On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation

2003 ◽  
Vol 70 (5) ◽  
pp. 676-680 ◽  
Author(s):  
Y.-S. Wang ◽  
G.-Y. Huang ◽  
D. Dross
Keyword(s):  
Integral Transform ◽  
Mixed Boundary ◽  
Plane Deformation ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Griffith Crack ◽  
Elastic Solids ◽  
Fourier Integral Transform ◽  
Graded Interfacial Zone

An analytical model is developed for a functionally graded interfacial zone between two dissimilar elastic solids. Based on the fact that an arbitrary curve can be approached by a continuous broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and continuous on the interfaces between sublayers. With this new multilayered model, we analyze the problem of a Griffith crack in the interfacial zone. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a Cauchy singular integral equation. The stress intensity factors are calculated. The paper compares the new model to other models and discusses its advantages.

Mixed Multi-Layered Model for Fracture Analysis of Functionally Graded Interfacial Zone under Anti-Plane Loading

2012 ◽  
Vol 452-453 ◽  
pp. 1154-1158
Author(s):  
Ke Di ◽  
Yue Cheng Yang
Keyword(s):  
Present Model ◽  
Mixed Boundary ◽  
Crack Problem ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Layered Model ◽  
Mixed Boundary Problem ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Equation ◽  
Graded Interfacial Zone

In this paper, a new mixed multi-layered model is put forward to study the crack problem of the functionally graded interfacial zone between tow homogeneous half-spaces. In the model, the interfacial zone is divided into some sub-layers with the properties of each layer varying in linear and exponential manners alternately. By applying Fourier transform and using the transfer matrix method, the mixed boundary problem of anti-plane fracture can be reduced to a Cauchy singular integral equation, which is solved numerically. Stress intensity factors of some examples are derived. The results show that the present model is effective and accurate and compared with the liner multi-layered model, the present one can save more CPU time in computation.

Mode I Crack Problem for a Functionally Graded Orthotropic COATING-Substrate Structure

2014 ◽  
Vol 936 ◽  
pp. 1999-2006
Author(s):  
Li Fang Guo ◽  
Xing Li ◽  
You Zheng Yang
Keyword(s):  
Integral Transform ◽  
Crack Problem ◽  
Integral Equation Method ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Mode I ◽  
Mode I Crack ◽  
Substrate Structure ◽  
Fourier Integral Transform ◽  
Principal Directions

In this paper, the Fourier integral transform-singular integral equation method is presented for the Mode I crack problem of the functionally graded orthotropic coating-substrate structure. The elastic property of the material is assumed vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. Numerical examples are presented to illustrate the effects of the crack length, the material nonhomogeneity and the thickness of coating on the stress intensity factors.

Sliding Frictional Contact of Functionally Graded Magneto-Electro-Elastic Materials Under a Conducting Flat Punch

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Ju Ma ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang
Keyword(s):  
Frictional Contact ◽  
Integral Transform ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Flat Punch ◽  
Coupled Equations ◽  
Fourier Integral Transform ◽  
Coulomb Type

This paper presents the two-dimensional sliding frictional contact between a rigid perfectly conducting flat punch and a functionally graded magneto-electro-elastic material (FGMEEM) layered half-plane. The electric potential and magnetic potential of the punch are assumed to be constant within the contact region. The magneto-electro-elastic (MEE) material properties of the FGMEEM layer vary as an exponential function along the thickness direction, and the Coulomb type friction is adopted within the contact region. By using the Fourier integral transform technique, the problem is reduced to coupled Cauchy singular integral equations of the first and second kinds for the unknown surface contact pressure, electric charge, and magnetic induction. An iterative method is developed to solve the coupled equations numerically and obtain the surface MEE fields. Then, the interior MEE fields are also obtained according to the surface MEE fields. Numerical results indicate that the gradient index and friction coefficient affect both the surface and interior MEE fields significantly.

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