A Bayesian Model for the Probability Distribution of Fatigue Damage in Tubular Joints

2004 ◽  
Vol 126 (3) ◽  
pp. 243-249 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Roberto Montes-Iturrizaga
Keyword(s):  
Fracture Mechanics ◽  
Probability Distributions ◽  
Error Variance ◽  
Crack Size ◽  
Offshore Structures ◽  
Density Functions ◽  
Time Varying ◽  
Tubular Joints ◽  
Mechanics Model ◽  
Distribution Of Stress

A Bayesian framework is used for updating the probability distributions of the parameters of a fracture mechanics model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. An error model, defined as the logarithmic difference between measured crack size during inspection and crack size predicted by the fracture mechanics model, is assumed to have a normal distribution with known mean and uncertain variance. The distribution of the error variance is modeled by a conjugate distribution for samples of normal variables with known mean and uncertain variance. Based on these assumptions, an analytical model is obtained using a Bayesian approach for the updated distributions of the parameters of the fracture mechanics model and of crack size based. The capabilities of the model are illustrated by means of examples using the Paris-Erdogan formulation for crack growth. The examples illustrate the effects of inspection times, measured crack size, and the distribution of stress ranges on the updated density functions of crack size, time varying reliability and expected cost of failure.

Analytical Models for the Probability Distributions of Fatigue Parameters and Crack Size of Offshore Structures Based on Bayesian Updating

2002 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Roberto Montes-Iturrizaga
Keyword(s):  
Crack Detection ◽  
Probability Distributions ◽  
Crack Depth ◽  
Error Variance ◽  
Crack Size ◽  
Offshore Structures ◽  
Probability Of Detection ◽  
Posterior Distributions ◽  
Fatigue Model ◽  
Normally Distributed

In this paper a bayesian framework is used for updating the probability distributions of the parameters of a fatigue model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. For crack detection, the uncertainties are taken into account by means of probability-of-detection (POD) curves. According to the bayesian procedure, if during an inspection no crack is detected, the updated (posterior) distributions depend on the prior ones at time of such inspection and on the POD. On the other hand, if during an inspection a crack is detected and measured, the corresponding predicted crack depth at that time is estimated given values of parameters of a selected fatigue model and of the initial crack depth. Then, a sample value of the model and sizing error associated with the inspection performed, defined as the logarithmic difference between the measured and the predicted crack size, is calculated. Such error is considered to be a normally distributed random variable with known mean and uncertain variance. The distribution of the error variance is taken as a conjugate one for samples of normally distributed variables with known mean and uncertain variance. Based on these assumptions, an analytical expression is obtained for the updated (posterior) distributions of the parameters of the fatigue model and of crack size. It is shown that the updated distributions depend on POD and on the prior and updated parameters of the error variance distribution. Finally, the bayesian method proposed here is illustrated taking as a fatigue model the Paris-Erdogan relation, which estimates crack growth based on linear elastic fracture mechanics. Joint failure is considered to occur when the crack depth reaches the thickness of the element where the crack propagates. The evolution of reliability with time is assessed.

Effect of Uncertainties on the Reliability of Fatigue Damaged Systems

2004 ◽  
Author(s):  
Francisco L. Silva-Gonza´lez ◽  
Ernesto Heredia-Zavoni
Keyword(s):  
Fracture Mechanics ◽  
Failure Modes ◽  
Crack Size ◽  
Initial Crack ◽  
Wave Forces ◽  
Scale Parameters ◽  
Uncertain Variables ◽  
Mechanics Model ◽  
Distribution Of Stress

Fluctuating stresses and strains due to wave forces cause accumulated fatigue damage in tubular joints of marine platforms. Considering the uncertainties in the loads, material properties, initial crack sizes, and stress intensity factors, etc., may affect significantly the reliability assessment of marine jacket platforms. In this paper, we assessed the effect of uncertainties about such fatigue variables on the time evolution of the reliability of series and parallel systems considering correlation between failure modes. The fracture mechanics Paris-Erdogan model is used to model crack growth and a FORM method is used for computing the safety index. The uncertain variables analyzed are: initial crack size, material parameters C and m in the fracture mechanics model and the shape and scale parameters of the Weibull density function used for the long-term distribution of stress range.

Analysis of Corrosion Fatigue Crack Growth in Welded Tubular Joints

1985 ◽  
Vol 107 (2) ◽  
pp. 212-219 ◽  
Author(s):  
S. J. Hudak ◽  
O. H. Burnside ◽  
K. S. Chan
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
Corrosion Fatigue ◽  
Offshore Structures ◽  
Corrosion Fatigue Crack ◽  
Tubular Joints ◽  
Mechanics Model ◽  
Weld Toe

An improved fracture mechanics model for fatigue crack growth in welded tubular joints is developed. Primary improvements include the use of a wide-ranged equation for the fatigue crack growth rate properties and the incorporation of the influence of local weld-toe geometry into the stress intensity factor equations. The latter is shown to explain the dependence of the fatigue life on the size of tubular joints. Good agreement between predicted and measure fatigue lives of full-scale joints tested in air further supports the applicability of the fracture mechanics approach to offshore structures. Although the model should also be applicable to corrosion fatigue, additional imput data and verification testing are needed under these conditions. Factors which could improve the model are discussed.

scholarly journals Fracture Mechanical Behavior of Cracked Cantilever Roof with Large Cutting Height Mining

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Zenghui Zhao ◽  
Wei Sun ◽  
Mingzhong Zhang ◽  
Xiaojie Gao ◽  
Shaojie Chen
Keyword(s):  
Fracture Mechanics ◽  
Cantilever Beam ◽  
Crack Size ◽  
Affected Area ◽  
Mechanics Model ◽  
Large Mining Height ◽  
Mining Disturbance ◽  
Seam Mining ◽  
Cutting Height ◽  
Mining Height

Accurately predicting the roof collapse span is crucial in ensuring the safe production of thick seam mining with large mining height, which is easy in forming a “cantilever beam” structure. Considering roof damage caused by roadway excavation and coal seam mining disturbance, the fracture mechanics model of large mining height roof cantilever beam with nonpenetrating cracks was established. The roof was divided into two parts: the crack-affected area and the crack-unaffected area. The analytical expression of the boundary between the two areas was established by fracture mechanics methods. Based on the boundary equation, the influences of crack size, crack inclination, roof lithology, and roof thickness on the roof crack-affected area were analyzed in detail. Finally, the accuracy of the theoretical model was verified by numerical experiments using the extended finite element method. The results demonstrate that the size of the area affected by the vertical crack increases with the increase of the crack size and the thickness of the roof. The influence of the crack decreases with the increase of roof lithology. The probability of early periodic collapse of a thin roof with the crack is increased. When the crack is completely located in the interior of the roof, the crack-affected area shrinks greatly with the decrease of the crack inclination. When the crack inclination is small, the crack will not cause the early collapse of the roof. Overall, the conclusions obtained are of great significance for predicting the collapse span of a cantilever roof with initial damage in large mining height.

Fatigue Fracture Mechanics Modeling and Structural Integrity Assessment of Offshore Welded Tubular Joints

1989 ◽  
Vol 111 (3) ◽  
pp. 170-176 ◽  
Author(s):  
J. C. P. Kam ◽  
D. A. Topp ◽  
W. D. Dover
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Nondestructive Testing ◽  
Crack Growth ◽  
Large Scale ◽  
Structural Integrity ◽  
Offshore Structures ◽  
Integrity Assessment ◽  
Tubular Joints

Evaluation of the structural integrity of offshore structures requires information on the reliability of nondestructive testing, the accuracy of fatigue crack growth modeling and other data. The University College London Underwater NDE Centre has been set up to provide information on the effectiveness and reliability of different nondestructive testing methods. To achieve this aim, a large library of cracked specimens will be assembled. In the preliminary phase of producing this library, a series of large-scale welded tubular joints were fatigue tested and the crack growth was fully monitored with the ACPD technique. This paper will describe briefly the background to the crack library and present the data obtained from fatigue tests. It will also describe a new model for fatigue crack growth prediction in tubular joints using fracture mechanics. This model allows the prediction of the size effect noted previously in the stress/life curves for tubular joints.

scholarly journals Random Outcome and Stochastic Analysis of Some Fatigue Crack Growth Data

2001 ◽  
Vol 17 (2) ◽  
pp. 61-68
Author(s):  
W. F. Wu ◽  
C. C. Ni ◽  
H. Y. Liou
Keyword(s):  
Fatigue Crack ◽  
Fracture Mechanics ◽  
Crack Size ◽  
Experimental Result ◽  
Exceedance Probability ◽  
Growth Data ◽  
Probabilistic Fracture Mechanics ◽  
Mechanics Model ◽  
Proposed Model ◽  
Analytical Result

ABSTRACTFatigue crack propagation data of a batch of AISI 4340 steel specimens are released in the present paper. The statistical nature of the data is specially emphasized, and a probabilistic fracture mechanics model is introduced to analyze the data. The stochastic differential equation associated with the model is then solved. The solution gives us the crack exceedance probability as well as the probability distribution of the random time to reach a specified crack size. These quantities are useful in the reliability assessment of structures made of the tested material. Comparing the analytical result with the experimental result, it is found that the proposed probabilistic fracture mechanics model can reasonably explain the experimental data. For those data that cannot be fitted well by the proposed model, methods of improvement are proposed in the present paper as well.

Fracture Mechanics Analysis of Fatigue Crack Repaired Joints

2004 ◽  
Author(s):  
J. Efrai´n Rodri´guez-Sa´nchez ◽  
William D. Dover ◽  
Feargal P. Brennan ◽  
Alejandro Rodri´guez-Castellanos
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Fracture Mechanics ◽  
Structural Integrity ◽  
Offshore Structures ◽  
Assessment Process ◽  
Tubular Joints ◽  
Mechanics Analysis ◽  
Crack Repair ◽  
Inspection Data

Fatigue life predictions based on fracture mechanics calculations are required to satisfy an increasing level of safety demanded by industry. These predictions are mainly used to schedule NDT inspections and with inspection data make structural integrity assessments. The periodic inspection-assessment process can lead to the implementation of a fatigue crack repair by crack removal. Fracture mechanics analysis is used again to determine whether or not a repair will be effective. For the case of tubular joints, in offshore structures, once repairs have been shown to be ineffective it is usually required to install a clamp to maintain the continuity of joint members if the structure is still required for production. In this paper a fracture mechanics analysis of crack repaired joints based on Y factors is presented. The analysis is used to predict fatigue life after crack removal and is validated against T-butts experimental data. The analysis is also extrapolated for the prediction of fatigue life of crack repaired tubular joints.

Fracture Mechanics Analysis of Fatigue Crack Repaired Joints

2004 ◽  
Vol 127 (2) ◽  
pp. 182-189 ◽  
Author(s):  
J. Efraín Rodríguez-Sánchez ◽  
William D. Dover ◽  
Feargal P. Brennan ◽  
Alejandro Rodríguez Castellanos
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Fracture Mechanics ◽  
Structural Integrity ◽  
Offshore Structures ◽  
Assessment Process ◽  
Tubular Joints ◽  
Mechanics Analysis ◽  
Crack Repair ◽  
Inspection Data

Fatigue life predictions based on fracture mechanics calculations are required to satisfy an increasing level of safety demanded by industry. These predictions are mainly used to schedule NDT inspections and with inspection data make structural integrity assessments. The periodic inspection-assessment process can lead to the implementation of a fatigue crack repair by crack removal. Fracture mechanics analysis is used again to determine whether or not a repair will be effective. For the case of tubular joints, in offshore structures, once repairs have been shown to be ineffective it is usually required to install a clamp to maintain the continuity of joint members if the structure is still required for production. In this paper a fracture mechanics analysis of crack repaired joints based on Y factors is presented. The analysis is used to predict fatigue life after crack removal and is validated against T-butts experimental data. The analysis is also extrapolated for the prediction of fatigue life of crack repaired tubular joints.

W-Peakedness: A Simulation based Study

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Suboohi Safdar ◽  
Dr. Ejaz Ahmed
Keyword(s):  
Probability Distributions ◽  
Extensive Study ◽  
Descriptive Statistics ◽  
Target Point ◽  
Density Functions ◽  
Central Value ◽  
Distribution Shape ◽  
Simulation Based ◽  
Different Shapes ◽  
Kurtosis Coefficient

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

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