Densification linear

When a foam is compressed, the stress-strain curve shows three regions (Fig. 25.9). At small strains the foam deforms in a linear-elastic way there is then a plateau of deformation at almost constant stress and finally there is a region of densification as the cell walls crush together. 

Person 1 In process A, the bulk density is 2.43 g/cm green and 3.84 fired. Calculate the volume shrinkage, linear shrinkage, and the densification ratio for this process. 

The shrinkage that often accompanies densification is controlled by different mechanisms in the three stages of sintering. In the initial stage of sintering, the linear shrinkage, AL/Lq, is described by... 

The Heckel equation describes the densification process with first-order kinetics. A linear equation is obtained with a slope which is inversely proportional to the yield strength. The slope of the Heckel equation provides information on the plastic deformation of the powder. It has also been published that the slope of the Heckel equation can be correlated with the elastic modulus (Young s modulus). 

The consequence of this volume conservation equation is that the porosity after dissolution varies linearly with the initial porosity. Increasing the volume fraction of liquid forming additive and increasing the solubility will lead to lower porosity and higher densification. The minimum volume fraction of liquid forming additive necessary for maximum densification is given by... 

If an equilibrated glass is subjected to only a few-degree change in temperature AT, the glass structure will not be far from equilibrium even immediately after the temperature change and the process of relaxation toward equilibrium can be described by a linear spectrum of relaxation times. The shape of the relaxation spectrum governing densification... 

Densification of carbon black by compression increases the dispersive component of surface free energy. This process is initially not proportional to density, but after some threshold value at around 0.7 g/cm the dispersive component has a linear... 

Small strains are typically confined to the linear response region, after which the region of plastic collapse takes over. At high strains, the material will typically experience a densification response in which the cell walls have been fully crushed and the bulk material properties begin to be exhibited. As one would expect, the greater the relative density, the smaller the role played by the collapse of the cell walls. At somewhere near 0.3 relative density, the cells are sufficiently apart that the collapse mechanisms are insignificant (illustrated in Figure 6.31). 

Figure 12. Linear shrinkage and skeletal density of a multicomponent borosilicate xerogel during heating in air at 2 °C/min. Skeletal densification accounts for all the shrinkage observed between 250 and 550 °C. (Reproduced with permission from reference 84. Copyright 1986.)...

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... 

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