Strain Histories and Strain Distributions in a Cup Drawing Operation

In the axisymmetrical cup drawing process, the principal directions of the strains are fixed with respect to the work material at every point and in every stage of the process; in other words, the strains are entirely coaxial ones—if the small strains in simple shear due to friction are ignored. For a properly chosen set of orthogonal space coordinates, therefore, the strains may be plotted in triangular coordinates. In such a coordinate system for strains, the loci for constant penetrations show the strain distributions, and those for constant initial radial positions show the strain histories. In these loci it is easy to see thinning and thickening, circumferential expansion and contraction, neck formation, variation in thickness, and other points of interest to the sheet metal engineer. Typical examples of strain histories and strain distributions in a cup drawing operation are shown. The method is applicable to any axisymmetrical sheet metal forming process.