A theory of plastic anisotropy based on yield function of fourth order (plane stress state)—II

It is shown from various view points that many of the disadvantages of the conventional theory based on a quadratic yield function can be satisfactorily removed by the use of a yield function of fourth order. Incremental equivalent strain is defined by , and cannot generally be expressed simply by the strain increment components d_ij. In contrast with the conventional theory, coefficients in the yield function f cannot be determined from the r-values only in uniaxial tensile tests, but yield stresses in these tests and for example in an equi-biaxial tension for the same are also required. This fact ensures that the curve for arbitrary loading is uniquely determined by the uniaxial tension curve in the rolling direction (R.D.), and thus such an intrinsic difficulty of the conventional theory as dependence of the curve on types of loading does not arise. Some formulae for the determination of the coefficients in f are given. Relationships between types of earing in axi-symmetrical deep-drawing and the coefficients of f are examined in detail and it is emphasized that only very special cases are included in the conventional yield function and thus use of it is very limited.