Stress intensity factor analysis for an interface crack between dissimilar anisotropic materials under thermal stress

Ikeda, Tôru; Yamanaga, Koh; Miyazaki, Noriyuki

doi:10.1299/jsmecmd.2003.16.761

Cited by 9 publications

(12 citation statements)

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“…There exist variety of post processing techniques, within the framework of the EFG method, to compute the SIFs for a crack in isotropic and homogenous materials [48,49] and complex SIF for an interface crack [50][51][52][53][54][55]. The popular interaction integral/M-integral [56] technique is used to extract the complex SIF associated with an interface crack under mechanical and thermal loading.…”

Section: Interaction Integral To Extract Sifs and T-stressmentioning

confidence: 99%

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

Muthu

Maiti

Falzon

et al. 2016

Engineering Analysis with Boundary Elements

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A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported. KEY WORDS: EFG, SIF, T-stress, interface crack, MTPS, crack propagation. INTRODUCTIONComposite materials are often subjected to extreme mechanical and thermal loading conditions that make them susceptible to damage through crack formation. Studies on the modelling of fracture in composites, range from nanoscale to macroscale analysis. Useful insight into the study of fracture may be gained through analysis at the microscale. At this level, the constituent materials are represented separately, i.e. the material is non-homogenous usually consisting of dissimilar materials or bi-materials separated by an interface [1].A propagating crack at the microscale may often impinge on the bi-material interface at an angle. The associated singular stress field consists of two different orders of singularity which may be either complex conjugates or real [2][3]. In addition, a crack tip that meets an interface of two materials may grow along it or penetrate into the neighbouring material. The criterion for such a crack to kink into the neighbouring material is different from the criterion governing the crack propagation in a homogenous material. The development of a proper numerical 2 method and an efficient approach to predict the angle of crack propagation, including kinking of an interface crack, can be very useful in the study of fracture of composites.Mesh-based methods like the finite element method (FEM) and the boundary element method (BEM) pose difficulties for crack propagation problems due to extensive meshing and remeshing. Although the extended finite element method (XFEM), based on the partition-of-unity approach, eliminated some of the difficulties, the enrichment functions depend on the crack tip loc...

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Section: Interaction Integral To Extract Sifs and T-stressmentioning

confidence: 99%

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

Muthu

Maiti

Falzon

et al. 2016

Engineering Analysis with Boundary Elements

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“…Therefore, the virtual crack extension method (14) and the virtual crack closure method (15) (16) , which are used in conjunction with conventional FEM analysis, cannot be applied to evaluate the energy release rate. The domain form of the energy release rate …”

Section: Evaluation Of Energy Release Ratementioning

confidence: 99%

“…In elastic problems, the energy release rate, which is one of fracture mechanics parameters, can be evaluated by the post processing for the results of X-FEM analysis, as well as FEM. Since the crack geometry does not always perfectly coincide with the element boundary in X-FEM models, neither the virtual crack closure method (14) nor the virtual crack extension method (15) (16) can be applied directly. Therefore, the domain integral method (17) (18) is used to evaluate the…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Nagashima

Miura

2008

JCST

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The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for efficiently solving fracture mechanics problems. In the present study, the constraint condition enforcement for X-FEM analysis considering symmetry is presented. Since the interpolation functions utilized in X-FEM analysis include the enrichment basis functions, the freedoms of the node on the symmetric plane should be constrained properly in the X-FEM model with symmetric conditions. Moreover, evaluation of the energy release rate by the domain integral method should be performed considering the symmetry conditions. In the present paper, the constraint conditions for three-dimensional X-FEM analysis considering symmetric conditions are summarized, and numerical examples using symmetric X-FEM models are shown. The proposed procedure can be used to perform efficient X-FEM analyses of practical fracture problems.Key words: Extended FEM, Fracture Mechanics, Energy Release Rate, Symmetric Conditions IntroductionThe extended finite element method (X-FEM)(1)-(3) can approximate the discontinuous displacement field near cracks independently of the finite element mesh by using the interpolation functions, which can describe the displacement field near cracks in structures. Therefore, the crack modeling for stress analyses can be performed more easily by X-FEM, as compared to conventional FEM. As the information with respect to the crack geometry is required in order to determine the interpolation functions in X-FEM, the level set method (4) , which expresses the geometry implicitly as the zero contour of the level set function, can be used in order to simplify the computation process in X-FEM analysis (5) . The X-FEM analyses in conjunction with the level set method (6) have been applied to the three-dimensional elastic stress and crack propagation analyses for planar and non-planar crack with complex geometry (7) (8) . Moreover, X-FEM has come to be applied to geometrically nonlinear (9) (10) and materially nonlinear problems (10)-(13) . In elastic problems, the energy release rate, which is one of fracture mechanics parameters, can be evaluated by the post processing for the results of X-FEM analysis, as well as FEM. Since the crack geometry does not always perfectly coincide with the element boundary in X-FEM models, neither the virtual crack closure method (14) nor the virtual crack extension method (15) (16) can be applied directly. Therefore, the domain integral method (17) (18) is used to evaluate the Vol. 2, No. 1, 2008 211 energy release rate Journal of Computational Science and Technology(1)- (3), (6)- (8) .The symmetrical conditions can be considered in order to reduce the number of nodes and elements and perform effective analyses in X-FEM as well as FEM when the geometry and boundary conditions have the symmetry properties. However, because the interpolation functions utilized in X-FEM analyses include the enrichment basis functions a...

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“…It is di cult to derive the exact solutions for cracked bodies of nite dimension. On numerical aspect, a lot of studies have been performed based on the nite element method [15][16][17][18][19][20][21][22][23][24][25] and the boundary element method [26][27][28][29] to solve the interface crack problems of nite dimension. The methods mentioned above may be categorized as the direct methods, which have a common disadvantage.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

Chai

et al. 2016

Journal of Thermal Stresses

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Di erent from previous two-dimensional thermal weight function (TWF) method, a three-dimensional (3D) TWF method is proposed for solving elliptical interface crack problems in bimaterial structures under a transient thermal loading. The present 3D TWF method based on the Betti's reciprocal theorem is a powerful tool for dealing with the transient thermal loading due to the stress intensity factors (SIFs) of whole transient process obtained through the static nite element computation. Several representative examples demonstrate that the 3D TWF method can be used to predict the SIFs of elliptical interface crack subjected to transient thermal loading with high accuracy. Moreover, numerical results indicate that the computing e ciency can be enhanced when dealing with transient problems, especially for large amount of time instants.ARTICLE HISTORY

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Stress intensity factor analysis for an interface crack between dissimilar anisotropic materials under thermal stress

Cited by 9 publications

References 0 publications

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

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