Relationship Between Workhardening Characteristics, Shape and Instability of Hydroformed Thin Shells

Abstract

In this paper, a pattern is observed which relates the stress-strain curve of sheet materials to the shape and instability of hydroformed axisymmetrical thin shells. According to this pattern, prolate shells are obtained when the effective strain at the pole has a value within the linear (or almost linear) portion of the stress-strain curve; while oblate shells are obtained when the polar effective strain is at the curved portion of the stress-strain curve. With the aid of Ludwik and Hollomon equations, a family of stress-strain curves of various n-values is constructed and the curves are divided into four zones which indicate the shape of shells and its evolution with deformation, the transition point toward instability and the onset of instability. From the fracture strain of a given material during hydroforming, the observed pattern also indicates whether or not instability is present.