A NUMERICAL-ANALYSIS OF NECK FORMATION IN TENSILE SPECIMENS

Numerical analyses on the phenomenon of necking in tensile specimens u sually introduce a geometric or deformation defect that initiates flow localization, or treat the onset of necking as a bifurcation in the m athematical solution. These approaches do not, however, appear to be e ssential in analysing the neck formation. A finite-element analysis wi thout introducing defects or a bifurcation solution is shown in the pr esent paper to be readily responsive to the initiation of necking on f ulfilling the critical criterion for neck initiation. In the present F E analysis, the appropriate elements are made to converge to a pre-spe cified node within the respective elements as an equivalent step to wh at 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 condi tion. This work is of industrial significance as the necking profile i n tension has an important bearing in determining the ductile behaviou r of a material.