Low cycle loading of a flat sample with a continuous displacement velocity field considering material compressibility condition

DOI: 10.34759/trd-2023-130-10

Аuthors

Kanashin I. V.^*, Grigorieva F. L.^**, Khromov A. I.^***, Grigoriev Y. Y.^****

Komsomolsk-na-Amure State University, 27, Lenina str., Komsomolsk-on-Amur, 681013, Russia

*e-mail: naj198282@mail.ru
**e-mail: Grigoreva.al@email.knastu.ru
***e-mail: khromovai@list.ru
****e-mail: fct@knastu.ru

Abstract

Low cycle loading of a flat specimen with a continuous displacement velocity field, taking into account the material compressibility condition. Subject of study — Determination of crack initiation moment conditions under low-cycle loading of a flat specimen with a continuous displacement velocity field under flat deformation and flat stressed state with consideration of material compressibility. The purpose of this work is to investigate the processes of tension, compression and sequential tension-compression of a flat sample with a continuous field of displacement velocities under flat deformation and a flat stress state, taking into account the compressibility of the material at small deformations. The compressibility of the material associated with the law of conservation of mass, formulated in the form of the continuity equation, leads to a change in density in the process of loading, in accordance with which the logarithm of the material derivative of density over time is added to the system of equations determining the field of displacement velocities.

The following methods were used in the study: analytical method for determining velocity and strain fields, propagating wave method for solving homogeneous differential equations.

The following results were obtained in the course of the study:

• relations for determination of plastic deformations in problems of uniaxial deformation of a flat specimen with a continuous displacement velocity field taking into account compressibility of the material under flat deformation conditions;
• relations for determination of plastic strains in problems of uniaxial deformation of a plane specimen with a continuous velocity field of displacements, taking into account compressibility of the material in a plane stress state.

The results of the study can be applied in the development of mathematical models of behavior of elements of real structures in the problems of modern mechanical engineering and construction, as well as in evaluating their strength.

Keywords:

rigid plastic body, flat sample, flat deformation, flat stress state, compressibility condition, continuous displacement velocity field, finite-strain Almansi tensor

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