A numerical analysis of neck formation in tensile specimens

Numerical analyses on the phenomenon of necking in tensile specimens usually introduce a geometric or deformation defect that initiates flow localization, or treat the onset of necking as a bifurcation in the mathematical solution. These approaches do not, however, appear to be essential in analysing the neck formation. A finite-element analysis without introducing defects or a bifurcation solution is shown in the present paper to be readily responsive to the initiation of necking on fulfilling the critical criterion for neck initiation. In the present FE analysis, the appropriate elements are made to converge to a pre-specified node within the respective elements as an equivalent step to what goes on inside the specimen at the point of incipient necking. The above method is seen to reproduce the usual hour-glass shaped necking profile for an axisymmetric round bar with a shear-free-grip end condition. This work is of industrial significance as the necking profile in tension has an important bearing in determining the ductile behaviour of a material.