Visualization of the Unified Strength Theory

摘要

The Unified Strength Theory (UST) provides the fundamentals for the systematic study of various strength hypotheses and yields criteria for isotropic materials. It shows relationship between known models (Mohr-Coulomb, Pisarenko-Lebedev, Twin-Shear Theory of Yu), and apart from these known models, this model contains also classical models like the normal stress hypothesis, VON MlSES, Tresca and Schmidt-Ishlinsky. The UST can be adapted for different types of materials. Thus, it is a suitable tool for the analysis of experimental data. For the UST, the inelastic Poisson's ratio and the maximum hydrostatic tension stress will be computed as a function of model parameters which simplifies the comparison with another model. The correlations between uniaxial, biaxial and hydrostatic stress will be illustrated and compared with classical models. For all classical models and for the UST, the uniaxial and biaxial tension failure stress and also the uniaxial and biaxial compression failure stress are equal. In this sense, the UST can be classified as a classical model. The failure behavior of new materials like some polymers and alloys differs from the classical one. The UST can be extended to such failure behavior. For this purpose, the Unified Yield Criterion (UYC) as part of the UST will be modified so that all known criteria of incompressible material behavior can be approximated. With the help of a simple substitution, the UYC can be further developed for compressible material behavior. Different convex lines can be adjust for the form of the meridian. With this substitution, the hydrostatic tension stress will be restricted with one of the parameters. Furthermore, the model can be applied for the description of failure behavior of ceramics, hard foams and sintered materials. For this application, both the hydrostatic tension and compression stress will be restricted too. Some reference values for hydrostatic loading are established. For the visual comparison of different parameter setting of the models, graphical methods can be used. The UST will be represented in the principal stress space. Further considerations will be carried out in the BURZYNSKI-plane and in the π -plane. For engineering applications, the BURZYNSKI-plane is preferred to the meridional cut. For better analysis and a direct comparison of fitted models to the experimental values, the line of the plane stress state will be shown in the BURZYNSKI-plane and in the π -plane.