Green Density-based Sintering Predictions
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Prediction of density–time curves, i.e., using the sintering curves for one green density to predict those of another during isothermal sintering, was demonstrated for 3 mol% yttria-stabilized zirconia and titania, as well as for data from the literature on various ceramic powder compacts. The predictions utilized only a median green pore size term as the scaling parameter for densification rates between samples of different green densities. Despite the simplicity of the approach, the resulting predictions of density–time curves were in relatively good agreement with the measured data.
I. INTRODUCTION
Differential equations for describing densification
Prediction of sintering behavior, i.e., prediction of density as a function of time and temperature using only easily measurable characteristics of the starting powder compacts, has been an elusive goal of sintering research for many decades. At least three types of sintering predictions can be attempted: (i) “first principles” predictions, which involve characterizing the green body and using known material properties (diffusion coefficients, surface energies, etc.) to predict sintered densities from any green density under any heating schedule without prior sintering experiments (e.g., Swinkels and Ashby1), (ii) predictions for one green density under an arbitrary sintering schedule—these generally involve using several prior sintering experiments and fitting an activation energy to the data (e.g., master sintering curves2); and (iii) predictions for multiple green densities using one sintering experiment on one body of a given green density to predict the density of another body of another green density under the same sintering conditions. The third type of prediction has not been explored very fully in the literature, and thus the main objective of the present study is to use a simple, modified Herring’s scaling law3 to predict green density effects on sintering.
There exist in the literature several equations for densification rate that involve parameters that change with green density.4–6 Unfortunately, these equations either contain parameters that need to be stereologically measured at each instant during sintering to predict what will happen in the next instant (practically impossible) or involve a term such as sintering stress with an unknown dependence upon green density. Sintering stress has been empirically found to vary approximately linearly with green density (at least for zinc oxide),4 but a simple universal relation (one that holds for a variety of materials) between green density and sintering stress has yet to be determined. Therefore a densification rate equation that contains only variables with a known dependence on green density are preferred. In the present work, we use an alternate, empirically determined form of densification rate relation,7
II. MATHEMATICAL APPROACH
For density predictions between bodies of different green densities, a relationship between densification rate and some parameter that scales with green density is requir
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