Cohesive separation

In some cases crack advance in a polymer could occur by close-to-ideal de-cohesion or, alternatively, by ideal cavitation when the local crack-tip stress reaches either the ideal de-cohesion strength or, alternatively, the cavitation strength Tc- These ideal strengths can be estimated from the universal 

For glassy polymers other than PP, it can be expected that the corresponding levels of ud/ o and Uc/ b are still likely to be around 0.035, suggesting that in most un-oriented polymers fracture occurs ultimately under circumstances that are much less than ideal. 

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Now while we admit that there is no limit to our concef ion of the dmsibility of matter, this does not prove that there mw not be a limit, in point of fact, to its actual divisibility. For, let us consider a moment what division really is and we shall find that it can only he defined as the separation of one portion of matter from oUrers. Now as matter, in its usual forms, undoubtedly consists of particles held together, more or less firmly, by cohesion, it is plain that we can easily, by overcoming cohesion, separate those particles from each other, and this is ordinary division. 

As expected, the energy release rate J and lump-sum cohesive law can be experimentally determined if the crack tip separation 8, the loadhne rotation Op of the adherends, and the global peel load P are simultaneously recorded during the fracture test. It is noted that this interface constitutive relationship is the equivalent interface cohesive law, not necessarily the intrinsic cohesive law. This is because, in addition to the intrinsic cohesive separation, possible plastic deformation in the adhesive layer contributes to the entire normal separation between the two adherends during the fracture test. Of course, with the decrease of the adhesive thickness, it is expected that this equivalent interface cohesive law will finally approach the intrinsic cohesive law [66]. 

It is well established that, in the peeling of pressure-sensitive tapes off solids, fflaments of adhesive exist, extending from the adhesive layer on the tape backing, down to the solid. i" ) See Figure 4. (An exception to the formation of filaments may be observed with certain tapes that are designed for cohesive separation, and have very thick layers of adhesives. During... 

Gardon(35,36) has determined the peeling force and the mode of separation as a function of separation rate and of adhesive thickness, for cellophane films bonded together by an acrylic adhesive. He found a transition from cohesive separation to mixed or interfacial separation, with increasing crosshead speed and with decreasing thickness of the adhesive layer. A transition from cohesive to mixed or adhesive failure was also observed with decreasing temperature. These observations are in exact agreement with the predictions that we have just indicated above. Similar results have been reported by Kaelble.(i3,34)... 

FIGURE 11. Aubrey and Sherrifif s report of the relation between viscoelasticity and peel adhesion. Master curve of peel force against pulling rate at 296 K for the system 6 4 NRiPiccolyte SI 15, showing superposition of experimental data (o) cohesive separation, ( ) adhesive separation. ... 

To summarize in regard to Table 1 and Figure 11, it is clear that the qualitative prediction, that there will be a transition between (a) cohesive separation or interfacial separation, with a large force requirement, and (b) interfacial separation with a low force requirement, is in agreement with experiment. 

Asphaltenes are obtained in the laboratory by precipitation in normal heptane. Refer to the separation flow diagram in Figure 1.2. They comprise an accumulation of condensed polynuclear aromatic layers linked by saturated chains. A folding of the construction shows the aromatic layers to be in piles, whose cohesion is attributed to -it electrons from double bonds of the benzene ring. These are shiny black solids whose molecular weight can vary from 1000 to 100,000. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

Polyurethane adhesives are known for excellent adhesion, flexibihty, toughness, high cohesive strength, and fast cure rates. Polyurethane adhesives rely on the curing of multifunctional isocyanate-terrninated prepolymers with moisture or on the reaction with the substrate, eg, wood and ceUulosic fibers. Two-component adhesives consist of an isocyanate prepolymer, which is cured with low equivalent weight diols, polyols, diamines, or polyamines. Such systems can be used neat or as solution. The two components are kept separately before apphcation. Two-component polyurethane systems are also used as hot-melt adhesives. 

Since the locus of failure can clearly distinguish between adhesive and cohesive failures, the following discussion separates loss of adherence into loss of adhesion and loss of cohesion. In the loss of cohesion it is the polysiloxane network that degrades, which can be dealt with independently of the substrate. The loss of adhesion, however, is dependent on the cure chemistry of the silicone, the chemical and physical properties of the substrates, and the specific mechanisms of adhesion involved. 

A useful way to approach these individual point defect energies is to define the energy per mole or cohesive energy of perfect material with respect to separated free atoms, Cmoi-We can then arbitrarily divide this between the atoms of type A and B so that ... 

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