On the decomposition of the J-integral for 3D crack problems

Huber, Otto; Nickel, Jeffrey C.; Kühn, G.

doi:10.1007/bf00017849

Cited by 57 publications

(26 citation statements)

References 14 publications

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“…This approach has been frequently used along with the domain representation of the J-integral for the computation of SIFs (Raju and Shivakumar, 1990;Shivakumar and Raju, 1992;Nikishkov and Atluri, 1987b;Huber et al, 1993). However, decomposing the crack tip field into symmetric and antisymmetric fields introduces error, and is mainly applicable to a mesh that is symmetric with respect to the crack face.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…The J 1 integral (or J integral) can also be used to extract mixed mode SIFs, with some auxiliary operation. One approach is to decompose the displacement and stress fields into symmetric and antisymmetric portions with a structured mesh along the crack front, then the three modes of the J integral can be extracted directly [114][115][116][117]. The other method known as the M integral (or interaction energy integral), was developed by introducing asymptotic fields as an auxiliary solution [108] has been extended in (X)FEM [118,31] and BEM [119].…”

Section: Computation Of Stress Intensity Factorsmentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

194

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Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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“…To prove path or domain independence of such transformations explicitly is often more cumbersome (e.g. Huber et al 1993;Rigby and Aliabadi 1998) than the convenient direct use of (5). To prove (4), we have, in short, for the terms in P l j the steps…”

Section: Decomposition Of the Energy Momentum Tensormentioning

confidence: 99%

“…to obtain the stress intensity factors K I , K II and K III from J . The most general and numerically stable method (Huber et al 1993), which is exploited here, is the decomposition method (Ishikawa et al 1979). In this method, J is first split into two parts J = J S + J A where J S and J A are calculated from the symmetric and anti-symmetric elastic fields about the crack plane, respectively.…”

mentioning

confidence: 99%

Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading

Eriksson

2007

Int J Fract

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Vanishing divergence of Eshelby's (energy momentum) tensor allows formulation of path or domain independent integral expressions of the crack extension force. In this work, a decomposition scheme of this tensor is presented, which results in zero divergence decomposed parts that allow formulation of expressions yielding the Mode I, II and III crack tip parameters J and K , with particular emphasis on Mode III, at present. By using the Mode III decomposed part of Eshelby's tensor and the virtual crack extension method, a path and a domain independent integral, both new, for the crack extension force of a plane circular crack in axi-symmetric Mode III loading, are derived as examples of application.

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On the decomposition of the J-integral for 3D crack problems

Cited by 57 publications

References 14 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

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading

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