Diffusion of impurity in material under vibration loads

D. A. Indeytsev ; Yu. A. Mochalova

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 292-305.

Résumé

Within the framework of the continuum mechanics, the authors develop a two-component impurity-containing model and investigate the mutual influence of impurity diffusion and the basic structure strains. They derive the equation of impurity motion — the generalized diffusion equation, which allows them to take into account not only impurity transport due to the basic structure motion, but also the effect of strain on the diffusion coefficient. The paper considers modeling problems that qualitatively describe two most important phenomena that are observed experimentally under vibration on materials with an admixture, localization of the impurity concentration, and the drop in the generalized rigidity of the sample. In both problems, approximate analytical solutions are obtained that are in good agreement with earlier numerical studies and experimental data.

Détail

Keywords: continuum mechanics, two-component material model, diffusion, deformation, approximate analytical solutions.

Bibliographie

[1] Blekhman I.I., Vibrational Mechanics, Word Scientific, Singapore, 2000 | MR

[2] Polyanskiy A.M., Polyanskiy V.A., Popov-Diumin D.B., “Diagnostics of mechanical condition of structural material by method of high-temperature hydrogen vacuum-extraction”, Proceedings of the Sixth International Congress on Thermal Stresses (Vienna, Austria, 589–592), 2005

[3] Aifants E.C., “On the problem of diffusions in solids”, Acta Mechanica, 37 (1980), 265–296 | DOI | MR

[4] Indeitsev D. A., Naumov V. N., Semenov B. N., Belyaev A. K., “Thermoelastic waves in a continuum with complex structure”, ZAMM, 89 (2009), 279–287 | DOI | Zbl

[5] Indeitsev D. A., Mochalova Yu. A., “Mechanics of multi-component media with exchange of mass and non-classical supplies”, Dynamics of Mechanical Systems with Variable Mass., Springer, 2014, 165–194 | MR

[6] Levin V. A., Nonlinear computational mechanics of strength, v. 1, Models and methods. Formation and development of defects, ed. Levin V. A., Phizmatlit, M., 2014, 452 pp.

[7] Indeitsev D. A., Osipova E.V., “Hydrogen embrittlement under load as a first-order phase transition”, Doclady Physics, 51 (2009), 1901–1906

[8] Indeitsev D.A., Semenov B.N., Sterlin M.D., “The phenomenon of localization of diffusion process in a dynamically deformed solid”, Doclady Physics, 57 (2012), 171–173

[9] J. David Logan, An introduction to nonlinear partial differential equations, Wiley-Interscience, 2008, 397 pp. | MR | Zbl

[10] Abramowitz M., Stegun I. A., Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover, New York, 1972 | MR

[11] Polyanin A. D., Manzhirov A. V., Handbook of Mathematics for Engineers and Scientists, Chapman and Hall/CRC Press, Boca Raton–London, 2007 | MR | Zbl

[12] Belyaev A.K., Polyanskiy V.A., Yakovlev Yu.A., “Stresses in pipeline affected by hydrogen”, Acta Mechanica, 223 (2012), 1611–1619 | DOI | MR | Zbl

[13] Indeitsev D., Mochalova D., “Stress Stage Influence on Diffusion Process in Materials”, Proc. of ICNAAM 2014 (22–28 September 2014, Rhodes, Greece), AIP Conference Proceedings, 1648, 2015, 300004 | DOI | MR

[14] Levin V. A., Nonlinear computational mechanics of strength, v. 1, Models and methods. Formation and development of defects, ed. Levin V. A., Phizmatlit, M., 2014, 452 pp.