Phase angle in the Cu/polyimide/alumina system

A linear elastic fracture mechanics analysis was extended to determining the phase angle of an interface crack between Cu/polyimide in the elasto-plastic peel test of Cu/polyimide/alumina structure. Then, the fracture mechanics solutions of the phase angle for the thin film/substrate structure were extended to the Cu/polyimide/alumina structure by assuming the path independence of J-integral, which turned out to be quite true with or without polyimide. The peel crack propagation occurred under the mixed mode in all cases with phase angles virtually independent of the metal film thickness, which is in good agreement with our earlier work [1] showing nearly constant interfacial fracture energy with the film thickness. The presence of the polyimide layer increased the mode mixity shifting the phase angle by 11–12°, which indicates that ignoring the polyimide interlayer may result in some underestimation of the real phase angle of multilayer films under the peel test.