Film cracking due to residual stress

If a thin film is bonded to a substrate, and if that film is subject to a residual tensile stress as a result of elastic mismatch with the substrate, then the stress can be partially relaxed by formation of cracks in the film. In this section, the behavior of through-the-thickness cracks within the film is considered. First, the behavior of an isolated, fuUy formed crack is examined and, subsequently, the mechanics of formation of an array of cracks is considered. 

---

The discussion of stress concentration near a film edge in the next section is followed by a brief review of linear elastic fracture mechanics concepts, a prelude to a discussion of delamination and cracking due to film residual stress. A survey of these topics set in the context of fracture mechanics has been presented by Hutchinson and Suo (1992). The chapter also includes descriptions of various experimental techniques for evaluating the fracture resistance of interfaces between films and substrates. In addition, representative experimental results on the interface fracture resistance, as a function of interface chemistry and environment, are presented for a variety of thin film and multilayer systems of scientific and technological interest. 

Stress corrosion cracking also involves localized breakdown of the protective film. The corrosion is narrowly confined within the metal due to stress factors which may arise from either residual Internal stress or applied external stress. In some cases the stress failure can be accelerated by chemical factors, such as surface adsorption or hydrogen dissolution from cathodic hydrogen leading to embrittlement. 

The formation of a through-the-thickness crack in a film subjected to a residual or applied tensile stress relieves that stress in the film material at points adjacent to the crack path. At points in the film at some distance from the crack path, the stress remains unrelaxed due to the constraint of the substrate. Consequently, a long crack that is parallel to the first formed crack can also form. Indeed, an array of parallel cracks over the entire film surface is likely, and the point of the discussion in this section is to provide an estimate of the dependence of the spacing between cracks in such an array on the film thickness hf and the mismatch stress a. The discussion is limited to the case when the equi-biaxial mismatch stress is uniform throughout the film, the elastic properties of the film and substrate are nominally the same, and hg/hf is sufficiently large so that the behavior is insensitive to the substrate thickness hg. Furthermore, it is assumed that the cracks grow through the thickness of the film to the depth hj, but that they do not penetrate into the substrate. There is no fundamental barrier to relaxation of these limitations, but the relatively simple system is sufficiently rich in physical detail to reveal the principal features of behavior. 

---