Anistropic creep modeling based on elastic projection operators with applications to CMSX-4 superalloy

Abstract

This paper presents a unified framework for creep modeling of anisotropic materials, which is specified in more detail to the cases of isotropy, cubic symmetry and transverse isotropy. To this end an additive decomposition of the elastic and inelastic strain tensors into dilational and isochoric Kelvin modes is assumed. Each of these modes is obtained from fourth-order projection operators, resulting from solution of the eigenvalue problem for the anisotropic fourth-order elasticity tensor. The amount of strain rate for each mode is modeled with a Norton-type ansatz in terms of an equivalent stress. The formulation for the equivalent stress in terms of quadratic forms with aid of the projection operators is compared with polynomial expressions from the literature. The experimental phenomenon of primary creep is taken into account by a back stress tensor of Armstrong–Frederick type, which is also decomposed into Kelvin modes. As a consequence of the mode decomposition the classical radial-return method of isotropic elasto-plasticity is generalized to the different cases of anisotropy. Furthermore the implications on parameter identification are addressed. Two numerical examples are concerned with a superalloy CMSX-4.