Equivalent strain and stress history in torsion tests

Bulk and plane torsion tests are being used in industry to determine the flow curve of metals up to very high plastic strains. Despite their wide usage the experimental results obtained in torsion tests are still not being evaluated uniformly. Differences arise basically due to the conversion of the measured angle of twist into the corresponding equivalent strain. This paper shows that the often used equivalent strain expression by Nádai and Davis as well as Eichinger is invalid, since the so-called redundant shear during torsion deformation has been ignored. Also, the histories of different stress measures such as the convected and rotated stress tensors are computed to discuss the reasons for differences between the flow curves obtained from torsion and simple tension tests.