Comput.Meth.Appl.Mech.Engng. 194, 2591-2603, 2005
T. Daxner¹, F.G. Rammerstorfer¹ and F.D. Fischer²
¹Institute of Lightweight Design and Structural
TU Wien, Vienna, Austria
²Institute of Mechanics, Montanuniversität Leoben,
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
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 of
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 expanded 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.