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 function ally graded materials (FGMs) with a view to improving the brittle fracture characteristics of these materials. First, a method is developed to calcula te the stress intensity factor of an edge crack in semi-infinite homogeneou s 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 app roximation method is established to simulate the nonhomogeneity of semiinfi nite FGMs by an equivalent eigenstrain. The stress intensity factor is calc ulated for this equivalent eigenstrain. Finally, the stress intensity facto r of the original semiinfinite FGMs is obtained by principle of superpositi on. By equating the stress intensity factor to the intrinsic fracture tough ness of the FGMs, the apparent fracture toughness is calculated for prescri bed composition profiles of the semi-infinite FGMs. Conversely, the composi tion profiles of prescribed apparent fracture toughness are also determined .