Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

scholarly journals Nanomechanics of a screw dislocation in a functionally graded material using the theory of gradient elasticity

2013 ◽  
Vol 21 (5-6) ◽  
pp. 187-194 ◽  
Author(s):  
Kamyar M. Davoudi ◽  
Hossein M. Davoudi ◽  
Elias C. Aifantis
Keyword(s):  
Screw Dislocation ◽  
Functionally Graded Material ◽  
Dislocation Line ◽  
Gradient Elasticity ◽  
Functionally Graded ◽  
Short Article ◽  
Graded Material ◽  
The Fourier Transform ◽  
Stress Function Method ◽  
Analytical Expressions

AbstractThe modest aim of this short article is to provide some new results for a screw dislocation in a functionally graded material within the theory of gradient elasticity. These results, based on a displacement formulation and the Fourier transform technique, complete earlier findings obtained with the stress function method and extends them to the case of the second strain gradient elasticity. Rigorous and easy-to-use analytical expressions for the displacements, strains, and stresses are obtained, which are free from singularities at the dislocation line.

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

scholarly journals Thermal Analysis of a Functionally Graded Coating/Substrate System Using the Approximated Transfer Approach

Coatings ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 51 ◽  
Author(s):  
Hui Wang ◽  
Qinghua Qin
Keyword(s):  
Boundary Conditions ◽  
Heterogeneous Material ◽  
Fundamental Solutions ◽  
Kernel Functions ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Hybrid Finite Element Method ◽  
Polygonal Element ◽  
Graded Coating ◽  
Graded Material

As a heterogeneous material, functionally graded material (FGM) behaves as continuously changed material properties in certain directions from one composition to another, and hence it has received much more attention for biomedical applications and thermal protections to achieve innovative functions that conventional homogeneous material cannot accomplish. However, due to the particularly small thickness ratio of coating to substrate in practice, the conventional mesh discretization of the coating region is inefficient. To simplify the meshing procedure and increase the efficiency of analysis, the approximated transfer algorithm based on the concept of finite difference is developed for transferring boundary conditions applied on the coating surface to the interface of coating and substrate. As a result, only the substrate with transferred convection boundary conditions needs to be solved numerically, i.e., by the fundamental-solution based hybrid finite element method (HFS-FEM) with high accuracy and feasible polygonal element construction, in which only integrals along the element boundary are evaluated because of the application of fundamental solutions of the problem as kernel functions of interior approximated fields. Finally, numerical experiments including the single-layered, multi-layered and functionally graded coatings are carried out to verify the accuracy and applicability of the present method.

The effect of a hole on certain stress distributions in aeolotropic and isotropic plates

1944 ◽  
Vol 40 (2) ◽  
pp. 172-188 ◽  
Author(s):  
S. Holgate
Keyword(s):  
Circular Hole ◽  
Infinite Plate ◽  
Complex Stress ◽  
Stress Distributions ◽  
Finite Form ◽  
Isotropic Materials ◽  
Isotropic Plates ◽  
General Manner ◽  
Alternative Method ◽  
Stress Functions

1. The problems of stress distributions in an infinite plate containing a circular hole were solved in a general manner by Bickley(1) for isotropic materials. An alternative method, using complex stress functions, was later given by Green(5) and extended so as to apply to aeolotropic materials. In the present paper Green's method is employed to determine the stress distributions that arise when the stresses are produced by isolated forces acting at points on, or near to, the edge of the circular hole, and though some of the solutions are cumbersome they are all obtained in finite form.

Fabrication and Properties of W-Cu Functionally Graded Material by Tape-Casting

2014 ◽  
Vol 616 ◽  
pp. 66-71
Author(s):  
Qiang Guo Luo ◽  
Yang Dai ◽  
Shu Long Liu ◽  
Kan Yu ◽  
Qiang Shen ◽  
...  
Keyword(s):  
Functionally Graded Material ◽  
Tape Casting ◽  
Copper Surface ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Equivalent Thermal Conductivity ◽  
Casting Technique ◽  
Cu Content ◽  
Graded Material ◽  
High Tungsten Content

In this paper, the W-Cu functionally graded material (FGM) was prepared by using the non-aqueous tape-casting technique combined with vacuum hot-pressing sintering. The graded composite material with high density, uniform transition and graded component was designed by 7 layers with the copper content range from 40 to 100 wt. %. Then the structures and properties of the composite were characterized. The scanning acoustic microscope (SAM) results for the W-Cu graded material showed that the interface between different layers was of high smoothness and parallel. The SEM-EDS results of cross section show that the W and Cu content changed gradually along the laminating direction after sintering. The equivalent electrical conductivity and the equivalent thermal conductivity of the W-Cu graded material were 0.3976×108 S/m and 323.5 W/(m·K), respectively, which were much higher than that of the W-40 wt. % Cu homogeneous composite. The Vickers hardness of the high tungsten content surface and the high copper surface were 163 HV and 80 HV, respectively, which were same with that of the homogeneous material.

The Verification of Computing J-Integral in Functionally Graded Material

2011 ◽  
Vol 268-270 ◽  
pp. 863-868 ◽  
Author(s):  
Z.C. Xuan ◽  
Y.H. Li ◽  
Q.J. Zhang ◽  
M. Guan
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Quadratic Term ◽  
Verification Method ◽  
Optimal Value ◽  
Graded Material ◽  
Element Computation ◽  
The Difference ◽  
Finite Element Computation

We present a verification method for the finite element computation of the J-integrals in functionally graded material. An interval is obtained for the J-integral by an output bound procedure for the quantity of interest. The difference between homogeneous material and functionally graded material is that the parameter before the quadratic term in the error equation is a function of coordinates, not a constant in the homogeneous material. An optimal value for of the parameter is calculated for obtaining efficient bounds on the J-integral.

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