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Strength of Materials

, Volume 30, Issue 4, pp 364–373 | Cite as

Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 1. Prescribed motion

  • M. S. Koval'chenko
Scientific and Technical Section

Abstract

The behavior of an open mechanical dissipative system formed by a viscoelastic hardening body and an elastic working element used for the energy transfer between the testing machine and the deformed body is described by a third-order dynamic differential equation with controlling parameters that depend on the reduced mass and stiffness of the system, its viscous resistance, the degree of strain hardening, the type of the stressed state of the body, and the dissipation of energy in a viscous ambient medium. We analyze the dynamics of uniaxial tension of the deformed body below and above its elasticity limit for the case where the forces induced in the process of motion are determined by the kinematics of the testing machine with prescribed motion. We establish the dynamic nature of the nonlinear section of the tensile stress-strain diagram beyond the elasticity limit of the viscoelastic body corresponding to the so-called “nonlinear elasticity”. It is shown that the appearance of this section is connected with a transient relaxation process. Upon the termination of this process, the forces acting in the system are determined by the viscous flow of the body corresponding to its yield limit. Above the elasticity limit of the body, we observe the formation of a bistable state of the system caused by changes in the controlling parameters and lag effects and leading to its macroscopic acoustic activity.

Keywords

Strain Hardening Viscous Flow Elasticity Limit Rheological Model Constant Strain Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. Nicolis and I. Prigogine,Exploring Complexity. An Introduction [Russian translation], Mir, Moscow (1990).Google Scholar
  2. 2.
    G. Lamb,Hydrodynamics [Russian translation], Gostekhizdat, Moscow-Leningrad (1947).Google Scholar
  3. 3.
    B. Jaoul,Etude de la Plasticite et Application de Metaux, Dunod, Paris (1965).Google Scholar
  4. 4.
    M. S. Koval'chenko, “Dynamics of the influence of mechanical factors on materials. 1. General theory,”Poroshk. Metallurg., No. 7, 41–48 (1993).Google Scholar
  5. 5.
    G. A. Korn and T. M. Korn,Mathematical Handbook for Scientists and Engineers [Russian translation], Nauka, Moscow (1973).Google Scholar
  6. 6.
    A. Angot,Complements de Mathematiques. A L'usage des Ingeniers de L'Electrotechnique et des Telecommunications [Russian translation], Nauka, Moscow (1965).Google Scholar
  7. 7.
    V. A. Ditkin and A. P. Prudnikov,Integral Transformations and Operational Calculus [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  8. 8.
    V. I. Arnold,Theory of Catastrophes [in Russian], Nauka, Moscow (1990).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • M. S. Koval'chenko

There are no affiliations available

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