Kinked cracks in bonded half-planes modeled by an integral equation method

Zang, Weilin; Gudmundson, Peter

doi:10.1007/bf00040856

Cited by 5 publications

(12 citation statements)

References 10 publications

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“…The strategy is closely related to that of Zang and Gudmundson [6], and it is essentially a boundary element method in which the crack line integrals are treated in a special fashion to eliminate the difficulties associated with the application of the standard boundary element technique to fracture problems. The resulting equations contain integrals associated with the fracture which can be interpreted in terms of a distribution of dislocations and a distribution of concentrated forces along the crack line.…”

Section: Discussionmentioning

confidence: 99%

“…The use of complex variable techniques for this purpose not only allows the manipulations to be carried out in a straightforward manner, it also allows for a more straightforward and convenient interpretation of the multi-valued functions which arise. Indeed, an important distinction between the treatment of the multi-valued functions given here and that used in [6] is that the branch cuts for the multi-valued functions are defined as finite cuts along the crack lines rather than as an infinite cut which emanates from the source point and extends to infinity. The advantage of this interpretation of the multi-valued functions is two-fold.…”

Section: Discussionmentioning

confidence: 99%

“…[10]), we adopt instead a procedure in which the hypersingularity is avoided by eliminating the Cauchy type kernel from (1) before forming the displacement gradients. The procedure follows the work of Zhang and Gudmundson [6], although the development presented here is more general than that which they employ. Toward performing the requisite regularization, let S~#.~ be the stress fundamental solution for a unit concentrated force so that the stress field due to a force Pc is given by or#, = p~S~#.~, and introduce a (multi-valued) stress function C~ such that 2…”

Section: Alternative Formulationmentioning

confidence: 99%

“…More recently, a re-formulation of the boundary element method specifically for twodimensional fracture problems has been given by Zang and Gudmundson [6]. In their approach, the two crack surfaces are 'combined' and then a partial integration procedure introduced by Ghosh et al [7] is applied to 'regularize' the crack line integrals (also see [8], [9]).…”

Section: Introductionmentioning

confidence: 99%

“…The technique which is developed is essentially a modified boundary element scheme in which boundaries other than the crack lines are modeled by conventional boundary integrals, while the cracks are modeled via integral equations involving a distribution of dislocations and a distribution of concentrated forces. The formulation is closely related to that given by Zang and Gudmundson [6], although the development and implementation differ in several important respects which leads to a more complete and robust numerical strategy.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A boundary element method for two dimensional linear elastic fracture analysis

Chang

Mear

1996

Int J Fract

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A boundary element method is developed for the analysis of fractures in two-dimensional solids. The solids are assumed to be linearly elastic and isotropic, and both bounded and unbounded domains are treated. The development of the boundary integral equations exploits (as usual) S omigliana's identity, but a special manipulation is carried out to 'regularize' certain integrals associated with the crack line. The resulting integral equations consist of the conventional ordinary boundary terms and two additional terms which can be identified as a distribution of concentrated forces and a distribution of dislocations along each crack line. The strategy for establishing the integral equations is first outlined in terms of real variables, after which complex variable techniques are adopted for the detailed development. In the numerical implementation of the formulation, the ordinary boundary integrals are treated with standard boundary element techniques, while a novel numerical procedure is developed to treat the crack line integrals. The resulting numerical procedure is used to solve several sample problems for both embedded and surface-breaking cracks, and it is shown that the technique is both accurate and efficient. The utility of the method for simulating curvilinear crack propagation is also demonstrated.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Alternative Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A boundary element method for two dimensional linear elastic fracture analysis

Chang

Mear

1996

Int J Fract

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Prediction of interfacial crack path: a direct boundary integral approach and experimental study

1994

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This paper presents the development of a higher-order direct boundary integral-displacement discontinuity method for crack propagation in layered elastic materials. The method is based on the dual boundary integral equations of linear elasticity which are solved by means of a quadratic boundary element formulation. The analytical solution for a point force within a bonded half-plane region is used to derive the kernel functions of the boundary integral equations. Square-root displacement-discontinuity elements are used to model the crack tips, and stress intensity factors may be computed using the numerically predicted values of the displacement discontinuity components at the midpoints of these crack-tip elements. An algorithm based on the maximum tensile-stress criterion is then developed and incorporated into the boundary element model to predict the paths of cracks propagating in layered elastic materials.In the experimental part of this study, crack profiles for straight-through-cracked, compact-tension specimens of the anodically bonded silicon/Pyrex glass system are measured by profilometry. The plane strain prediction of the crack-propagation path is compared with the experimentally measured crack profiles. Consistent with the prediction, the interfacial crack is observed to kink away from the strong, anodicaUy-bonded interface and propagate into the more compliant glass layer. The predicted initial kink angle of 26 ° agrees very well with the average measured value of 280 . The measured path of the crack is also in very good agreement with the predicted path over about the first 120 microns of crack growth with increasing deviation observed beyond that.

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Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity

Chen

Lin

2006

Acta Mechanica

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Kinked cracks in bonded half-planes modeled by an integral equation method

Cited by 5 publications

References 10 publications

A boundary element method for two dimensional linear elastic fracture analysis

A boundary element method for two dimensional linear elastic fracture analysis

Prediction of interfacial crack path: a direct boundary integral approach and experimental study

Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity

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