Necking in the tensile test. Correction formulae and related error estimation

This paper deals with analytical modelling of the classical tensile test which is still considered as one of the main experimental procedures to determine the flow curve of elasto-plastic materials. Together with numerical simulation of the deformation process, it allows us to estimate the accuracy of the well-known classical formulae when they are used to evaluate the experimental data under stage of the neck formation. For this aim, errors related with the application of each individual simplifying assumption on the value of the average normalised axial stress were analysed. From critical analysis of one of the assumptions (curvature radius formulae of the longitudinal stress trajectory), a new empirical formula has been derived. It depends on the same measured parameters, however, leads to higher accuracy than any of the classical formulae. In addition, a new formula obtained from analytical investigation, i.e. in Lagrange approach, is discussed.