Probabilistic analysis of off-center cracks in cylindrical structures

Chen, G.; Firmature, R.; Rahman, Sharif

doi:10.1016/s0308-0161(99)00076-9

International Journal of Pressure Vessels and Piping

2000

DOI: 10.1016/s0308-0161(99)00076-9

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Probabilistic analysis of off-center cracks in cylindrical structures

G. Chen

R. Firmature

Sharif Rahman³

Abstract: This paper presents a probabilistic methodology for fracture-mechanics analysis of off-center cracks in pipes subject to pure bending moment. It is based on: (1) a new analytical approximation of the J-integral; (2) statistical models of uncertainties in loads, material properties, and crack geometry; and (3) standard computational methods of structural reliability theory. The proposed analytical equations were applied to a probabilistic fracture-mechanics analysis of off-center cracks in pipes. The second-ord… Show more

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Cited by 14 publications

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“…This shows the performance of CFRP pressure vessel is related not only with fiber strength but also with material properties of resin matrix, tension and solidifying system of winding process.Because of CFRP (Carbon Fiber Reinforced Plastics) have many advantages which are high specific strength, high specific modulus, ablation resistance and low cost. Although the thing that composite materials have been substitutes for metal shell springs up soon, the application is much wide [1][2][3][4][5][6] .…”

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confidence: 99%

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The Burst Tests and Theory Analysis of CFRP Pressure Vessel

Zhang

Zuo

Zheng

et al. 2012

AMM

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8 pressure vessels of carbon fiber reinforced plastics (CFRP) have been manufactured with in the winding technology of same continuous carbon fiber–-amine system, new same flexible formula and same tension system. And the hydraulic bursting tests with the specimens were done in accordance with GB6058-85. The parameters of fiber strength, winding angle, geometric sizes and burst pressure were obtained by the tests. The theoretical analysis was done by conventional design method and reliability design method. The results show that: the theoretical calculating thickness of CFRP pressure vessel with by same parameters is thicker than practical thickness. This shows the performance of CFRP pressure vessel is related not only with fiber strength but also with material properties of resin matrix, tension and solidifying system of winding process. Because of CFRP (Carbon Fiber Reinforced Plastics) have many advantages which are high specific strength, high specific modulus, ablation resistance and low cost. Although the thing that composite materials have been substitutes for metal shell springs up soon, the application is much wide[1-6].

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mentioning

confidence: 99%

“…Because of CFRP (Carbon Fiber Reinforced Plastics) have many advantages which are high specific strength, high specific modulus, ablation resistance and low cost. Although the thing that composite materials have been substitutes for metal shell springs up soon, the application is much wide [1][2][3][4][5][6] .…”

mentioning

confidence: 99%

The Burst Tests and Theory Analysis of CFRP Pressure Vessel

Zhang

Zuo

Zheng

et al. 2012

AMM

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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 analysis of off-center cracks in cylindrical structures

Cited by 14 publications

References 16 publications

The Burst Tests and Theory Analysis of CFRP Pressure Vessel

The Burst Tests and Theory Analysis of CFRP Pressure Vessel

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

Stochastic meshless analysis of elastic?plastic cracked structures

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