Skip to main content
SpringerLink
Log in

Coupling diffusion–reaction–mechanics model for oxidation

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Considering the chemical reaction during metal oxidation at high temperature, a coupled diffusion–reaction–mechanics model of the metallic oxidation is developed, which is different from the existing mechanochemistry coupling model. Seen from the coupled model, the hydrostatic pressure depending on the diffusion and reaction is a harmonic function if the body force is ignored. Analytical solutions of the concentration and hydrostatic pressure in the steady state are obtained. Then a numerical example in the unsteady state is performed by means of the finite difference method. Numerical results show that the distribution of the concentration in the thin plate is nonlinear due to the interactions among diffusion, reaction and stress.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Saillard A., Cherkaoui M., Capolungo L., Busso E.P.: Stress influence on high temperature oxide scale growth: modeling and investigation on a thermal barrier coating system. Philos. Mag. 90, 2651 (2010)

    Article  Google Scholar 

  2. Entchev P.B., Lagoudas D.C., Slattery J.C.: Effects of non-planar geometries and volumetric expansion in the modeling of oxidation in titanium. Int. J. Eng. Sci. 39, 695 (2001)

    Article  Google Scholar 

  3. Garikipati K., Rao V.S.: Recent advances in models for thermal oxidation of silicon. J. Comput. Phys. 174, 138 (2001)

    Article  MATH  Google Scholar 

  4. Golmon S., Maute K., Dunn M.L.: Numerical modeling of electrochemical–mechanical interactions in lithium polymer batteries. Comput. Struct. 87, 1567 (2009)

    Article  Google Scholar 

  5. Cui Y., Wei Q.Q., Park H.K., Lieber C.M.: Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species. Science 293, 1289 (2001)

    Article  Google Scholar 

  6. Walter E.C., Penner R.M., Liu H., Ng K.H., Zach M.P., Favier F.: Sensors from electrodeposited metal nanowires. Surf. Interface Anal. 34, 409–412 (2002)

    Article  Google Scholar 

  7. Bakkers E.P.A.M., Borgström M.T., Verheijen M.A.: Epitaxial growth of III-V nanowires on group IV substrates. MRS bull. 32, 117 (2007)

    Article  Google Scholar 

  8. Zhu G.N., Wang Y.G., Xia Y.Y.: Ti-based compounds as anode materials for Li-ion batteries. Energy Environ. Sci. 5, 6652 (2012)

    Article  Google Scholar 

  9. Zhang J.Z.: Metal oxide nanomaterials for solar hydrogen generation from photoelectrochemical water splitting. MRS bull. 36, 48 (2011)

    Article  Google Scholar 

  10. Ling Y.C., Wang G.M., Reddy J., Wang C.C., Zhang J.Z., Li Y.: The influence of oxygen content on the thermal activation of hematite nanowires. Angew. Chem. 124, 4150 (2012)

    Article  Google Scholar 

  11. Saillard A., Cherkaoui M., El Kadiri H.: Stress-induced roughness development during oxide scale growth on a metallic alloy for SOFC interconnects. Model. Simul. Mater. Sci. Eng. 19, 015009 (2011)

    Article  Google Scholar 

  12. Freund L.B., Nix W.D.: A critical thickness condition for a strained compliant substrate/epitaxial film system. Appl. Phys. Lett. 69, 173 (1996)

    Article  Google Scholar 

  13. Zhang T.Y., Lee S., Guido L.J., Hsueh C.H.: Criteria for formation of interface dislocations in a finite thickness epilayer deposited on a substrate. J. Appl. Phys. 85, 7579 (1999)

    Article  Google Scholar 

  14. Panicaud B., Grosseau-Poussard J., Dinhut J.: General approach on the growth strain versus viscoplastic relaxation during oxidation of metals. Comput. Mater. Sci. 42, 286 (2008)

    Article  Google Scholar 

  15. Maharjan S., Zhang X., Wang Z.: Effect of oxide growth strain in residual stresses for the deflection test of single surface oxidation of alloys. Oxidation Metals 77, 93 (2012)

    Article  Google Scholar 

  16. Clarke D.R.: The lateral growth strain accompanying the formation of a thermally grown oxide. Acta Mater. 51, 1393 (2003)

    Article  Google Scholar 

  17. Hu S.M.: Stress-related problems in silicon technology. J. Appl. Phys. 70, R53 (1991)

    Article  Google Scholar 

  18. Evans A.G., Hutchinson J.W.: The thermomechanical integrity of thin films and multilayers. Acta Metall. Mater. 43, 2507 (1995)

    Article  Google Scholar 

  19. Hsueh C.H., Evans A.G.: Residual stresses and cracking in metal/ceramic systems for microelectronics packaging. J. Am. Ceram. Soc. 68, 120 (1985)

    Article  Google Scholar 

  20. Volkert C.A.: Stress and plastic flow in silicon during amorphization by ion bombardment. J. Appl. Phys. 70, 3521 (1991)

    Article  Google Scholar 

  21. Volkert C.A.: Density changes and viscous flow during structural relaxation of amorphous silicon. J. Appl. Phys. 74, 7107 (1993)

    Article  Google Scholar 

  22. Evans H.E.: Stress effects in high temperature oxidation of metals. Int. Mater. Rev. 40, 1 (1995)

    Article  Google Scholar 

  23. Bull S.J.: Modeling of residual stress in oxide scales. Oxid. Metals. 49, 1 (1998)

    Article  Google Scholar 

  24. Wang D., Wu X., Wang Z., Chen L.: Cracking causing cyclic instability of LiFePO4 cathode material. J. Power Sources. 140, 125 (2005)

    Article  Google Scholar 

  25. Krishnamurthy R., Srolovitz D.J.: Stress distributions in growing oxide films. Acta Mater. 51, 2171 (2003)

    Article  Google Scholar 

  26. Stephen L.C.: Mechanochemistry: A tour of force. Nature. 487, 176 (2012)

    Article  Google Scholar 

  27. Hickenboth C.R., Moore J.: Biasing reaction pathways with mechanical force. Nature. 446, 423 (2007)

    Article  Google Scholar 

  28. Hu S.L., Shen S.P.: Non-equilibrium thermodynamics and variational principles for fully coupled thermal–mechanical–chemical processes. Acta Mech. 224, 2895 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. Suo Y.H., Shen S.P.: General approach on chemistry and stress coupling effects during oxidation. J. Appl. Phys. 114, 4905 (2013)

    Article  Google Scholar 

  30. Sallès-Desvignes I., Bertrand G., Montesin T., Favergeon J.: Coupling between diffusion, stress field and chemical reaction in a metal– gas oxidation. Solid State Phenom. 72, 9 (2000)

    Article  Google Scholar 

  31. Prussin S.: Generation and distribution of dislocations by solute diffusion. J. Appl. Phys. 32, 1876 (1961)

    Article  Google Scholar 

  32. Li J.C.M.: Physical chemistry of some microstructural phenomena. Metall. Trans. A. 9, 1353 (1978)

    Article  Google Scholar 

  33. Lee S.B., Wang W.L., Chen J.R.: Diffusion-induced stresses in a hollow cylinder: constant surface stresses. Mater. Chem. Phys. 64, 123 (2000)

    Article  Google Scholar 

  34. Wang W.L., Lee S.B., Chen J.R.: Effect of chemical stress on diffusion in a hollow cylinder. J. Appl. Phys. 91, 9584 (2002)

    Article  Google Scholar 

  35. Larche F.C., Cahn J.W.: The interactions of composition and stress in crystalline solids. J. Res. Natl. Bur. Stand. 89, 467 (1984)

    Article  Google Scholar 

  36. Yang F.Q.: Interaction between diffusion and chemical stresses. Mater. Sci. Eng. A. 409, 153 (2005)

    Article  Google Scholar 

  37. Rhines F.N., Wolf J.S.: The role of oxide microstructure and growth stresses in the high-temperature scaling of nickel. Metall. Trans. 1, 1701 (1970)

    Article  Google Scholar 

  38. Yang F.Q.: Effect of local solid reaction on diffusion-induced stress. J. Appl. Phys. 107, 103516 (2010)

    Article  Google Scholar 

  39. Landau L.D., Lifschitz E.M.: Theory of Elasticity, 3rd ed. Oxford, England (1986)

    Google Scholar 

  40. Timoshenko S.P., Goodier J.N.: Theory of elasticity. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  41. Morales-Rodriguez, R.: Thermodynamics Fundamentals and its Application in Science. InTech, Rijeka (2012)

  42. Li J.C.M.: Chemical potential for diffusion in a stressed solid. Scr. Metall. 15, 21 (1981)

    Article  Google Scholar 

  43. Zhang X., Shyy W., Sastry A.M.: Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc. 154, A910 (2007)

    Article  Google Scholar 

  44. Bhandakkar T.K., Gao H.: Cohesive modeling of crack nucleation under diffusion induced stresses in a thin strip: implications on the critical size for flaw tolerant battery electrodes. Int. J. Solids Struct. 47, 1424 (2010)

    Article  MATH  Google Scholar 

  45. Devereux O.F.: Topics in metallurgical thermodynamics. Wiley, (1983)

  46. De Groot S.R., Mazur P.: Non-equilibrium thermodynamics. Courier Dover, New York (1984)

    Google Scholar 

  47. Simon A.M.: A criticism of the postulated quadratic steady-state concentration profile for strain gradient induced hydrogen diffusion in metallic membranes. Int. J. Hydro. Energy. 22, 27 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Xi’an university of Science and Technology, Xi’an, 710054, China

    Yaohong Suo

  2. State Key Lab for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Yaohong Suo & Shengping Shen

  3. School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108, China

    Yaohong Suo

Authors
  1. Yaohong Suo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengping Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengping Shen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suo, Y., Shen, S. Coupling diffusion–reaction–mechanics model for oxidation. Acta Mech 226, 3375–3386 (2015). https://doi.org/10.1007/s00707-015-1366-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1366-7

Keywords

Search

Navigation