Dynamic Crack-Tip Stress and Displacement Fields Under Thermomechanical Loading in Functionally Graded Materials

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Kwang Ho Lee ◽  
Vijaya Bhaskar Chalivendra ◽  
Arun Shukla
Keyword(s):  
Functionally Graded Materials ◽  
Maximum Shear Stress ◽  
Crack Tip ◽  
Functionally Graded ◽  
Dynamic Crack ◽  
Loading Conditions ◽  
Thermomechanical Loading ◽  
Displacement Fields ◽  
Graded Materials ◽  
Stress And Displacement Fields

Thermomechanical stress and displacement fields for a propagating crack in functionally graded materials (FGMs) are developed using displacement potentials and asymptotic analysis. The shear modulus, mass density, and coefficient of thermal expansion of the FGMs are assumed to vary exponentially along the gradation direction. Temperature and heat flux distribution fields are also derived for an exponential variation of thermal conductivity. The mode mixity due to mixed-mode loading conditions around the crack tip is accommodated in the analysis through the superposition of opening and shear modes. Using the asymptotic stress fields, the contours of isochromatics (contours of constant maximum shear stress) are developed and the results are discussed for various crack-tip thermomechanical loading conditions.

Stress and Displacement Fields at a Transient Crack Tip Propagating in Functionally Graded Materials

2007 ◽  
Vol 345-346 ◽  
pp. 481-484
Author(s):  
Kwang Ho Lee ◽  
Gap Su Ban
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Stress Fields ◽  
Displacement Fields ◽  
Graded Materials ◽  
Transient Motion ◽  
Stress And Displacement Fields ◽  
Displacement Potentials ◽  
Nonhomogeneous Materials

Stress and displacement fields for a transient crack tip propagating along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density under a constant Poisson's ratio are developed. The equations of transient motion in nonhomogeneous materials are developed using displacement potentials and the solution to the displacement fields and the stress fields for a transient crack propagating at nonuniform speed though an asymptotic analysis.

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.

scholarly journals Extended radial point interpolation method for dynamic crack analysis in functionally graded materials

2015 ◽  
Vol 18 (2) ◽  
pp. 59-66
Author(s):  
Nha Thanh Nguyen ◽  
Bang Kim Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Interpolation Method ◽  
Functionally Graded ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Graded Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

Functionally graded materials (FGMs) have been widely used as advanced materials characterized by variation in properties as the dimension varies. Studies on their physical responses under in-serve or external loading conditions are necessary. Especially, crack behavior analysis for these advanced material is one of the most essential in engineering. In this present, an extended meshfree radial point interpolation method (RPIM) is applied for calculating static and dynamic stress intensity factors (SIFs) in functionally graded materials. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. To assess the static and dynamic stress intensity factors, non-homogeneous form of interaction integral with the nonhomogeneous asymptotic near crack tip fields is used. Several benchmark examples in 2D crack problem are performed such as static and dynamic crack parameters calculation. The obtained results are compared with other existing solutions to illustrate the correction of the presented approach.

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