Finite boundary effects in problem of a crack perpendicular to and terminating at a bimaterial interface

Chen, Shaohua; Wang, Tzuchiang; Kao-Walter, Sharon

doi:10.1007/s10409-004-0007-5

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Fracture criteria such as SIF and crack opening displacement can be obtained. In general, the SIF values computed from the FEMOL solution are close to theoretical predictions with a percentage difference depending on the crack length [11,12].…”

Section: Resultssupporting

confidence: 48%

Cracking analysis of fracture mechanics by the finite element method of lines (FEMOL)

Moran

2005

ACTA MECH SINICA

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The Finite Element Method of Lines (FEMOL) is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor (SIF) and crack opening displacement (COD) are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

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Section: Resultssupporting

confidence: 48%

Cracking analysis of fracture mechanics by the finite element method of lines (FEMOL)

Moran

2005

ACTA MECH SINICA

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“…Chen et al (2003) used a dislocation simulation approach to derive the basic equations for a crack perpendicular to the interface in a finite solid. Chen et al (2005) solved the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries by employing dislocation simulation method and boundary collocation approach. Ouyang and Lee (1996) presented an analysis of screw dislocations near a crack penetrating through an interface based on the solution of a homogeneous solid.…”

Section: Introductionmentioning

confidence: 99%

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

Xiao

Xie

2008

International Journal of Solids and Structures

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a b s t r a c tA method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips' singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann-Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K IIIu increases steeply to infinity.

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“…Figure 1.2: Schematics indicating the cracking behavior and failure in ceramic matrix composite (Liu, 2015) Within the framework of linear elastic fracture mechanics (LEFM), the stress intensity factors are essential parameters providing the measure of the dominant elastic fields in a local region surrounding the crack edge. Various researchers employed the concept of LEFM to develop solution techniques for determining the stress intensity factors for cracks in dissimilar media (e.g., Lee et al, 1987;Huang and Kardomateas, 2001;Chang and Wu, 2003;Chen et al, 2005;Xiao et al, 2005;Hao, 2006;Noda et al, 2006;Rungamornrat, 2006;Chang and Xu, 2007;Yue et al, 2007;Marsavina and Sadowski, 2008;Chen et al, 2010;Tu et al, 2013;Liu, 2015).…”

Section: Motivation and Significancementioning

confidence: 99%

Analysis of near interface cracks by weakly singular boundary integral equation method

Watanavit

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This thesis presents a weakly singular boundary integral equation method for analysis of sub-interface cracks in a three-dimensional, linearly elastic, multi-material domain. The formulation is established in a general framework allowing finite bodies, general material anisotropy and loading conditions, arbitrarily shaped cracks, and curved material interface to be treated. A system of integral equations governing the unknown data on the boundary, the crack surface and the material interface are established using a pair of weakly singular, weak-form displacement and traction integral equations and the continuity along the material interface. A symmetric Galerkin boundary element method together with the standard finite element technique is implemented to solve the governing integral equations. Special near-front approximation is employed to enhance the approximation of the relative crack-face displacement in the neighborhood of the crack front. The solved crack-face data is then used to post-process for the stress intensity factors and the T-stress along the crack front. A selected set of results is presented not only to demonstrate the accuracy, convergence and capability of the proposed technique but also to explore the influence of the material stiffness and the distance to the material interface on the fracture data along the crack front.?

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Finite boundary effects in problem of a crack perpendicular to and terminating at a bimaterial interface

Cited by 4 publications

References 15 publications

Cracking analysis of fracture mechanics by the finite element method of lines (FEMOL)

Cracking analysis of fracture mechanics by the finite element method of lines (FEMOL)

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

Analysis of near interface cracks by weakly singular boundary integral equation method

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