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.

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 Fields for Physical Weak-- Discontinuous Crack of FGM Plate with Reissner’s Effect

2013 ◽  
Vol 664 ◽  
pp. 841-845
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Engineering Application ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Graded Materials ◽  
Crack Problems ◽  
Asymptotic Expansion Method

The physical weak-discontinuous problem of an interfacial crack between homogeneous material and functionally graded materials (FGMs) is studied based on Reissner’s plates considering transverse shear deformation effect. The crack-tip higher order asymptotic fields of homogeneous materials and FGMs regions are obtained by the asymptotic expansion method, respectively. Finally, the whole crack tip high order fields are assembled and given. The results provide a theoretical basis for solving interfacial crack problems of FGMs plates and their engineering application.

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.

The Higher Order Asymptotic Fields for Anti-Plane Oblique Crack with Physical Weak-Discontinuity

2011 ◽  
Vol 217-218 ◽  
pp. 1309-1313
Author(s):  
Yao Dai ◽  
Shi Min Li ◽  
Peng Zhang ◽  
Xiao Chong
Keyword(s):  
Asymptotic Series ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Weak Discontinuity ◽  
Homogeneous Material ◽  
Graded Materials ◽  
Crack Tip Fields ◽  
Common Structure ◽  
Oblique Crack

An arbitrarily oriented anti-plane crack with its tip at the physical weak-discontinuous line of the structure which is made up of homogeneous material and functionally graded materials (FGMs) is studied. The analytic solution of the higher order crack tip fields (similar to the Williams’ solution of homogenous material) is obtained by applying the asymptotic series expansion. When non-homogeneous material parameters are degenerated, the solutions become the same as the asymptotic crack tip fields of the homogeneous material. Therefore, the solutions are the basic results of non-homogeneous fracture mechanics, and provide a theoretical basis for solving the fracture problems of one common structure with physical weak-discontinuity.

Higher Order Crack-Tip Fields of Reissner’s Linear Functionally Graded Materials Plates

2012 ◽  
Vol 549 ◽  
pp. 914-917
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Lei Zhang ◽  
Xiao Chong ◽  
Hong Qian Chen
Keyword(s):  
Functionally Graded Materials ◽  
Crack Problem ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Graded Materials ◽  
Fracture Theory ◽  
Bending Fracture ◽  
Asymptotic Expansion Method

Reissner’s plate bending fracture theory with consideration of transverse shear deformation effects is adopted for the crack problem of functionally graded materials (FGMs) plates. Assume that the crack is perpendicular to the material property gradient. By applying the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to Williams’ solutions of homogeneous materials are obtained.

The Higher Order Crack-Tip Field for Reissners Power FGMs Spherical Shell

2013 ◽  
Vol 748 ◽  
pp. 354-357
Author(s):  
Yao Dai ◽  
Zhang Lei ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Spherical Shell ◽  
Governing Equation ◽  
Crack Problem ◽  
Crack Tip ◽  
Expansion Method ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Crack Tip Field ◽  
Asymptotic Expansion Method

The crack problem of power functionally graded spherical shell with Reissners effect is studied. Based on the Reissners theory, the governing equation of power functionally graded spherical shell is given. The eigen-solution of the crack tip field is obtained by using the asymptotic expansion method. The result is similar to Williams solution for homogeneous material.

The Higher Order Asymptotic Crack-Tip Field for Reissner’s Linear Functionally Graded Shell

2012 ◽  
Vol 549 ◽  
pp. 826-829
Author(s):  
Yao Dai ◽  
Lei Zhang ◽  
Jun Feng Liu ◽  
Xiao Chong ◽  
Hong Qian Chen
Keyword(s):  
Experimental Investigation ◽  
Engineering Application ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Crack Tip Field ◽  
Crack Problems ◽  
Asymptotic Expansion Method ◽  
Functionally Graded Shell

The eigen-problem of a crack in functionally graded Reissner’s spherical shell is analyzed. By adopting the asymptotic expansion method, the higher order crack tip asymptotic fields which are similar to the Williams’ solutions of plane crack problems in homogenous materials are obtained. The grade direction is assumed to be parallel to the crack. The results can be widely adopted in numerical analysis, experimental investigation and the engineering application of FGM shell structure.

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