On the tensile plastic instability in axi-symmetric deformation of sheet metals

Abstract

The general theory on the sufficient condition for uniqueness to the boundary-value problem of a rigid-plastic solid is applied to the axi-symmetric deformation of thin sheet metals. It is a generalization of the conventional treatment of plastic instability in that it includes the virtual mode of axi-symmetry which is not necessarily a continuation of the mode immediately prior to instability. The virtual work equation is established and applied to thin tubes under internal fluid pressure, independent axial load and/or torque. An important conclusion is that the plastic instability criterion originally obtained by Swift is acceptable in the light of the theory of the present paper. The same is true for the spherical shells subjected to internal pressure, which is another example of a uniformly distributed stress field. As illustrations of the stress fields which are not uniform, the hydraulic bulge and bore expanding tests are treated in an explanatory manner. Further, the theory is extended to include thin tubes of an anisotropic material in the last section.