Sintering forces acting among particles during sintering by grain-boundary/surface diffusion

The microstructural evolution during sintering involves the formation and pinch-off of pore channels. The sintering of 3 particles in 3 dimensions is a simple model for studying the pinch-off of a pore channel. We simulate the solid-state sintering of 3 particles by using Brakke's Surface Evolver program, which incorporates coupled grain-boundary diffusion and surface diffusion. The pinch-off of pore channel divides the sintering process into 2 stages; the initial stage and the later stage. The contact area has a noncircular shape bounded by both surface triple junction and triple junction in the later stage. A general method is presented to determine the sintering force acting on the noncircular contact. The mechanical approach of densification, where the relative motion of particles is driven by both sintering force and applied force, is applicable not only for the initial stage, but also for the later stage.