Void model framework

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. 

The occurrence of creep-controlled crack growth, in an inert environment, has been demonstrated. It can occur even at modest temperatures, and has been linked to localized creep deformation and rupture of ligaments isolated by the growth of inclusion-nucleated voids ahead of the crack tip. Landes and Wei [2] and Yin et al. [3] have made a formal connection between the two processes, and provided a modeling framework and experimental data to link the kinetics of creep to creep-controlled crack growth. Further work is needed to develop, validate, and extend this understanding. In particular, its extension to high-temperature applications needs to be explored. 

The stability, growth, and transport of voids during composite processing is reviewed. As a framework for this model, the autoclave process was selected, but the concepts and equations may be applied equally effectively in a variety of processes, including resin transfer molding, compression molding, and filament winding. In addition, the problem of resin transport and its intimate connection with void suppression are analyzed. 

More crystallographic variations of the water models are the vacant lattice, framework or cage models which include interstitial water molecules within a four-connected network. In one of these models, the void in the ice-like structure is occupied by a water molecule which at any particular instant may be nonbonded... 

As pointed out in Section I, the pore space can generally be treated as a lattice of voids interconnected by necks in a three-dimensional network (Figs. 2 and 3). It is often possible to consider that the pore volume is concentrated in voids, whereas necks do not possess a volume of their own (Fig. 2). In the framework of this model, the filling of every void on the adsorption branch of the isotherm is determined only by the individual void characteristics and does not depend on the neck-size distribution. In particular, voids with radii lower than the Kelvin radius, r < Vp, are completely filled and those with r > Kp are filled only partly via the reversible sorption... 

During desorption, as the relative vapor pressure is reduced, pore solids in which capillary condensation occurs often show a hysteresis loop. The simplest interpretation of this phenomenon is given by the ink-bottle model (6). In the framework of this model (Fig. 12) the adsorption and desorption processes are controlled, respectively, by the void and neck sizes. Thus, desorption from a given pore occurs at a lower pressure than adsorption. 

VPI-5 is an aluminophosphate framework with very large one-dimensional pores defined by 18-member ring[22]. The crystal structure report[7j of synthesized VPI-5 revealed the possible role of water molecules as templates. The use of VPI-5 as a molecular sieve and as a catalyst primarily depend on the removal of the occluded water molecules without the destruction of the framework structure. Prasad et al.[23] reported from their TGA experiment that the seven distinct types of water molecules could be desorbed from VPI-5 in a step-wise fashion, in the temperature range of 35 to 60°C. The cluster model calculations[24] have revealed the actual electronic interaction of water molecules with VPI-5 framework. CG technique also indicated that the void volume in VPI-5 could be controlled by the partial removal of water molecules. 

The optical properties and thickness of the films were quantified using spectroscopic ellipsometry (M-2000, J.A. Woollam). Film porosity was calculated from the Bruggemann effective medium approximation (BEMA) model [11,54], assuming that only two phases existed amorphous silica and voids. The refractive index of the film was determined and directly translated into the film porosity, knowing the refractive index of the wall framework. The wall was assumed to be solely amorphous silica with a reported refractive index of 1.458. The film porosity calculated was found to be in the range of 50-60%. 

Figure 10.18 Figures from Savage and Lun (1988) illustrating the framework of their model—a systems of layers of particles sheared passed one another with random voids of different sizes (upper right) and the process of capture of particles from one layer into the layer below (lower left). Dy + D is the capture diameter of the region, where Dy is the associated void diameter, and D is the mean particle diameter.

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