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 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.

Finite Element Investigation of Quasi-Static Crack Growth in Functionally Graded Materials Using a Novel Cohesive Zone Fracture Model

2002 ◽  
Vol 69 (3) ◽  
pp. 370-379 ◽  
Author(s):  
Z.-H. Jin ◽  
G. H. Paulino ◽  
R. H. Dodds,
Keyword(s):  
Finite Element ◽  
Crack Growth ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Growth Response ◽  
Functionally Graded ◽  
Fracture Model ◽  
Cohesive Fracture ◽  
Graded Materials ◽  
Cohesive Fracture Model

This work studies mode I crack growth in ceramic/metal functionally graded materials (FGMs) using three-dimensional interface-cohesive elements based upon a new phenomenological cohesive fracture model. The local separation energies and peak tractions for the metal and ceramic constituents govern the cohesive fracture process. The model formulation introduces two cohesive gradation parameters to control the transition of fracture behavior between the constituents. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with standard isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive fracture model and computational scheme to analyze crack growth in compact tension, C(T), and single-edge notch bend, SE(B), specimens with material properties characteristic of a TiB/Ti FGM. Young’s modulus and Poisson’s ratio of the background solid material are determined using a self-consistent method (the background material remains linear elastic). The numerical studies demonstrate that the load to cause crack extension in the FGM compares to that for the metal and that crack growth response varies strongly with values of the cohesive gradation parameter for the metal. These results suggest the potential to calibrate the value of this parameter by matching the predicted and measured crack growth response in standard fracture mechanics specimens.

Model Development of the Application of Finite Element – Eigenvalue Method to the Determination of Transient Temperature Field in Functionally Graded Materials

2007 ◽  
Vol 18-19 ◽  
pp. 253-261
Author(s):  
John A. Akpobi ◽  
C.O. Edobor
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Functionally Graded Materials ◽  
Model Development ◽  
Element Model ◽  
Steady State Solution ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Graded Materials ◽  
Eigenvalue Method

In this paper, a finite elment-eigenvalue method is formulated to solve the finite element models of time dependent temperature field problems in non-homogeneous materials such as functionally graded materials (FGMs). The method formulates an eigenvalue problem from the original finite element model and proceeds to calculate the associated eigenvectors from which the solution can be obtained. The results obtained highly accurate and are exponential functions of time which when compared with the exact solution tended fast to the steady state solution.

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.

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