Numerical determination of strain localisation during finite element simulation of deep-drawing operations

This paper presents a purely numerical criterion to determine the onset of necking during finite element simulation of a deep-drawing process. In fact, the proposed detection procedure is based on fine analysis of plastic strain distributions observed along flat samples during classical tensile tests on various materials. This distribution is evaluated by using a CCD camera and a correlation program. This tool processes successive digital images of the surface of the sample during testing. It is shown that strain field determination allows both the computation of the usual stress-strain relation even during longitudinal localisation and clearly highlights developments of elastically unloaded zones, apart from the necked area where localisation occurs. Thus the numerical criterion described in this paper consists simply in counting the unloaded elements during numerical simulation using a post-processing program. The occurring localisation in a real deep-drawing operation is thus precisely detected during the corresponding finite element simulation.