Constitutive models for viscous sintering

The free sintering rate of porous glass has been analyzed on the basis of several models employing widely varying geometrical assumptions, yet the results are remarkably similar, and are in good agreement with experimental studies. Therefore, it is not necessary to have detailed knowledge of the microstructure to make accurate predictions of the sintering kinetics of glass. In many practical cases, the sintering body is subjected to constraints, such as attachment to a substrate, inclusions of rigid particles, or inhomogeneity in the pore or particle size. To analyze the sintering rates in those circumstances, it is necessary to develop constitutive models for the porous glass. Simple models represent the viscosity of the porous glass as a function of the porosity and the viscosity of the liquid phase, but more sophisticated models take account of the size of the contacts between particles. The results of these models are quite different, so it is essential to know the geometry of the system in order to chose the appropriate constitutive model. Examples are given of the successful application of such models to analyze problems of constrained sintering that are of practical interest.