A procedure for regularization of singular integral equation of the multiple crack problem in an infinite plate

1987 ◽  
Vol 34 (3) ◽  
pp. R53-R56 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problem ◽  
Infinite Plate ◽  
Multiple Crack

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE CURVED EDGE CRACKS EMANATING FROM BOUNDARY OF HALF-PLANE

2006 ◽  
Vol 03 (02) ◽  
pp. 205-217 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Edge Crack ◽  
Crack Problem ◽  
Infinite Plate ◽  
Complex Potentials ◽  
Edge Cracks ◽  
Edge Crack Problem

This paper provides, an elastic solution for multiple curved edge cracks emanating from the boundary of the half-plane. After placing the distributed dislocations at the prospective sites of cracks in an infinite plate, the principal part of the complex potentials is obtained. By using the concept of the modified complex potentials, the complementary part of the complex potentials can be derived. The whole complex potentials satisfy the traction free condition along the boundary of half-plane automatically. This is a particular advantage of the suggested method. This concept or method of the modified complex potentials is a counterpart of the Green's function method, which is universal in mathematical physics. The direct usage of this method cannot provide a solution in detail. Comparing with the line edge crack case, the following points are significant in the presented study. The relevant kernels in the integral equation are more complicated than in the line edge crack case and the relevant integrations in the problem should be completed on curves. This paper solves a rather complicated problem, the multiple curved edge crack problem, and gives the final solution. A singular integral equation is formulated with the dislocation distribution being unknown function and the traction being the right hand term. The singular integral equation is solved by using the curve length method in conjunction with the semiopening quadrature rule. Periodic curved edge crack problem is also addressed. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

SINGULAR INTEGRAL EQUATION METHOD FOR A MOVING CRACK PROBLEM IN ANTIPLANE ELASTICITY OF FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (03) ◽  
pp. 475-492 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Functionally Graded Materials ◽  
Material Property ◽  
Singular Integral ◽  
Crack Problem ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Antiplane Elasticity

In this paper, elastic analysis for a Yoffe moving crack problem in antiplane elasticity of the functionally graded materials (FGMs) is presented. The crack is assumed to move with a constant velocity V. The traction applied on the crack face is arbitrary. The Fourier transform method is used to derive an elementary solution. Furthermore, using the obtained elementary solution a singular integral equation for the problem is obtained. After the singular integral equation is solved, the stress intensity factor (SIF) can be evaluated immediately. In the case of evaluating the SIFs at the leading crack tip and the trailing crack tip, the difference between the two cases is investigated. From the numerical solution of the SIFs, the influence caused by the velocity V and the FGM material property β1 are addressed. It is found that when the FGM material property β1 = 0, i.e. the homogeneous case, the SIFs at the crack tips do not depend on the moving velocity of the crack. Finally, numerical examples are given.

Application of Singular Integral Equation to a Crack Moving near a Hole in a Two-Dimensional Infinite Plate

2018 ◽  
Vol 774 ◽  
pp. 113-118
Author(s):  
Masayuki Arai ◽  
Kazuki Yoshida
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Path ◽  
Infinite Plate ◽  
Propagation Path ◽  
Straight Crack ◽  
Distributed Dislocation ◽  
Moving Direction ◽  
Dislocation Technique

In this study, crack path simulation was conducted based on a singular integral equation formulated by a continuous distributed dislocation technique. The problem investigated in this study was to predict the propagation path of a crack moving in an infinite elastic plate with a circular hole, under uniform tensile loading. In order to perform this prediction, a probing method was developed to search for a crack moving direction where the mode II stress intensity factor would be almost zero, enabling the crack to automatically extend in that direction. Some cases for different locations of an initial straight crack were simulated using the program developed.

EVALUATION OF THE T-STRESS FOR MULTIPLE CRACKS IN AN INFINITE PLATE USING SINGULAR INTEGRAL EQUATION

2014 ◽  
Vol 11 (05) ◽  
pp. 1350073 ◽  
Author(s):  
Y. Z. CHEN ◽  
Z. X. WANG
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Infinite Plate ◽  
Multiple Cracks ◽  
Numerical Examples ◽  
T Stress ◽  
Crack Tips ◽  
Remote Loading ◽  
Crack Faces

This paper studies T-stress problem for multiple cracks in an infinite plate with the remote loading. After some manipulations, the problem can be modeled by dislocation distributions along the crack faces. A singular integral equation is formulated for the problem, where the unknowns are the dislocation distribution along the crack faces. The SIFs (stress intensity factor) can be evaluated from the solution of singular integral equation. From a definition for T-stress in the crack back position method and the solution of the singular integral equation, the T-stresses at crack tips can be evaluated accordingly. An explicit formula for the T-stress is provided. Several numerical examples are provided. Accuracy of computation is examined by an example.

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