Isothermal Consolidation

The derivation is formally the same for the hexagonal and square arrangements, only requiring the use of the correct expressions of Vy, L, and Uf). The value of the viscous pressure thus obtained is  

In this equation, C is a constant that depends on the towpreg properties, the press operation, and the Hber/polymer arrangement. The variables hjf and Vy are the final composite thickness and fiber volume fiaction, respectively. For hexagonal and square packing, the values of C are, respectively  

For the utilization of the model, it is also necessary to consider the momentary shear rate, y, of the molten polymer through the fiber interstices. As can be seen from Eqs. (1) and (2), the pressure necessary to consolidate a towpreg with a hexagonal fiber/polymer arrangement is approximately 4/3 of that for a square arrangement. At this stage, using the viscosity, it is possible to express the temperature dependence of the pressure by Eq. (2) and to consider an isothermal and a non-isothermal approach. 

When the consolidation is isothermal, all composite layers are considered to be at the mold temperature. Then, using Eq. (1), the momentary pressure can be analytically determined if the fiber and polymer particle radii, the final molding thickness, and fiber volume fraction are known. 

The polymer viscosity, tj, at each mold temperature is derived by means of an Arrhenius power law. Finally, the expression modeling the evolution of the viscous pressure during isothermal consolidation can be obtained by introducing the value of t] in Eq. (1). 

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The material properties to be homogenized and upscaled are drawn from Biot s theory extended for non-isothermal consolidation (Guvanasen and Chan 2000). The modified crack tensor theory of Oda (1986) has been modified to include other transport and thermoelastic properties specified by Guvanasen and Chan (2000). 

Abstract motif is a three-dimensional finite-element code developed to simulate groundwater flow, heat transfer and solute transport in deformable fractured porous media. The code has been subjected to an extensive verification and updating programme since the onset of its development. In this paper, additional verification and validation works with an emphasis on thermo-hydro-mechanical processes are presented. The verification results are based on cases designed to verify thermo-hydro-mechanical coupling terms, and isothermal and non-isothermal consolidations. A number of validation case studies have been conducted on the code. Example results are repotted in this paper. 

Two transient simulations were conducted in addition to the one-element verification cases. The two simulations comprise one-dimensional isothermal consolidation simulation and one-dimensional non-isothermal consolidation simulation. These two simulations were designed to examine the coupling between two dominant modules the equilibrium module and the flow module. The heat transport module is weakly coupled to the flow module via the velocity terms and unilaterally coupled with the equilibrium module via the thermal expansion terms. 

Figure I. Isothermal consolidation verification head vs distance at 15 s.

More fundamental studies with the material under special consideration here, i.e. GF/PP commingled yams or fabrics, were thoroughly preformed with regard to its isothermal consolidation behavior and to an optimization of its flexural stiffness by Cain et at. [6]. In the following, some further details about impregnation, consolidation and resulting properties of GF/PP will be discussed. 

J. P. Nunes, A. M. Brito, A. S. Pouzada, C. A. Bernardo (2001) Non-isothermal consolidation of carbon fiber towpregs and composites, Polym. Compos. 22, 71. 

Wankat and Koo (110) have shown that the efficient mass transfer achievable with small ( 10 micron diameter) monodisperse packing can provide excellent resolution on very short columns, even when adsorption isotherms are nonlinear. For high-throughput processes, the most efficient columns resemble squat disks or pancakes (109). The ultimate "column" geometry may well be a membrane or consolidated packing with mobile phase flow through monodisperse pores. 

D warp interlock fabrics, constituted by commingled yams, can be preformed at room temperature and this cool forming tends to be better controlled and seems to be more economical (Vanclooster et al., 2009a,b Padvaki et al., 2010 Thomanny and Ermanni, 2004 Zhu et al., 2011). The increase of temperature and the resin consolidation phases after the forming can be achieved under isothermal conditions thanks to a closed mould. By this way, it appears easier to avoid defects during the non-isothermal thermoforming process, especially for thick preform. 

There are basically three techniques for studying the pore structure of a porous body. The first is what is known as mercury intrusion exploration of the pore structure. The second is the use of gas adsorption studies in which pore structure is derived from condensation isotherms. The third method is a study of sections made through the porous body or the consolidated powder system with subsequent image analysis. In this section we will first explore all mercury intrusion technology and then image analysis of sectioned material. A discussion of the method based upon gas adsorption studies will be deferred until Chapter 10. 

A theoretical model was developed to simulate the consolidation by compression molding, both in isothermal and non-isothermal conditions. - The model assumes a towpreg lamina as an array of fibers with attached particles (Figure 5a). The stacking of a number of these laminae together with different possible arrangements leads to a preform (Figure 5b). 

In Figure 10, pressure data obtained from consolidation tests at 260 °C are compared with simulations for the isothermal and non-isothermal models using two different closing speeds. It is seen that the predictions of the non-isothermal model are closer to the experimental results, especially at the start of compression. The worst fit corresponds to the isothermal simulation at the higher closing speed. 

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