The Hencky equivalent strain and its inapplicability to the interpretation of torsion testing experiments

Abstract

Experiments were carried out on a 0.06%C plain C steel to determine the shear stress–shear strain behaviour. The results obtained at 1200°C and a shear strain rate of 0.866 s⁻¹ are described. The experimental data are converted into equivalent stress–equivalent strain form using the von Mises and Hencky formalisms. It is shown that when the equivalent stress is of interest, as in the calculation of rolling load, only the von Mises formulation can be used without the introduction of large errors. This is required so that the incremental work done/unit volume of material can remain constant in both the shear and equivalent uniaxial tension formulations. The problem with the Hencky formalism with regard to simple shear is that the orientations of the Hencky principal strains and principal strain increments do not coincide and also vary continuously. As a consequence, the absolute values of the strain increments cannot simply be summed and the description of the equivalent strain applicable to large strain torsion proposed by Onaka [Philos. Mag. Lett. 90 (2010) p.633] cannot be used to predict mechanical properties along other strain or loading paths. The problems associated with the definitions of the Hencky equivalent stress and Hencky work increment are also discussed.

Keywords:

• equivalent strain
• simple shear deformation
• torsion testing
• rolling load
• von Mises equivalent strain increment
• von Mises equivalent stress
• Hencky equivalent strain increment
• Hencky equivalent stress

Acknowledgements

The authors are grateful to the Natural Sciences and Engineering Council of Canada for financial support and to Professor Laszlo Toth of the Université de Metz for suggesting the analytic approach employed in Appendix 2.