MATHEMATICAL MODELING OF SHEET METAL DEFORMATION

For the better understanding of sheet metal deformation during forming operations a mathematical model is presented. The purpose of this modeling is to predict the forming limit diagram (FLD) which represents the limiting strain states achievable during sheet forming operations. The model is based upon a previously developed analysis by Jones and Gillis (JG). The deformation is idealized into three phases: (I) homogeneous deformation up to maximum load; (II) deformation localization under constant load; (III) local necking with a precipitous drop in load. In phase III local necking is described by a Bridgman type neck.; The present model extends the JG theory which was applied to the right hand side of the FLD only, the main difference in treating the two different sides of the FLD lies in the assumptions regarding the width direction deformations.; It is also assumed that the principal axes of deformation coincide with the principal axes of material anisotropy throughout the test. Both the actual neck geometry and the criterion for determining the limit strain are modified from the earlier analysis in order to agree more closely with actual press shop practice. The most important feature of present model, however, is the calculation of the left hand side of the FLD which was not done in the previous analysis.; Results from this analysis are compared with the experimental ones for aluminum-killed (AK) steel and three aluminum alloys.; Using the mathematical model the effects of varying material properties are studied. The properties considered are the strain hardening exponent, n, the strain rate sensitivity parameter, m, and the plastic anisotropy ratio, r.; An important theoretical result that derives from this analysis is the extension of the Considere criterion for maximum load into two dimensional cases and for generally anisotropic materials. It is also shown that when maximum load is reached in the major strain direction the value of major strain is independent of the (constant) strain rate ratio. At maximum load the major strain had the same value in every case and that value was precisely as predicted by the analysis. (Abstract shortened with permission of author.)...