Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes (original) (raw)
Related papers
Engineering Fracture Mechanics, 1999
The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a non-homogeneous interface was formulated for singular integral equations with Cauchy kernels and integrated using the Lobatto-Chebyshev collocation technique. Mixed-mode Stress Intensity Factors and Strain Energy Release Rates were calculated. The Stress Intensity Factors were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various non-homogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.
Multiple moving cracks in a functionally graded strip
Applied Mathematical Modelling, 2012
This paper considers several finite moving cracks in a functionally graded material subjected to anti-plane deformation. The distributed dislocation technique is used to carry out stress analysis in a functionally graded strip containing moving cracks under anti-plane loading. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. By utilizing the Fourier sine transformation technique the stress fields are obtained for a functionally graded strip containing a screw dislocation. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by several moving cracks. Numerical examples are provided to show the effects of material properties, the crack length and the speed of the crack propagating upon the stress intensity factor.
Antiplane analysis of a functionally graded strip with multiple cracks
International Journal of Solids and Structures - INT J SOLIDS STRUCT, 2006
The stress fields are obtained for a functionally graded strip containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The stress components exhibit Cauchy as well as logarithmic singularities at the dislocation location. The dislocation solution is utilized to formulate integral equations for the strip weakened by multiple smooth cracks under anti-plane deformation. Several examples are solved and stress intensity factors are obtained.
Analysis of Multiple Cracks in an Infinite Functionally Graded Plate
1999
A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate (thickness). The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity. This publication is available from the NASA Center for AeroSpace Information, (301) 621-0390.
Mechanics of Materials, 2001
This paper presents the dynamic stress intensity factor of a cylindrical interface crack located between two coaxial dissimilar homogeneous cylinders that are bonded with a functionally graded interlayer and subjected to a torsional impact loading. The shear modulus and mass density of the functionally graded interlayer are taken to vary continuously between those of the two coaxial cylinders. The mixed boundary value problem involved is reduced to a singular integral equation with a Cauchy-type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The expressions for the dynamic stress intensity factor at the crack tips are derived in detail and the results are displayed after solving the singular integral equation numerically and performing numerical Laplace inversions. It is found that the relative magnitudes of the adjoining material properties, the graded interlayer thickness, and the crack length, all have signi®cant eects on the dynamic stress intensity factor. Ó
Elastodynamic analysis of a functionally graded half-plane with multiple sub-surface cracks
Acta Mechanica Solida Sinica, 2012
The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors are obtained.
Mixed-mode stress intensity factors for a crack in an anisotropic bi-material strip
International Journal of Solids and Structures, 2004
This paper provides a method for obtaining the mixed-mode stress intensity factors for a bi-material interface crack in the infinite strip configuration and in the case where both phases are fully anisotropic. First, the dislocation solution in a bi-material anisotropic infinite strip is investigated (the boundary of the strip is parallel to the bi-material interface). A surface distributed dislocation approach is employed to ensure the traction-free conditions at the strip bounding surfaces. Subsequently, the derived dislocation solution is applied to calculate the mixed-mode stress intensity factors of a crack located at, or parallel to, the interface in the bi-material anisotropic infinite strip. The crack itself is modelled as a distribution of the derived dislocation solutions for the strip. Results are presented and the effects of material mismatch, the length of the crack and the material interface on the stress intensity factors are investigated.
An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space
International Journal of Solids and Structures, 2010
In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating's material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.
Fracture analysis of a functionally graded interfacial zone under plane deformation
International Journal of Solids and Structures, 2004
A new multi-layered model for fracture analysis of functionally graded materials (FGMs) with the arbitrarily varying elastic modulus under plane deformation has been developed. The FGM is divided into several sub-layers and in each sub-layer the shear modulus is assumed to be a linear function while the PoissonÕs ratio is assumed to be a constant. With this new model, the problem of a crack in a functionally graded interfacial zone sandwiched between two homogeneous half-planes under normal and shear loading is investigated. Employment of the transfer matrix method and Fourier integral transform technique reduce the problem to a system of Cauchy singular integral equations. Stress intensity factors of the crack are calculated by solving the equations numerically. Comparison of the present new model with other existing models shows some of its advantages.
Periodic crack problem for a functionally graded half-plane an analytic solution
International Journal of Solids and Structures, 2011
The plane elasticity problem of a functionally graded semi-infinite plane, containing periodic imbedded or edge cracks perpendicular to the free surface is considered. Cracks are subjected to mode one mechanical or thermal loadings, which are represented by crack surface tractions. Young's modulus, conduction coefficient, coefficient of thermal expansion are taken as exponentially varying functions of the depth coordinate where as Poisson ratio and thermal diffusivity are assumed to be constant. Fourier integrals and Fourier series are used in the formulation which lead to a Cauchy type singular integral equation. The unknown function which is the derivative of crack surface displacement is numerically solved and used in the calculation of stress intensity factors. Limited finite element calculations are done for verification of the results which demonstrate the strong dependence of stress intensity factors on geometric and material parameters.