<![CDATA[In the field of crack mechanics, predicting the direction of the crack when the propagation crack occurs is important because this will evaluate the crack when it propagates whether it penetrates into important areas, the danger of the structure or not. This paper will refer to three theories that predict the propagation direction of cracks: the theory of maximum tangential normal stress, the theory of maximum energy release and the theory of minimum strain energy density. At the same time, the finite element method (FEM)- ANSYS program will be used to calculate stress intensity factors (SIFs), strain energy release rate- J-integral, simulate stress field, displacement near a crack tip, and crack propagation phenomenon based on the above theories. The calculated results were compared with the results in other scientific papers and experimental results. This research used ANSYS program, an Experimental method combined with FEM based on the above energy theories to simulate J-integral, the SIFs and crack propagation. The errors of SIFs of a functionally-graded material (FGM)rectangular plate has a Internal Crack of 0.33% for , 0.43% for , the J-integral of 1.62% and crack propagation angle of 0.15%. The FEM gave good errors compared to Experimental and Exactly methods.]]>
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