The Plastic Flow Condition Including the Poisson’s Ratio

The scheme of deforming based on division of the general material rigidity into two components is proposed. The first component implements relations between different directions of deforming, while the second one determines the material deforming along the selected direction alone. A condition for beginning of plastic flow is obtained which includes the first invariant of the stress tensor and the Poisson’s ratio. The specific potential energy is divided into two components: "own" energy and "bond" energy. The energy additivity for such division is proved. As opposed to criteria of the type of the Schleicher-Mises criterion, the condition of plastic-flow beginning follows from the proposed scheme of deforming without specifying any additional conditions and the observed effects can be described with sufficient accuracy. The condition of plasticity is investigated for certain types of stress states: uniform compression, one-axis tension, pure shear and their combined loading. For some types of loading, it is shown that test results for metals are in a good agreement with the proposed plasticity condition.

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