Fatigue limit estimated using finite lives

Lorén, Sara

doi:10.1046/j.1460-2695.2003.00659.x

Cited by 15 publications

(27 citation statements)

References 10 publications

(25 reference statements)

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“…The variance of the logarithm of the finite life is τ 2 . There are two differences between this model and the model in Ref. [1].…”

Section: Model For Estimate the Fatigue Limit Distributionmentioning

confidence: 97%

“…The second difference is that the variance of the logarithm of the finite life N f is constant. Here a limited stress range is considered so the difference compare to nonconstant variance is not that large 1 . Therefore, constant variance is used for simplification.…”

Section: Model For Estimate the Fatigue Limit Distributionmentioning

confidence: 99%

“…In Ref. [1] the distribution of the fatigue limit has been estimated on the basis of the stress level and the finite life given by the staircase test.…”

Section: Introductionmentioning

confidence: 99%

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Modelling curved S–N curves

Lorén

Lundström

2005

Fatigue Fract Eng Mat Struct

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A B S T R A C T The fatigue limit distribution is estimated using fatigue data and under the assumption that the fatigue limit is random. The stress levels for the broken and unbroken specimens are used. For the broken specimen the number of cycles to failure is also used. By combining the finite life and fatigue limit distribution it is possible to get the probability of not surviving a certain life. This probability is used to estimate a curved S-N curve by using the method of likelihood. The whole S-N curve is estimated at the same time. These curves show the predictive life given a certain stress level. The life and the quantile of the fatigue limit distribution are also predicted by using profile predictive likelihood. In this way the scatter around the S-N curve as well as the uncertainty of the S-N curve are taken into account.Keywords fatigue limit; finite life; predictive profile likelihood; staircase test. N O M E N C L A T U R E1 = indicator function C = set of censored observations e yx = n x f , g = density function l y = likelihood function L p , L ps = profile predictive likelihood L p ,L ps = normalized profile predictive likelihood N f = finite life n ro = run-out level n x = life given a stress level S q = probability S = stress level S ∞ = fatigue limit U = set of uncensored observations x = ln e (S) y = ln e (N ) y ro = ln e (n ro ) Z = random variable θ = parameter µ = mean of fatigue limit distribution ν (x) = mean of logarithm of the finite life distribution σ 2 = variance of fatigue limit distribution τ 2 = variance of logarithm of the finite life distribution = standard normal cumulative distribution · = estimate Correspondence: Sara Lorén.

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“…The variance of the logarithm of the finite life is τ 2 . There are two differences between this model and the model in Ref. [1].…”

Section: Model For Estimate the Fatigue Limit Distributionmentioning

confidence: 97%

Section: Model For Estimate the Fatigue Limit Distributionmentioning

confidence: 99%

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Modelling curved S–N curves

Lorén

Lundström

2005

Fatigue Fract Eng Mat Struct

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“…(1) depends on the cdfs of the continuous rvs l X , t X , Y int and Y surf . According to what proposed in the literature [9][10][11][12] for the fatigue strength, both l X and t X can be assumed as Normal distributed (i.e., the fatigue limit and the transition stress are Log-Normal distributed). In particular, let l X have mean value l X  and standard deviation l X  , and t X have mean value t X  and standard deviation t X  , then:…”

Section: Duplex S-n Curves: Statistical Modelmentioning

confidence: 99%

“…In the literature [9][10][11], different types of continuous distribution have been proposed for the number of cycles to failure. Usually, either a 2-parameter Weibull distribution or a Log-Normal distribution are used for the cycles to failure rv.…”

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confidence: 99%

Duplex S-N fatigue curves: statistical distribution of the transition fatigue life

Paolino¹,

Tridello²,

Geng³

et al. 2014

Frattura Ed Integrità Strutturale

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In recent years, very-high-cycle fatigue (VHCF) behavior of metallic materials has become a major point of interest for researchers and industries. The needs of specific industrial fields (aerospace, mechanical and energy industry) for structural components with increasingly large fatigue lives, up to 10 10 cycles (gigacycle fatigue), requested for a more detailed investigation on the experimental properties of materials in the VHCF regime. Gigacycle fatigue tests are commonly performed using resonance fatigue testing machines with a loading frequency of 20 kHz (ultrasonic tests). Experimental results showed that failure is due to cracks which nucleate at the specimen surface if the stress amplitude is above the conventional fatigue limit (surface nucleation) and that failure is generally due to cracks which nucleate from inclusions or internal defects (internal nucleation) when specimens are subjected to stress amplitudes below the conventional fatigue limit. Following the experimental evidence, the Authors recently proposed a new statistical model for the complete description of S-N curves both in the high-cycle-fatigue (HCF) and in the VHCF fatigue regions (Duplex S-N curves). The model differentiates between the two failure modes (surface and internal nucleation), according to the estimated distribution of the random transition stress (corresponding to the conventional fatigue limit). No assumption is made about the statistical distribution of the number of cycles at which the transition between surface and internal nucleation occurs (i.e., the transition fatigue life). In the present paper, the statistical distribution of the transition fatigue life is obtained, according to the statistical model proposed. The resulting distribution depends on the distance between the HCF and the VHCF regions and on the distribution of the random transition stress. The estimated distribution can be effectively used to predict, with a specified confidence level, the number of cycles for which an internal nucleation may probabilistically occur in a VHCF test and it is also informative for properly choosing the end of HCF tests in terms of number of cycles. A numerical example, based on experimental datasets taken from the literature, is provided.

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