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# Computation of Three Dimensional J_Integral in Functionally Graded Material With Finite Element Method

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Ghadimi, Zahra
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2011

435
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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 41691 (45)
- University: Sharif University of Technology
- Department: Aerospace Engineering
- Advisor(s): Hosseini Kordkheili, Ali
- Abstract:
- The J-integral, as a powerful tool in fracture mechanics, is used to analysis of fracture behavior of materials. In order to, evaluate of three dimensional J-integral, an integral evaluation of line and surface is required. However, because surface integral evaluation requires the calculation of the second derivative of displacement field, an commercial finite element codes cannot calculate it.In this thesis, a method for computing 3D J-integral is presented using finite element analysis. In the analysis, the second derivative evaluation of displacement field is employed. In this method, error-minimal points for stress computation are not suitable for second derivative displacement computation and the average value of the Central node of neighbouring elements of each node is considered to be the final value of the node. The material is assumed to be isotropic with constant Poisson's ratio and exponentially-varying elastic modulus in the radial direction. The J-integral is computed on the basis of the results of a finite element analysis using 20-node isoperimetric graded elements. Normal vector to the crack surface assumed perpendicular to the direction of the gradient for nonhomogeneous material. Due to material property variation in r direction, the J-integral is path-dependent and for evaluate it with use of standard form of J-integral, requires very fine mesh. Therefore it is necessary to capture the effects of material nonhomogeneity. In this Thesis, a new method is implemented in calculating the modified J-integral of a circular crack in functionally graded solids. The modified J-integral at any counter with relatively coarse mesh, has same value the results are compared to well-known reference values
- Keywords:
- J-Integral ; Finite Element Method ; Graded Materials ; Three Dimensional State ; Second Derivation

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