A method of generating analytical yield surfaces of crystalline materials

An analytical representation of the yield loci of single crystals obeying the Schmid law is examined. It involves an exponent n. The study is conducted first in the fcc case, but it can be extended to more complex modes of slip. A method of predicting the plastic behaviour of polycrystals from the knowledge of their texture is then derived. It leads to completely analytical formulae and is compatible with the assumption of uniform stress. In case n = 2, it is equivalent to Hill's 1948 yield criterion but experiments show that the values of the best-fitting n are higher than 2. These larger values account for phenomena which cannot be predicted by the quadratic criterion, such as ‘anomalous behaviour’. Further reflection leads us to propose an alternative method of averaging, characterized by the introduction of a second exponent m. The effect of m is to realize a fair balance between the contributions of the various crystallographic components to the global mechanical behaviour. The comparison with experimental data from two aluminium sheets shows that it leads to an improvement in the predictions of the values of the strain rate ratio.