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

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