Constrained network model for predicting densification behavior of composite powders

Abstract

Inert particles that do not contribute to the densification of a composite powder compact are visualized as located on network sites; the network is defined by the distribution of the particles in the powder matrix. Because the distances between neighboring network sites are not identical, the strain produced by the sintering powder between all inert particle pairs cannot be the same as that for the powder compact without the inert particles. The constrained network model is based on the hypothesis that the densification of the composite will be constrained by the network and will mimic that of the network. The shrinkage of the network, and thus the densification of the composite, is estimated with a periodic network. A distance between the minimum and maximum site pairs within the unit cell defines the distance between site pairs in the random network where the powder between the particles densifies in the same manner as that for the powder without the inert particle. When the particles form a continuous touching network, composite shrinkage and densification is nil. The chosen lattice must also conform to this condition. A simple relation was developed relating the densification behavior of the composite to that of the matrix without the inert particles and the parameter associated with the chosen lattice. By choosing the lattice formed by the tetrakaidecahedron unit cell (volume fraction of particles for a touching network = 0.277), remarkable agreement was achieved for the experimental data concerning the densification behavior of the ZnO/SiC composite system reported by De Jonghe et al. [L. C. De Jonghe, M. N. Rahaman, and C. H. Hsueh, Acta Metall. 34, 1467 (1986)]. The universal nature of this lattice for other composites is discussed with respect to site percolation theory. The application of this concept to powder compacts containing either whiskers or agglomerates is briefly discussed.