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

Abstract

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 Taylor and Quinney[3], 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. The available studies of the Poynting-Swift effect are shown to be in general accord with the proposed yield function and total deformation type constitutive equation. In particular, for sufficiently small shear strains it has been shown that simple torsion of both a thin-walled tube and a solid rod is characterised by an axial elongation which is proportional to the square of the twist. It is also shown that the available experimental results are in quantitative agreement with the predictions of the proposed constitutive equation.