Composition profile for improving the brittle fracture characteristics in semi-infinite functionally graded materials

In this study, we analyze the composition profile of semi-infinite functionally graded materials (FGMs) with a view to improving the brittle fracture characteristics of these materials. First, a method is developed to calculate the stress intensity factor of an edge crack in semi-infinite homogeneous media with distributed eigenstrain under a far-field uniform applied load. The crack. is represented by the distribution of edge dislocations, and a singular integral equation with a Cauchy-type kernel is obtained using the complex potential functions of the edge dislocations. Second, a useful approximation method is established to simulate the nonhomogeneity of semiinfinite FGMs by an equivalent eigenstrain. The stress intensity factor is calculated for this equivalent eigenstrain. Finally, the stress intensity factor of the original semiinfinite FGMs is obtained by principle of superposition. By equating the stress intensity factor to the intrinsic fracture toughness of the FGMs, the apparent fracture toughness is calculated for prescribed composition profiles of the semi-infinite FGMs. Conversely, the composition profiles of prescribed apparent fracture toughness are also determined.