A fuzzy approach for drawing S-N curves in the finite life region

Abstract

A B S T R A C T In this work a fuzzy approach has been developed in order to estimate the probability of fatigue failure. In particular, with the proposed method the S-N curves of a material in the finite life region can be drawn. The experimental data are represented in terms of fuzzy sets and are fitted using a fuzzy linear regression. Data scattering and uncertainty in the empirical failure model are reflected in the definition of membership functions. Several examples are shown to illustrate the procedure. Failure probabilities and fatigue curves obtained by the fuzzy method are similar to those obtained by traditional statistical analysis, based on normal distributions of strength with standard deviation that remains constant with different load levels. In particular, the results obtained indicate that the possibilities offered by fuzzy systems are also applicable for estimating the Wöhler curve of a material under fatigue stresses. To evaluate its reliability, the proposed method is compared with the traditional one, with particular attention to the case in which a small amount of experimental data is available. The new fuzzy method is slightly less accurate than traditional statistical analysis to outline S-N curves in the finite life region. This is mainly due to the fact that the method is influenced by the nonuniformity of data dispersion at each level of stress. = Arithmetic mean between S Lmin and S Lmax N L = Arithmetic mean of the various N L at a given level of stress a m = Centre of triangular fuzzy number N = Cycle number N L = Decimal logarithm of N S L = Decimal logarithm of S D m1 = Distribution of the means D m2 = Distribution of the medians d er = Error distribution R = Fuzzy event 'strength is smaller than the stress amplitude' c L = Left width of triangular fuzzy number α = Material parameter in the S-N curve β = Material parameter in the S-N curve A 0 = Material parameter in the S-N curve A 1 = Material parameter in the S-N curve M = Mean of D m1 distribution M e = Mean of D m2 distribution μ() = Membership function of a fuzzy set Correspondence: G. Zonfrillo.