Construction of plasticity diagrams taking into account the mechanics of deformation localization under uniaxial tension

Abstract

Ogorodnikov V. A., Sukhorukov S. I., Arkhipova T. F. Construction of plasticity diagrams taking into account the mechanics of deformation localization under uniaxial tension. Material working by pressure. 2020. № 1 (50). Р. 147-153.

The plasticity diagrams used in the phenomenological criteria of deformability of metals without fracture as material characteristics are considered. Plasticity diagrams are obtained experimentally by testing materials for tensile, torsion, compression and other types of tests, followed by approximation. In tests under uniaxial tension, fracture is often preceded by localization of deformations in the form of a “neck” formation. In this case, the stress state in the neck becomes volumetric and there are problems of calculations. There is a need to take into account when calculating both indicators of the stress state and the accumulated intensity of deformation at the time of failure.

The paper discusses issues related to the mechanics of the development of neck formation under tension. An analysis is made of the influence of various factors, namely, the stress state diagram, the deformation gradient, and the history of deformation on the value of the limiting intensity of deformations.

A procedure has been developed for calculating ultimate strains in constructing plasticity diagrams under conditions of strain localization under uniaxial growing action. The “anomalous” increase in plasticity with increasing stress state is explained by the influence of three factors: the strain gradient, the strain history, and the third invariant of the stress tensor.

The ductility diagram of steel St. 3 demonstrates the quantitative effect of three factors on the value of ultimate strain in a sample stretched to failure. The total value of the overestimation of the ultimate strain is 35 %.