The driving force for delamination

Suppose next that extensibility of the film is taken into account. If the bonded film supports a uniform equi-biaxial mismatch stress 7 then the elastic energy density per unit area of interface far ahead of the line of separation compared to h is W+ = a hf/Mf = t /h Mf. For points far behind the separation point, the nonzero stress components are Oxx = q/h and ayy = + (1 — these values are based on the constraint that 

Note that this result reduces to (4.34) when 0 — 0, as it should. 

---

Strain energy release rate, which is the driving force for delamination propagation and denoted by the symbol G) [1,4]. Assessment of the long-term performance of FRP composites for aerospace apphcations requires consideration of the effects on their delamination resistance of both service loads and environmental exposure. 

An imderstanding of the fundamentals governing adhesion is important regardless of the application. These involve two opposing effects elastic strain energy in the layers, which results ft om stresses in the layers and provides the driving force for delamination and the layer s adherence, which is the resistance to separation at the interface between two layers and is intimately related to the work of adhesion (lTad) which was described in Chapter 3. 

Fig. 4.24. Ratio of the driving force for delamination to its steady-state value approached far from the film edge versus the delamination zone size for three values of D. The configuration is shown in the inset. Adapted from Yu et al. (2001).

Fig. 4.36. Schematic diagram of a bilayer film on the surface of a relatively thick substrate. The second film can contribute to the driving force for delamination of the first film from the substate and/or alter the stress state phase angle at the edge of the delamination zone.

The local conditions at the edge of the line of separation can again be represented by the situation depicted in Figure 5.2 where ta and ma are the stress resultants at the edge of the detached region. At this level of observation, the driving force for delamination has been given by (5.21) where At = — Equilibrium of the detached portion of the film implies... 

A main objective in developing the boundary layer solution is to determine the bending moment at the edge of the bulge, which is needed to determine the driving force for further delamination of the film. The bending moment is determined from the solution to be... 

Fig. 4.47. The ratio of driving force for the kink crack in Figure 4.46(b) versus kink angle, is normalized by the value of energy release rate Q for continued growth of the delamination crack in the interface.

Combining (5.15) through (5.17) and noting that = cr hi, the total driving force for each edge of the delamination is written as... 

Fig. 5.15. Mode-adjusted driving force for circular delamination, defined as the nondimensional quantity versus the normalized circular buckle...

Other than the standard or the inverted blister test, the island blister test (Allen and Senturia 1989), the peninsula blister test (Dillard and Bao 1991), and the constrained blister test (Chang et al. 1989) have been proposed (Lacombe 2006). These tests are schematically shown in O Fig. 22.3. In the island blister test, a small inner island induces larger driving force for the propagation of the delamination front than that on the periphery (the crack initiation point for the standard blister test), which results in effective demationation at the interface between the film and the substrate. The peninsula blister test is a modification of the island blister test and improves the stability of the delamination. In the constrained blister test, a transparent rigid cover plate prevents the film from bursting while the observation of the delamination front is possible. For theoretical treatment of some of these tests, refer to the documents by Williams (1997). 

Lastowka LA, Sheehan AF, Schneider JM (2001) Seismic evidence for partial lithospheric delamination model of Colorado Plateau uplift. Geophys Res Let 28(7) 1319-1322 Lithgow-Bertelloni C, Silver PG (1998) Dynamic topography, plate driving forces and the African Superswell. Nature 395 269-271... 

For the case of a straight-sided buckle, the ratio of the delamination driving force G a) to the phase-angle-dependent delamination resistance r( / ) was shown in Figure 5.7 for a particular choice of the parameter r/c introduced in (5.20) and for three values of the system parameter f/m/ric-A similar representation could be produced for the case of a circular buckle. 

If delamination at the edges of the bulging strip is driven by controlling the volume V of the pressurizing fluid between the film and its substrate, the dependence of driving force G a) on width a is quite different from that shown in Figure 5.30. For the case of small deflections, w x) is given explicitly in (5.57) in terms of pressure p and various system parameters. Therefore, the relationship between volume V as defined in (5.75) and pressure can be established as... 

---