The Poynting-Swift effect in relation to initial and post-yield deformation (Q1058353)

The material behaviour predicted by the constitutive equation of a general elastic material is considered in relation to the combined extension and torsion of a thin-walled tube and a solid rod. This state of combined stressing is considered in relation to material behaviour at small strains, and at finite strains in the context of initial yield and the Poynting-Swift effect. A composite yield condition has been postulated on general grounds which, over a given range of application, is identical to the von Mises yield criterion, or some modified form of it, and over the remaining range of application takes the form of a 12- sided, linear, piece-wise continuous yield condition. The theory is applied to the classical combined-stress experiments of \textit{G. I. Taylor} and \textit{H. Quinney} [Philos. Trans. R. Soc. Lond., A 230, 323-362 (1931; Zbl 0003.08003)], using a total deformation-type constitutive equation. It is shown that the proposed yield condition when combined with the new constitutive equation, is in full agreement with the useable experimental data obtainable from these particular combined- stress measurements.