Effects of elastic unloading on multiple necking in tensile bars

The deformation of round tensile bars subject to dynamic loading is studied numerically using two different plasticity theories: J₂-flow theory and J₂-deformation theory. Time development of neck localization is visualized and a comparison of the necking patterns obtained using the two different constitutive models is presented. The possibility of using J₂-deformation theory as an alternative to J₂-flow theory to model the dynamic behaviour of tensile bars subject to high rate deformation is investigated and the effects of elastic unloading are discussed. Influence of specimen geometry and initial thickness imperfections is also considered. The effects of elastic unloading on multiple necking are of particular interest, since elastic unloading may serve as a restricting factor regarding the growth of multiple neck localizations. In the present analysis, multiple necking is found to appear using both J₂-flow theory and J₂-deformation theory. The use of stubby bars leads to similar necking patterns when comparing the results obtained with J₂-flow theory and J₂-deformation theory. For slender bars subject to certain loading conditions a larger number of necks is obtained when J₂-deformation theory is applied rather than J₂-flow theory. In addition, results of simulations near the ideal-plastic limit are discussed as well as results where the yield stress is varied.