Strength and Failure Characteristics of Metal Membranes in Circular Bulging

Abstract

Abstract Circular hydraulic bulges were formed from a group of materials having widely varying strain-hardening rates. The complete development of the shapes and strain distributions was determined experimentally, and the stress and radius of curvature at the pole were calculated as a function of the maximum strain. An analysis of the data revealed that strain gradients and, therefore, the bulge heights were influenced by the stress-strain characteristics of the metal. It was also found that the bulge contour was closely approximated by a sphere only at strains in the vicinity of the instability strain. Instability was exhibited by all materials having a sufficient ductility at strains varying from ϵ3 = −0.47 for 75S-O to ϵ3 = −0.64 for annealed low-carbon steel. The phenomenon of instability was related to both the development of the shape and the strain distribution. The previously reported differential equation for instability in a circular bulge was found to yield strains which agreed with the maximum load strain and the instability strains derived from the analysis of the shape and strain distributions. These instability strains were not found to be simply related to the necking strains in uniaxial tension. The height and maximum strains (forming limits) obtainable in bulging were found to be greatly reduced by the presence of surface flaws or a large grain size.