Elastic-viscoplastic notch correction methods

Neuber’s type methods are dedicated to obtain fast estimation of elastic–plastic state at stress concentrations from elastic results. To deal with complex loadings, empirical rules are necessary and do not always give satisfying results. In this context, we propose a new approach based on homogenization techniques. The plastic zone is viewed as an inclusion in an infinite elastic matrix which results in relationships between the elastic solution of the problem and estimated stress–strain state at the notch tip. Three versions of the notch correction method are successively introduced, a linear one which directly uses Eshelby’s solution to compute stresses and strains at the notch, a non-linear method that takes into account plastic accommodation through a β-rule correction and, finally, the extended method that is based on the transformation field analysis methods. All the notch correction methods need calibration of localization tensors. The corresponding procedures are proposed and analyzed. The methods are compared on different simulation cases of notched specimens and the predictive capabilities of the extended method in situations where plasticity is not confined at the notch are demonstrated. Finally, the case of a complex multiperforated specimen is addressed.