Equilibrium depth and spacing of cracks in a tensile residual stressed thin film deposited on a brittle substrate

The depth and spacing of cracks in a tensile residual stressed thin film bonded on a brittle substrate are analyzed thermodynamically using the minimum energy theorem on the basis that the film has the same mechanical properties as the substrate. The results show that the cracks penetrate into the substrate. Simple and approximate relationships between three dimensionless parameters, i.e., the normalized crack depth and spacing, and the cracking resistance number, are derived, which determine the fracture behavior of the film.