Crack-Tip Singular Fields in Functionally Graded Materials

2014 ◽  
pp. 798-805
Author(s):  
Zhihe Jin
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Graded Materials

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

The Crack-Tip Fields of Reissner’s Plates of Radial Functionally Graded Materials

2011 ◽  
Vol 217-218 ◽  
pp. 1319-1323
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Peng Zhang
Keyword(s):  
Functionally Graded Materials ◽  
Plate Theory ◽  
Crack Tip ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Governing Equations ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Crack Tip Fields

For homogeneous material plates and non-homogeneous material plates, the crack-tip field plays an important role in the research of fracture mechanics. However, the governing equations become the system of the sixth order partial differential ones with the variable coefficients when the material gradient is perpendicular to the thickness direction of plates. In this paper, they are derived first. Then, the crack-tip fields of the plates of radial functionally graded materials (FGMs) are studied and the higher order crack-tip fields are obtained based on the Reissner’s plate theory. The results show the effect of the non-homogeneity on the crack-tip fields explicitly and become the same as solutions of the homogeneous material plates as the non-homogeneous parameter approaches zero.

The Higher Order Crack-Tip Field for Reissner's Bidirectional FGMs Spherical Shell

2013 ◽  
Vol 748 ◽  
pp. 341-344
Author(s):  
Yao Dai ◽  
Zhang Lei ◽  
Xiao Chong
Keyword(s):  
Spherical Shell ◽  
Functionally Graded Materials ◽  
Superposition Principle ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Crack Problems

The crack tip fields for a cracked functionally graded materials spherical shell considering Reissners effect are obtained. Similar to Williams solution for homogeneous material, the eigen-solution of the crack tip field for bi-directional FGMs spherical shell is obtained by stress superposition principle. This result can be used to deal with the crack problems for FGMs shell.

A completely meshless analysis of cracks in isotropic functionally graded materials

2009 ◽  
Vol 224 (3) ◽  
pp. 581-590 ◽  
Author(s):  
H Koohkan ◽  
G H Baradaran ◽  
R Vaghefi
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Least Squares Approximation ◽  
Equilibrium Equations ◽  
Graded Materials ◽  
Linear Elastic ◽  
Support Domain ◽  
A New Technique ◽  
Good Agreement

In the present study, a completely meshless analysis of two-dimensional cracks in non-homogeneous, isotropic, and linear elastic functionally graded materials (FGMs) is developed. The meshless local Petrov—Galerkin method is applied and the equilibrium equations are considered to drive the local symmetric weak formulations. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. Also, a new technique for defining local sub-domain and support domain is proposed. Using the technique, more nodes are considered in the direction of material variation and extra nodes are located near the crack tip of the FGM body to obtain an accurate meshless model. The based functions are also enriched in order to capture singularities around the crack tip. Several numerical examples containing both mode-I and mixed-mode conditions are presented and the results are compared with the available solutions in the literature which shows a good agreement.

The Crack-Tip Higher Order Fields of Linear FGM Plates with Reissner’s Effect

2012 ◽  
Vol 476-478 ◽  
pp. 1421-1424
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Lei Zhang ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Functionally Graded Materials ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Plate Bending ◽  
Graded Materials ◽  
Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials(FGMs) plates for a crack parallel to material gradient. By means of the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to the famous Williams’ solutions to homogeneous materials are obtained.

A Simplified Method for Calculating the Crack-Tip Field of Functionally Graded Materials Using the Domain Integral

1999 ◽  
Vol 66 (1) ◽  
pp. 101-108 ◽  
Author(s):  
P. Gu ◽  
M. Dao ◽  
R. J. Asaro
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Crack Tip ◽  
Functionally Graded ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Fine Mesh ◽  
Domain Integral ◽  
Standard Domain

A finite element based method is proposed for calculating stress intensity factors of functionally graded materials (FGMs). We show that the standard domain integral is sufficiently accurate when applied to FGMs; the nonhomogeneous term in the domain integral for nonhomogeneous materials is very small compared to the first term (the standard domain integral). In order to obtain it, the domain integral is evaluated around the crack tip using sufficiently fine mesh. We have estimated the error in neglecting the second term in terms of the radius of the domain for the domain integration, the material properties and their gradients. The advantage of the proposed method is that, besides its accuracy, it does not require the input of material gradients, derivatives of material properties; and existing finite element codes can be used for FGMs without much additional work. The numerical examples show that it is accurate and efficient. Also, a discussion on the fracture of the FGM interlayer structure is given.

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