Interfacial toughness and mode mixity

When I was a graduate student, I spent several months to measure interfacial toughness between metalic (Cu and Au) films and thick substrates(Si and Polycarbonate). My methods were bulge test (blistering test) and 4-point bending test. I had many problems such as making an initial crack(pre-cracking), changing load phase angle applied to specimens, preparing/patterning thin films, constructing my own test apparatus, etc. The biggest problem was to measure the interfacial toughness over a wide range of loading phase angle. For a bimaterial with a non-zero oscillatory index(epsilon), we don't know the phase angle for a minimum interfacial toughness beforehand. Therefore, we need to measure the interfacial toughness over a wide range of phage angle. For engineering purpose, we need a minimum interfacial toughness value for reliability design because this value will lead to a conservative design of systems.

The attached file was written based on the above considerations(it's not an experimental paper, but an analysis one). It describes an interfacial toughness model which provides some useful guidelines for finding a minimum interfacial toughness. It assumes that the main contribution for the phase angle dependency of interfacial toughness is plastic dissipation. Using plastic zone size around an interface crack, it defines two stress modes which are corresponding to Mode I and II for epsilon =0, but are not orthogonal to each other for nonzero epsilon.

I think some descriptions in the paper are not good(this is one of my first papers), but it contains some useful ideas for interfacial toughness model. Any comments and advices are welcomed.