Plastic flow in the elliptical bulge test

Abstract

A theoretical analysis is presented of plastic flow at the pole of an elliptical bulge as it forms through a die from applying normal pressure to thin metallic sheets. The inherent anisotropy present in as-rolled sheets of three steels and a brass is characterized from in-plane r-values. The latter were found from tensile tests for directions parallel and perpendicular to the direction of rolling. The validity of the theory is appraised from experiments which examine the extent to which it can provide equivalence between pole flow for elliptical bulges, with five different aspect ratios, and the flow in tension. For each material, all tests are equivalent to 20% plastic strain, i.e. the full range of uniform tensile strain. As greater strains (up to ε ̄ P ⋍ 80% ) are achieved from bulge forming, the flow curves diverge downward with increasing die aspect ratio. This geometrical effect on flow is such that narrower elliptical die apertures require greater maximum pressures to attain instability but appear to flow under lower equivalent stresses. It is suggested that as the strain gradients increase, the assumption that the two principal radii of curvature which encompass the pole and the 1 in. radius on which the spherometer contact is made, become suspect. A correction is made by employing an equivalent gauge length. In practice, a smaller radius would be required to define the pole curvatures more accurately. Alternatively, larger die apertures could be used.