Predicting the yield surface in a two-dimensional stress system : a student's laboratory experiment

Abstract

This paper is concerned with the determination of the yield surface in a two-dimensional stress field within an undergraduate Mechanics of Materials student laboratory experiment. In this experiment, the two-dimensional stress field is obtained by subjecting a steel specimen to a combined bending and torsion load. The motivation for the paper was the lack of correlation between the von Mises and Tresca yield criteria and the principal stresses calculated at the load at which students were predicting material yielding. The latter yield loci were based on the uniaxial 0.2% proof stress. The lack of correlation was creating a lot of frustration amongst students. This is undesirable, especially within an undergraduate student experiment. Two hypotheses for the lack of agreement were considered. The first hypothesis was the uncertainty involved in the method that the students were using to predict the onset of material yielding. The second hypothesis was that the specimens being used for the experiment had anisotropic properties, given that little information on their manufacture was provided. The need for determining accurate yield stress values and on methodologies found in literature that are used to determine the material proof stress or lower yield stress in a uniaxial tensile test are discussed. Four methods taken from literature are used and adapted to detect the first yield of the specimen under a combined bending and torsional load. The resulting experimentally yield loci are compared with the theoretical von Mises and Tresca isotropic yield loci over half of the second quadrant of the two-dimensional principal stress field plot. Correlation between the four methods was quite good but not so when compared with the von Mises and Tresca’ loci. A lack of correlation occurred for an increasing torsional load indicating a possible anisotropy in the material properties. These results hinted towards the second hypothesis. A number of tensile test specimens were hence heat treated so as to induce isotropy in the material properties. The combined loading experiments were repeated using the heat-treated samples. A very good correlation was obtained between the experimental yield points for the two-dimensional stress field and the von Mises and Tresca yield loci. This good correlation for the heat-treated specimens confirmed the authors’ second hypothesis on the anisotropic properties in the as-received state and, therefore, the requirement to heat treat the specimens for a meaningful student undergraduate laboratory activity.