Abstract
Solutions are obtained for two elastic plane strain problems relevant to the cracking of a thin film bonded to a dissimilar semi-infinite substrate material. The first problem is that of a crack in the film oriented perpendicular to the film/substrate interface with the crack tip touching the interface. The second problem is that of a crack of the same geometry, but with length less than the film thickness, so that the crack tip is within the film. These problems are used to model several modes of crack extension in thin films bonded to thick substrate materials. Complete results from the solution of each problem are given over the full range of practical elastic mismatches. Dimensionless quantities important in describing the cracking of thin films are introduced and accurate approximate formulas based on the solution results are given for them. Applications are discussed, including criteria for avoiding thin film crack extension and a formula for the curvature change induced by the cracking of a thin film bonded to a substrate of finite thickness. The solution results, approximate formulas and information on their application provide the details necessary for the analysis of practical thin film cracking problems.
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