Flow Stresses in Sheet Material Formed Into Nearly Spherical Shapes

The relationship between the geometry and the membrane stresses of a thin shell under internal or external pressure is analyzed through the concept of prolateness. Prolateness is a quantitative measure of the local deviation from the spherical surface and it varies in a complex manner throughout a thin shell formed by hydraulic pressure. It is found that for the metals tested the surface is locally a sphere only at the pole and at an annular ring; elsewhere, it is oblate or prolate. The stress distributions in the shell being formed are also determined. Their variation as the forming progresses reveals that the material deforms quite differently at the beginning and at the end of the process.