Material Fracture Life Prediction Using Linear Regression Techniques Under High Temperature Creep Conditions

  • Roberto Fernandez MartinezEmail author
  • Pello Jimbert
  • Jose Ignacio Barbero
  • Lorena M. Callejo
  • Igor Somocueto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11896)


9–12% Cr martensitic steels are widely used for critical components of new, high-efficiency, ultra-supercritical power plants because of their high creep and oxidation resistances. Due to the time consuming effort of obtaining creep properties for new alloys under high temperature creep conditions, in both short-term and long-term testing, it is often dealt with simplified models to assess and predict the future behavior of some materials. In this work, the total time to produce the material fracture is predicted according to models obtained using several linear techniques, since this property is really relevant in power plants elements. These models are obtained based on 344 creep tests performed on modified P92 steels. A multivariate analysis and a feature selection were applied to analyze the influence of each feature in the problem, to reduce the number of features simplifying the model and to improve the accuracy of the model. Later, a training-testing validation methodology was performed to obtain more useful results based on a better generalization to cover every scenario of the problem. Following this method, linear regression algorithms, simple and generalized, with and without enhanced by gradient boosting techniques, were applied to build several linear models, achieving low errors of approximately 6.75%. And finally, among them the most accurate model was selected, in this case the one based on the generalized linear regression technique.


Linear regression Generalized linear regression Enhanced linear regression 



The authors wish to thanks to the Basque Government through the KK-2018/00074 METALCRO.


  1. 1.
    Sachadel, U.A., Morris, P.F., Clarke, P.D.: Design of 10% Cr martensitic steels for improved creep resistance in power plant applications. J. Mater. Sci. Technol. 29(7), 767–774 (2013)CrossRefGoogle Scholar
  2. 2.
    Morris, P.F., Sachadel, U.A., Clarke, P.D.: Design of heat treatments for 9–12% Cr steels to optimise creep resistance for power plant applications. In: Proceedings of 9th Liège Conference on Materials for Advanced Power Engineering, Liège, Belgium, pp 554–564 (2010)Google Scholar
  3. 3.
    Mayer, K.H., Bendick, W., Husemann, R.V., Kern, T., Scarlin, R.B.: International Joint Power Generation Conference, PWR, vol. 33, pp. 831–841. ASME, New York (1998)Google Scholar
  4. 4.
    Gold, M., Jaffee, R.I.: Materials for advanced steam cycles. J. Mater. Energy Syst. 6(2), 130–145 (1984)CrossRefGoogle Scholar
  5. 5.
    Viswanathan, R., Bakker, W.: Materials for ultrasupercritical coal power plants - boiler materials: Part 1. J. Mater. Eng. Perform. 10(1), 81–95 (2001)CrossRefGoogle Scholar
  6. 6.
    Lanin, A.A., Grin, E.A.: An approach to assessment of the lifetime characteristics of steels under creep conditions using fracture mechanics criteria. Therm. Eng. 65(4), 239–245 (2018)CrossRefGoogle Scholar
  7. 7.
    Hald, J.: Prospects for martensitic 12% Cr steels for advanced steam power plants. Trans. Indian Inst. Met. 69(2), 183–188 (2016)CrossRefGoogle Scholar
  8. 8.
    Kimura, K., Kushima, H., Sawada, K.: Long-term creep deformation property of modified 9Cr–1Mo steel. Mater. Sci. Eng., A 510, 58–63 (2009)CrossRefGoogle Scholar
  9. 9.
    Sklenička, V., Kuchařová, K., Svoboda, M., Kloc, L., Buršık, J., Kroupa, A.: Long-term creep behavior of 9–12%Cr power plant steels. Mater. Charact. 51(1), 35–48 (2003)CrossRefGoogle Scholar
  10. 10.
    Fujita, T., Asakura, K., Sawada, T., Takamatsu, T., Otoguro, Y.: Creep rupture strength and microstructure of Low C-10Cr-2Mo heat-resisting steels with V and Nb. Metall. Trans. A 12(6), 1071–1079 (1981)CrossRefGoogle Scholar
  11. 11.
    Liu, Y., Tsukamoto, S., Sawada, K., Abe, F.: Role of boundary strengthening on prevention of type IV failure in high cr ferritic heat-resistant steels. Metall. Mater. Trans. A 45(3), 1306–1314 (2014)CrossRefGoogle Scholar
  12. 12.
    Mishnev, R., Dudova, N., Kaibyshev, R.: On the origin of the superior long-term creep resistance of a 10% Cr steel. Mater. Sci. Eng., A 713, 161–173 (2018)CrossRefGoogle Scholar
  13. 13.
    Abe, F.: Creep behavior, deformation mechanisms, and creep life of Mod.9Cr-1Mo steel. Metall. Mater. Trans. Phys. Metall. Mater. Sci. 46(12), 5610–5625 (2015)CrossRefGoogle Scholar
  14. 14.
    Aghajani, A., Somsen, Ch., Eggeler, G.: On the effect of long-term creep on the microstructure of a 12% chromium tempered martensite ferritic steel. Acta Mater. 57(17), 5093–5106 (2009)CrossRefGoogle Scholar
  15. 15.
    Tamura, M., Kumagai, T., Miura, N., Kondo, Y., Shinozuka, K., Esaka, H.: Effect of martensitizing temperature on creep strength of modified 9Cr steel. Mater. Trans. 52(4), 691–698 (2011)CrossRefGoogle Scholar
  16. 16.
    Sawada, K.: Effect of W on recovery of lath structure during creep of high chromium martensitic steels. Mater. Sci. Eng., A 267(1), 19–25 (1999)CrossRefGoogle Scholar
  17. 17.
    Sklenicka, V., Kucharova, K., Svobodova, M., Kral, P., Kvapilova, M., Dvorak, J.: The effect of a prior short-term ageing on mechanical and creep properties of P92 steel. Mater. Charact. 136, 388–397 (2018)CrossRefGoogle Scholar
  18. 18.
    Haney, E.M., et al.: Macroscopic results of long-term creep on a modified 9Cr–1Mo steel (T91). Mater. Sci. Eng., A 510–511, 99–103 (2009)CrossRefGoogle Scholar
  19. 19.
    Fedoseeva, A., Dudova, N., Kaibyshev, R.: Creep strength breakdown and microstructure evolution in a 3% Co modified P92 steel. Mater. Sci. Eng., A 654, 1–12 (2016)CrossRefGoogle Scholar
  20. 20.
    Fernandez Martinez, R., Iturrondobeitia, M., Ibarretxe, J., Guraya, T.: Methodology to classify the shape of reinforcement fillers: optimization, evaluation, comparison, and selection of models. J. Mater. Sci. 52(1), 569–580 (2017)CrossRefGoogle Scholar
  21. 21.
    Fernandez Martinez, R., Lostado Lorza, R., Santos Delgado, A.A., Piedra Pullaguari, N.O.: Optimizing presetting attributes by softcomputing techniques to improve tapered roller bearings working conditions. Adv. Eng. Softw. 123, 13–24 (2018). Scholar
  22. 22.
    Fernandez Martinez, R., Jimbert, P., Ibarretxe, J., Iturrondobeitia, M.: Use of support vector machines, neural networks and genetic algorithms to characterize rubber blends by means of the classification of the carbon black particles used as reinforcing agent. Soft. Comput. (2018). Scholar
  23. 23.
    Hair, J.F., Black, W.C., Babin, B.J., Anderson, R.E.: Multivariate Data Analysis, 7th edn. Pearson, Upper Saddle River (2010)Google Scholar
  24. 24.
    Fernandez Martinez, R., Martinez-de-Pison Ascacibar, F.J., Pernia Espinoza, A.V., Lostado Lorza, R.: Predictive modeling in grape berry weight during maturation process: comparison of data mining, statistical and artificial intelligence techniques. Span. J. Agric. Res. 9(4), 1156–1167 (2011)CrossRefGoogle Scholar
  25. 25.
    Fernandez Martinez, R., Okariz, A., Ibarretxe, J., Iturrondobeitia, M., Guraya, T.: Use of decision tree models based on evolutionary algorithms for the morphological classification of reinforcing nano-particle aggregates. Comput. Mater. Sci. 92, 102–113 (2014)CrossRefGoogle Scholar
  26. 26.
    Jolliffe, I.T.: Principal Component Analysis, 2nd edn. Springer, New York (2002). Scholar
  27. 27.
    Wilkinson, G.N., Rogers, C.E.: Symbolic descriptions of factorial models for analysis of variance. Appl. Stat. 22, 392–399 (1973)CrossRefGoogle Scholar
  28. 28.
    Chambers, J.M.: In: Chambers, J.M., Hastie, T.J. (eds.) Statistical Models in S. Wadsworth & Brooks/Cole (1992)Google Scholar
  29. 29.
    Friedman, J.H.: Greedy function approximation: a gradient boosting machine. Technical report, Department of Statistics, Sequoia Hall, Stanford University, Stanford California 94305 (1999)Google Scholar
  30. 30.
    Friedman, J.H.: Stochastic gradient boosting. Technical report, Department of Statistics, Sequoia Hall, Stanford University, Stanford California 94305 (1999)Google Scholar
  31. 31.
    Wang, Z.: HingeBoost: ROC-based boost for classification and variable selection. Int. J. Biostat. 7(1), 13 (2011)MathSciNetCrossRefGoogle Scholar
  32. 32.
    McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman and Hall, London (1989)zbMATHCrossRefGoogle Scholar
  33. 33.
    Dobson, A.J.: An Introduction to Generalized Linear Models. Chapman and Hall, London (1990)zbMATHCrossRefGoogle Scholar
  34. 34.
    Hasti, T. J., Pregibon, D.: In: Chambers, J.M., Hastie, T.J (eds.) Statistical Models in S. Wadsworth & Brooks/Cole (1992)Google Scholar
  35. 35.
    Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S. Springer, New York (2002). Scholar
  36. 36.
    Fox, J.: Applied Regression Analysis and Generalized Linear Models, 3rd edn. McMaster University, SAGE Publications, Inc, Los Angeles (2015)Google Scholar
  37. 37.
    Freund, Y., Schapire, R.E.: Experiments with a new boosting algorithm. In: Proceedings of 13th International Conference on Machine Learning, San Francisco, CA, pp. 148–156 (1996)Google Scholar
  38. 38.
    Buehlmann, P.: Boosting for high-dimensional linear models. Ann. Stat. 34, 559–583 (2006)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Buehlmann, P., Yu, B.: Boosting with the L2 loss: regression and classification. J. Am. Stat. Assoc. 98, 324–339 (2003)CrossRefGoogle Scholar
  40. 40.
    Buehlmann, P., Hothorn, T.: Boosting algorithms: regularization, prediction and model fitting. Stat. Sci. 22(4), 477–505 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Hothorn, T., Buehlmann, P., Kneib, T., Schmid, M., Hofner, B.: Model-based boosting 2.0. J. Mach. Learn. Res. 11, 2109–2113 (2010)MathSciNetzbMATHGoogle Scholar
  42. 42.
    Hofner, B., Mayr, A., Robinzonov, N., Schmid, M.: Model-based boosting in R: a hands-on tutorial using the R package mboost. Comput. Stat. 29(1–2), 3–35 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    R Development Core Team: R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2017).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.College of Engineering in BilbaoUniversity of the Basque Country UPV/EHUBilbaoSpain
  2. 2.Industry and Transport DivisionFundacion TECNALIA Research & InnovationDerioSpain

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