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This paper presents a numerical method to model a general system containing cracks and voids in an infinite elastic plate under remote cyclic loads. By extending Bueckner's principle suited for a crack to a general system containing cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus, the results in terms of the stress intensity factors can be calculated by considering the latter problem, which is analyzed easily by using the hybrid displacement discontinuity method (a boundary element method). Further, a fatigue growth technique of a mixed-mode crack is combined with the numerical approach to simulating a void-crack interaction problem under cyclic loads. Test examples are included to illustrate that the numerical method is very simple and effective for analyzing a void-crack interaction problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner’s principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given. [Copyright &y& Elsevier]

Abstract: This note is concerned with a surface semi-circular crack by using finite element method. Attention is specifically paid to the effect of the boundaries parallel to the crack on the stress intensity factors (SIFs). The numerical results illustrate that when the boundaries parallel to the crack are closer to the crack surface the effect of the boundaries parallel to the crack on the SIFs must be considered. [Copyright &y& Elsevier]

Abstract: This note is specifically concerned with cracks emanating from a surface semi-spherical cavity in an infinite body (see ) by using the boundary element software FRANC3D developed by a fracture mechanics investigation group of Cornell University. The numerical results can reveal the effect of the geometry of the surface cavity on the stress intensity factors. [Copyright &y& Elsevier]

Abstract: By using the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author, this note presents the stress intensity factors (SIFs) of a rectangular tensile plate with single edge crack. Further this note studies the SIFs of crack emanating from an edge half-circular hole. By comparing the calculated SIFs of the single edge half-circular-hole crack with those of the single edge crack, a shielding effect of the half-circular hole on the SIFs of the single edge crack is discussed. It is found that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems in finite plate. [Copyright &y& Elsevier]

Abstract: In this paper, an effective numerical method for analyzing interacting multiple cracks and complex crack configurations in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple-crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by taking into account the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are included to illustrate that the method is very simple and effective for analyzing interacting multiple cracks and complex crack configurations in an infinite linear elastic media under remote uniform stresses. Specifically, analysis of perpendicular cracks under general in-plane loading is performed using the numerical approach and many numerical results are given in the form of tables. [Copyright &y& Elsevier]

Abstract: A numerical analysis of cracks emanating from a circular hole (Fig. 1) or a square hole (Fig. 2) in rectangular plate in tension is performed by means of the displacement discontinuity method with crack-tip elements (a boundary element method) presented recently by the author. Detail solutions of the stress intensity factors (SIFs) of the two plane elastic crack problems are given, which can reveal the effect of geometric parameters of the cracked bodies on the SIFs. By comparing the SIFs of the two crack problems with those of the center crack in rectangular plate in tension (Fig. 3), in addition, an effect of the circular hole or the square hole on the SIFs of the center crack is discussed in detail. The numerical results reported here also illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems in finite plate. [Copyright &y& Elsevier]

Abstract: In this paper, numerical analysis of a few complex crack problems is made by using a boundary element method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or the right crack-tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical results of a few complex crack problems, such as “a singly branched crack in an infinite plate”, “interaction between a circular hole and a crack in an infinite plate”, “a pair of branched cracks emanating from an elliptical hole in a rectangular plate under biaxial uniform tensions” and “fatigue growth analysis of a branched crack emanating form the corner of a square hole”, indicate that the numerical approach is very efficient and accurate for analyzing complex plane elasticity crack problems. [Copyright &y& Elsevier]

Abstract: This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given. [Copyright &y& Elsevier]

Abstract: This paper is concerned with complex stress intensity factors at bifurcated cracks by using the boundary element method, which consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. To prove the efficiency of the suggested approach and provide more results of the stress intensity factors, analysis of an asymmetric branched crack bifurcated from a main crack is carried out. The present numerical results show that the numerical approach to the computation of stress intensity factors of complex plane crack problems is simple, yet very accurate. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the stress intensity factors (SIFs) of cracks emanating from an elliptical hole in an infinite or a finite plate under biaxial loads by using a boundary element method, which consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. A few numerical examples are included to show that the present approach is very efficient and accurate for the calculating the SIFs of crack problems in an infinite or a finite plate. The present numerical results of cracks emanating from an elliptical hole under biaxial loads can reveal the effect of the elliptical aspect ratio and the transverse load on the SIFs. [Copyright &y& Elsevier]

Abstract: This paper concerns stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure calculated by means of a boundary element method, which consists of constant displacement discontinuity element presented by Crouch and Starfied and crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors of plane elasticity crack problems. Specifically, the numerical results of stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure are given. [Copyright &y& Elsevier]

This study concerns with a crack emanating from a corner of a square hole in an infinite plate subjected to internal pressure by means of a boundary element method which consists of the constant displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and other boundaries. Test examples are included to show that the numerical approach is very efficient and accurate for stress intensity factor calculation of plane complex crack problems in both infinite and finite domains. Specifically, the numerical results of stress intensity factors of a crack emanating from a corner of a square hole in an infinite plate subjected to internal pressure are given. [Copyright &y& Elsevier]

This note concerns with stress intensity factors of cracks emanating from a square hole in rectangular plate under biaxial loads by means of the boundary element method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results illustrate that the present approach is very effective and accurate for calculating stress intensity factors of complicated cracks in a finite plate and can reveal the effect of the biaxial load and the cracked body geometry on stress intensity factors. [Copyright &y& Elsevier]

In this paper, a numerical analysis of perpendicular cracks under general in-plane loading is performed by using a hybrid displacement discontinuity method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results show that the numerical approach is simple, yet very accurate for calculating numerically stress intensity factors for perpendicular cracks under general in-plane loading. [Copyright &y& Elsevier]

This article concerns with the interference effect of arbitrary multiple parabolic cracks in plane elasticity by using a new boundary element method. The boundary element method consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results of stress intensity factors for “the interference effect of two collinear parabolic cracks”, “the interference effect of three collinear parabolic cracks”, “the interference effect of two parallel parabolic cracks”, “the interference effect of three parallel parabolic cracks” and “the interference effect of two parabolic cracks” show that the numerical approach presented in the present study is simple, yet very accurate for analyzing the interference effect of arbitrary multiple parabolic cracks in plane elasticity. [Copyright &y& Elsevier]

Abstract: This note is concerned with a surface semi-circular crack by using the fracture analysis software FRANC3D developed by a fracture mechanics investigation group of Cornell University. Attention is specifically paid to the effect of the boundaries parallel to the crack on the stress intensity factors (SIFs). [Copyright &y& Elsevier]

A letter to the editor is presented in response to the article regarding the use of hybrid displacement discontinuity or boundary element method which provides rectangular tensile sheets numerical analysis with double edge cracks.

Abstract: By using a hybrid displacement discontinuity method, the interactions of two collinear circular hole cracks in infinite plate subjected to internal pressure are investigated in this paper. Numerical examples are included to illustrate that the numerical approach is very simple and effective for calculating the stress intensity factors (SIFs) of crack problems. In particular, the interaction problem of two collinear circular hole cracks is investigated in detail. Many numerical results are given and discussed. It is found that a circular hole has a shielding effect on the SIFs of crack(s) emanating from the hole. The finding perhaps has an important meaning in engineering. [Copyright &y& Elsevier]