Statistical aspects of fatigue life and endurance limit

Abstract

A B S T R A C T Based on the assumption that the fatigue life and endurance limit is mainly controlled by the materials particle distribution, different possible statistical distributions to describe the fatigue have been assessed. Some distributions lead to high statistical uncertainty or physically non-realistic size effects. It is shown that, if the maximum particle size distribution is described by a Frechet distribution, both the fatigue life, as well as the endurance limit are described by a Weibull distribution. N O M E N C L A T U R EC 1 and C 2 = constants K 0 = normalising constant n = number of particles or sample sizē n = average number of particles n Vo = average number of particles in reference volume N = number of cycles N 0 = normalising parameter N c = critical fatigue life N eff = effective fatigue life corresponding to crack growth N f = fatigue life N i = fatigue life corresponding to initiation m = exponent p = discrete probability P = cumulative probability P n = probability of having n particles in sample P rmax = probability that the maximum particle size is smaller or equal to r max r = rank number or particle sizē r = average particle size r 0 = normalising particle size r c = critical particle size r limit = limiting particle size r max = maximum particle size in sample r ref = reference particle size V = sample volume V 0 = reference volume α = Gumbel location parameter β = Gumbel scale parameter γ = constant ≈ −0.577216 a = crack extension Correspondence: K. Wallin.

A methodology to determine a conditional probability density distribution surface from S–N data

“…Data of fatigue test (S-N data) generally show considerable dispersion even under rigidly controlled conditions [1,2]. Although the well-known S-N curve can express parts of material's fatigue properties, the dispersion of the fatigue life cannot be known from it.…”

“…The scattering of the fatigue properties can be expressed by fatigue life or fatigue strength distribution. It is sufficient to note that usually the scatter, especially in terms of fatigue life but also endurance limit, is described assuming a Weibull or log-normal distribution [1]. In general, the fatigue life is often described by a Weibull distribution, while the logarithm of fatigue life and the fatigue limit are often described by a normal distribution.…”

A physically based extreme value characterization of material fatigue

“…These statistical distributions are often compared to each other, e.g. [9], without paying sufficient attention to the underlying process or their asymptotic nature. However, their application may be inappropriate if the asymptote conditions, i.e.…”

“…Under the i.i.d. and the Poisson assumptions the exact CDF of the extreme value A max may be expressed as [9,13] F Amax ðaÞ ¼ expfÀKQðaÞg ð2Þ…”

“…Commonly, standard statistical distributions (e.g. normal, log-normal, Weibull and Gumbel) have been utilized for the characterization and modeling of these aspects [1][2][3][4][5][6][7][8][9].…”