Fatigue crack growth reliability by probabilistic finite elements

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

doi:10.1016/0045-7825(91)90225-u

Cited by 56 publications

(19 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Rao¹,

Rahman²

2002

Computational Mechanics

View full text Add to dashboard Cite

show abstract

“…More recently, the problem of structural reliability for fatigue crack propagation has been de"ned as an optimization problem [11]. This approach, however, implies the necessity of verifying that global and not only local optimum has been obtained, which is not obvious in non-convex problems.…”

Section: Introductionmentioning

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.

View full text Add to dashboard Cite

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.

show abstract

“…However, MCS is computationally expensive method to solve the structural problems consisting of defects like cracks. This problem can be overcome with the help of adopting adaptive sampling techniques [44,45]. …”

Section: Msif Statistics Response For Multiple Random Variablesmentioning

confidence: 99%

Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method

Lal

Shailesh

2016

Curved and Layered Structures

View full text Add to dashboard Cite

Abstract:The second order statistics of mixed mode stress intensity factors (MSIF) of single edge V-notched angle ply laminated composite plate subjected to uniaxial tensile load with uncertinity in the system properties using displacement correlation method (DCM) is evaluated. The random system properties such as material properties, crack opening and crack length are modelled as combined uncorrelated and correlated random system variables. A C nite element method (FEM) based on higher order shear deformation plate theory (HSDT) is used for basic formulation. The Taylor series based rst order perturbation technique (FOPT), second order perturbation technique (SOPT) are used and direct Monte Carlo simulation (MCS) is performed to evaluate the statistics (mean and coe cient of variance) of the mixed mode SIFs. The present work signi es the accurate analysis of frature behaviour by in uence of di erent random variables and bre orientations on the fracture behaviour in angle ply laminates.

show abstract

Fatigue crack growth reliability by probabilistic finite elements

Cited by 56 publications

References 18 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

Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method

Contact Info

Product

Resources

About