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 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.

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.

Elastodynamic Interaction of Two Offset Interfacial Cracks in Bonded Dissimilar Media With a Functionally Graded Interlayer Under Antiplane Shear Impact

2014 ◽  
Vol 81 (8) ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Inverse Laplace Transform ◽  
Dynamic Mode ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Interfacial Cracks ◽  
Graded Interlayer ◽  
The Impact

The impact response of bonded media with a functionally graded interlayer weakened by a pair of two offset interfacial cracks is investigated under the condition of antiplane deformation. The material nonhomogeneity in the graded interlayer is represented in terms of power-law variations of shear modulus and mass density between the dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the crack problem to solving a system of Cauchy-type singular integral equations in the Laplace domain. The crack-tip behavior in the physical domain is recovered through the inverse Laplace transform to evaluate the dynamic mode III stress intensity factors as a function of time. As a result, the transient interaction of the offset interfacial cracks spaced apart by the graded interlayer is illustrated. The peak values of the dynamic stress intensity factors are also presented versus offset crack distance, elaborating the effects of various material and geometric parameters of the bonded system on the overshoot characteristics of the transient behavior in the near-tip regions, owing to the impact-induced interaction of singular stress fields between the two cracks.

On the Mechanical Modeling of the Interfacial Region in Bonded Half-Planes

1988 ◽  
Vol 55 (2) ◽  
pp. 317-324 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Crack Surface ◽  
Mixed Boundary ◽  
Crack Problem ◽  
External Loading ◽  
Interfacial Region ◽  
Mechanical Modeling ◽  
Intensity Factors ◽  
Single Crack ◽  
Collinear Cracks ◽  
Mixed Boundary Problem

In this paper the crack problem for two bonded dissimilar homogeneous elastic half-planes is considered. It is assumed that the interfacial region can be modeled by a very thin layer of nonhomogeneous material. Even though the formulation given is rather general, in the particular model used the elastic properties of the interfacial layer are assumed to vary continuously between that of the two semi-infinite planes. The layer is assumed to have a series of collinear cracks parallel to the nominal interface. The related mixed boundary problem is formulated for arbitrary crack surface tractions which can be used to accommodate any general external loading condition through a proper superposition. A single crack problem for two different material combinations is solved as examples, and Modes I and II stress-intensity factors, the energy release rate and the direction of a probable crack growth are calculated.

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.

scholarly journals ON AN ANTIPLANE CRACK PROBLEM FOR FUNCTIONALLY GRADED ELASTIC MATERIALS

2010 ◽  
Vol 52 (1) ◽  
pp. 69-86
Author(s):  
DAVID L. CLEMENTS
Keyword(s):  
Integral Equations ◽  
Elastic Moduli ◽  
Crack Problem ◽  
Iterative Solution ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Elastic Materials ◽  
Spatial Coordinates ◽  
Anisotropic Elastic ◽  
Anisotropic Elastic Material

AbstractThis paper examines an antiplane crack problem for a functionally graded anisotropic elastic material in which the elastic moduli vary quadratically with the spatial coordinates. A solution to the crack problem is obtained in terms of a pair of integral equations. An iterative solution to the integral equations is used to examine the effect of the anisotropy and varying elastic moduli on the crack tip stress intensity factors and the crack displacement.

Interfacial cracking in a graded coating/substrate system loaded by a frictional sliding flat punch

2009 ◽  
Vol 466 (2115) ◽  
pp. 853-880 ◽  
Author(s):  
Hyung Jip Choi ◽  
Glaucio H. Paulino
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Contact Pressure ◽  
Contact Stress ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Flat Punch

An analysis of a coupled plane elasticity problem of crack/contact mechanics for a coating/substrate system with functionally graded properties is performed, where the rigid flat punch slides over the surface of the coated system that contains a crack. The graded material is treated as a non-homogeneous interlayer between dissimilar, homogeneous phases of the coated medium and the crack is assumed to exist along the interface between the interlayer and the substrate. Based on the Fourier integral transform method and the transfer matrix approach, formulation of the current coupled mixed boundary value problem lends itself to the derivation of a set of three simultaneous Cauchy-type singular integral equations. In the numerical results, the emphasis is placed on the investigation of interactions between the contact stress field and the crack-tip behaviour for various combinations of material, geometric and loading parameters of the coated system. Specifically, effects of interfacial cracking on the distributions of the contact pressure and the in-plane stress component along the coating surface are examined and the mixed-mode stress intensity factors evaluated from the crack-tip stress field with the square-root singularity are provided as a function of punch location. Further addressed is the quantification of the singular character of contact pressure distributions at the trailing and leading edges of the flat punch in terms of the punch-edge stress intensity factors. Implicit in this particular analysis of the coupled crack/contact problem presented henceforth is that the crack closure behaviour under the compressive contact stress field is not taken into account, ignoring the influence of crack-face contact and friction.

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.

scholarly journals The Crack Problem in Bonded Nonhomogeneous Materials

1991 ◽  
Vol 58 (2) ◽  
pp. 410-418 ◽  
Author(s):  
F. Erdogan ◽  
A. C. Kaya ◽  
P. F. Joseph
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Plane Elasticity ◽  
Primary Objective ◽  
Intensity Factors ◽  
Shear Moduli ◽  
Square Root Singularity

In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r−α, 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.

scholarly journals The Crack Problem for a Nonhomogeneous Plane

1983 ◽  
Vol 50 (3) ◽  
pp. 609-614 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Integral Equation ◽  
Poisson’S Ratio ◽  
Crack Problem ◽  
Surface Displacement ◽  
Plane Elasticity ◽  
Poisson's Ratio ◽  
Cauchy Type ◽  
Crack Tips ◽  
Square Root Singularity ◽  
Crack Surface Displacement

In this paper the plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson’s ratio of the medium is constant and the Young’s modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy-type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson’s ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. On the other hand, the results are highly affected by the parameter β describing the material nonhomogeneity in E (x) = E0exp(βx).

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