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In this paper, the Meshless Local Petrov-Galerkin (MLPG) method is used to analyze the fracture of an isotropic FGM plate. The stress intensity factor of Mode I and Mode II are determined under the influence of various non-homogeneity ratios, crack length and material gradation angle. Both the moving least square (MLS) and the direct method have been applied to estimate the shape function and to impose the essential boundary conditions. The enriched weight function method is used to simulate the displacement and stress field around the crack tip. Normalized stress intensity factors (NDSIF) are calculated using the path independent integral, J*, which is formulated for the non-homogeneous material. The Edge-Cracked FGM plate is considered here and analyzed under the uniform load and uniform fixed grip conditions. To validate results, at first, homogeneous and FGM plate with material gradation along crack length was analyzed and compared with exact solution. Results showed good agreement between MLPG and exact solution.

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Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.