**Published:** Jan 1982

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**Source: **STP753-EB

The accurate conversion of the torque/twist data obtained from torsion tests into equivalent stress/equivalent strain data is required for reliable formability predictions, particularly at large strains. The first stage in this process is the derivation of the shear stress/shear strain curve from the torque/twist data. A new method is proposed which performs this first operation. It is based on the observation that the radii of cylindrical bars remain straight during testing, and also on the hypothesis that the state of the material at a given radius is not influenced by the state of the surrounding layers. This method appears to reduce significantly the errors inherent in the previous methods.

The second stage involves converting the shear stress/strain curve into an equivalent stress/equivalent strain relationship, with due consideration for the very large strains involved. For this purpose, the equivalent strain ε^{eq} is calculated from the incremental changes in the strain components during torsion. This analysis leads to the relation

It is also shown that, when the corrected conversions are used, the rate of work hardening calculated from torsion tests is *lower* than that obtained from uniaxial testing. This discrepancy is attributed to three causes: (*a*) at low strains, the torsion equivalent stresses calculated using the von Mises relationship are 6.5 percent lower than those obtained from the crystallographically based Bishop and Hill formulation, which is judged to be more accurate; (*b*) the difference in the textures developed in torsional and tensile deformation leads to Taylor factors that evolve differently with strain, and which cause the tension and torsion equivalent stresses to diverge at large strains, even if the *true* rates of work hardening (in terms of the critical resolved shear stresses) are the *same* in the two modes of deformation; (*c*) there is a possibility that there is less dislocation accumulation at large strains in torsion than in tension because less dislocation intersection is required by the torsion as opposed to the tension end textures. The lower work hardening rates determined in torsion lead in turn to lower forming limit predictions for deformation along other strain paths.

**Keywords:**

formability, simple shear, pure shear, torsion testing, tension testing, equivalent strain, equivalent stress, shear stress, work hardening, texture, flow stress, hardness state, dynamic recrystallization

**Author Information:**

Canova, GR *Graduate student and professor, McGill University, Montreal,*

Shrivastava, S *Assistant professor, McGill University, Montreal,*

Jonas, JJ *Graduate student and professor, McGill University, Montreal,*

G'Sell, C *Maître assistant, Laboratoire de Physique du Solide, Ecole des Mines, Parc de Saurupt, Nancy,*

**Paper ID:** STP28395S

**Committee/Subcommittee:** E28.02

**DOI:** 10.1520/STP28395S