Dilatation stresses

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

We can distinguish between two types of stresses on an interface a shear stress and a dilatational stress. In a shear stress experiment, the interfacial area is kept constant and a shear is imposed on the interface. The resistance is characterized by a shear viscosity, similar to the Newtonian viscosity of fluids. In a dilatational stress experiment, an interface is expanded (dilated) without shear. This resistance is characterized by a dilatational viscosity. In an actual dynamic situation, the total stress is a sum of these stresses, and both these viscosities represent the total flow resistance afforded by the interface to an applied stress. There are a number of instruments to study interfacial rheology and most of them are described in Ref. [1]. The most recent instrumentation is the controlled drop tensiometer. 

A linear decrease of KIc with an increase in crosslink density was reported for model PU based on triisocyanate and diols of various molar masses (Bos and Nusselder, 1994), and for epoxy networks (Lemay et al., 1984). It was suggested that the dilational stress field at the crack tip may induce an increase in free volume and a devitrification of the material. A linear relationship between GIc and M XJ2 was verified for these systems, although other empiric equations were found in other cases (Urbaczewski-Espuche et al., 1991). 

The volume decrease accompanying formation of intermetallic compounds produces a bulk dilation stress over the whole thickness of growing layers. Thermal expansion of the couple constituents during heating up as well as their contraction during cooling down in the course of successive anneals of the same couple produces a shear stress. These inevitably lead to the rupture of Ni-Zn and Co-Zn diffusion couples, with the latter effect being most disastrous. 

The stress bias criterion [24,25] refers implicitly to two mechanisms of microvoid formation in a dilatational stress field and stabilization of the microvoids through a deviatoric stress component and local plasticity. Its definition is... 

Under dilatational stresses and in contact with solvents, polymers exhibit a cavitational mode of plasticity called environmental crazing. This phenomenon occurs at small strains in the order of a few percent well below the yield point of the polymer. Environmental crazes are normally observed at the surface of a specimen where the penetrating solvent produces a polymer-solvent mixture. Environmental crazing has been extensively discussed in the literature (see e.g. However, one basic problem in studying this phenomenon arises from the fact that the macroscopic state of the sample at craze initiation may differ considerably from the local one which is, in general, poorly defined. 

A high dilatational stress can be built up to nucleate a craze on the specimen surface if there are defects such as scratches or groves. Figure 8 shows a schematic illustration of the dilatational stress concentration at the root of such a defect. If Poisson s ratio is 0.5, the dilatational stress s is given by ... 

Fig. 8. Surface craze formed by elastic dilatational stress at the root of notch under plane strain...

Fig. 34. Yield stress and critical dilatational stress required for crack nucleation in PEEK...

It is well known that the mechanical behavior of glassy amorphous polymers is strongly influenced by hydrostatic pressure. A pronounced change is that polymers, which fracture in a brittle manner, can be made to yield by the application of hydrostatic pressure Additional experimental evidence for the role of a dilatational stress component in crazing in semicrystalline thermoplastics is obtainai by the tests in which hydrostatic pressure suppresses craze nucleation as a result, above a certain critical hydrostatic pressure the material can be plastically deformed. 

To avoid these mathematical details and focus on the key concepts of tablet stress analysis this discussion will examine the simplest of viscoelastic models using the method outlined by Fluggie (97). To begin the analysis, the boundary conditions which apply to tablet compaction, will be used to set up the stress and strain tensors Equations (26) and (27). Then the dilation and distortion uations (28-31) will be used lo obtain dilation and distortion tensors. After obtaining the dilational and distortional stress and strain tensors, a Kelvin viscoelastic model will be used to relate the distortional stress to distortional strain and the dilational stress to dilational strain. 

Using the bulk and shear modulus to relate dilational stress to dilational strain and distortional stress to distortional strain yields ... 

It is interesting that, upon rubber modification, the CET resin matrix can no longer form dilatation bands (18). Only rubber-particle cavitation and matrix shear yielding are detected. This observation implies that a dilatational stress component is required to trigger the formation of dilatation bands. In other words, upon rubber-particle cavitation, the dilatational stress component in the matrix is reduced. This suppresses the formation of dilatation bands. This conjecture finds support in the work of Glad (27), who investigated thin-film deformation of epoxy resins with various cross-link densities and could not find any signs of dilatation bands in his study. 

The transverse stress t is thus equivalent to a dilation stress parallel to plus... 

The stress field around an edge dislocation is more complex, with both shear and dilatational stresses. For example, from Fig. 6.9, one expects o-, to be compressive in the region above the slip plane due to the insertion of the extra half-plane. 

In general, the development of crazes is associated with dilatational stresses (Kambour, 1973). In one case, crystalline poly(ethylene terephthalate), so-called shear crazes have been reported to lie along shear bands induced by yielding. While such crazes are not yet understood, it is reasonable to assume that a dilatational stress component must somehow be involved. If such crazes exist in other systems, however, the argument in this section should not be affected. 

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