Local solution of the stress and strain fields in the necking section of cylindrical bars under uniaxial tension

The problem of finding the stress and strain fields over the minimum cross section of necked cylindrical bars under uniaxial tensile load has been solved locally using a new fast numerical method. The scheme delivers both the accuracy of the finite element analysis and the applicability of simple closed-form analytical solutions. The required inputs are the distributions of curvature radii for both isostatic and material lines. It is numerically observed that the mathematical formulas available in the literature fail to adequately predict these distributions. Introducing the stress normalized strain-hardening rate as the most decisive parameter affecting the curvature radii, a database and interpolation technique have been developed in order to estimate the necessary information based on the results of the previously FE analyzed samples. Finally, a practical case has been solved and compared with the FE results.