A constitutive model for anisotropic materials based on Neuber’s rule Original Research Article

Phenomenological approaches to fatigue damage prediction often rely on the assessment of local stress–strain concentrations in structural components. To avoid complex plastic analysis in fatigue assessment, approximate constitutive models have been developed to evaluate the local inelastic response of the material and which allow for an adequate lifetime prediction in a competitive time. One of these approximate methods is the Neuber rule, which has originally been elaborated for the uniaxial loading state of isotropic materials. This paper addresses an approximate method for multiaxial loading of anisotropic materials. The proposed approach is based on a tensorial formulation of the Ramberg–Osgood equation and a generalization of the uniaxial Neuber hypothesis by assuming the equivalence of the deviatoric strain energy density for the elastic and inelastic solution in the notch region. After a decomposition of the stress tensor into a normalized direction tensor and a stress invariant, a nonlinear expression is obtained which can be iterated for the unknown inelastic stress state. It is shown that the proposed anisotropic Neuber rule includes the multiaxial isotropic and the classical uniaxial formulation as special cases. Furthermore, aspects of parameter identification are discussed for directionally solidified Nickel-based superalloys with transverse isotropic properties and single crystal materials with cubic anisotropy. Two numerical examples demonstrate the applicability of the proposed approach.