A simplified method for calculating the crack-tip field of functionally graded materials using the domain integral

A finite element based method is proposed for calculating stress intensity factors of functionally graded materials (FGMs). We show that the standard domain integral is sufficiently accurate when applied to FGMs; the nonhomog eneous term in the domain integral for nonhomogeneous materials is very sma ll compared to the first term (the standard domain integral). In order to o btain it, the domain integral is evaluated around the crack tip using suffi ciently fine mesh. We have estimated the error in neglecting the second ter m in terms of the radius of the domain for the domain integration, the mate rial properties and their gradients. The advantage of the proposed method i s that, besides its accuracy, it does not require the input of material gra dients, derivatives of material properties; and existing finite element cod es can be used for FGMs without much additional work. The numerical example s show that it is accurate and efficient. Also, a discussion on the fractur e of the FGM interlayer structure is given.