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In this paper, the cracked thick-walled functionally graded cylinder has been analyzed using the finite element method. The internally pressurized cylinder contains fully longitudinal cracks. The analyses have been done with two, four, six and eight longitudinal cracks at the inner surface of the cylinder in four different conditions. For this  purpose, using  the  USDFLD  subroutine coding in  ABAQUS  software,  the variations of  properties of  the functionally graded material are considered based on a power-law function model in the cracked cylinder. The inner  and  outer  surfaces of  the  cylinder  are  made of  aluminium  oxide and  titanium  carbide respectively. The continuous composition of the  two  materials has  been considered in  the  form of varying elastic  modulus and Poisson’s ratio along the radial direction as the power-law function. The J-integral has been used to calculate the stress intensity factors, taking into account the variable properties at the crack tip. The effect of non-homogeneity of the properties, the number of the cracks and cracks’ relative depth on the stress intensity factors have been evaluated. The results have been compared with  those of other available literature to verify the finite element modelling, in which very good agreement has been found. The results show that similar to the isotropic cylinder with multiple longitudinal cracks, in the cylinder of functionally graded material, the two-crack model has the highest amount of stress intensity factors and the variation of Poisson’s ratio has to be taken into account in the shallow cracks.

Analysis of stress intensity factors for functionally graded cylinders with multiple longitudinal cracks using finite element method