On the anomalous behaviour of anisotropic sheet metals

Abstract

Using Hill's 1948 criterion [1] for anisotropic yielding and the strain ratio, r, it has been shown that the ratio of the balanced biaxial yield stress, [sigma]b, to the uniaxial tensile yield stress, [sigma]u, should be > 1 if r > 1 and r r b to [sigma]u was always > 1 in that study. This was termed anomalous behaviour. Hill has proposed a new criterion[3] that not only appears to provide greater flexibility than does his earlier version but can also encompass anomalous behaviour which the earlier version cannot.Four simplified cases of the 1979 criterion have been proposed[3] and to date only one has been subjected to experimental assessment. However, the goals of those studies were not concerned with anomalous behaviour per se. In this paper, all four cases are analysed to determine the interrelationships of the parameters r and m (exponent in Hill's new criterion) required to encompass anomalous behaviour. It is found that for each of the four cases anomalous behaviour is predicted for a range of (m, r) combinations which are presented graphically in this paper.