Cailletaud (2010) to fulfill the effects of fast microstructure evolutions occurring upon high temperature non-isothermal loadings. New internal variables were introduced in the crystal plasticity framework to take into account microstructure evolutions such as γ′ dissolution/precipitation and dislocation recovery processes which are known to control the creep behavior and life. Nevertheless, this model did not consider the γ′ directional coarsening, one of the main microstructural evolutions occurring specifically at high temperature. In addition, no kinematic hardening was considered to describe the mechanical behavior, leading to a poor description of cyclic loadings. This paper details the development of a new model by introducing new internal variables for both modeling the γ′ directional coarsening and the evolutions of isotropic and kinematic hardening under complex loading paths. This model was calibrated using monotonous and cyclic experiments performed on [0 0 1] oriented single-crystal samples and both under isothermal and non-isothermal conditions. Thereby, it is able to predict microstructural evolutions for complex thermal and mechanical loadings as well as internal stress evolutions whatever the thermomechanical history. The model efficiency was highlighted by comparing FEM simulation and experimental results of a non-isothermal creep test on a notched sample (i.e. under complex mechanical stress state).