Determination of Limiting Deformations at Testing Cylindrical Samples for Tension


  • I. Iu. Kyrytsya Vinnitsa National Technical University
  • O.V. Petrov Vinnitsa National Technical University, Ukraine
  • I.V. Vishtak Vinnitsa National Technical University
  • S.I. Sukhorukov Vinnitsa National Technical University



limiting deformations, stress state indicators, deformations gradient, deformation history, stress tensor, deformation tensor, plasticity diagram, tension testing


This paper proposes a method for calculating limiting deformations under conditions of localized deformation during tensile testing. The method for calculating limiting deformations was used to construct plasticity diagrams under conditions of strain localization under uniaxial tension.

The plasticity diagram is one of the material functions that forms the technological map of the material. The plasticity diagram displays the properties of a material depending on the degree of deformation and the stress state scheme.

According to the studies carried out in this work, it was established that the critical increase in plasticity with increasing stress state indicator is explained by the influence of three factors: the strain gradient, the history of deformation and the third invariant of the stress tensor.

The obtained dependencies make it possible to construct plasticity diagrams for materials whose destruction is preceded by localized deformation in the form of a "neck".

This work establishes the quantitative influence of these three factors on the magnitude of the limiting deformations of a sample stretched to the point of failure.

Application plasticity diagrams constructed using the proposed methods for cold plastic deformation processes, depending on the type of deformation path and the features of metal rheology, clarifies the value of the used plasticity resource of the metal, which allows to reduce the number of defective products for processes whose modes are calculated according to limit deformations.


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How to Cite

Kyrytsya, I. I., Petrov, O., Vishtak, I., & Sukhorukov, S. (2024). Determination of Limiting Deformations at Testing Cylindrical Samples for Tension. Problems of Tribology, 29(1/111), 6–15.