Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition

2010 ◽  
Vol 37 (1) ◽  
pp. 50-53 ◽  
Author(s):  
Y.Z. Chen ◽  
X.Y. Lin ◽  
Z.X. Wang
Keyword(s):  
Boundary Condition ◽  
Functionally Graded Materials ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Crack Problem ◽  
Functionally Graded ◽  
Graded Materials ◽  
Antiplane Elasticity

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.

Thermoelastic Fracture Mechanics for Nonhomogeneous Material Subjected to Unsteady Thermal Load

1999 ◽  
Vol 67 (1) ◽  
pp. 87-95 ◽  
Author(s):  
B. L. Wang ◽  
J. C. Han ◽  
S. Y. Du
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Crack Problem ◽  
Laminated Composite ◽  
Functionally Graded ◽  
Comprehensive Treatment ◽  
Numerical Illustration ◽  
Graded Materials ◽  
Nonhomogeneous Material ◽  
Crack Problems

This article provides a comprehensive treatment of cracks in nonhomogeneous structural materials such as functionally graded materials. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material nonhomogeneity, we present an algorithm for solving the system based on the Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problems in the functionally graded materials with arbitrarily varying material properties. The algorithm can be applied to steady state or transient thermoelastic fracture problem with the inertial terms taken into account. As a numerical illustration, transient thermal stress intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of nonhomogeneous material with properties varying in the thickness direction. [S0021-8936(00)01601-9]

Implementation of Crack Problem of Functionally Graded Materials with ABAQUSTM

2011 ◽  
Vol 284-286 ◽  
pp. 297-300 ◽  
Author(s):  
Hong Liang Zhou
Keyword(s):  
Functionally Graded Materials ◽  
Interface Crack ◽  
Crack Problem ◽  
Functionally Graded ◽  
Closure Technique ◽  
Graded Materials ◽  
Finite Element Software ◽  
User Subroutine ◽  
Implementation Method ◽  
Crack Element

An implementation method of the virtual crack closure technique (VCCT) for fracture problems of non-homogeneous materials such as functionally graded materials (FGMs) with commercial finite element software ABAQUSTMis introduced in this paper. In order to avoid the complex post proceeding to extract fracture parameters, the interface crack element based on the VCCT is developed. The heterogeneity of FGMs is characterized though user subroutine UMAT and the interface crack element is implemented by user subroutine UEL. Several examples are analyzed to demonstrate the accuracy of the present method.

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.

Higher Order Crack-Tip Fields of Reissner’s Linear Functionally Graded Materials Plates

2012 ◽  
Vol 549 ◽  
pp. 914-917
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Lei Zhang ◽  
Xiao Chong ◽  
Hong Qian Chen
Keyword(s):  
Functionally Graded Materials ◽  
Crack Problem ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Graded Materials ◽  
Fracture Theory ◽  
Bending Fracture ◽  
Asymptotic Expansion Method

Reissner’s plate bending fracture theory with consideration of transverse shear deformation effects is adopted for the crack problem of functionally graded materials (FGMs) plates. Assume that the crack is perpendicular to the material property gradient. By applying the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to Williams’ solutions of homogeneous materials are obtained.

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).

On the Receding Contact Between a Homogeneous Elastic Layer and a Half-plane Substrate Coated with Functionally Graded Materials

2019 ◽  
Vol 17 (01) ◽  
pp. 1844008 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi
Keyword(s):  
Integral Equations ◽  
Functionally Graded Materials ◽  
Half Plane ◽  
Elastic Layer ◽  
Mixed Boundary ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Engineering Structures ◽  
Graded Materials ◽  
Receding Contact

Mechanical contact threatens the integrity of engineering structures. In particular, receding contact is one of the primary causes that are responsible for the delamination of multilayered elastic structures. This paper aims to analyze the receding contact between a homogeneous elastic layer and a half-plane reinforced by a functionally graded coating. The multilayered structure is indented by a rigid stamp of convex profile. Governing equations and mixed boundary conditions of the double contact problem are converted into a pair of singular integral equations by Fourier integral transforms. The dual integral equations are numerically solved by Gauss–Chebyshev quadrature for the contact pressure and contact length at both interfaces of contact. Taking a circular punch as a case study, the developed algorithm is first validated against classical models available in the literature. Extensive parametric studies are subsequently performed to illustrate the effects of indentation load, geometry and material properties of individual components. Numerical results suggest the possibility of optimizing multilayered structures by the introduction of functionally graded materials (FGMs) as coatings or transitional layers.

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