Prediction of Localised Non-Linear Stress and Strain at the Critical Location of Mechanical Members— A Neuber's Rule Study

The present study aims to solve a polynomial equation known as Neuber's rule in conjunction with Ramberg-Osgood relation to estimate the plastic stress and strain at the stress concentration point of a mechanical component subjected to monotonic loading condition. Structural components such as plate with centrally punched circular hole and plate with edge notch exhibited material non-linearity due to large imposed boundary forces, as ascertained from non-linear stress strain curves obtained by performing finite element analysis. In order to implement the Neuber's rule, linear static finite element analysis is first performed with suitable sub-steps and the maximum von-Mises stress values thus obtained for each sub step is substituted in the rule to evaluate plastic stress. The plastic strains are evaluated by using Ramberg relations that takes into account the estimated plastic stress from the rule.  As a benchmarking case study, a multilinear FE analysis is performed and the results are compared with the analytical non-linear stress strain curves. The comparison resulted in errors less than five percent, thus ascertaining the accuracy of the estimated stress values from the Neuber's rule. The results obtained from the case studies indicate that the implementation of the simpler Neuber's rule and Ramberg relation is computationally efficient in comparison with the multilinear finite element analysis performed to estimate stress and strain states, for the ductile materials such as engineering steel and aluminium.