Anti-plane analysis of a functionally graded strip with multiple cracks

Fotuhi, Ali Reza; Fariborz, S.J.

doi:10.1016/j.ijsolstr.2005.03.066

Cited by 35 publications

(23 citation statements)

References 10 publications

(12 reference statements)

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“…Researchers have paid attention to some particular problems for FGMs. For example, crack problems for an elastic medium made of FGMs were investigated in [Erdogan and Wu 1997;Jain et al 2004;Fotuhi and Fariborz 2006].…”

Section: Introductionmentioning

confidence: 99%

Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

Chen

2011

J. Mech. Mater. Struct.

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This paper provides a general solution for a multiply-layered cylinder made of functionally graded materials. The Young's modulus is assumed to be an arbitrary function of r , and the Poisson's ratio takes a constant value. The first step is to study the single-layer case (a < r < b). A transfer matrix is defined, relating the values of radial stress and displacement at the initial point (r = a) to those at the end point (r = b). The matrix is evaluated on the basis of two fundamental solutions, which are evaluated numerically. The final solution is obtained by using many transfer matrices for layers, continuation conditions between layers, and boundary conditions at inner and outer boundaries. Several numerical examples are provided.

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Section: Introductionmentioning

confidence: 99%

Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

Chen

2011

J. Mech. Mater. Struct.

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“…In an attempt to address the issues pertaining to the fracture analysis of bonded media with such transitional interfacial properties, a series of solutions to certain crack problems were obtained by Erdogan and his associates [2,3] . To our best knowledge, only a few open literature studied the multiple-crack problems in functionally graded materials [4]- [7] . For instances, the dynamic behavior of a functionally graded piezoelectric strip with periodic cracks vertical to the boundary was studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Anti-plane analysis of a functionally graded strip with multiple cracks was given Ref. [7]. However, the number of cracks is infinite and the form of cracks is symmetric in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…However, the number of cracks is infinite and the form of cracks is symmetric in Refs. [4]- [7]. These fracture problems are solved by the representative crack unit method and the integral transform technique for the periodic cracks [4]- [7] .…”

Section: Introductionmentioning

confidence: 99%

“…[4]- [7]. These fracture problems are solved by the representative crack unit method and the integral transform technique for the periodic cracks [4]- [7] . To our knowledge, understanding of the multi-cracks interaction problem in a functionally graded material plane is very insufficient compared with homogeneous materials.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

Yang

2009

JMMP

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In this paper, the basic solutions of multiple parallel symmetric finite length cracks in a functionally graded material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, respectively, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors at the crack tips depend on the crack lengths, spacing of the cracks and the functionally graded parameter. It is also revealed that the crack shielding effect presents in functionally graded materials.

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Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Mousavi

2015

Z Angew Math Mech

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Dislocation‐based analysis of cracked magnetoelectroelastic solid under remotely uniform anti‐plane mechanical with in‐plane electromagnetic loading is presented. The solution to the generalized dislocation including screw dislocation and electric and magnetic jumps within an incompatible framework are reviewed from the literature. In order to model the system of multiple cracks in the solid, the dislocations are distributed along the crack faces. Then the densities of the dislocations are evaluated by applying the crack‐face boundary conditions. Both permeable and impermeable conditions are discussed. The entire field components including shear stress, electric displacements and magnetic inductions are determined for the cracked material, which is an advantage comparing to the methods which only provide crack tip field components. The field intensity factors are also formulated for both permeable and impermeable conditions. Finally examples including horizontal crack, inclined crack and multiple cracks are studied.

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Anti-plane analysis of a functionally graded strip with multiple cracks

Cited by 35 publications

References 10 publications

Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

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