ABSTRACT
One of the features of interfacial fracture that has become appreciated in recent years is the importance of the symmetry of the crack-tip stress field. In particular, three modes of deformation are possible at the tip of a crack: modes I, II, and III, which correspond to normal, in-plane shear, and anti-plane shear, respectively. In axisymmetric and plane-strain geometries, which are appropriate for the blister and peel tests, there is no anti-plane shear and it is convenient to express the ratio of the other two modes by a phase angle, ip, defined as
where K\ and K\\ are the mode-I and mode-II stress-intensity factors [15]. If the phase angle is 0°, pure mode-I conditions exist at the crack tip; if the phase angle is 90°, pure mode-II conditions exist. Experimental observations suggest that the toughness of an interface is frequently not a constant but depends on the phase angle. It should be emphasized that there is no a priori reason to assume that the fracture resistance is independent of the mode of loading, since the size and shape of any dissipative region
near the crack tip (which is responsible for most of the toughness) will depend on the details of the elastic stress field. There appears to be no unique relationship between the failure criterion and the phase angle; it must be determined experimentally as part of the procedure of characterizing the interface of interest. One purely empirical expression that links the toughness of an interface to the phase angle, and appears to capture at least some of the essential elements of observed mixed-mode failure behavior, is
properties of the film and substrate are identical, and that the film is sufficiently hard so as to ensure small-scale yielding conditions.
