Probabilistic pipe fracture evaluations for leak-rate-detection applications

Rahman, Sharif; Ghadiali, N.; Paul, Darrell; Wilkowski, G.

doi:10.2172/50938

Cited by 29 publications

(18 citation statements)

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“…The latter probability is more dif®cult to compute since it must be obtained by incorporating crack-growth simulation in a nonlinear ®nite element analysis. However, if suitable approximations of J can be developed analytically, the crack-instability failure probability can be easily calculated, as demonstrated by previous research in probabilistic pipe fracture evaluations [5,6].…”

Section: Random Parameters and Fracture Responsementioning

confidence: 99%

“…Table 2 lists the means, COV, and probability distributions of tensile parameters (E, a, n), fracture toughness parameter (J Ic ), and bending moment (M). As mentioned previously, the statistics of the material properties were obtained from actual TP304 stainless steel data at 2888C (550 F) [5]. However, the probabilistic characteristics of M were chosen arbitrarily.…”

Section: Example 2: a Through-wall-cracked Cylinder Specimenmentioning

confidence: 99%

“…Accordingly, probabilistic EPFM analyses based on both methods have been reported. For example, in the U.S. Nuclear Regulatory Commission's Short Cracks in Piping and Piping Welds Program [4], a probabilistic model was developed by the ®rst author for elastic±plastic analysis of circumferential through-wall cracks in pipes for leakbefore-break applications [5]. This model involves a J-estimation method, statistical representation of uncertainties in loads, crack size, and material properties, and ®rst-and second-order reliability methods (FORM/SORM).…”

Section: Introductionmentioning

confidence: 99%

“…Both load and material properties were assumed to be random. Table 1 shows the means, coef®cients of variation (COV), and probability distributions of these random parameters, obtained from recently performed statistical characterization of actual material property data [5]. The random variables were also assumed to be statistically independent.…”

mentioning

confidence: 99%

“…(1)) has only two independent parameters. In this study, a and n were assumed to vary randomly, while s 0 was held deterministic [5].…”

mentioning

confidence: 99%

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Probabilistic fracture mechanics for nonlinear structures

Rahman

Kim

2001

International Journal of Pressure Vessels and Piping

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Section: Random Parameters and Fracture Responsementioning

confidence: 99%

Section: Example 2: a Through-wall-cracked Cylinder Specimenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…(1)) has only two independent parameters. In this study, a and n were assumed to vary randomly, while s 0 was held deterministic [5].…”

mentioning

confidence: 99%

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Probabilistic fracture mechanics for nonlinear structures

Rahman

Kim

2001

International Journal of Pressure Vessels and Piping

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Probabilistic fracture mechanics by Galerkin meshless methods ? part II: reliability analysis

Rahman¹,

Rao²

2002

Computational Mechanics

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This is the second in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper, a stochastic meshless method is presented for probabilistic fracture-mechanics analysis of linear-elastic cracked structures. The method involves an element-free Galerkin method for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique described in the companion paper [1]. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted probability of fracture initiation based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using meshless methods.Keywords Probabilistic fracture mechanics, Stochastic meshless method, Element-free Galerkin method, Stressintensity factor, J-integral, Probability of failure IntroductionProbabilistic fracture mechanics (PFM) is becoming increasingly popular for realistic evaluation of fracture response and reliability of cracked structures. Using PFM, statistical uncertainties can be incorporated in engineering design and evaluation, a long-standing need in the stochastic-mechanics community. The theory of fracture mechanics provides a mechanistic relationship between the maximum permissible load acting on a structural component to the size and location of a crack -either real or postulated -in that component. Probability theory determines how the uncertainties in crack size, loads, and material properties, when modeled accurately, affect the integrity of cracked structures. PFM, which blends these two theories, accounts for both mechanistic and stochastic aspects of the fracture problem, and hence, provides a more rational means to describe the actual behavior and reliability of structures than traditional deterministic methods [2].While development is ongoing, a number of methods have been developed or implemented for estimating statistics of various fracture response and reliability. Most of these methods are based on linear-elastic fracture mechanics (LEFM) and a finite element method (FEM) that employs the stress-intensity factor (SIF) as the primary crack-driving force [2][3][4][5][6][7]. For example, using SIFs from an FEM code, Grigoriu et al.[3] applied first-and secondorder reliability methods (FORM/SORM) to predict the probability of fracture initiation and a confidence interval of the direction of crack extension. The method can account for random loads, material properties, and crack geometry. However, the r...

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Stochastic meshless analysis of elastic?plastic cracked structures

Rao

Rahman

2003

Computational Mechanics

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This paper presents a stochastic mesh-free method for probabilistic fracture-mechanics analysis of nonlinear cracked structures. The method involves enriched element-free Galerkin formulation for calculating the J-integral; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method (FORM) for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique. Numerical examples based on mode-I fracture problems have been presented to illustrate the proposed method. The results from sensitivity analysis indicate that the maximum difference between sensitivity of the J-integral calculated using the proposed method and reference solutions obtained by the finite-difference method is about three percent. The results from reliability analysis show that the probability of fracture initiation using the proposed sensitivity and meshless-based FORM are very accurate when compared with either the finite-elementbased Monte Carlo simulation or finite-element-based FORM. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently using meshless methods.Keywords Probabilistic fracture mechanics, Mesh-free method, Element-free galerkin method, J-integral, Sensitivity of J-integral, Probability of failure IntroductionProbabilistic fracture mechanics (PFM) is becoming increasingly popular for realistic evaluation of fracture response and reliability of cracked structures. The theory of fracture mechanics provides a mechanistic relationship between the maximum permissible load acting on a structural component to the size and location of a crackeither real or postulated -in that component. Probability theory determines how the uncertainties in crack size, loads, and material properties, when modeled accurately, affect the reliability of cracked structures. PFM, which blends these two theories, accounts for both mechanistic and stochastic aspects of the fracture problem, and hence, provides a more rational means to describe the actual behavior and reliability of structures than traditional deterministic methods [1].While development is ongoing, a number of methods have been developed for estimating statistics of various fracture response and reliability. Most of these methods are based on linear-elastic fracture mechanics (LEFM) and the finite element method (FEM) that employs the stressintensity factor (SIF) as the primary crack-driving force [1][2][3][4][5]. For example, using SIFs from an FEM code, Grigoriu et al. [2] applied first-and second-order reliability methods (FORM/SORM) to predict the probability of fracture initiation and a confidence interval of the direction of crack extension. The method can account for random loads, material properties, and crack geometry. However, the randomness in crack geometry was modeled by response surfa...

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Probabilistic pipe fracture evaluations for leak-rate-detection applications

Cited by 29 publications

References 0 publications

Probabilistic fracture mechanics for nonlinear structures

Probabilistic fracture mechanics for nonlinear structures

Probabilistic fracture mechanics by Galerkin meshless methods ? part II: reliability analysis

Stochastic meshless analysis of elastic?plastic cracked structures

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