An analysis of interface cracks between dissimilar isotropic materials using conservation integrals in elasticity

Yau, J. F.; Wang, S.S.

doi:10.1016/0013-7944(84)90048-1

Cited by 106 publications

(41 citation statements)

References 13 publications

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“…The M-integral formulation was first presented by Yau et al [71]. Later this formulation was extended by Yau and Wang [72] for interface cracks between two homogeneous isotropic two-dimensional bodies. More recently, a three-dimensional M-integral using asymptotic stress was presented by Freed and Bank-Sills [73].…”

Section: A Methodology Based On a Conservative M-integralmentioning

confidence: 99%

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Krueger

Shivakumar

Raju

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established.

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Section: A Methodology Based On a Conservative M-integralmentioning

confidence: 99%

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Krueger

Shivakumar

Raju

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…The node density of the case with 206,195 nodes was locally refined near the crack tip, and the others were nearly homogeneous. Table 1 provides the stress intensity factors (SIFs) for the numerical results recalculated by the M-integral method [22], and Fig. 9 illustrates the von Mises stress distribution in a section of y = 0 for the case with 206,195 nodes.…”

Section: Near-tip Crack Field Problemmentioning

confidence: 99%

“…(21) and (22) are linear, so δ u can be obtained by using a numerical solution of algebraic equations. The operators r Ω (u) and r Γ (u) are also constructed in each step up to the unknown function u (k) .…”

Section: Point Collocation Schemementioning

confidence: 99%

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Three-Dimensional Crack Propagation Analysis Using Meshless Point Collocation Method

Tanaka¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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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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An analysis of interface cracks between dissimilar isotropic materials using conservation integrals in elasticity

Cited by 106 publications

References 13 publications

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Three-Dimensional Crack Propagation Analysis Using Meshless Point Collocation Method

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

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