Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.