The equivalent strain in high pressure torsion

The results of experiments carried out by means of high pressure torsion (HPT) are frequently described in terms of the Eichinger “equivalent” strain. When employed in conjunction with equivalent stresses derived using von Mises in conjunction with the Fields and Backofen analysis, the values of the work done/unit volume associated with the Eichinger-based flow curves are shown to be only a small fraction of the actual work done. By contrast, the values of the work done/unit volume that correspond to the shear stress/shear strain as well as the von Mises flow curves are in full agreement with the torque/twist work done/unit volume. When the principle of work conjugacy is employed, the Eichinger strain-based work done values are necessarily in agreement with the shear stress/shear strain and torque/twist results, but then the “equivalent” stresses are unrealistically high. It is concluded that only the von Mises equivalent stresses and strains should be employed in the description of HPT results and that the Eichinger “equivalent” strain should not be used for this purpose.