PSI - Issue 2_A

Petteri Kauppila et al. / Procedia Structural Integrity 2 (2016) 887–894 P. Kauppila et al. / Structural Integrity Procedia 00 (2016) 000–000

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surface of the weld between the header pipe and the tube nozzle in all situations, although it should be noted that these models do not take the special characteristics of a welded joint into account. According to the results, the values of the damage parameter calculated using the model 1 are slightly higher than the values calculated using the model 2. In any case, the values of the damage parameters calculated using the model 1 are only 3-7 percentage points greater than the values calculated using the model 2, and thus the results of the both models are relatively accurate for practical applications. A material can be considered to be essentially fully damaged when the value of the damage parameter exceeds the value 0.3 and the onset of tertiary creep phase has occurred. Despite the slight di ff erence in the values of the damage parameter for the models, the equivalent creep strains at the most damaged location are almost equal between models 1 and 2. From an engineering point of view, the both developed models yield practically equal results within the temperature range 500-600 ◦ C. However, the model 2 is accurate only in relatively high creep temperatures and it becomes slightly inaccurate at lower temperatures, which is a result of the assumed Monkman-Grant relationship. The model 1 is more accurate also in low creep temperatures mainly because of its greater flexibility due to higher number of calibration parameters. Acknowledgements. This work was carried out in the research program Flexible Energy Systems (FLEXe) and sup ported by Tekes and the Finnish Funding Agency for Innovation. The aim of FLEXe is to create novel technological and business concepts enhancing the radical transition from the current energy systems towards sustainable systems. FLEXe consortium consists of 17 industrial partners and 10 research organisations. The programme is coordinated by CLIC Innovation Ltd. www.clicinnovation.fi Altenbach, H., Gorash, Y., Naumenko, K., 2009. Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges. Acta Mechanica 195, 263–274. Arndt, J., Haarmann, K., Kottmann, G., Vaillant, J., Bendick, W., Kubla, G., Arbab, A., Deshayes, F., 2000. The T23 / T24 Book. 2nd ed., Vallourec & Mannesmann Tubes. Betten, J., 2005. Creep Mechanics. Springer-Verlag, Berlin. da Costa Andrade, E., 1910. On the viscous flow in metals, and allied phenomena. Proceedings of the Royal Society A 84, 1–12. Fre´mond, M., 2002. Non-Smooth Thermomechanics. Springer, Berlin. Garofalo, F., 1965. Fundamentals of Creep and Creep-Rupture in Metals. Macmillan series in Materials Science, Macmillan, New York. Gorash, Y., 2008. Development of a creep-damage model for non-isothermal long-term strength analysis of high-temperature components operating in a wide stress range. Ph.D. thesis. Martin-Luther-Universita¨t. Halle-Wittenberg, Germany. Hayhurst, D., 1972. Creep rupture under multiaxial states of stress. Journal of Mechanics and Physics of Solids 20, 381–390. Hayhurst, D., 1994. The use of continuum damage mechanics in creep analysis for design. Journal of Strain Analysis 25, 233–241. Kachanov, L., 1958. On the creep fracture time. Iz. An SSSR Ofd. Techn. Nauk. , 26–31(in Russian). Kachanov, L., 1986. Introduction to continuum damage mechanics. volume 10 of Mechanics of Elastic Stability . Martinus Nijho ff Publishers. Kouhia, R., Marjama¨ki, P., Kivilahti, J., 2005. On the implicit integration of inelastic constitutive equations. International Journal for Numerical Methods in Engineering 62, 1832–1856. Lemaitre, J., 1992. A Course on Damage Mechanics. Springer-Verlag, Berlin. Lemaitre, J., Chaboche, J.L., 1990. Mechanics of Solid Materials. Cambridge University Press. Murakami, S., 2012. Continuum Damage Mechanics. volume 185 of Solid Mechanics and Its Applications . Springer Netherlands. Nabarro, F., Villers, H., 1995. The Physics of Creep and Creep Resistant Alloys. Taylor & Francis Ltd. Naumenko, K., 2006. Modeling of high temperature creep for structural analysis applications. Ph.D. thesis. Martin-Luther-Universita¨t. Halle Wittenberg, Germany. Ottosen, N., Ristinmaa, M., 2005. The Mechanics of Constitutive Modeling. Elsevier. Riedel, H., 1987. Fracture at High Temperatures. MRE Materials Reserch and Engineering, Springer-Verlag, Berlin, Heidelberg. Wallin, M., Ristinmaa, M., 2001. Accurate stress updating algorithm based on constant strain rate assumption. Computer Methods in Applied Mechanics and Engineering 190, 5583–5601. References