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Saturation of a plate with an environmental impurity under mechanical loading conditions

Abstract

We analyze a model of saturation of a thin plate with an alloying element under uniform loading with a distributed constant load. The appearance of internal stresses accompanying the diffusion processes is taken into account as well as the effect of the stresses on the mass transfer. The exact solution of the mechanical equilibrium problem has allowed us to reduce the model to a nonlinear diffusion problem with a convective term responsible for mass transfer under the action of stresses. We have found that the external loading significantly affects the process if the magnitude of the distributed load is greater than that of the internal stresses, which, in turn, depends on the material properties and the diffusant type. The time-dependence curves of the average strains in the direction of the acting load are typical of the phenomena of diffusion creep.

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References

  1. 1.

    G. D. C. Kuiken, Thermodynamics of Irreversible Processes. Applications to Diffusion and Rheology (Wiley, New York, 1994).

    Google Scholar 

  2. 2.

    Ya. E. Geguzin, Diffusion Zone (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  3. 3.

    N. I. Bezukhov, Foundations of the Theory of Elasticity, Plasticity, and Creep (Vyssh. Shkola, Moscow, 1961) [in Russian].

    Google Scholar 

  4. 4.

    B. A. Boley and J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960; Mir, Moscow, 1964).

    MATH  Google Scholar 

  5. 5.

    V. S. Eremeev, Diffusion and Stresses (Energoatomizdat, Moscow, 1984) [in Russian].

    Google Scholar 

  6. 6.

    T. D. Shermergor, Theory of Elasticity of Micro-Inhomogeneous Media (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  7. 7.

    A. G. Knyazeva, “Diffusion and Rheology in Locally Equilibrium Thermodynamics,” Mat. Modelirovanie Sist. Prots., No. 13, 45–60 (2005).

  8. 8.

    A. G. Knyazeva, “Cross Effects in Solid Media with Diffusion,” Zh. Prikl. Mekh. Tekhn. Fiz. 44(3), 85–99 (2003) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 44 (3), 373–384 (2003)].

    MATH  MathSciNet  Google Scholar 

  9. 9.

    A. G. Knyazeva, Introduction to Locally Equilibrium Thermodynamics of Physical and Chemical Transformations in Deformable Media (Izd-vo TGU, Tomsk, 1996) [in Russian].

    Google Scholar 

  10. 10.

    A.G. Knyazeva and Ya.G. Donskaya, “ADiffusion-Deformation Model for the Growth of a Spherical Nucleus of a Solid-State Reaction Product,” Fiz. Goreniya Vzryva 33(2), 52–68 (1997) [Comb. Expl. Shock Waves (Engl. Transl.) 33 (2), 168–182 (1997)].

    Google Scholar 

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Correspondence to A. G. Knyazeva.

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Original Russian Text © A.G. Knyazeva, M.A. Mikolaychuk, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 5, pp. 43–57.

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Knyazeva, A.G., Mikolaychuk, M.A. Saturation of a plate with an environmental impurity under mechanical loading conditions. Mech. Solids 46, 692–704 (2011). https://doi.org/10.3103/S0025654411050050

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Keywords

  • plane stress state
  • diffusion
  • coupled problem