Transient dynamic analysis of a cracked functionally graded material by a BIEM

Zhang, Ch.; Savaidis, A.; Savaidis, Georgios; Zhu, Han

doi:10.1016/s0927-0256(02)00395-6

Cited by 73 publications

(23 citation statements)

References 13 publications

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“…That a pure tensile load on the crack resulting from the P-wave should produce a rather small (but non-zero) K I I factor is at first surprising, but it is a manifestation of coupling effects inherent in the inhomogeneous structure of the surrounding material. In fact, recent investigations by Zhang et al [18][19][20][21][22] have established precisely this type of behavior for general FGM cases. In addition, the reverse effect is present too, in that a pure shear loading from SV-waves on the face of buried crack produces a K I factor as well.…”

Section: Parametric Studymentioning

confidence: 77%

“…Up to now, relatively little research seems to have been carried out for devising effective methods, both analytical and numerical, in order to solve static and dynamic problems involving inhomogeneous media [1][2][3][4][5][6][7][8]. The same holds true regarding work that focuses on studying formation of defects and development of cracks in these materials [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. More specifically, in [13][14][15][16] we see the development of three basic classes of numerical methods for dealing with dynamic problems involving various FGM (such as media with material gradients described by an exponential law, inhomogeneous layers bonded to upper and lower homogeneous strata, etc.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the combined effect of anisotropy and inhomogeneity is also addressed through these classes of numerical methods. 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%

See 2 more Smart Citations

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: Parametric Studymentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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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“…[3]. The boundary integral equation method was used to investigate the dynamic response of the crack problem in an NM [4] . The investigation in Ref.…”

Section: Introductionmentioning

confidence: 99%

A moving crack in a nonhomogeneous material strip

Wang

Han

2006

Acta Mech. Solida Sin.

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This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.

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“…Wu et al [2002] proposed an extended dynamic J integral for functional graded materials. Zhang et al [2003] used a boundary integral equation method to investigate the dynamic response of FGM crack problems. investigated the dynamic fracture of a crack in a functionally graded piezoelectric interface.…”

Section: Introductionmentioning

confidence: 99%

A mode III moving crack between a functionally graded coating and a homogeneous substrate

Wang

Han

2006

JOMMS

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This paper considers an anti-plane moving crack between a functionally graded coating and a homogeneous substrate. The shear modulus and the mass density of the FGM coating are considered for a class of functional forms for which the equilibrium equation has an analytical solution. The problem is solved by means of singular integral equation technique. Results are plotted to show the effect of material nonhomogeneity and crack moving velocity on the crack tip field. The angular variation of the near-tip stress field is of particular interest, and the crack bifurcation behaviour is also discussed. It is shown that choice of an appropriate fracture criterion is essential for studying the stability of a moving crack in FGMs. Different fracture criteria could give opposite predictions for crack stability. It seems that the maximum cleavage stress near the crack tips is a reasonable failure criterion for a moving crack in FGMs.

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Transient dynamic analysis of a cracked functionally graded material by a BIEM

Cited by 73 publications

References 13 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

A moving crack in a nonhomogeneous material strip

A mode III moving crack between a functionally graded coating and a homogeneous substrate

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