J. Phys. IV France 110 (2003) 287
Linear stability analysis of multiple necking in rapidly expanded thin tubeS. Mercier and A. Molinari
Laboratoire de Physique et Mécanique des Matériaux, UMR 7554 du CNRS, ISGMP, Université de Metz, Ile du Saulcy, 57045 Metz, France
Fragmentation of rings subjected to radial expansion is analysed for material having a viscoplastic with strain hardening behavior. Using a linear stability technique, the growth rate of a perturbation is evaluated and dynamic necking is captured. Due to the interplay between biaxial flow effect and inertia, a finite wavelength associated to the largest growth rate is selected, which will define the size of fragments. The effect of the ring radius is clearly shown. Finally, calculations obtained with the present approach provide fragment size in agreement with experimental data .
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