Skip to main content
Log in

NONLINEAR COUPLED MODEL OF SURFACE TREATMENT BY A PARTICLE BEAM TAKING INTO ACCOUNT THE FORMATION OF A NEW PHASE

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A model of the initial stage of surface treatment of a material by a particle beam is presented which takes into account the mutual influence of elastic, thermal, and diffusion waves and the formation of a new phase in the surface layer of the substrate. Examples of problem solution for different combinations of model parameters are given, and the dynamics of the process under the action of two successive pulses is illustrated. Possible partial variants of the model are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

REFERENCES

  1. Mechanics of Coupled Fields in Construction Elements, Ed. by A. N. Guz’ (Nauk. Dumka, Kiev), pp. 1987–1989 [in Russian].

  2. D. I. Bardzokas, A. I. Zobnin, N. A. Senik, and M. L. Fil’shtinskii, Mathematical Modeling in Problems of Mechanics of Coupled Fields (KomKniga, Moscow, 2005) [in Russian].

    Google Scholar 

  3. B. A. Boley and H. J. Weiner, “Theory of Thermal Stresses," (Wiley–New York–London, 1960).

    MATH  Google Scholar 

  4. Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics (Nauk. Dumka, Kiev, 1976) [in Russian].

    Google Scholar 

  5. H. Lord amd Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity," J. Mech. Phys. Solids 15, 299–309 (1967).

    Article  ADS  Google Scholar 

  6. W. Nowacki, “Dynamical Problems of Thermodiffusion in Solids. 1,"Bull. Acad. Pol. Sci. Ser. Sci. Technol. 22, 55–64 (1974).

    MathSciNet  MATH  Google Scholar 

  7. B. M. Darinskii and T. D. Shermergor, “On the Theory of Diffusion Relaxation in Polycrystals," Prikl. Mekh. Tekh. Fiz., No. 5, 84–89 (1965) [J. Appl. Mech. Tech. Phys., No. 5, 54–57 (1965); https://doi.org/10.1007/BF00913383].

    Article  ADS  Google Scholar 

  8. F. Larché and J. W. Cahn, “A Linear Theory of Thermochemical Equilibrium of Solids under Stress," Acta Metallurg. 21 (8), 1051–1063 (1973). DOI: 10.1016/0001-6160(73)90021-7.

    Article  Google Scholar 

  9. G. Rambert, J.-C. Grandidier, and E. C. Aifantis, “On the Direct Interactions between Heat Transfer, Mass Transport and Chemical Processes within Gradient Elasticity," Europ. J. Mech. A Solids 26, 68–87 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  10. J. N. Sharma, N. Kumari, and K. K. Sharma, “Diffusion in a Generalized Thermoelastic Solid with a Cylindrical Cavity," Prikl. Mekh. Tekh. Fiz. 54 (5), 154–168 (2013) [J. Appl. Mech. Tech. Phys. 54 (5), 819–831 (2013); https://doi.org/10.1134/S0021894413050155].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. A. V. Zemskov and D. V. Tarlakovskii, “Two-Dimensional Nonstationary Problem of Elastic Diffusion for an Isotropic One-Component Layer," Prikl. Mekh. Tekh. Fiz. 56 (6), 102–110 (2015) [J. Appl. Mech. Tech. Phys. 56 (6), 1023–1030 (2015); https://doi.org/10.1134/S0021894415060127].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. G. A. Vershinin, T. S. Grekova, G. I. Gering, et al., “Analysis of the Formation of Concentration Fields in Titanium During Implantation of Aluminum Ions Through a Gas-Metal Film Deposited on the Target Surface,"Poverkhnost’. Rentgen., Sinkhrotron. i Neitron. Issled., No. 3, 68–71 (2012).

  13. N. V. Bukrina, A. G. Knyazeva, and V. P. Sergeev, “Experimental and Numerical Studies of the Formation of Transition Zones during the Bombardment of a Nitride Coating with a Combined Ion Beam," Poverkhnost’. Rentgen., Sinkhrotron. i Neitron. Issled., No. 1, 83–92 (2009).

  14. E. S. Parfenova and A. G. Knyazeva, “Non-Isothermal Mechanodiffusion Model of the Initial Stage of the Process of Introduction of the Particle Beam Penetration into a Target Surface," Vychisl. Mekh. Sploshn. Sred 12 (1), 36–47 (2019). DOI: 10.7242/1999-6691/2019.12.1.4.

    Article  Google Scholar 

  15. E. S. Parfenova and A. G. Knyazeva, “Influence of Chemical Reaction Parameters on the Interaction of Thermal, Diffusion and Mechanical Waves under Conditions of Surface Treatment by a Particle Beam," Vychisl. Mekh. Sploshn. Sred 14 (1), 77–89 (2021). DOI: 10.7242/1999-6691/2021.14.1.7.

    Article  Google Scholar 

  16. V. N. Demidov and A. G. Knyazeva, “Transfer Coefficients for a Three-Component Deformable Alloy," Vestn. Perm. Gos. Tekhn. Univ. Mekhanika, No. 3, 84–99 (2011).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Knyazeva.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 4, pp. 124-133. https://doi.org/10.15372/PMTF20210412.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Knyazeva, A.G., Parfenova, E.S. NONLINEAR COUPLED MODEL OF SURFACE TREATMENT BY A PARTICLE BEAM TAKING INTO ACCOUNT THE FORMATION OF A NEW PHASE. J Appl Mech Tech Phy 62, 633–641 (2021). https://doi.org/10.1134/S002189442104012X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S002189442104012X

Keywords

Navigation