Material Modelling of Sheet Metal by Bi-Axial Loading Tests

Abstract

A new material description for sheet metal forming has been developed. The material description exists of the Vegter yield criterion and a physically based hardening rule. In contrast to most former criteria, the Vegter yield criterion is based on measurements of multi-axial yield stress states. The yield criterion is extended with a physically based hardening rule, in which the flow stress depends on the strain and strain rate. To measure the multi-axial stress states a biaxial test equipment is being designed. The test equipment will be capable of imposing a shear deformation and a plane strain deformation, including combinations of both deformations. To check whether the bi-axial test equipment will give reliable results, a Finite Element model of a part of the test piece and the clamp equipment is constructed.

Stress–strain responses for continuous orthogonal strain path changes with increasing sharpness

“…Due to the large width to height ratio in the deformation zone, the sample is subjected to a plane strain condition in horizontal direction. More detailed information about the test equipment can be found in Pijlman et al [8], Pijlman [9]. The strains are determined from the surface of the deformation zone.…”

A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states

“…Kinematic hardening can be incorporated easily by subtracting the back stress from the total stress and using the resulting effective stress instead of r in the yield locus. This was elaborated for the current model by Pijlman (2001), but will not be used in this paper for clarity.…”

“…The authors determine the reference points with unidirectional experiments only (Vegter, 1991;Vegter et al, 1999aVegter et al, , 2003Pijlman, 2001). The equi-biaxial stress point and strain ratio are obtained from compression in the normal direction of a stack of sheet specimens, assuming that the hydrostatic stress has no effect on the plastic deformation (Tozawa, 1978;An and Vegter, 1998;Barlat et al, 2003).…”

“…The complex geometry of the yield locus for some materials requires the definition of complicated non-quadratic yield functions. In this paper another approach is proposed, initially developed for planar isotropic sheet material (Vegter et al, 1995) and later extended for planar anisotropic material (Pijlman et al, 1998;Vegter et al, 1999b;Pijlman, 2001). The yield locus in the plane stress and principal stress space (r 1 , r 2 ) is explicitly described by a set of quadratic Be ´zier interpolations between pre-determined stress states.…”

Strain path dependency in sheet metal. Experiments and models

“…To investigate the mechanical behaviour of sheet metal while undergoing strain path changes, a more advanced experiment than the uniaxial tensile test is required. At the University of Twente a biaxial testing device was developed that loads a specimen of sheet metal in tension and shear (Pijlman, 2001). The truly exceptional advantage of the TWENTE BIAXIAL TESTER is that continuous strain path changes can be applied while still measuring the stresses.…”