IMPURITY DIFFUSION IN MATERIAL UNDER VIBRATION LOADS
https://doi.org/10.22405/2226-8383-2017-18-3-290-303
Abstract
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.
About the Authors
D. A. Indeytsev
Institute for Problems in Mechanical Engineering RAS
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor, corresponding member of Russian Academy of Sciences, scientific head
Yu. A. Mochalova
Institute for Problems in Mechanical Engineering RAS
Russian Federation
Russian Federation
candidate of physical and mathematical sciences, сsenior research
References
1. Abramowitz, M. & Stegun, I. A. 1972, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover, New York
2. Aifants, E.C.1980, "On the problem of diffusions in solids’,Acta Mechanica, 37, pp. 265–296
3. Blekhman, I.I. 2000, Vibrational Mechanics, Word Scientific, Singapore
4. Belyaev, A.K., Polyanskiy, V.A. & Yakovlev, Yu.A. 2012 "Stresses in pipeline affected by hydrogen’. Acta Mechanica, 223, pp. 1611–1619
5. Indeitsev, D.A. & Osipova, E.V. 2009, "Hydrogen embrittlement under load as a first-order phase transition’, Doclady Physics, 51, pp. 1901–1906
6. Indeitsev, D.A., Naumov, V.N., Semenov, B.N. & Belyaev, A.K. 2009, "Thermoelastic waves in a continuum with complex structure’, ZAMM, 89, pp.279–287
7. Indeitsev, D.A., Semenov, B.N. & Sterlin, M. D. 2012, "The phenomenon of localization of diffusion process in a dynamically deformed solid’. Doclady Physics, 57, pp. 171–173
8. Indeitsev, D.A., Mochalova Yu.A. 2014, "Mechanics of multi-component media with exchange of mass and non-classical supplies’, In: Dynamics of Mechanical Systems with Variable Mass, Springer, pp. 165–194
9. Papanicolaou G.P. 1995, "Diffusion in Random Media’. In: Surveys in Applied Mathematics, Springer, pp 205–253
10. Polyanin A.D., Manzhirov A.V.: 2007, Handbook of Mathematics for Engineers and Scientists, Boca Raton-London: Chapman and Hall/CRC Press
11. Polyanskiy, A.M., Polyanskiy, V.A. & Popov-Diumin, D.B. 2005, "Diagnostics of mechanical condition of structural material by method of high-temperature hydrogen vacuum-extraction’ (Proc. of the Sixth International Congress on Thermal Stresses) Vienna, Austria, pp.589–592
12. Indeitsev D.A. & Mochalova Yu.A. 2017 "On the Problem of Diffusion in Materials Under Vibrations’, Chapter Mechanics for Materials and Technologies, Volume 46 of the series Advanced Structured Materials, pp 183-193.
13. Indeitsev, D. & Mochalova D. 2015, "Stress Stage Influence on Diffusion Process in Materials’, (Proc. of ICNAAM 2014, 22-28 September 2014, Rhodes, Greece) AIP Conference Proceedings 1648, 300004
14. Levin V.A. 2014, Nonlinear computational mechanics of strength, Vol.1, Models and methods. Formation and development of defects, Ed. Levin, V.A. Phizmatlit, Moscow, 452p.
Review
For citations:
Indeytsev D.A., Mochalova Yu.A. IMPURITY DIFFUSION IN MATERIAL UNDER VIBRATION LOADS. Chebyshevskii Sbornik. 2017;18(3):290-303. (In Russ.) https://doi.org/10.22405/2226-8383-2017-18-3-290-303
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