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.

Interaction Between Interfacial Cavity/Crack and Internal Crack—Part II: Simulation

2003 ◽  
Vol 72 (3) ◽  
pp. 394-399 ◽  
Author(s):  
P. B. N. Prasad ◽  
Norio Hasebe ◽  
X. F. Wang
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Singular Integral Equation ◽  
Internal Crack ◽  
Uniform Loading ◽  
Distributed Dislocation ◽  
Point Dislocation ◽  
Dislocation Technique

This paper discusses the interaction of an interfacial cavity/crack with an internal crack in a bimaterial plane under uniform loading at infinity. The point dislocation solution is used to simulate internal crack by using the distributed dislocation technique. The resulting singular integral equation is solved numerically and the stress intensity factor variations are plotted for some cases of internal crack interacting with interfacial cavity/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.

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.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

2017 ◽  
Vol 24 (2) ◽  
pp. 448-464 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi ◽  
Zhixin Liu
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Singular Integral ◽  
Material Properties ◽  
Elastic Layer ◽  
Coated Substrate ◽  
Receding Contact ◽  
Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

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