Non-Isothermal Consolidation

Using Eqs. (1) and (2), the momentary deformation rate of each layer j, h, can be calculated by solving the system of n equations  

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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. 

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. 

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. 

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). 

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. 

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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