On the Applicability of Neuber’s Rule for Low-Cycle Fatigue

Neuber’s rule is commonly applied in fatigue analysis to estimate the plasticity of purely elastic FEA results. In certain cases, this is more efficient than running elastic-plastic models. However, the applicability of Neuber’s rule is not well understood for complex models and may not always be appropriate. In this paper, the applicability of Neuber’s rule is investigated. The background of Neuber’s rule is discussed, theoretical limitations are derived, and algorithmic outlines of the procedures are presented. Neuber’s plasticity correction procedure is applied to both the Ramberg-Osgood elastic-plastic constitutive relation and the advanced Chaboche isotropic/kinematic nonlinear hardening relation. Throughout the manuscript, the aspects of each model are discussed from an educational perspective, highlighting each step of the implementation in sufficient detail for independent reproduction and verification. This level of detail is often absent from similar publications and, it is hoped, may lead to the wider dissemination of Neuber’s rule for plasticity correction. The final component of the paper presents a multiaxial correction of the Chaboche hardening model. To the best of the authors’ knowledge, this is the first published application of Neuber’s rule to the multiaxial plasticity correction of the Chaboche combined isotropic/kinematic hardening model. Examples are used to illustrate the behavior of the method and to present some of the commonly overlooked components when assessing the applicability of Neuber’s method.