Asymptotic Stress Fields for Stationary Cracks Along the Gradient in Functionally Graded Materials

2002 ◽  
Vol 69 (3) ◽  
pp. 240-243 ◽  
Author(s):  
V. Parameswaran ◽  
A. Shukla
Keyword(s):  
Shear Stress ◽  
Stress Field ◽  
Functionally Graded Materials ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Stress Fields ◽  
Shear Mode ◽  
Graded Materials ◽  
Opening Mode ◽  
Constant Maximum

Stress field for stationary cracks, aligned along the gradient, in functionally graded materials is obtained through an asymptotic analysis coupled with Westergaard’s stress function approach. The first six terms of the stress field are obtained for both opening mode and shear mode loading. It is observed that the structure of the terms other than r−1/2 and r0 are influenced by the nonhomogeneity. Using this stress field, contours of constant maximum shear stress are generated and the effect of nonhomogeneity on these contours is discussed.

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.

Random Dynamic Analysis of a Crack in a Functionally Graded Materials Layer for Plane Problem Using Shear Stress

2013 ◽  
Vol 756-759 ◽  
pp. 64-67
Author(s):  
Hui Zhan Zhang ◽  
Jin Ling Zhang ◽  
Jia Zhen Zhang ◽  
Zhen Gong Zhou
Keyword(s):  
Shear Stress ◽  
Dynamic Analysis ◽  
Plane Problem ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Fourier Transforms ◽  
Fundamental Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Graded Materials

Dynamic analysis is performed for a crack in a functionally graded materials layer for plane problem using shear stress. The material properties of the functionally graded materials layer vary randomly in the thickness direction, and the cracks are parallel to the materials faces. A pair of dynamic loadings applied on the elastic planes faces are treated as stationary stochastic processes of time. By dividing the functionally graded materials layer into several sub-layers, this problem is reduced to the analysis of laminated composites containing a crack, the material properties of each layer being random variables. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. The stress intensity factor history with its statistics is analytically derived. Numerical calculations are provided to show the effects of related parameters.

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