Brittle Fracture Reliability by Probabilistic Finite Elements

Besterfield, Glen; Liu, Wing K; Lawrence, Mark; Belytschko, Ted

doi:10.1061/(asce)0733-9399(1990)116:3(642)

Cited by 41 publications

(14 citation statements)

References 22 publications

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“…First-and second-order reliability methods [11], frequently used in PFM [12][13][14][15][16][17][18], require the gradient and/or Hessian of the performance function with respect to random parameters. In linear-elastic fracture mechanics (LEFM), the performance function is built on SIFs.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic fracture mechanics by Galerkin meshless methods ? part I: rates of stress intensity factors

Rao¹,

Rahman²

2002

Computational Mechanics

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This is the first in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper (Part I), a Galerkin-based meshless method is presented for predicting first-order derivatives of stress-intensity factors with respect to the crack size in a linear-elastic structure containing a single crack. The method involves meshless discretization of cracked structure, domain integral representation of the fracture integral parameter, and sensitivity analysis in conjunction with a virtual crack extension technique. Unlike existing finite-element methods, the proposed method does not require any second-order variation of the stiffness matrix to predict first-order sensitivities, and is, consequently, simpler than existing methods. The method developed herein can also be extended to obtain higher-order derivatives if desired. Several numerical examples related to mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that firstorder derivatives of stress-intensity factors using the proposed method agree very well with reference solutions obtained from either analytical (mode I) or finite-difference (mixed mode) methods for the structural and crack geometries considered in this study. For mixed-mode problems, the maximum difference between the results of proposed method and finite-difference method is less than 7%. Since the rates of stress-intensity factors are calculated analytically, the subsequent fracture reliability analysis can be performed efficiently and accurately.

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Section: Introductionmentioning

confidence: 99%

Probabilistic fracture mechanics by Galerkin meshless methods ? part I: rates of stress intensity factors

Rao¹,

Rahman²

2002

Computational Mechanics

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“…In the present case, it is very simple to perform the integral (19) analytically over the domain (20) getting: …”

Section: Corrections To the B-pfem Modelmentioning

confidence: 99%

Corrections to B-models for fatigue life prediction of metals during crack propagation

Bea

Doblaré

Villanueva

et al. 1999

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper a new model for the prediction of the Cumulative Distribution Function (CDF) of fatigue life of structural elements during the crack propagation stage is described. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdano! and Kozin [1] (B-models). The initial and "nal crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads may be considered as random variables. In this initial approach, a linear approximation of the random variable &fatigue life' and a truncated uniform distribution for the crack length variable are considered. Two corrections to this model are discussed: a second-order approximation of the fatigue life to compute its variance, and a modi"cation of the Probability Density Distribution (PDD) of the crack length, which is now derived from the truncated uniform distributions of the initial and "nal crack lengths. Some examples for mode I are compared to the ones obtained using a Monte Carlo scheme with 400 000 samples, showing a good agreement and a much better performance of the corrected version of the model, specially for big standard deviations.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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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Brittle Fracture Reliability by Probabilistic Finite Elements

Cited by 41 publications

References 22 publications

Probabilistic fracture mechanics by Galerkin meshless methods ? part I: rates of stress intensity factors

Probabilistic fracture mechanics by Galerkin meshless methods ? part I: rates of stress intensity factors

Corrections to B-models for fatigue life prediction of metals during crack propagation

Stochastic meshless analysis of elastic?plastic cracked structures

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