Estimation of the fatigue strength distribution in high-cycle multiaxial fatigue taking into account the stress–strain gradient effect

Based on the weakest link concept, a probabilistic approach in high-cycle multiaxial fatigue is developed to predict, for a given number of cycles, the probability distribution of the fatigue strength for metallic structural components. A three-parameter Weibull distribution is combined with the energy-based and volumetric high-cycle multiaxial fatigue criterion proposed by Banvillet et al. in 2002 [Banvillet A, Palin-Luc T, Lasserre S. A volumetric energy based high cycle multiaxial fatigue criterion. Int J Fatigue 2003;26(8):755–69; Banvillet A, Palin-Luc T, Lasserre S, Vittori JF. Energy based high cycle multiaxial fatigue criterion depending on stress–strain distribution. In: Blom AF, editor. Fatigue 2002: eighth international fatigue congress, vol. 1, EMAS: Stockholm; 2002, p. 283–90]. Whatever the stress state and the loading type are, the corresponding fatigue strength probability distribution can be deduced from three usual experimental fatigue limits. The scale effect is also predicted. Experimental probability distributions and theoretical predictions of the fatigue strength of smooth specimens are in good agreement for the five materials investigated: the 30NiCrMo16 and 35CrMo4 quenched and tempered steels, the C20 annealed steel, the EN-GJS800-2 nodular cast iron and the Ti–6Al–4V titanium alloy.