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.

Collinear Crack Problem in Antiplane Elasticity for a Strip of Functionally Graded Materials

2004 ◽  
Vol 20 (3) ◽  
pp. 167-175 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Problem ◽  
Functionally Graded ◽  
Elementary Solution ◽  
Collinear Crack ◽  
Graded Materials ◽  
Antiplane Elasticity

AbstractIn this paper, elastic analysis for a collinear crack problem in antiplane elasticity of functionally graded materials (FGMs) is present. An elementary solution is obtained, which represents the traction applied at a point “x” on the real axis caused by a point dislocation placed at a point “t” on the same real axis. The Fourier transform method is used to derive the elementary solution. After using the obtained elementary solution, the singular integral equation is formulated for the collinear crack problem. Furthermore, from the solution of the singular integral equation the stress intensity factor at the crack tip can be evaluated immediately. In the solution of stress intensity factor, influence caused by the materials property “α” is addressed. Finally, numerical solutions are presented.

scholarly journals Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

2020 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Youn-Sha Chan ◽  
Edward Athaide ◽  
Kathryn Belcher ◽  
Ryan Kelly
Keyword(s):  
Integral Equations ◽  
Functionally Graded Materials ◽  
Singular Integral ◽  
Mixed Mode ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Mixed Mode Fracture ◽  
Graded Materials

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

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