Issue 37

F. Berto et alii, Frattura ed Integrità Strutturale, 37 (2017) 69-79; DOI: 10.3221/IGF-ESIS.37.10 78 C ONCLUSIONS large bulk of experimental fatigue results relevant to axisymmetric notched samples subjected to multiaxial loadings, both proportional and non-proportional, have been re-analysed and compared with the fatigue strength data relevant to smooth and notched samples subjected to pure tension and pure torsion loadings. All specimens were made of titanium grade 5 alloy (Ti-6Al-4V). Altogether, more than 250 fatigue results, corresponding to 19 S-N curves, have been analysed in this contribution. First, the experimental results obtained from uniaxial and multiaxial fatigue tests have been examined on the basis of nominal stress amplitudes. Then, they have been re-analysed by means of the linear elastic strain energy density (SED) averaged over a control volume surrounding the notch root. The effect of the loading mode on the control volume size has been analysed in detail, showing that different control radii must be adopted under tension and torsion loading conditions, dealing with notched components made of Ti-6Al-4V titanium alloy. The averaged SED-based synthesis enables to obtain a quite narrow scatter band, characterized by an energy-based scatter index of 2.50. In particular, the fatigue design scatter band was derived by taking into account all experimental results relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions, regardless the nominal load ratio and the phase angle. R EFERENCES [1] Fatemi, A., Shamsaei, N., Multiaxial fatigue: An overview and some approximation models for life estimation, Int. J. Fatigue, 33 (2011) 948-958. [2] Nieslony, A., Sonsino, C.M., Comparison of some selected multiaxial fatigue assessment criteria, L.B.F. Report, No. FB-234 (2008). [3] Fatemi, A., Socie, D.F., A critical plane approach to multiaxial fatigue damage including out-of-phase loading, Fatigue Fract. Eng. Mater. Struct., 11 (1988) 149-165. [4] Fatemi, A., Kurath, P. P., Multiaxial fatigue life prediction under the influence of mean stresses, ASME J. Eng. Mater. Techn., 110 (1988) 380-388. [5] Łagoda, T., Macha, E., Bedkowski, W., A critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, Int. J. Fatigue, 21 (1999) 431-443. [6] Carpinteri, A., Spagnoli, A., Multiaxial high-cycle fatigue criterion for hard metals, Int. J. Fatigue, 23 (2001) 135-145. [7] Carpinteri, A., Spagnoli, A., Vantadori, S., Bagni, C., Structural integrity assessment of metallic components under multiaxial fatigue: The C-S criterion and its evolution, Fatigue Fract. Eng. Mater., 36 (2013) 870-883. [8] Ye, D., Hertel, O., Vormwald, M., A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, Int. J. Solids Struct., 45 (2008) 6177-6189. [9] Cristofori, A., Benasciutti, D., Tovo, R., A stress invariant based spectral method to estimate fatigue life under multiaxial random loading, Int. J. Fatigue, 33 (2011) 887–899. [10] Carpinteri, A., Spagnoli, A., Vantadori, S., Reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, Int. J. Fatigue, 67 (2014) 55-61. [11] Jasper, T.M., The value of the energy relation in the testing of ferrous metals at varying ranges and at intermediate and high temperature, Philos. Mag., 46 (1923) 609–627. [12] Ellyin, F., Cyclic strain energy density as a criterion for multiaxial fatigue failure, Brown, Miller, editors. Biaxial and Multiaxial Fatigue, London: EGF Publication, (1989) 571–83. [13] Ellyin, F., Fatigue damage, crack growth and life prediction, Edmonton: Chapman and Hall (1997). [14] Macha, E., Sonsino, C. M., Energy criteria of multiaxial fatigue failure, Fatigue Fract. Engng. Mater. Struct., 22 (1999) 1053–1070. [15] Pook, L.P., Sharples, J.K., The mode III fatigue crack growth threshold for mild steel, Int. J. Fract., 15 (1979) R223- R226. [16] Pook, L.P., The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading, Int. J. Fatigue, 7 (1985) 21-30. [17] Tong, J., Yates, J.R., Brown, M.W., Some aspects of fatigue thresholds under mode III and mixed mode and I loadings, Int. J. Fatigue, 18 (1986) 279-285. A