J-integral at loaded crack surfaces

Karlsson, A.; Bäcklund, Jan

doi:10.1007/bf00116006

Cited by 33 publications

(8 citation statements)

References 10 publications

(5 reference statements)

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“…It is worth noting that the crack-like J-integral analysis strictly requires the contour to start and end from a traction-free surface, and therefore does not consider any internal pressure that might be exerted at the twin-parent boundary. Thus, to maintain the path independence of the integral, the J-integral definition of the contour path should be extended to include the twin-parent boundary [104] (similar to hydraulic fracture [105]), as described by the 2 nd term of equation ( 3) where f 𝑐 is the twin surface (Γ 𝑐 ) traction vector.…”

Section: Discussionmentioning

confidence: 99%

J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction

et al. 2021

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Section: Discussionmentioning

confidence: 99%

J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction

et al. 2021

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“…38,[42][43][44] The quintessential example of such efficient energy-based approaches is the 𝐽-integral, which estimates the energy release rate of an extending self-planar crack. 42,[45][46][47][48][49][50][51][52] Unlike the displacement correlation method, the 𝐽-integral is more acceptably extensible to three -dimensional problems, and constitutes an important method in assessing failure in both non-linear and time-dependent materials. 41 The 𝐽-integral has been applied in the hydraulic fracturing context, [53][54][55][56][57][58][59][60] along with alternative energy-based approaches, 61,62 however it has remained elusive whether the aforementioned advantages can be exploited.…”

Section: Highlightsmentioning

confidence: 99%

“…Adopting energy‐based theories of failure in LEFM avoids these disadvantages and, instead, achieves significantly higher levels of accuracy and lower resolution requirements 38,42–44 . The quintessential example of such efficient energy‐based approaches is the J ‐integral, which estimates the energy release rate of an extending self‐planar crack 42,45–52 . Unlike the displacement correlation method, the J ‐integral is more acceptably extensible to three ‐dimensional problems, and constitutes an important method in assessing failure in both non‐linear and time‐dependent materials 41…”

Section: Introductionmentioning

confidence: 99%

An enhancedJ‐integral for hydraulic fracture mechanics

Pezzulli

Nejati

Salimzadeh

et al. 2022

Num Anal Meth Geomechanics

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This article revisits the formulation of the J‐integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J‐integral in finite element models overestimates the length of hydraulic fractures in the viscosity‐dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of the J‐integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of the J‐integral, termed the JHFM$J_{HFM}$ and JHFMA$J_{HFM}^A$‐integral, that demonstrate an enhanced ability to predict viscosity‐dominated propagation. In particular, such JHFM$J_{HFM}$‐integrals accurately extract stress intensity factors in both viscosity and toughness‐dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness‐viscous propagation regimes. Both techniques are combined to form an implicit front‐tracking JHFM$J_{HFM}$‐algorithm capable of quickly converging on the location of the fracture front independently to the toughness‐viscous regime of propagation. The JHFM$J_{HFM}$‐algorithm represents an energy‐based alternative to the aperture‐based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro‐mechanical finite element simulations at the reservoir scale.

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“…To address this issue, the solution proposed by Karlsson and Bäcklund (1978) was hereby adopted. Accordingly, a decomposition of the J Integral is assumed as:…”

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confidence: 99%

The Splitting Method and the GFEMin the Two-Dimensional Analysis of Linear Elastic Domains with Multiple Cracks

Cotta

Proença

2016

Lat. Am. j. solids struct.

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an essential role in terms of modeling this kind of phenomenon. In fact, it can be said nowadays that failure analysis governed by unstable propagation from a single crack is common practice.However, failure analysis may become a more serious issue when many cracks which interact with each other must be considered. Furthermore, as well having many cracks, it is often necessary to predict and compute a large number of possible scenarios of multiple cracks. These requirements can make the analysis very complex or almost impracticable. Choosing an efficient numerical approach plays a crucial role in enabling computational analysis, and the Finite Element Method is the most commonly adopted option. Moreover, there is still a lack of studies with regards to establishing a computational framework that combines a representative mechanical model with an efficient numerical approach to solve such problems. This issue is addressed in this work.Domain decomposition methods such as the overlapping and non-overlapping Schwarz alternating methods, Le Tallec (1994), Wang and Atluri (1996) were most successful in overcoming the above mentioned mechanical modeling difficulties. This class of methods has proven to be very efficient and accurate in terms of analyzing multiple crack problems, despite requiring an iterative procedure to impose the restriction of stress vector nullity at the crack faces.The Splitting Method, proposed by Andersson and Babuska (1996), (2005), also belongs to the class of decomposition methods, and is hereby adopted for several reasons. Firstly, a very important characteristic of this method is that it was designed to efficiently search and identify the worst scenario among a set of possible multisite crack scenarios. This means that each pattern of cracked domains can be analyzed without substantially increasing the computational effort. For each pattern, the results can be obtained from the resolution of a single linear system. Moreover, it is important to stress that this method does not require an iterative procedure to impose the nullity restriction of stress vectors at the crack faces.On the other hand, regarding numerical approaches, the methods derived from the Partition of Unity Finite Element Method, introduced by Babuska and Melenk (1995), (1997), such as the Generalized Finite Element Method or the Extended Finite Element Method (GFEM/ XFEM) have been successfully used in linear fracture mechanics problems, Duarte et al.(2000), Sukumar et al. (2000), Belytschko et al. (2009), Kim et al.(2012 and Barros et al.(2004). Using the GFEM, for example, the approximation to the solution can be improved locally by exploring a priori known accurate solutions, and therefore avoiding costly mesh refinements. For instance, concerning crack problems, the Westergaard Complex Stress Function scan be explored in order to reproduce stress fields more accurately in the proximity of the crack tip. In fact, in Alves (2010), the referred enrichment strategies were primarily used to improve accuracy to analyze frac...

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J-integral at loaded crack surfaces

Cited by 33 publications

References 10 publications

J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction

J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction

An enhancedJ‐integral for hydraulic fracture mechanics

The Splitting Method and the GFEMin the Two-Dimensional Analysis of Linear Elastic Domains with Multiple Cracks

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