Keywords: cohesive zone model, damage model, buckling, ductile fracture, contact, metal tube tearing.

When a tool is used to cut a sheet metal, or a tube according sometimes, buckling waves appear on the free edges. This wavy edge bears strong similarities with the geometry on the wreckage of some aircraft fuselage skins associated with damaged aircraft [1]. In order to understand this behaviour, the authors conducted a set of experiments, in which stainless steel tubes are cut according to a generator. An adequate instrumentation, including specific measurements (high elongation strain gages, digital image correlation) allowed the phenomena to be accurately stated, in particular the kinematics at the scale of the crack (ahead of crack tip) and at the level of the tube (wave lengths of buckling). Various geometries of tubes (diameter - thickness ratios) were tested. The numerical simulation takes into account large displacement such as the buckling phenomenon and material nonlinearities, material yielding associated with ductile tear propagation. The crack propagation is managed by the cohesive zone model (CZM), formulated and implemented into ABAQUS Standard using the user subroutine UEL [2,3] or by the DM existing in ABAQUS Standard [4]. The coupling of the shell continuum elements and these fracture models makes it possible to corroborate the experimental observations. The assumption of the mode I crack propagation is made. It is still a challenge to obtain the cohesive parameters (separation energy, cohesive strength), or the ductile damage parameters (fracture strain, displacement at failure) experimentally on thin sheets, thus these material properties managing the cracking are obtained by numerical retiming. These studies show that the displacement of cutting tool induced a circumferential extension of the tube that leads to a local necking in the radial direction finally causing the rupture. During the failure, a "plastic wake" appears, relatively wide, close and parallel to the crack lips. Constrained by other parts of the tube which remain elastic, sufficient axial residual compressive stresses produced in this plastic wake produce the undulations which represents local buckling.

1

Z. Zou, S.R. Reid, "Wavy-edged fractures in axially split aluminum tubes", International Journal of Solids and Structures, 42(16-17), 4519-4540, 2005. doi:10.1016/j.ijsolstr.2005.01.016

2

I. Scheider, "Cohesive model for crack propagation analyses of structures with elastic-plastic behavior: Foundations and implantation", GKSS research center Geesthacht, Dept. WMS, 1-41, 2001.

3

G. Alfano, "On the influence of the shape of the interface law on the application of cohesive-zone models", Composites Science and Technology, 66(6), 723-730, 2006. doi:10.1016/j.compscitech.2004.12.024

4

ABAQUS, "ABAQUS User's Manual (version 10.2)", Hibbitt, Karlsson, and Sorensen, Inc, Pawtucket, USA, 2010.

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