Circular delamination

Suppose that the film completely covers the substrate surface initially. Then, the film is cut through its thickness down to the substrate surface over a circle of radius b hf as indicated in Figure 4.25. The film material inside the circle is removed and, outside the circle of radius 6, a circular delamination front begins to grow outward. When the front is very near the film edge of radius b, the local conditions are very much like those discussed the preceding section, and the front advances spontaneously. 

The symmetry of the configuration depicted in Figure 4.25 with a circular delamination zone renders the analysis of delamination simple and transparent. If this symmetry is lost, the situation becomes more complex and the delamination zone shapes which can be observed are surprisingly rich in detail. For example, Choi and Kim (1992) introduced a cut into a polyimide film on a glass substrate and observed the resulting growth of a delamination front from the cut. Because the local conditions varied along... 

Fig. 5.12. (A) Schematic showing a uniform equi-biaxial force t a ahead of the circular delamination front and an extensional force fa and bending moment ma behind the front. (B) represents a state of uniform equi-biaxial compression. The superposition of (A) and (B) leads to the stress state shown in (G).

Fig. 5.13. Normalized energy release rate Q a)/Qra plotted as a function of the normalized buckle size a/a for the circular delamination.

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

Perhaps the most noteworthy aspect of the secondary buckling phenomenon illustrated here is that it is accompanied by an energy release rate at the edge of the zone of delamination that varies with position in the y—direction. This provides a mechanism by which a straight-sided delamination zone may develop a wavy shape through buckle-driven delamination, or a circular delamination zone may develop a lobed shape. The consequences of secondary buckling in thin films have not been studied systematically. 

Controlled circular delaminations of different diameters were introduced at the interface between the mica and the resin by using a screw that was threaded through the substrate, from the back face of the substrate to... 

W. L. (1985), Axisymmetric buckling and growth of a circular delamination in a compressed laminate, International Journal of Solids and Structures 21, 503-514. 

Figure 7-16 Schema of the mechanism of circular delamination (a) view from above, and (b) cross section.

Circular delamination is where a circular portion only peels off from the fired body as shown in Figure 7-16, and in extreme cases, a plate shaped piece delaminates. This probably occurs due to the fact that normally, since the conductor pattern is concentrated in the center of the green sheet so that the total thickness of the middle part only is greater and is raised higher, uneven pressure is applied during lamination. 

Internal interlayer delamination is where delamination occurs at the interface between the internal conductor and the ceramic, although the cracks do not reach to the outside of the substrate. The cause of the problem is an area of poor adherence between the green sheet and conductive paste in the laminated body. When there are many layers, or when the conductor on each layer is thick, there is a great difference in the thickness of the parts including the conductor and the parts with ceramic only, so that the laminated body is like a sandwich with a lot of filling (refer to Figure 7-17). Since this delamination occurs in order to release the stress within the laminated body, it takes a similar form to stepped interlayer delamination and circular delamination. 

A transverse concentrated load, P, is applied at the center of a clamped circular plate of radius R and thickness h with multiple circular delaminations, as shown in Rgure 3. The damaged portion is divided into N pieces of the same thickness by iV-1 equal in size delaminations of radius a. The values relating to the intact and delaminated portions are indicated by subscripts 0 and d, respectively. 

While the IR and MAS NMR spectra are consistent with the delaminated structure of ITQ-2 and ITQ-6, the Argon isotherms represented as a function of log P/P are highly informative on the changes in topologies experienced during delamination (Fig. 3). It can be seen there that ITQ-2 does not show the adsorption corresponding the large 12 MR cavities characteristics of the MWW structure, while preserves that of the intralayer 10 MR circular channels. Meanwhile, in the case of ITQ-6, the adsorption at the 10 MR pores of ferrierite has practically disappeared. 

Figure 4.11 Buckling of circular sub-laminate, diameter I, above delamination.

Suemasu H, Majima O. Multiple delaminations and their severity in circular axisym-metrical plates subjected to transverse loadings. J Compos Mater 19% 30(4) 441—53. 

Figure 4. A urea mediated mineralization process leads to high-affinity growth of CP on pHEMA-based hydrogel copolymers displaying various anionic residues. Hydrogels mineralized here were pHEMA with 5% Glu-MA (A), 5% Gly-MA (B) and 5% Ser-MA (C). Note that the deliberate fracturing of the composite (B) did not lead to delamination of any circular CP domains, suggesting an excellent gel-mineral interfacial adhesion strength.

Fig. 4.25. Schematic diagram of a delamination zone expanding outward from the free edge of a circular hole in the film. The expansion is driven by a residual stress in the film.

The relationship (4.45) between the final radius ap of the delamination zone and the corresponding separation energy F was established by adapting some general concepts of fracture mechanics. The same result can be obtained by direct appeal to energy methods. The total elastic energy in the film between the free surface at r = 6 and some remote circular boundary, say at r = i > a, is... 

In order to examine the phenomenon of film buckling and possible subsequent delamination, this section begins with a description of the simplest case of buckling under plane strain conditions. This is followed, in subsequent sections, by analysis of circular buckles, secondary buckling phenomena and buckles with perimeters of other shapes. 

The smallest circular zone of delamination which is unstable in the presence of a mismatch force < 0 is denoted by Om and is given by... 

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. 

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