Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Tribocorrosion in Pressurized High-Temperature Water: A Mass Flow Model Based on the Third-Body Approach


Pressurized water reactors (PWR) used for power generation are operated at elevated temperatures (280–300 °C) and under high pressure (120–150 bar). In addition to these harsh environmental conditions some components of the PWR assemblies are subject to mechanical loading (sliding, vibration and impacts) leading to undesirable and hardly controllable material degradation phenomena. In such situations wear is determined by the complex interplay (tribocorrosion) between mechanical, material and physical–chemical phenomena. Tribocorrosion in PWR conditions is at present little understood and models need to be developed in order to predict component lifetime over several decades. This paper present an attempt to model PWR tribocorrosion through the combination of a tribological third-body approach with a mechanistic description of the involved flows and the mass balance compartments corresponding to well-defined loci of the contact. The obtained model permits to gain better insight in the phenomenology and in the mechanisms of tribocorrosion of metals in PWR conditions. It also allows assessing the relative role of a variety of materials, mechanical and electrochemical parameters affecting the entire system. Quantitative predictions of the model were found to fit reasonably well experimental observations

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


|M o|3 :

Metal mass in the compartment 3 (g)

|M o|4 :

Metal mass in the compartment 4 (g)

\(F_{\text{N}}\) :

Normal force (N)

\(K_{{\phi_{1} }}\) :

Non-dimensional wear coefficient

\(K_{{\phi_{2} }}\) :

Proportionality constant of the flow ϕ 2

\(K_{{\phi_{3} }}\) :

Wear coefficient of the flow ϕ 3 (m2 N−1)

\(K_{{\phi_{4} }}\) :

Proportionality constant of the flow ϕ 4 (s−1)

\(K_{{\phi_{5} }}\) :

Proportionality constant of the flow ϕ 5 (s−1)

K p :

Parabolic oxidation constant (kg2 m−4 s−1)

\(t_{\text{cycle}}\) :

Time interval between two successive strokes (s)

\(v_{\text{s}}\) :

Sliding velocity (m s−1)

\(v_{\text{settling}}\) :

Settling velocity (m s−1)

\(\rho_{\text{f}}\) :

Fluid density (kg m−3)

\(\rho_{\text{metal}}\) :

Metal density (kg m−3)

\(\rho_{\text{oxide}}\) :

Density of the oxide (kg cm−3)

\(\rho_{\text{p}}\) :

Density of the particles (kg m−3)

ϕ 1 :

Flow of metal particles entering the friction film (kg s−1)

ϕ 2 :

Flow of oxidized metal particles entering friction film (kg s−1)

ϕ 3 :

Flow of particles detached from the friction film (kg s−1)

ϕ 4 :

Flow of particles re-deposed in the friction film (kg s−1)

ϕ 5 :

Flow of oxidized metal particles within the friction film (kg s−1)


Concentration of the reactant A (mol l−1)

a :

Attenuation factor

A :

Reactant in a chemical equation

A cross,section :

Cross-sectional area (m2)

B :

Product in a chemical equation


Compartment 1: contains mass of bulk metal (kg s−1)


Compartment 2: Contains mass of oxidized metal on the friction film (kg s−1)


Compartment 3: contains mass of non-oxidized metal in the friction film (kg s−1)


Compartment 4: contains mass of oxidized metal in water (wear) (kg s−1)

F :

Faraday constant (C mol−1)

g :

Gravitational acceleration (m s−2)

H :

Indentation hardness inside the wear track (N m−2)

k :

Reaction rate coefficient (s−1)

M 1(t):

Mass in the compartment 1 in function of time (g)

M 2(t):

Mass in the compartment 2 in function of time (g)

M 3(t):

Mass in the compartment 3 in function of time (g)

M 4(t):

Mass in the compartment 4 in function of time (g)

m alloy :

Mass of bare metal (kg)

M alloy :

Alloy’s molar mass (kg mol−1)



M mol :

Molar mass (kg mol−1)

m oxide :

Amount of oxide formed using a given amount of metal (kg)

M oxide :

Molar mass of the oxide (kg mol−1)

m s :

Mass of the formed oxide per unit of surface (Kg m−2)

n :

Oxidation valence of the metal

n X,alloy :

Number of moles of the element X in the alloy (mol)

n X,oxide :

Number of moles of the element X in the oxide (mol)

Q p :

Charge density (C m−2)

R :

Particle radius (m)

r ox :

Stoichiometric ratio

t :

Time (s)

V C4 :

Volume of the compartment 4 (m3)

µ :

Dynamic viscosity (Kg m−1 s−1)


  1. 1.

    Kaczorowski, D., Vernot, J.P.: Wear problems in nuclear industry. Tribol. Int. 39(10), 1286–1293 (2006)

  2. 2.

    Blau P.J., Hayrapetian A.V., Demkowicz M.J.: Development of a Predictive Wear Model for Grid-to-Rod Fretting in Light Water Nuclear Reactors. Tribo-Corrosion: Research, Testing, and Applications on April 19–20, 2012 in Atlanta, GA; STP 1563, Peter J. Blau, Jean-Pierre Celis, and Dirk Drees, Editors, pp. 139–158, doi:10.1520/STP156320120035, ASTM International, West Conshohocken, PA 2013

  3. 3.

    Frick, T.: Overview on the development and implementation of methodologies to compute vibration and wear of steam generator tubes. ASME Sympoisum on Flow-Induced Vibration vol 3, pp. 149–161 (1984)

  4. 4.

    Kim, K.T.: The study on grid-to-rod fretting wear models for PWR fuel. Nucl. Eng. Des. 239(12), 2820–2824 (2009)

  5. 5.

    Attia, H., Gessesse, Y.B., Osman, M.O.M.: New parameter for characterizing Ind correlating impact-sliding fretting wear to energy. Dissipation-experimental investigation, Wear 236, 419–429 (2007)

  6. 6.

    Le Calvar, M., Lemaire, E.: Evidence of tribocorrosion wear in pressurized water reactors. Wear 249(5-6), 338–344 (2001)

  7. 7.

    Berthier, Y., Vincent, L., Godet, M.: Velocity accommodation sites and modes in tribology. Eur. J. Mech. A Solid 11(1), 35–47 (1992)

  8. 8.

    Felder, R.M., Rousseau, R.W.: Elementary Principles of Chemical Processes. Wiley, New York (2004)

  9. 9.

    Bearup, D.J., Evans, N.D., Chappell, M.J.: The input-output relationship approach to structural identifiability analysis. Comput. Meth. Prog. Bio. 109(2), 171–181 (2013)

  10. 10.

    Dupin, M., Gosser, P., Walls, M.G., Rondot, B., Pastol, J.L., Faty, S., Ferreira, M.G.S., Belo, M.D.C.: Influence of pH on the chemical and structural properties of the oxide films formed on 316L stainless steel, alloy 600 and alloy 690 in high temperature aqueous environments. Ann. Chim. Sci. Mat. 27(1), 19–32 (2002)

  11. 11.

    Kritzer, P., Boukis, N., Dinjus, E.: Factors controlling corrosion in high-temperature aqueous solutions: a contribution to the dissociation and solubility data influencing corrosion processes. J. Supercrit. Fluid 15(3), 205–227 (1999)

  12. 12.

    Kaczorowski, D., Combrade, P., Vernot, J.P., Beaudouin, A., Crenn, C.: Water chemistry effect on the wear of stainless steel in nuclear power plant. Tribol. Int. 39(12), 1503–1508 (2006)

  13. 13.

    Kaczorowski, D., Georges, J.M., Bec, S., Tonck, A., Vannes, A.B., Vernot, J.P.: Wear of a stainless steel in pressurised high temperature water. C. R. Phys. 2(5):739–747 (2001)

  14. 14.

    Ziemniak, S.E.: Metal oxide solubility behavior in high temperature aqueous solutions. J. Solut. Chem. 21(8), 745–760 (1992)

  15. 15.

    Lina, A., Moinereau, D., Delaune, X., Phalippou, C., Reynier, B., Riberty, P.: The influence of water flow on the impact/sliding wear and oxidation of PWR control rods specimens. Wear 251, 839–852 (2001)

  16. 16.

    Lister, D.H., Davidson, R.D., Mcalpine, E.: The mechanism and kinetics of corrosion product release from stainless-steel in lithiated high-temperature water. Corros. Sci. 27(2), 113–140 (1987)

  17. 17.

    Landolt, D.: Corrosion and Surface Chemistry of Metals. EPFL Press, Lausanne (2006)

  18. 18.

    Chitty, W.J., Vernot, J.P.: Tribocorrosion issues in nuclear power generation. In: Landolt, D., Mischler, S. (eds.) Tribocorrosion of passive metals and coatings. Woodhead Publishing, Sawston (2011)

  19. 19.

    Perret, J. : Modélisation de la tribocorrosion d’aciers inoxydables dans l’eau à haute pression et haute température. Thèse EPFL N° 4727 Lausanne 2010

  20. 20.

    Chitty, W.: NTCT-F R08.1107: Avancement des essais R&D sur le tribomètre AURORE équipé de mesure électrochimique; 2008

  21. 21.

    Perret, J., Boehm-Courjault, E., Cantoni, M., Mischler, S., Beaudouin, A., Chitty, W., Vernot, J.P.: EBSD, SEM and FIB characterisation of subsurface deformation during tribocorrosion of stainless steel in sulphuric acid. Wear 269(5–6), 383–393 (2010)

  22. 22.

    Guadalupe Maldonado, S., Mischler, S., Chitty, W.-J., Falcand, C., Hertz, D.: Mechanical and chemical mechanisms in the tribocorrosion of Stellite type alloy. Wear 308(1), 213–221 (2013)

  23. 23.

    Favero, M., Stadelmann, P., Mischler, S.: Effect of the applied potential of the near surface microstructure of a 316L steel submitted to tribocorrosion in sulfuric acid. J. Phys. D Appl. Phys. 39(15), 3175–3183 (2006)

  24. 24.

    Bidiville, A., Favero, M., Stadelmann, P., Mischler, S.: Effect of surface chemistry on the mechanical response of metals in sliding tribocorrosion systems. Wear 263, 207–217 (2007)

  25. 25.

    Buscher, R., Tager, G., Dudzinski, W., Gleising, B., Wimmer, M.A., Fischer, A.: Subsurface microstructure of metal-on-metal hip joints and its relationship to wear particle generation. J. Biomed. Mater. Res. B 72B(1), 206–214 (2005)

  26. 26.

    Mischler, S., Debaud, S., Landolt, D.: Wear-accelerated corrosion of passive metals in tribocorrosion systems. J. Electrochem. Soc. 145(3), 750–758 (1998)

  27. 27.

    Steinfeld, J.I., Hase, W.L.: Chemical Kinetics and Dynamics. Prentice Hall, Upper Saddle River (1999)

  28. 28.

    Kaczorowski, D.: Usures d’un acier inoxydable austénitique dans l’eau à haute pression et haute température. Thèse ECL N° 2002-10, Lyon 2002

  29. 29.

    Guadalupe Maldonado, S.: Tribocorrosion in pressurized high temperature water: a mass flow model based on the third body approach. Thèse EPFL N° 6430, Lausanne 2014

  30. 30.

    Kermouche, G., Kaiser, A.L., Gilles, P., Bergheau, J.M.: Combined numerical and experimental approach of the impact-sliding wear of a stainless steel in a nuclear reactor. Wear 263, 1551–1555 (2007)

  31. 31.

    Hsu, S.M., Shen, M.C.: Wear Maps. In: Bushan, B. (ed.) Modern Tribology Handbook. CRC, Boca Raton (2001)

  32. 32.

    Wei, J.J., Xue, Q.J.: The friction and wear properties of Cr2O3 coating with aqueous lubrication. Wear 199, 157–159 (1996)

  33. 33.

    Liu, H.W., Xue, Q.J.: Wear mechanisms of zirconia/steel reciprocating sliding couple under water lubrication. Wear 201, 51–57 (1996)

  34. 34.

    Lancaster, J.K.: A review of the influence of environmental humidity and water on friction, lubrication and wear. Tribol. Int. 23, 371–389 (1990)

  35. 35.

    Robertson, J.: The mechanism of high-temperature aqueous corrosion of stainless-steels. Corros. Sci. 32(4), 443–465 (1991)

Download references

Author information

Correspondence to S. Mischler.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Guadalupe, S., Falcand, C., Chitty, W. et al. Tribocorrosion in Pressurized High-Temperature Water: A Mass Flow Model Based on the Third-Body Approach. Tribol Lett 62, 10 (2016).

Download citation


  • Tribocorrosion
  • Nuclear reactor
  • Modeling
  • Wear
  • Third body
  • Stainless steel