An Evaluation of the Neuber and Glinka Relations for Monotonic Loading

The Neuber relation is widely used to compute elastoplastic stresses and strains at stress concentrations, but a newer relation has been developed by Glinka. Prediction of local strain response is important because low cycle, fatigue life models are based on the strain range. The effects of notch root constraint on the response have been difficult to predict or measure. This paper evaluates the abilities of six models of notch root behavior by comparing them with experimental results over a range of constraints. The models are: the Neuber model, the Neuber model as modified by Walker, the Glinka models for plane stress and for plane strain, and two modifications of the Glinka models that are presented in this paper. Comparisons are made with strains measured at the roots of notches by resistance gages or by laser-based interferometry; data come from previous works as well as some new results of the authors. The constraints vary from plane stress to plane strain with several intermediate cases. Conclusions must take into account the fact that elastoplastic strain measurements have scatter arising from the gage length relative to the grain size. But, in general, one can say that the Neuber model is best for plane stress and the Glinka plane-strain model is best for very large constraint. Response for intermediate amounts of constraint are predicted better by one of the other models.