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The direct application of finite element method to crack problems will produce errors, which cannot be neglected. One of the major sources of the errors is crack tip singularity, The numerical solution of path independent JIntegral method is considered to be based on conservation law of energy in conservative fields. Combination of such method with finite element method creates a very powerful tool to analyze cracks with complex shapes and model geometries. In the present research after a short review of fracture mechanics history in general and J-Integral in particular, cracks in composite materials which are divided into internal cracks and interlaminar cracks are
analyzed using J-IntegraI. For numerical solution of J-Integral two computer programs are written using MA TLAB software. Input data for these programs, stress-strains and coordinates of nodal points come from output files of finite element analysis. These programs
read their input data directly from the output files of finite element program. Comparison between results of the present study and existing results in literature shows the ability of this method in analyzing plane crack in three-dimensional space.