PSI - Issue 5

Tomasz Tomaszewski et al. / Procedia Structural Integrity 5 (2017) 840–847 Tomasz Tomaszewski et al. / StructuralIntegrity Procedia 00 (2017) 000 – 000

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The mean errors summarized in Table 8 allow for general assessment of the correctness of applying the given model. Due to the non-parallelism of the characteristics, a percent error was calculated for the extreme ranges of the fatigue life tested in respect of high-cycle fatigue. The results of these calculations are presented on Fig. 8, taking into account the safe area, unsafe area, and the confidence interval. The applied model of highly stressed volume allows to shift the σ a -N characteristics in the proper direction, and make linear change to fatigue life. The estimated fatigue limit is lower than the input values. This is confirmed by the results of experimental tests. The estimated fatigue characteristics σ a -N is parallel to the base characteristics. The percent errors calculated are dependent on fatigue life. As it is shown on the diagram (Fig. 8), the estimated characteristics is within the confidence interval of the reference characteristics only at the level of higher fatigue life. 1.4310 acid resistant steel exhibited sensitivity to changing the cross-section size both in respect of axial loads (statistical size effect) as well as bending loads (geometrical size effect). K HC coefficient was used for describing the differences in fatigue life, whose mean value is higher for bending loads (1.275) than for axial loads (1.086). This is in accordance with the theoretical assumptions. For smaller specimens, the stress value is smaller at the assumed length a 0 of the stress gradient. Analyzing the size effect in terms of its definition it may be concluded that, in the case of bending loads, for material sensitive to the size effect, the impact of statistical and geometrical size effect cumulates. The simplest approach that takes into account the size effect is applying a correction coefficient determined empirically, or applying an analytical model indicated for the given area of analyses. However, this proves to be insufficient for loads other than axial loads. Such approach may lead to significant errors in estimating fatigue strengths. The highly stressed volume model allows for linear change of the fatigue limit. In the case of non-parallel fatigue characteristics, the errors in estimating fatigue properties are varied. The obtaining of results with smaller error would be possible provided that the size effect models that take into account the dispersion of results and change of the angle of the estimated characteristics, other than the base characteristics, would be used. Carpinteri, A., Spagnoli, A., 2009. Size effect in S-N curves: A fractal approach to finite-life fatigue strength. International Journal of Fatigue. 31, 927-933. Götz S., Eulitz K.-G., 2013. Concepts to estimate the endurance limit of notched parts – statistical evaluation using a broad database for PM steels. International Journal of Fatigue. 52, 1-10. Härkegård, G., Halleraker, G., 2010. Assessment of methods for prediction of notch and size effects at the fatigue limit based on test data by Böhm and Magin. International Journal of Fatigue. 32, 1701-1709. Kloos, K.H., Buch, A., Zankov, D., 1981. Pure geometrical size effect in fatigue tests with constant stress amplitude and in programme tests. Materialwissenschaft und Werkstofftechnik. 12, 40-50. Kuguel, R., 1961. A relation between the theoretical stress concentration factor and the fatigue notch factor deduced from the concept of highly stressed volume. ASTM Proceeding. 61, 732-748. Makkonen, M., 2003. Notch size effects in the fatigue limit of steel. International Journal of Fatigue. 25, 17-26. Nogami, S., Nishimura, A., Wakai, E., Tanigawa, H., Itoh, T., Hasegawa, A., 2013. Development of fatigue life evaluation method using small specimen. Journal of Nuclear Materials. 441, 125-132. Olbricht, J., Bismarck, M., Skrotzki, B., 2013. Characterization of the creep properties of heat resistant 9-12% chromium steels by miniature specimen testing. Materials Science & Engineering A. 585, 335-342. Peter, D., Otto, F., Depka, T., Nörtershäuser, P., Eggeler, G., 2011. High temperature test rig for inert atmosphere miniature specimen creep testing. Materialwissenschaft und Werkstofftechnik. 42(6), 493-499. Sonsino, C.M., Fischer, G., 2005. Local assessment concepts for the structural durability of complex loaded components. Materialwissenschaftund Werkstofftechnik. 36, 632-641. Tomaszewski, T., Sempruch, J., 2017. Fatigue life prediction of aluminium profiles for mechanical engineering. Journal of Theoretical and Applied Mechanics. 55(2), 497-507. Tomaszewski, T., Sempruch, J., Piątkowski , T., 2014. Verification of selected models of size effect based on high-cycle fatigue testing on mini specimens made of EN AW-6063 aluminum alloy. Journal of Theoretical and Applied Mechanics. 52(4), 883-894. Tomaszewski, T., Strzelecki, P., 2016. Study of the size effect for non-alloy steels S235JR, S355J2+C and acid-resistant steel 1.4301. AIP Conference Proceedings. 1780, 020008-1-020008-8. 5. Conclusion References