Plasticity Analysis of Sheet Metal Forming

Abstract

The paper surveys the application of plasticity theory to sheet metal forming problems and attempts to highlight those areas where knowledge is lacking. From an engineering standpoint the most valuable analyses would seem to be those which predict trends in deformation behaviour. It is only rarely that the material properties and lubrication characteristics are known with sufficient accuracy to make correlations between theory and practice worthwhile in a particular case. There would, however, seem to be definite advantages in the same research team following both theoretical and experimental paths.

The processes considered are deep-drawing (with a flat-headed punch), stretch forming (by hydraulic pressure, with a hemispherical punch, and in-plane stretching) and general sheet pressing. The easiest theoretical problems to solve are those where the deformation is stable. The most interesting and difficult problems deal with failure which can take the form of wrinkling and puckering, tensile instability, limit strain or final fracture.

In engineering the load required for a given process is usually determined with sufficient accuracy from a simple approximate analysis and in carrying out a more detailed analysis we are primarily interested in the prediction of the strain distributions and in their correlation with experimental measurements of strain. This is one method of making certain that an appropriate yield criterion and its associated flow rule have been selected. It is impossible to ignore anisotropy when discussing sheet metal forming. The theory of orthotropic anisotropy describes the deformation of deep-drawing steels quite well but is unsatisfactory for most other materials. In particular when the r-value is less than unity we must look at other yield criteria and flow rules to describe the plastic flow of such materials.