Physics-based modeling of γ/γ′ microstructure evolution and creep constitutive relation for single crystal superalloy

In this study, a physics-based model is proposed to predict the γ/γ′ microstructure evolution of single crystal (SC) superalloy at medium temperature and high stress level. Considering multiple hardening mechanisms, the crystal plasticity (CP) model accounting for γ/γ′ microstructure evolution is developed to predict the creep strain. Creep fracture and interrupted tests are conducted for a kind of Nickel-based SC superalloy firstly. Based on the microscopic observation of the tested specimens, the γ/γ′ microstructure evolutions including dissolution and rafting behaviors of γ/γ′ phases are observed. Besides, the hardening mechanisms during plasticity accumulation can be revealed as the coupling of dislocation bypassing, dislocation hardening and γ′ phases shear. Based on the unit cell model (UCM), the dimensional parameters evolution of γ/γ′ phases is modeled. The Fick's law is employed to describe the dissolution of γ′ phase, and the rafting behavior is modeled based on the release of elastic-plastic energy. The diffusion coefficient is derived to consider the effects of both temperature and stress. Applying the γ/γ′ microstructure evolution as the input, the CP-based constitutive model accounting for the multiple hardening mechanisms is developed. The Orowan stress denoting the resistance of dislocation bypassing is modified to account for both horizontal and vertical channel width. Finally, the proposed model is validated by the test results. The γ/γ′ microstructure evolution model is verified by the statistical data including fraction, length and width of γ′ phases within the temperature range of 850–900 °C and stress range of 550–660 MPa. Further, the modified CP model is validated using creep strain curves within the temperature range of 760–900 °C and stress range of 500–660 MPa. The predicted results are in good agreement with the test data.