scholarly journals Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
R. Patra ◽  
S. P. Barik ◽  
M. Kundu ◽  
P. K. Chaudhuri
Keyword(s):  
Integral Transform ◽  
Crack Opening ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Cauchy Type ◽  
Elastic Parameters ◽  
Concentrated Force ◽  
Functionally Graded Layer ◽  
Integral Transform Technique

This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressure p0 along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude P/2 with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parameters λ and μ are assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically.

Mode III crack problem in a functionally graded coating-homogeneous substrate structure

2008 ◽  
Vol 222 (3) ◽  
pp. 329-337 ◽  
Author(s):  
L Ma ◽  
L-Z Wu
Keyword(s):  
Integral Transform ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Internal Crack ◽  
Mode Iii ◽  
Functionally Graded Coating ◽  
Substrate Structure ◽  
Graded Coating ◽  
Gradient Parameter

The current paper describes an anti-plane problem for an internal crack and an edge crack perpendicular to the interface of a functionally graded coating-homogeneous substrate structure for the material whose properties are one-dimensionally dependent. Integral transform and dislocation density functions are employed to reduce the problem to a solution of a system of singular integral equations. Numerical results show the effect of the material gradient parameter and crack configuration on the stress intensity factors of the functionally graded coating-homogeneous substrate structure.

Delamination of Compressively Stressed Orthotropic Functionally Graded Material Coatings Under Thermal Loading

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Bora Yıldırım ◽  
Suphi Yılmaz ◽  
Suat Kadıoğlu
Keyword(s):  
Functionally Graded Material ◽  
Bond Coat ◽  
Thermal Loading ◽  
Layer Structure ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Correlation Technique ◽  
Fracture Parameters ◽  
Graded Material

The objective of this study is to investigate a particular type of crack problem in a layered structure consisting of a substrate, a bond coat, and an orthotropic functionally graded material coating. There is an internal crack in the orthotropic coating layer. It is parallel to the coating bond-coat interface and perpendicular to the material gradation of the coating. The position of the crack inside the coating is kept as a variable. Hence, the case of interface crack is also addressed. The top and bottom surfaces of the three layer structure are subjected to different temperatures and a two-dimensional steady-state temperature distribution develops. The case of compressively stressed coating is considered. Under this condition, buckling can occur, the crack can propagate, and the coating is prone to delamination. To predict the onset of delamination, one needs to know the fracture mechanics parameters, namely, Mode I and Mode II stress intensity factors and energy release rates. Hence, temperature distributions and fracture parameters are calculated by using finite element method and displacement correlation technique. Results of this study present the effects of boundary conditions, geometric parameters (crack length and crack position), and the type of gradation on fracture parameters.

Transient non-Fourier thermoelastic fracture analysis of a cracked orthotropic functionally graded strip

2021 ◽  
pp. 108128652110246
Author(s):  
Wenzhi Yang ◽  
Amin Pourasghar ◽  
Zengtao Chen
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Thermal Stresses ◽  
Heat Propagation ◽  
Functionally Graded ◽  
Internal Crack ◽  
Phase Lag ◽  
Dual Phase ◽  
Cauchy Type ◽  
Functionally Graded Strip

In this work, the fracture problem of an orthotropic functionally graded strip containing an internal crack parallel to its surfaces subjected to thermal shocks is examined. To eliminate the paradox of infinite heat propagation speed and take the microstructural interactions of thermal energy carriers into account, the non-Fourier, dual-phase-lag theory is employed to investigate the transient heat conduction and the associated thermal stresses response. By utilizing Laplace transform and Fourier transform, the thermoelastic problems are finally reduced to the Cauchy-type singular integral equations, which are solved by the Lobatto–Chebyshev technique numerically. The temperature field and thermal stress intensity factors are evaluated by the numerical inversion of Laplace transform to illustrate the effects of two thermal lags and nonhomogeneous parameters. The results show the fracture risks accompanied by the dual-phase-lag heat conduction can be higher than the classical analysis and it would be more conservative to consider non-Fourier effects in designing the orthotropic functionally graded materials.

scholarly journals Analytical Solution of a Crack Problem in a Radially Graded FGM

2009 ◽  
Vol 631-632 ◽  
pp. 115-120
Author(s):  
Suat Çetin ◽  
Suat Kadıoğlu
Keyword(s):  
Stress Intensity ◽  
Plane Strain ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Approximate Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Homogeneous Layer ◽  
Intensity Factors ◽  
Functionally Graded Layer

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a functionally graded layer bonded to a homogeneous substrate. Functionally graded coating contains an edge crack perpendicular to the interface. It is assumed that plane strain conditions prevail and the crack is subjected to mode I loading. By introducing an elastic foundation underneath the homogeneous layer, the plane strain problem under consideration is used as an approximate model for an FGM coating with radial grading on a thin walled cylinder. The plane elasticity problem is reduced to the solution of a singular integral equation. Constant strain loading is considered. Stress intensity factors are obtained as a function of crack length, strip thicknesses, foundation modulus, and inhomogeneity parameter.

An Analysis of Cracking in a Layered Medium With a Functionally Graded Nonhomogeneous Interface

1996 ◽  
Vol 63 (2) ◽  
pp. 479-486 ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Layered Medium ◽  
Crack Problem ◽  
Crack Size ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Interfacial Region ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Transitional Layer ◽  
Homogeneous Surface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method of formulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.

scholarly journals Moving Griffith crack in an orthotropic strip with punches at boundary faces

2005 ◽  
Vol 2005 (19) ◽  
pp. 3157-3167
Author(s):  
S. Mukherjee ◽  
S. Das
Keyword(s):  
Constant Pressure ◽  
Integral Transform ◽  
Finite Thickness ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Griffith Crack ◽  
Orthotropic Strip ◽  
Finite Hilbert Transform ◽  
Integral Transform Technique ◽  
State Propagation

Integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of a Griffith crack centrally situated along the midplane of orthotropic strip of finite thickness2hand subjected to point loading with centrally situated moving punches under constant pressure along the boundaries of the layer. The problem is reduced to the solution of a pair of simultaneous singular integral equations with Cauchy-type singularities which have finally been solved through the finite Hilbert transform technique. For largeh, analytical expression for the stress intensity factor at the crack tip is obtained. Graphical plots of the numerical results are also presented.

Crack Problem for a Functionally Graded Orthotropic Coating-Substrate Structure

2007 ◽  
Vol 353-358 ◽  
pp. 263-265 ◽  
Author(s):  
Li Cheng Guo ◽  
Lin Zhi Wu ◽  
Hong Jun Yu
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Orthotropic Material ◽  
Integral Transform ◽  
Crack Problem ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Transform Method ◽  
Substrate Structure ◽  
Integral Transform Method

The crack problem for a functionally graded orthotropic coating-substrate structure under an in-plane load is studied. The orthotropic coating is assumed to contain a crack perpendicular to the interface. Integral transform method is used to obtain singular integral equation. Stress intensity factors (SIFs) are evaluated. The influences of orthotropic material constants and the geometry parameters on SIFs are analyzed.

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.

The Surface Crack Problem for a Plate With Functionally Graded Properties

1997 ◽  
Vol 64 (3) ◽  
pp. 449-456 ◽  
Author(s):  
F. Erdogan ◽  
B. H. Wu
Keyword(s):  
Crack Opening ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Opening Displacement ◽  
Nonhomogeneous Layer ◽  
Edge Cracks ◽  
Graded Properties ◽  
Plane Elasticity Problem

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.

Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part II: Crack Parallel to the Material Gradation

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Youn-Sha Chan ◽  
Glaucio H. Paulino ◽  
Albert C. Fannjiang
Keyword(s):  
Elasticity Theory ◽  
Strain Gradient ◽  
Crack Opening ◽  
Crack Problem ◽  
Gradient Elasticity ◽  
Functionally Graded ◽  
Numerical Results ◽  
Surface Strain ◽  
Mode Iii ◽  
Gradient Elasticity Theory

A Mode-III crack problem in a functionally graded material modeled by anisotropic strain-gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ℓ and ℓ′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived assuming that the shear modulus G is a function of x, i.e., G=G(x)=G0eβx, where G0 and β are material constants. A hypersingular integrodifferential equation is derived and discretized by means of the collocation method and a Chebyshev polynomial expansion. Numerical results are given in terms of the crack opening displacements, strains, and stresses with various combinations of the parameters ℓ, ℓ′, and β. Formulas for the stress intensity factors, KIII, are derived and numerical results are provided.

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