Stochastic crack growth models for applications to aircraft structures

Yang, Jann N.; Manning, Shannon D.; Hsi, W. H.; Rudd, JL

doi:10.1007/978-94-017-2764-8_4

Cited by 20 publications

(12 citation statements)

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“…Furthermore, X .N g / can be taken as a stationary lognormal random process. 11 If the lognormal random process is completely correlated at any two load cycles, X .N g / becomes a lognormal random variable X and, thus, Eq. (6) becomes…”

Section: With the Anderson-darling (A-d) Statistic Calculated Asmentioning

confidence: 99%

“…Following the procedures proposed by Yang et al 11 for single fastener hole specimens, a stochastic damage growth model is established for lap splices with MSD. In this model, sophisticatedfracture mechanics analysis for each specimen at every growth time is not required,so that the approachis less complex than risk analysis using deterministic crack growth prediction and distributed initial aw sizes.…”

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confidence: 99%

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Stochastic Damage Growth Model for Fuselage Splices with Multisite Damage

Xiong

Shi

2001

AIAA Journal

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Research has been conducted on methods for risk assessment of fuselage splice joints containing multisite damage (MSD), and extensive test data from MSD specimens have been obtained. The objective is to propose a test databased methodology for probabilistic analysis of lap splices with MSD. In the probabilistic analysis, the failure characteristics of nine noncorroded MSD specimens under fatigue loading were examined, and a failure criterion was proposed involving an aggregated lead crack in a segment where the rst linkup occurred. A curve-tting technique was used to characterize the growth behavior of the aggregated lead crack in each specimen. The total fatigue life of each specimen was divided into two stages: damage starting and damagegrowth. The starting life was assumed to follow a lognormal distribution derived from the test data. In the growth stage, a stochastic damage growth model was developed based on the censored test data. This model, along with the derived distribution of the visible damage starting life, was used to predict the probability of failure for the MSD specimens tested. Comparisonsbetween the data from analysis and test were made and are presented to demonstrate the effectiveness of the developed model. Nomenclaturea = length of aggregate crack a cr = critical crack length f N 0 .¢ ¢ ¢/ = probabilistic density function of visible damage starting life K max = maximum stress intensity factor N = number of load cycles N g = damage growth life N t = total fatigue life N 0 = visible damage starting life Q N 0 = median value of observed visible damage starting life P.¢ ¢ ¢/ = cumulative distribution function Q; b = deterministic constants in damage growth function q = logarithm of Q R = stress ratio of loading spectrum U = logarithm of crack length u i ; v i = random numbers between zero and unity X = lognormal random variable associated with damage growth rate Y = logarithm of damage growth rate Z = normal random variable associated with damage growth rate Z 0 = normal random variable associated with visible damage starting life 1K = stress intensity factor range ¹ N 0 = mean value of visible damage starting life ¹ Y = mean value of Y ¹ Z = mean value of Z ¹ Z 0 = mean value of Z 0 ¾ N 0 = standard deviation of visible damage starting life ¾ Y = standard deviation of Y ¾ Z = standard deviation of Z ¾ Z 0 = standard deviation of Z 0 8.¢ ¢ ¢/ = standard normal distribution function

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Section: With the Anderson-darling (A-d) Statistic Calculated Asmentioning

confidence: 99%

mentioning

confidence: 99%

Stochastic Damage Growth Model for Fuselage Splices with Multisite Damage

Xiong

Shi

2001

AIAA Journal

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“…Mathematically, the reliability of the whole system R, at time t * > T can be written as : (27) 6. Cost modelling Decision strategies based on expected cost, or on expected values of any measure of utility are reasonable if one thinks on the long term.…”

Section: Structural Reliabilitymentioning

confidence: 99%

An Application of Bayesian Decision Theory to the Design and Inspection of Marine Structures

Kawano

Itagaki

Ishizuka

1994

J. SNAJ, Nihon zousen gakkai ronbunshu

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SummaryLife of structures which are subject to fatigue failures involves high degree of uncertainty and risk. In order to design such systems it is necessary to take into account several stochastic elements. As the structure ages, the relationship among initial cost, inspections, maintenance and reliability level becomes important, and it has to be studied in order to achieve a good design from the costeffectiveness point of view. This paper analyses this relationship and proposes a method to take the best decision among a set of alternatives regarding structural dimensions using a new class of Bayesian loss functions that are based on the concepts of under and over design.

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“…Bogdanoff and Kozin 1 have accounted for the random nature of fatigue cracks using the Markov process and compare the results of a randomized Paris' law approach with the Markov model. 2 Yang and Manning 3 and Yang et al 4 have modeled the stochastic nature of the crack growth using a lognormal process. Ortiz and Kiremidjian 5 use a stationary mean Gaussian process error term which depends on the crack length as part of the fatigue crack growth law and Tang and Spencer 6 use an error term which is a general random process in time.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic approach to growth and detection of a truncated distribution of initial crack lengths based on Paris' law

Cohen

Kulkarni

Achenbach

2011

Structural Health Monitoring

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A method for incorporating probabilistic considerations into fatigue life prognosis based on experimental information for Paris' law is presented in this article. A truncated probability distribution of initial crack lengths is introduced to obviate a complication of the use of Paris' law. This formulation allows the calculation of several probabilities for various values of the truncation length, including the probability of the existence of a crack larger than a predetermined critical crack length and the probability of a crack in a prescribed domain of crack lengths, and the effect of an inspection on these probabilities. A probabilistic consideration for the fact that the Paris' law parameters are not constants but distributions is also addressed using a stochastic version of Paris' law and a Monte Carlo simulation. Finally, a novel Bayesian approach which highlights the effect of probability of detection, critical crack length, and applied stress versus the number of elapsed fatigue cycles is presented and ramifications explored. This article provides insight on how various factors affect diagnosis and prognosis in a probabilistic manner.

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Stochastic crack growth models for applications to aircraft structures

Cited by 20 publications

References 0 publications

Stochastic Damage Growth Model for Fuselage Splices with Multisite Damage

Stochastic Damage Growth Model for Fuselage Splices with Multisite Damage

An Application of Bayesian Decision Theory to the Design and Inspection of Marine Structures

Probabilistic approach to growth and detection of a truncated distribution of initial crack lengths based on Paris' law

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