Dynamic neck formation in elastic-plastic tensile bars

Abstract: The time development of neck formation in ductile elastic-plastic bars is analyzed numerically in order to obtain a qualitative description of the features of dynamic neck localization under impact conditions. The full time history is visualized using contour plots of the time development of a strain rate parameter. Both axisymmetric and planar bars are studied. Several types of neck development are discussed. The analysis shows that multiple neck formation occurs for a range of parameters when long thin bars are used. For shorter bars two necks are frequently observed and with sufficiently high end velocities necking occurs essentially always at the loaded end of the bar. In certain cases with planar bars the growing localization zone is found to have wave character as it travels along the bar. For the case of axisymmetric bars the effects of background inertia are investigated. It is found that in the present analysis the effect of background inertia does not significantly change the necking pattern observed unless the effect is artificially increased by three orders of magnutude so that it becomes of the order of the yield stress.