Constitutive modelling of orthotropic plasticity in sheet metals

The classical quadratic yield criterion for orthotropic metals is known not to be sufficiently flexible in practice. By the simple expedient of admitting non-integer exponents, however, an improved criterion was devised for sheet with in-plane isotropy (so-called normal anisotropy). On the other hand, an acceptable proposal has not been forthcoming for sheet with in-plane anisotropy (so-called planar anisotropy). It is suggested here that improvement should be sought by incorporating a compatible dependence on orientation in a homogeneous yield function of arbitrary degree. In so doing, the practicalities of forming technology are respected by keeping the number of arbitrary parameters as small as possible. A new criterion is constructed along these lines and its implications are explored in detail. Additionally, a simple means of representing anisotropic yield criteria of any kind is presented with supporting general theorems.