This paper shows the two calculation method of J Integral in elastic-plastic behavior of central crack in 2-dimensional problem. The analysis of the J integral and the increment of J for a plate with a central crack under cyclic fatigue loadings are carried out by using path integration based on the numerical results of Finite Element (FE) analysis. The J integral is calculated by both elastic analysis and elasto-plastic analysis. The accuracy of numerical results for the increment of J is proved by comparison with the simplified method results. In this study, we also analyzed the J-integral using the virtual crack extension method based on the finite element method. Analysis model is a two-dimensional flat plate with a central crack, and by changing the crack length in the different FE analysis, the fundamental feature of J-integral by the virtual crack extension method under cyclic fatigue analysis is discussed.

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