A continuum model for the anisotropic creep of single crystal nickel-based superalloys

In this paper, we extend the constitutive theory developed by Prasad et al. [Prasad SC, Rao IJ, Rajagopal KR. A continuum model for the creep of single crystal nickel-base superalloys. Acta Mater 2005;53(3):669–79], to describe the creep anisotropy associated with crystallographic orientation in single crystal nickel-based superalloys. The constitutive theory is cast within a general thermodynamic framework that has been developed to describe the response of materials capable of existing in multiple stress free configurations (“natural configurations”). Central to the theory is the prescription of the forms for the stored energy and rate of dissipation functions. The stored energy reflects the fact that the elastic response exhibits cubic symmetry. The model takes into account the fact that the symmetry of single crystals does not change with inelastic deformation. The rate of dissipation function is also chosen to be anisotropic, in that it reflects invariance to transformations that belong to the cubic symmetry group. The model is used to simulate uniaxial creep of single crystal nickel-based superalloy CMSX-4 for loading along the 〈0 0 1〉, 〈1 1 1〉 and 〈0 1 1〉 orientations. The predictions of the theory agree well with the experimental data.