Instability analysis for ellipsoidal bulging of sheet metal

Abstract

This chapter presents a theory of instability for ellipsoidal bulging of orthotropic sheet metals. It provides the limiting strains and peak pressure for a pole failure when an instability condition applies. Predictions to the pressure versus bulge height curves are compared with experimental results for four sheet materials: stainless steel, brass and carbon steels with and without zinc cladding. A general approach is adopted in terms of the die axis length ratio, the sheet's r-values, the Hollomon hardening constants and any inclination of the die's minor axis to the material's rolling direction. The theory of instability given requires equivalence in the flow behaviour for all test conditions reported in. From this a sub-tangent is derived to provide the equivalent instability strain that is converted into (i) the ultimate pressure and (ii) the limiting, inplane surface strains. The latter show that greater strains are possible from forming under pressure than from in-plane stretching. Thus, the attainment of a peak pressure is a desirable condition for forming since very large strains can be achieved with the correct material.