Biaxial Plastic Stress-Strain Relations of a Mild Steel for Variable Stress Ratios

Abstract

Abstract The main objective in the study reported in this paper was to provide further experimental checks on the validity of the simple flow theory of plasticity. In this investigation, biaxial stresses were produced by subjecting tubular specimens to internal pressure and axial tension. The tests were made on specimens machined from cold-drawn seamless-steel tubing. Most of the tests were performed under variable biaxial-stress ratios but in order to provide the necessary control data and basic biaxial strength properties, a series of constant stress-ratio tests also was conducted. Eight different types of variable stress-ratio tests were devised to determine the validity of the simple flow theory. The results of these tests do not support the theory. A test also was made to check the validity of the distortion-energy criterion as used in the simple flow theory. The differences between the theoretical and experimental results for this test were too great to be explained as due to experimental error or material anisotropy. A special variable stress-ratio test also was conducted to compare certain requirements of both the slip and simple flow theory. The results from this test were in poor agreement with the simple flow theory and in approximate agreement with the slip theory. An investigation was made to determine the validity of the so-called “loading function” as required by the various plasticity theories. These test results do not agree with the concept of the isotropic expansion of loading functions.