Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics

Banks‐Sills, Leslie

doi:10.1115/1.4000798

Cited by 59 publications

(18 citation statements)

References 44 publications

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“…Chen and Shield (1977) and Yau et al (1980) introduced this method for 2D cracks, and Nakamura and Parks (1989) extended it to 3D crack configurations. Interaction integral methods are perhaps the most accurate, reliable and readily implementable methods to extract SIFs in mixed-mode 2D and 3D crack problems (Walters et al, 2005;Banks-Sills, 2010;Bremberg and Faleskog, 2015). Consider two states of equilibrium for the cracked body deformation: (i) an actual state obtained by the FE solution of the actual boundary value problem (u i , i j , σ i j ); and (ii) an auxiliary state given by the known asymptotic fields which are functions of the SIFs (u…”

Section: Interaction Integral To Extract Stress Intensity Factorsmentioning

confidence: 99%

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

Nejati

Paluszny

Zimmerman

2015

International Journal of Solids and Structures

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Please cite this article as: Nejati, M., Paluszny, A., Zimmerman, R.W., A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes, International Journal of Solids and Structures (2015), doi: http://dx.doi.org/10. 1016/j.ijsolstr.2015.05.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes Abstract A novel domain integral approach is introduced for the accurate computation of pointwise Jintegral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2 − 3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

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Section: Interaction Integral To Extract Stress Intensity Factorsmentioning

confidence: 99%

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

Nejati

Paluszny

Zimmerman

2015

International Journal of Solids and Structures

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“…For quarter point singular elements as shown in Figure 1(b), mixed mode SIFs can be estimated as follows using the COD and CSD as [8] and [35][36][37][38][39][40] …”

Section: Displacement Correlation Methods (Dcm)mentioning

confidence: 99%

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

Lal

Shailesh

2016

Curved and Layered Structures

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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.

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“…We repeat the numerical examples on a single fracture in an infinite plane in section 4 with Poisson's ratios ranging from 0 to 0.4, and the correction multipliers required for obtaining accurate SIF's for different mesh refinement levels are shown in Figure 12. A unified regression model is established by assuming the two constants in equation (20) to vary linearly with respect to the Poisson's ratio, and the regression results are The effects of the Poisson's ratio are more significant for mode-I than for mode-II. Even for mode-I, ignoring these effects by using the correction multipliers for ν=0.2 introduces less than 4% incremental error to the calculated SIF's for arbitrary Poisson's ratio.…”

Section: The Effects Of Mesh Configurations and The Poisson's Ratiomentioning

confidence: 99%

“…Many of the displacement-based methods were developed in the 1970's and 1980's in tandem with various special "quarter-point" finite element types [15][16][17][18][19] used in these methods. Though few new developments have been made for the displacement-based methods in the intervening decades [20], they continue to be widely used.…”

Section: Introductionmentioning

confidence: 99%

Generalized displacement correlation method for estimating stress intensity factors

Johnson

Settgast

et al. 2012

Engineering Fracture Mechanics

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Summary:Conventional displacement-based methods for estimating stress intensity factors require special quarter-point finite elements in the first layer of elements around the fracture tip and substantial near-tip region mesh refinement. This paper presents a generalized form of the displacement correlation method (the GDC method), which can use any linear or quadratic finite element type with homogeneous meshing without local refinement. These two features are critical for modeling dynamic fracture propagation problems where locations of fractures are not known a priori. Because regular finite elements' shape functions do not include the square-root terms, which are required for accurately representing the near-tip displacement field, the GDC method is enriched via a correction multiplier term. This paper develops the formulation of the GDC method and includes a number of numerical examples, especially those consisting of multiple interacting fractures. We find that the proposed method using quadratic elements is accurate for mode-I and mode-II fracturing, including for very coarse meshes. An alternative formulation using linear elements is also demonstrated to be accurate for mode-I fracturing, and acceptable mode-II results for most engineering applications can be obtained with appropriate mesh refinement, which remains considerably less than that required by most other methods for estimating stress intensities.

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Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics

Cited by 59 publications

References 44 publications

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

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

Generalized displacement correlation method for estimating stress intensity factors

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