Effects of imperfections on buckling delamination

Axisymmetric buckling of a thin film on a flat substrate surface becomes possible when there exists an interface separation with minimum radius as given in (5.35). Analysis of this phenomenon is predicated on the tacit assumption that the film is nominally uniform in thickness and that the interface is nominally flat in other words, it is assumed that no large scale 

Hutchinson et al. (2000) have performed finite element simulations of energy release rates for interface imperfections in the form of axisymmetric undulations of different wavelengths and amplitudes. Their results suggest 

When 5min is equated with the interface fracture energy at the appropriate local stress state phase angle V , a critical wavelength or radius for the interface imperfection ao = a r, can be extracted by combining (5.41) and (5.17) to yield 

This result implies that when the imperfection wavelength is smaller than ttcr, the energy release rate is not sufficiently high to induce buckling. On the 

It is noted that Ucr as given by (5.42) is independent of the film thickness h(, which is counter to experimental evidence. Hutchinson et al. (2000) circumvent this problem by postulating that max = 2F gives the 

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