Plasticity and creep of pressurized membranes: A new look at the small-deflection theory

The Mechanics of the bulge test at small deflections has not been adequately investigated in the past, especially when the stress dependence on strain and/or strain-rate is represented by a power law. For this type of material response, and for die apertures of any shape, we prove new theorems relating to the extremal characterization and uniqueness of the solution, and to a general correspondence between the respective solutions for viscoplasticily or creep on the one hand and time-independent plasticity on the other. The basic problem is here solved exactly for a circular membrane, and to a close approximation for elliptical ones; the results of extensive numerical calculations are presented in full. With this background the influence of material response and tool geometry on the inherent inhomogeneity of the test can be clearly seen. A proper appreciation of these effects is of course essential when interpreting observational data.