Fumihiro Wakai

Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan

Frenkel and Kuczynski laid the foundation for understanding the sintering phenomena in particle scale, emphasizing the center-to-center approach and the neck growth in the initial stage. In the late 1980s the development of continuum mechanics led to a paradigm shift; the macroscopic strain rate is proportional to the driving force called sintering stress, and is inversely proportional to bulk viscosity. Both sintering stress and bulk viscosity are physical quantities that can be measured experimentally. From this mechanical point of view, the relative velocity between two spherical particles is described as a response to the sintering force acting on a circular contact, and is inversely proportional to the square of contact area, when the sintering occurs by coupled grain boundary diffusion and surface diffusion. It is well known that the sintering depends not only on temperature, applied stress, particle/pore size, relative density, but also on complex microstructure.  Therefore, it is a challenge for the modern sintering theory to understand how the macroscopic sintering stress and bulk visocity arise from microstructural evolution in the course of sintering. The question remains unanswered: is the concept of sintering force can be extended to the later stage where complex topological transformations of micrustructure occur? for example, pinch-off of pore channel, formation and disappearance of closed pore, grain boundary sliding, particle rearrangements, coarsening and grain growth. We give here some answeres by using simple but accurate geometrical models. This knowledge will help to develop realistic simulation method, and can be used to  check the validity of simulations such as discrete element method (DEM), kinetic Monte Carlo simulation + DEM, and phase field model + DEM, all of which incorporate the micromechanics in particle scale.