Sintering Kinetics Across Pore Closure Transition Accounting for Continuous Increase in Grain Coordination with Density

Abstract

The influence of dihedral angle and particle coordination on the evolution of densification rate is investigated throughout the intermediate and final stages of sintering. From a review of literature data, heuristic expressions are proposed for representing different trajectories of evolution of coordination from the onset of skeleton formation up to full density. The influence of dihedral angle and coordination on the threshold density for pore closure is established by revisiting the Plateau–Rayleigh instability criterion. The intermediate and final stages are modeled using representative volume elements that do not restrict coordination to integer values. Computational results enlighten the interplay between coordination and dihedral angle on the evolution of sintering stress, bulk viscosity, and sintering rate. The results allow quantifying the amplitude of the drop of densification rate at pore closure transition. The monotonous increase of coordination with relative density brings about a monotonous increase of sintering rate at constant particle size. Simulations emphasize the beneficial effect of higher initial density and coordination in the green part.

Influence of Dihedral Angle and Grain Coordination on Densification Rate During Intermediate and Final Sintering Stages

“…As discussed elsewhere, the critical density ρ pc corresponding to the transition between the intermediate stage and the final stage is a function of n c and ψ. As the precise value of ρ pc is not addressed in this study, the results presented in the following have been calculated over the range 0.75 ≤ ρ ≤ 0.95 for the intermediate stage and over the range 0.85 ≤ ρ ≤ 1 for the final stage.…”

“…This observation stresses the importance of properly accounting for the variation in n c with ρ in the modeling of sintering kinetics: this issue is further analyzed in Ref. .…”

“…This effect is primarily due to the increase in the area of the grain boundaries when q increases and when n c decreases. Indeed, for the intermediate stage, relation (18) shows that K increases as the fourth power of the ratio R gb /R G . For the final stage, the main contribution to the increase in K with increasing grain boundary arises from the term À4lnx = À4ln(R in /R out ) in relation (27).…”

“…24 This issue is not addressed in this study. It is addressed in the companion paper 18 when analyzing how the monotonous increase in n c with q affects densification kinetics during the two stages and across the pore closure transition. Figure 1(c) represents the average Vorono€ ı cell when q > q pc .…”

“…[according to relations (1) and (2)], K varies as R G À3 in the case of a rheology controlled by grain-boundary diffusion 2,11 [see below, relations (18) and (32)]. It thus follows from relation (3) that the sintering rate _ q varies as R G…”