Computation of the Necking in Bars Without Geometrical Imperfection - Tapas Kumar Datta (International Journal of Fracture Mechanics and Damage Science, 2024)
This paper presents a finite element analysis to compute the neck profiles of smooth, circular cylindrical bars in shear-free grip under uniaxial tensile load. The analysis uses 4-node quadrilateral element with linear displacement variation, as well as 8-node Serendipity quadrilateral element with curved sides and a quadratic variation of the displacement field, for power law hardening materials that follow von Mises plasticity. All the elements are based on isoparametric formulation. The analysis computes the reduction of area for given elongation and the results are compared with the data of percentage elongation and reduction of area (at fracture) for a few materials as available in literature to find close correspondence. This analysis simulates the neck profiles by implementing only that the elements away from the neck stop deforming.
Keywords: Finite element analysis; ductility; elongation; reduction-of-area; von Mises plasticity