A maximum likelihood method for estimating P_S_N curves

Ling, Jing; Pan, Jwo

doi:10.1016/s0142-1123(97)00037-6

Cited by 79 publications

(49 citation statements)

References 2 publications

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“…Thus about 50 specimens are required for the establishment of an S-N curve. In order to decrease the specimen numbers and test time, a single-point group testing method (SPGTM) [28][29][30] (shown in Fig. 3.7) was proposed for a p-S-N curve determination; seven specimens for the single-point tests and eight specimens for a group test are required to be fatigue tested.…”

Section: Single-point Likelihood Methodsmentioning

confidence: 99%

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Principles Underpinning Reliability based Prediction of Fatigue and Fracture Behaviours

Xiong

Shenoi

2011

Springer Series in Reliability Engineering

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Because of the stochastic nature of the damage processes, it is generally inadvisable to formulate a deterministic approach to predict fatigue damage and fatigue life. Thus, many stochastic mathematical expressions for fatigue life and fatigue damage process have been developed. specimens, fatigue data can be described by random variables to study the variability of damage and life and to analyse their average trends [1, 2]. With improvements in crack-size measurements, fatigue crack growth data can be described in a random time-space and state-space to depict local variations within a single specimen analyse. This has been done by a stationary lognormal process-based randomized approach of deterministic crack growth equation in power law and polynomial forms [7][8][9][10]. Under random spectrum loading, a fatigue cumulative process can be described by discrete Markov chain models [3,6] or continuous Markov process methods based on the solution of the Fokker-Planck equation [4,6,11,12]. The appropriateness and accuracy of these categories of stochastic models have been verified by statistically meaningful fatigue crack growth data sets with certain degrees of accuracy [7,8,[13][14][15]. In fact, all above categories of stochastic models have been obtained by randomizing the deterministic fatigue crack growth equation and using large sample numbers of statistically meaningful data sets from which to determine the random coefficients for the models.However, in many circumstances, due to time and resource constraints, it is infeasible to conduct extensive experimental investigations in order to generate the large numbers of data sets required by classical statistical processes. Hence, it is desirable to have a technique to address the paucity of data in assessing the structural probability of fatigue and fracture performance. In the chapter, a series of original and practical approaches of deterministic equation are proposed for the J. J. Xiong and R. A. Shenoi, Fatigue and Fracture Reliability Engineering, Springer Series in Reliability Engineering,

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Section: Single-point Likelihood Methodsmentioning

confidence: 99%

“…where Z(S) is the lognormal random variable following a Gauss distribution N[0, r 2 (S)] dependent on fatigue stress level S. The standard deviation r(S) to characterize the dispersion of fatigue life is generally assumed to be a linear relationship with ln S as [17,30]: …”

Section: Single-point Likelihood Methodsmentioning

confidence: 99%

Principles Underpinning Reliability based Prediction of Fatigue and Fracture Behaviours

Xiong

Shenoi

2011

Springer Series in Reliability Engineering

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“…Hence, a lot of investigations about the expression of P-S-N curve are presented in the literature. [14][15][16] Normally, the P-S-N curve is fitted based on fatigue test data in different stress levels, and it can characterize the randomness of fatigue property of the structure objectively.…”

Section: Introductionmentioning

confidence: 99%

Fatigue reliability evaluation of structural components under random loadings

Cheng

Tao

Chen

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part O:

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An efficient method for time-dependent fatigue reliability assessment of mechanical components under random loadings is proposed. Normally, fatigue damage induced by random loading is high-cycle fatigue problem. The randomness of high-cycle fatigue damage is treated in two aspects. The first one is the uncertainty quantification from the external random loading. The second one is the uncertainty quantification of the fatigue property of the structural component. The former is characterized by Gaussian distribution derived from the rainflow cycle distribution, median stress-life (S-N) curve, and the linear damage accumulation rule. The latter is described with the probabilistic stress-life (P-S-N) curve based on log-normal distribution. The proposed method has colligated these two aspects together to evaluate the expectation and confidence interval of fatigue reliability. Finally, a numerical example is provided to verify the effectiveness of the developed approach. A comparison with bootstrap method is also carried out. The comparative result has shown rational accuracy of the proposed method.

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“…、三参数方程 [2] 和 Langer 方程 [3] )，采用常规法 [4] 或极大似然法 [5][6][7] 建立应力水平相关的分组寿命数据或全体寿命数据的正态型可靠性统 * 国家自然科学基金(51175439)、高等学校博士学科点专项科研基金 …”

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Modeling of the Probabilistic Fatigue S-N Curves Using the Two Parameter Weibull Distribution

Zhao¹

2015

JME

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Abstract： Modeling and construction method of the probabilistic fatigue S-N curves are developed using the two parameter Weibull distribution for describing random rolling contact fatigue stress amplitude-life relations. Except for the statistical distributed regularities of the random relations, a least norm life confidence bound assessment is incorporated into the modeling for considering risk effect related to limited sampling size. The scale and shape parameters of the distribution, the statistical parameter for the confidence assessment, and the exponents of the S-N curves are all determined by the test data set. Applicability of the present method has been well verified by treating the rolling contact fatigue test S-N data of G20CrNi2Mo bearing steel. In addition, a skew statistical model is proved to be suitable for characterizing the statistical distributed regularities of the rolling contact fatigue life data.

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A maximum likelihood method for estimating P_S_N curves

Cited by 79 publications

References 2 publications

Principles Underpinning Reliability based Prediction of Fatigue and Fracture Behaviours

Principles Underpinning Reliability based Prediction of Fatigue and Fracture Behaviours

Fatigue reliability evaluation of structural components under random loadings

Modeling of the Probabilistic Fatigue S-N Curves Using the Two Parameter Weibull Distribution

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