Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate

El-Borgi, Sami; Hatira, Fafa Ben

doi:10.1023/b:frac.0000007373.29142.57

Cited by 49 publications

(28 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The buckling problem was solved analytically and the post-buckling problem was solved using a geometrically nonlinear finite element procedure. The same geometry was considered by the main author (El-Borgi et al 2003) who performed a first-order analysis to compute the stress intensity factors under the effect of thermo-mechanical loading. Shen (2003), studied the post-buckling behavior of a functionally graded cylindrical thin shell of finite length exposed to external pressure and in thermal environment.…”

Section: Introductionmentioning

confidence: 99%

Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate

2006

Self Cite

View full text Add to dashboard Cite

In an attempt to simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a functionally graded coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an isotropic stress-strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to give the critical buckling strain and the corresponding crack opening displacement shapes. The main objective of the paper is to study the influence of

show abstract

Section: Introductionmentioning

confidence: 99%

Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate

2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Poisson's ratio v is assumed to be a constant because the effect of its variation on the crack tip stress intensity factors was shown to be negligible [14,15]. The remaining thermomechanical properties depend on the y-coordinate only and are modeled by an exponential function [3,[11][12][13] k j = k 0 e δ j y , μ j = μ 0 e β j y , α j = α 0 e γ j y , j = 1, 2,…”

Section: Problem Formulationmentioning

confidence: 99%

“…The limiting values Bi → 0 represent perfect insulation along the crack surfaces. This thermal response problem with a fully insulated interface crack between a graded isotropic coating of finite thickness and a semi-infinite homogeneous isotropic substrate was investigated by EI-Borgi et al [11]. Figure 3 shows the temperature distribution along the crack plane y = 0 + and y = 0 − for δ 2 /δ 1 = −1.0.…”

Section: Crack Surface Temperaturementioning

confidence: 99%

“…The properties of practical FGMs, nevertheless, may vary in an arbitrary manner. Chen et al [10] investigated the mode I surface crack problem for an orthotropic-graded strip under transient loading.Considering the partial insulation along the crack surfaces, Borgi and Erdogan [11,12] considered the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading is considered by Borgi et al [13].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

Ding

Xing

2010

Arch Appl Mech

View full text Add to dashboard Cite

The fracture behavior of a functionally graded layered structure (FGLS) with an interface crack under thermal loading is investigated. Considering new boundary conditions, it is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The problem is formulated in terms of a system of singular integral equations. Numerical results are presented to show the influence of the material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors (TSIFs).Keywords Functionally graded layered structure (FGLS) · Thermal resistance · Thermal stress intensity factors (TSIFs) IntroductionOne of the purposes for developing functionally graded materials (FGMs) is to replace the conventional homogeneous materials to reduce the magnitude of residual and thermal stresses and thus to increase the bonding strength where the materials are subjected to extremely high thermal loading. In designing components involving FGMs, an important aspect of the problem is the question of mechanical failure, specifically the fracture failure [1]. Fatigue and fracture characterization of materials and related analysis require the solution of certain standard crack problems. So far, many crack problems in FGMs have been solved to obtain the crack tip thermal stress intensity factors (TSIFs) by assuming the elastic properties varying due to functional forms [2][3][4][5][6][7].Assuming the perfect thermal insulation of the crack surfaces, Noda and Jin [8] studied the crack problem for an infinite functionally graded material (FGM) subjected to a steady-state heat flux over the crack surfaces by assuming continuously varying thermal properties. Choi et al. [9] studied the crack problems in FGM-like nonhomogeneous materials under thermal loading. The properties of practical FGMs, nevertheless, may vary in an arbitrary manner. Chen et al. [10] investigated the mode I surface crack problem for an orthotropic-graded strip under transient loading.Considering the partial insulation along the crack surfaces, Borgi and Erdogan [11,12] considered the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading is considered by Borgi et al [13]. In their studies, the continuity conditions of the temperature field and heat flux along the crack axis, outside the crack and along the interface are considered.In this paper, consider new boundary conditions, assuming that the interface crack is partially insulated and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction

show abstract

“…Chen and Erdogan [1996] studied the problem of a graded coating on homogeneous substrate with an interface crack subjected to mechanically induced crack surface tractions. El-Borgi et al [2003] extended this problem by considering both thermal and mechanical loads and accounting for crack-closure effects. In [El-Borgi et al 2004b] we considered the problem of a graded coating bonded to a substrate subjected to a Hertzian contact pressure and with an internal crack embedded in the coating, and in [El-Borgi et al 2000] the mixed-mode crack parallel to the boundary of an infinite strip, with the elastic modulus varying exponentially in an arbitrary direction.…”

Section: Introductionmentioning

confidence: 99%

A surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions

El-Borgi

Abdelmoula

Dağ

et al. 2007

JOMMS

View full text Add to dashboard Cite

The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions is considered. The coating is graded along the thickness direction and modeled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The crack surfaces are subjected to arbitrary loadings which give rise to mixed fracture modes which can be uncoupled due to the fact that the crack axis is parallel to the material gradient. Therefore, the opening and sliding mode problems may be formulated separately. For each problem, the solution of the composite medium may be determined by obtaining the solution of the homogeneous substrate and that of the graded layer. The latter solution may be expressed as the sum of two solutions, namely an infinite graded medium with a crack and a graded strip without a crack. The resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically using Jacobi polynomials. The main objective of the paper is to study the effect of the layer thickness and nonhomogeneity parameter on the crack tip mixed-mode stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

show abstract

Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate

Cited by 49 publications

References 15 publications

Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate

Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

A surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions

Contact Info

Product

Resources

About