Generalized Strength Criteria as Functions of the Stress Angle

The equivalent stress concept allows the comparison of arbitrary multiaxial stress states with a uniaxial one. Based on this concept several limit surfaces were formulated. The trend in the formulation lies in the generalized criteria that contain classical hypotheses and are suitable for several materials. In this work, three generalized criteria are discussed. They are rewritten in order to more closely meet a set of plausibility assumptions. A schematic representation of the unified strength theory (UST) of Yu can be given as a convex combination of the classical hypotheses (Tresca, Schmidt-Ishlinsky, and Rankine). For this schema a criterion as a function of the stress angle is proposed. It describes a single surface without plane intersecting in the principal stress space. The introduced criterion is similar to the UST and like the UST is $C^0$-continuous. The Podgórski criterion as function of the stress angle is $C^1$-continuously differentiable and can be used as yield and strength criterion. The parameters of this criterion are real numbers restricted in order to obtain the convex shapes in the $\pi$-plane. The same parameters can be defined as complex numbers. With these complex parameters, this criterion describes an extended region of the convex shapes in the $\pi$-plane. The Altenbach-Zolochevski criterion as function of the stress angle will be modified in order to describe additional convex shapes in the $\pi$-plane. In contrast to the Altenbach-Zolochevski criterion, the modified criterion contains the Schmidt-Ishlinsky hypothesis as extremal yield function. Both criteria are $C^0$-continuous and can therefore be recommended as strength criteria. The suggested modifications of the discussed criteria extend their application area and simplify the fitting procedure. Therefore these criteria are recommended for practical use.