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From: "Instability phenomena during the conical expansion of circular cylindrical shells", by T. Daxner (1), F.G. Rammerstorfer (1), F.D. Fischer (2,3)
(1) Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Gusshausstr., 27-29 (E317), A-1040 Vienna, Austria
(2)Institute of Mechanics, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria
(3) Erich Schmid Institut der Österreichischen Akademie der Wissenschaften, Jahnstr. 12, A-8700 Leoben, Austria
Computer Methods in Applied Mechanics and Engineering, Vol 194, Nos 21-24, 10 June 2005, pp. 2591-2603
http://dx.doi.org/10.1016/j.cma.2004.07.047
ABSTRACT: Pushing a conical die into a tube is a forming process that is suitable for changing the shape of a thin cylindrical tube into that of a conical shell. The degree of expansion that is achievable without destroying the tube is limited by two mechanisms: (a) loss of global stability due to elasto-plastic ‘Concertina’ buckling of the straight part of the tube, and (b) diffuse necking caused by local loss of material stability in the conical part of the tube. The former mechanism is characterized by a periodic buckling pattern, that is similar to the one observed in typical crash elements, while the latter mechanism leads to the formation of periodic necks and subsequent failure by strain localization and rupture.
In this study experimental evidence for both kinds of instabilities is presented along with corresponding simulation results obtained with the finite element method. For long tube specimens ‘Concertina’ buckling was found to be the dominant instability mode while for short tube specimens failure by necking and rupture occurred. The critical circumferential strain for the onset of necking at the expanding tube end was markedly higher than the one expected from uniaxial tension results. This finding is attributed to the supporting effect of the tube sections that are subjected to lower strains.
See the next slide for an experimental configuration.
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