Effects of inertia on dynamic neck formation in tensile bars

Neck localization during high rate extension of round bars is analyzed numerically. An axisymmetric problem formulation is given and the material is described as rate independent and elastic–plastic. The time history of neck development is investigated and effects of geometry and initial thickness imperfections are visualized. Studies of both weakly and strongly developed necks are performed, revealing the occurrence of multiple necks in some loading cases. The influence on neck formation from background inertia (lateral inertia) corresponding to the inertia originating from homogeneous deformation of the bar is examined somewhat qualitatively by introducing an artificial volume load. Calculations show that in the present analysis, background inertia does not have any noticeable influence on the necking pattern unless the effect is artificially magnified by three orders of magnitude so that it becomes comparable to the yield stress.