Effects of anisotropy and diaphragm size on biaxial stress—strain curves for sheet metals

Abstract

When a circular diaphragm clamped at the edge is deformed by unilateral hydrostatic pressure the pole is under balanced biaxial tension if the absence of edge effects is assumed. The diaphragm test is an excellent way of obtaining the work-hardening characteristics of sheet metals to fairly high strains. Some previous investigators have tried to correlate the experimental and theoretical stress-strain characteristics of the pole of a diaphragm. In this present work 10 in. and 4 in. diameter dies and sheet metals with an average thickness of 0·040 in. have been used. Previous investigators used diaphragms of smaller sizes; but if the thickness—diameter ratio can be kept small the bending stresses will be negligible. All sheet metals are anisotropic and for simplicity anisotropy in the plane is neglected, so that an average R value can be adopted. Hill's theory of yielding and plastic flow for anisotropic materials has been used together with the uniaxial tension test values to predict the stress—strain characteristic at pole. The effects of the diameter of the die and the normal anisotropy of the sheet metals on the stress—strain characteristics at pole are discussed.