A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

Abstract

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.

Keywords:

• simple shear deformation
• torsion testing
• von Mises equivalent strain
• Hencky equivalent strain
• Hencky equivalent stress
• incremental plastic work

Acknowledgements

The authors are grateful to the Natural Sciences and Engineering Council of Canada for financial support and to Dr. Pampa Ghosh for assistance in manuscript preparation.