“…(Beuth [2]; Beuth and Klingbell [3]; Hu et al [4]; Hutchinson and Suo [5]; Nakamura and Kamath [6]; Thouless, Cao, and Mataga [7]; Thouless [8]; Thouless, Olsson, and Gupta [9]; Vlassak [10]; Xia and Hutchinson [11]; Ye et al [12];) These analyses are based on the assumptions that the film and substrate are elastic isotropic solids with dissimilar elastic moduli, the film is subject to a uniform, equib axial in-plane tensile lease the film. For a through-thickness single channel crack forming in a residually stressed film, the mode I steady state strain energy release rate at fracture, Iss , is given by, (Hu et al [4]); Thouless [8]; Beuth [2]; Hutchinson and Suo [5]), (1) In this equation, is the stress in the film, h is the film thickness, E f is the elastic modulus of the film, f Poissons ratio for the film, and g( , ) is nondimensionalized integral of the crack opening displacement. (Beuth [2]) The analysis was extended to multiple crack systems to account for crack interaction effects on strain energy release rates and is a function of crack spacing and film thickness.…”