A yield criterion for elastic pure-plastic polycrystalline materials is generated under simplified conditions by assuming that for yielding a certain fraction Qe of the total number of slip planes in the material has to be active. This fraction Qe is called the critical active quantity. We suppose Qc to be independent of the state of stress. The yield criterion is mathematically expressed as an integral, which is a function of Qe. This criterion can also be used for anisotropic materials.
For isotropic materials the ratio (r) of the yield stress in torsion to that in tension is calculated as a function of Qe. We find 0.5 < r < 0.61.
The value r = 0.5 (Tresca's criterion) is obtained for Qe = 0 alld Qe = 1. The value r = 0.577 (yon Mises criterion) is obtained for Qe = 0.34 and Qe = 0.79. The difference between two criteria with the same r is the magnitude of the yield stress. We think the value Qo = 0.79 corresponds to the experiments for f.c.c, materials, since a rough estimation gives Qe > 0.75 for yielding.
The independence of Qe on the state of stress brings on that r > 0.5 is more probable. This is caused by the slower increase to Qe in torsion compared with the case of tension.
From the theory follows that in the general case (Qe ~ 0) the middle principal stress has influence on yielding.
In this paper we don't determine Qe, but adapt its value to the experimental results. However, a rough estimation of Qo is given for isotropic materials.