Distortion Energy Theory Research Articles

Stress-strain relations in the plastic range for biaxial stresses

This paper gives the results of an experimental investigation on thin-walled aluminum alloy tubes subjected to combined tension and torsion. A specially designed testing machine was constructed for obtaining plastic load-strain relations to rupture for various ratios of the principal stresses ranging from 0 to -1.0. During each test, the ratios of the principal stresses were maintained essentially constant. Nominal stress-strain diagrams for the elastic range and true stress-strain diagrams for the plastic range were plotted for each test and each stress ratio. Values of yield strength, ultimate strength, fracture strength, ductility, and plastic stress-strain relations for the various biaxial stress ratios investigated were compared with theoretical values based upon uniaxial tension results. The yield strength values were found to be in good agreement with values predicted by the Von Mises-Hencky Distortion Energy Theory. The nominal ultimate strengths, fracture strengths, ductility, and plastic stress-strain relations were approximately in agreement with the values predicted by the distortion energy theory using St. Venant's plasticity relations.

Anisotropic Plastic Flow

Abstract The mathematical theory of plasticity has been generalized to apply to plastically anisotropic materials. The anisotropic flow theory has been shown to reduce to the resolved shear stress - shear strain relationship for single crystals, and to the distortion energy theory for isotropic polycrystals. Experimental data concerning the plastic flow of anisotropic polycrystalline aluminum indicate that the predictions of the anisotropic flow theory are in good agreement with experiment, and are significantly better than the predictions of the distortion energy theory. As plastic anisotropy is the rule rather than the exception, caution is indicated in interpreting the results of combined stress tests by means of the distortion energy theory.

Partially plastic thick-walled tubes

A theory is presented for the partial plastic yielding of thick-walled cylindrical tubes acted upon by any combination of internal pressure, external pressure and end load when the material follows an arbitrary stress-strain law. The solution combines (a) the distortion energy theory of plastic flow and (b) the effects of elastic compressibility of the plastic material. Numerical values for stresses and strains are given for certain special cases of internal pressure in thick-walled open-ended tubes for an idealized stress-strain law, and the results are compared with earlier approximate theories.

Strengthening of Circular Holes in Plates Under Edge Loads

Abstract In this paper, stress distributions are determined around strengthened circular holes in plates submitted to edge loads at infinity. Various proportions of circular strengthenings are considered, and three conditions of applied edge loads are investigated; uniform hydrostatic stress, uniform shearing stress, uniform axial stress. Stress distributions are found by methods of theory of elasticity, and the results are given in the form of stress-concentration factors. In order to reduce the results to a common basis, the stress-concentration factors have been defined by the ratio of the critical stress, computed by the distortion-energy theory, to the critical stress at infinity, which is the critical stress in the plate without hole.