An analytical study of the yield condition of bcc metal was carried out based on the Sachs model of polycrystalline aggregates. The yield stress ratio τ/σ of torsion to tension was calculated averaging the orientation factors among all grains. The resultant value of τ/σ was 0.573 for the uniform distribution of orientations, which is in good agreement with the value 0.577 obtained from von Mises' law and also with the experimental data. It turned out that the preferred orientation <110> or <100> resulting from uniaxial tension or rolling of bcc polycrystalline metals makes the value τ/σ larger than that of the uniform distribution of orientation. Discussions were made on the physical meaning of von Mises' law.
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