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.

The strain distributions and strain histories in the axisymmetrical sheet metal forming process have hitherto been difficult to study owing to the lack of a succinct system of representation. The use of a triangular coordinate system to represent the strains in axisymmetrical sheet metal products is explained. Strain distributions and strain paths in sheet steel products are presented for processes involving variations in blank diameter, load on the pressure plate and punch profile radius. It is shown, by studying the growth of draw-in, that the effect of an increase in blank diameter is the same as that of increasing the load on the pressure plate. The various effects of a change in the punch profile radius are also discussed through the diagrams showing the strain distributions and strain paths.

In the formability of sheet metal, distinction is made between the formability at the critical section, the formability of the material, and process efficiency. It is shown that draw-in has an adverse effect on the formability at the critical section, but greatly improves the gross process efficiency, which measures the extent to which the formability of the material is exploited in a particular process. The effect of draw-in on the strain distribution in the workpiece is shown in a triangular coordinate system for strains.