Mode I crack problem for a functionally graded orthotropic strip

Guo, Licheng; Wu, Linzhi; Zeng, Tao; Ma, Li

doi:10.1016/j.euromechsol.2003.12.006

Cited by 96 publications

(47 citation statements)

References 36 publications

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“…Subsequently, the integral representation formula (see [37]) is used to recover the scattered displacement field as follows: (33) We note here that the stress fundamental solution σ * y k ji was given in Eq. (23). Finally, the SIF is computed from the integral representation formula written in terms of the scattering traction field (see [37]), i.e.,…”

Section: Biem Formulation and Numerical Implementationmentioning

confidence: 99%

“…Following this work, applications by the aforementioned authors [17][18][19][20][21][22] include fracture behaviour of FGM, which is the topic of interest in this paper. Furthermore, the theoretical treatment of mode I crack problems in an orthotropic strip made of FGM appears in Guo et al [23], while the results of experimental work on FGM with a crack along the direction of the elastic gradient are given in Rousseau and Tippur [24].…”

Section: Introductionmentioning

confidence: 99%

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Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

2006

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Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson's ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ(x) = μ 0 exp (2ax 2 ), where μ 0 is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green's function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case.

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Section: Biem Formulation and Numerical Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

2006

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“…Wang et al [20] studied functionally graded strip weakened by a crack perpendicular to the boundary by dividing a strip into some layer with homogeneous properties along the thickness direction. Guo et al [21] considered the mode I crack problem for a functionally graded strip. It has been shown that material constants and the geometry parameters have significant effects on the stress intensity factors.…”

Section: Introductionmentioning

confidence: 99%

The mixed-mode analysis of a functionally graded orthotropic half-plane weakened by multiple curved cracks

2015

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The problem of functionally graded orthotropic half-plane with climb and glide edge dislocations is solved. Dislocations are used as the building blocks of defects to model cracks of modes I and II. Following a dislocation-based approach, the problem is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks. These integral equations enforce the crack-face boundary conditions and are solved numerically for the dislocation density. The numerical results include the stress intensity factors for several different cases of crack configurations and arrangements.

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“…the previous analytical fracture models, the material properties were usually assumed to be very particular functions (mainly exponential functions) (Delale & Erdogan 1983;Chen & Erdogan 1996;Erdogan & Wu 1997;Guo et al 2004Guo et al , 2005. Recently, Choi & Paulino (2008) investigated the thermoelastic contact problem of a FGM coating/substrate system, and the thermomechanical properties were assumed to be exponential functions so that the problem could be solved analytically.…”

Section: Introductionmentioning

confidence: 99%

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

2012

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This study aimed to develop a method to build a 'bridge' between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

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Mode I crack problem for a functionally graded orthotropic strip

Cited by 96 publications

References 36 publications

Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

The mixed-mode analysis of a functionally graded orthotropic half-plane weakened by multiple curved cracks

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

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