Hot pressing equations

This equation indicates that, at the initial stage, AC for hot pressing is similar to that for normal sintering, but ysv + is used instead of ysv- Because and a are constant, hot pressing equations can be derived from the sintering equations by simply changing ysv into ysv + Pi aln. 

Hot pressing equations can be derived from the creep equations with certain modifications. In practices, sintering data are usually present as density versus time to obtain densification rate. Because sintering compacts are porous before they are fuUy densified, the creep equations developed for dense solids should be modified to be suitable for hot pressing equations. First, the creep rate that is a linear strain rate should be related to the densification rate which is a volumetric strain rate. Second, the porosity should be compensated. In hot pressing, the mass M of the powder and the cross-sectional area A of the die, are constants, while the density... 

Table 8.6 Hot Pressing Equations Obtained by Modification of the Creep Equations...

Compared with Coble s hot pressing equations (Table 8.5), Eq. (8.118) has the same dependence on the material and physical parameters except for the value of the exponent for 4>. The difference in the exponents arises because Coble assumed that X = G, whereas the present derivation related X to G, through <]) ... 

This latter equation defines the relative roles in hot pressing densification of volume and grain boundary processes. 

The alteration of several titanate ceramics in pure water at 90 °C has been investigated by Leturcq et al. (2001). These experiments were performed under conditions of high surface area to volume ratio and lasted for over one year without replacement of the solution. Starting materials included melted Synroc-like materials and hot pressed Synroc-C. This study reported the normalized elemental mass losses, defined by the equation ... 

Once the elastic residual moment from Equation 8.30 or the viscoelastic residual moment history from Equation 8.39 have been determined, the final value may be applied elastically as platens open (hot pressing) or as the applied pressure is released (autoclave processing) to find the resulting cross-ply curvature. This curvature can then be correlated to experimental data. 

Most investigators agree that the strength and durability of isocyanate-bound wood panels are due to the chemical reaction of the isocyanate group with wood hydroxyls as illustrated by the above equation. Thus, the multifunctional isocyanate molecule forms a chemically bonded bridge between two or more adjacent wood particles. This reaction is only one of several involving isocyanates that can and probably do occur in a hot press during formation of particleboards when isocyanate binder is used. A very important reaction is that of isocyanate with water to produce a very unstable carbamic acid which immediately decomposes to form a primary amine and COg ... 

Fig. 2.51 Determination of activation energy for flow equation in the as-hot-pressed jS-Si3N4 [51]. With kind permission of John Wiley and Sons...

Models for hot pressing by diffusional mass transport under the driving forces of surface curvature and applied stress were formulated by Coble (39,40). In one approach, the analytical models for sintering were adapted to include the effects of an applied sdess, while in a second approach, hot pressing is viewed in a manner analogous to that of creep in dense solids and the creep equations... 

Coble did not specifically adapt the intermediate and final stage sintering models to account for hot pressing, but as described below, he used a different approach based on a modification of creep equations. However, as we shall show later, if the differential equations for matter transport are formulated with the proper dependence of the chemical potential on surface curvature and applied... 

In the hot pressing of powders, the data are normally acquired in the form of density versus time from which the densification rate can be determined. Furtha--more, considerable porosity is present over a large part of the process. The modification of the creep equations derived for dense solids therefore attempt to incorporate these two factors (1) relating the creep rate (a linear strain rate) to the densification rate (a volumetric strain rate) and (2) compensating for the presence of porosity. 

The mononitride is an electronic conductor with a room-temperature specific resistivity first reported as 10 Q m [15]. Electrical dc resistivity measurements (4 to 850 K) have been made on ThN specimens with porosities P = 8 to 13% that had been hot pressed at 1275°C and sintered at 1800°C in vacuum (10 Torr) for 6 h [16]. The results above 70 K, after correcting for porosity P with the formula R = Rq (1-P)/(1 + P/2), are represented by the equation... 

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