Crack problems in plane and antiplane elasticity using a singular integral equation

KSME Journal ◽  
1989 ◽  
Vol 3 (1) ◽  
pp. 10-14
Author(s):  
Mostafa A. Hamed ◽  
Barry Cummins
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Antiplane Elasticity ◽  
Crack Problems

The Solution of Crack Problems by Using Distributed Strain Nuclei

1996 ◽  
Vol 210 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A M Korsunsky ◽  
D A Hills
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problems ◽  
The Relationship ◽  
Distributed Strain

Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.

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.

Analysis of Branched Cracks

1978 ◽  
Vol 45 (4) ◽  
pp. 797-802 ◽  
Author(s):  
K. K. Lo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Complex Form ◽  
Function Technique ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Potential Formulation ◽  
Crack Problems

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.

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