An anisotropic elastic–plastic model for predicting the rafting behavior in Ni-based single crystal superalloys

Abstract

An anisotropic elastic–plastic model was developed to investigate the rafting behavior of Ni-based single crystal superalloys. This model was developed by introducing the plastic constitutive equation of face-centered cubic (FCC) single crystal in the framework of Eshelby's equivalent inclusion theory. The Hill's equivalent stress was calculated when applying a tensile or compressive loading along the [001] direction. The calculated results successfully predict the rafting direction for alloys with a positive or negative mismatch, consistent with pervious experimental and theoretical studies. Moreover, based on this model, the mismatch degree and the elastic-constant differences of the matrix and precipitate phases and their effects on the speed of rafting are carefully discussed. Regardless of a positive or negative mismatch alloy, the larger absolute value of mismatch degree can more effectively accelerate the process of rafting in Ni-based single crystal superalloys. However, when the alloys enter the plastic deformation stage, the variation in mismatch degree slightly affects the speed of rafting. For the elastic-constant differences (C11r′−C11r,C12r′−C12r,and C44r′−C44r), the smaller the value of C11r′−C11r, or the greater the value of C12r′−C12r, the more effective the acceleration of γ′ rafting; whereas the value of C44r′−C44r has no effect on the rafting of alloys. The research results provide a new theory and method for studying the rafting behavior and its influencing factors for Ni-based single crystal superalloys.