Prediction Of Multiple Necking During The Dynamic Extension Of A Round Bar Based On An Extension Of The Linear Stability Analysis : Characterization Of Interneck Distances

Linear stability analysis has been widely used to describe the onset of multiple necking and the number of necks appearing during expansion of rings, tubes or spheres. However, experimental observations, for instance on ring expansions obtained in CEA-Gramat, have shown distributions of inter-neck lengths instead of a unique distance between necks. The objective of the present work is to extend linear stability analysis (i.e. the characterization of the dominant necking mode) in order to take into account contributions of all perturbation modes during a dynamic loading. The evolution of all perturbation modes has thus led to the definition of potential necking sites. In the present work, the dynamic extension of a cylindrical bar is considered. This configuration can be related to a thin ring expansion. The main outcome of the present analysis is the proposition of a statistical framework leading to the definition of the distribution of pre-neck spacing. Such approach provides additional information such as the scattering of pre-neck distances.