Multiple necking during the dynamic expansion of hemispherical metallic shells, from experiments to modelling

Expansions of hemispheres driven by explosive charge have been conducted for two materials: copper and tantalum. Owing to high speed camera, the time occurrence, the angular position and the number of necks have been identified at the onset of necking. Tantalum and copper have been characterized from quasi-static to dynamic conditions at different temperatures and their behavior has been modelled using three different thermoviscoplastic flow laws (powerlaw, Zerilli–Armstrong, Preston–Tonks–Wallace). From numerical simulations of the expansion process, it has been shown that the onset of necking is located in an axisymmetric layer where plane strain conditions prevail. Since the layer has a small extension in latitude and the shell is thin, the stability problem can be assimilated to that of a plate stretched under dynamic plane strain conditions. A stability analysis is developed based on the concept of an effective rate sensitivity parameter which merges the thermal and the visco-plastic material characteristics. From the evolution of this parameter during loading, a new criterion for the onset of instability is postulated. This criterion, which is different to the usual one based on the evolution of the growth rate of small perturbations, is used to characterize multiple necking observed during the dynamic expansion of copper and tantalum hemispheres. A good agreement with experiments is obtained concerning the number of necks and the time of occurrence of instabilities.