A sub-granular scale model for solid state free sintering : results on the evolution of two grains
Résumé
A sub-granular model development for solid state sintering of ceramics is ongoing to describe grain and pore size
evolution during a free (or under gas pressure) sintering.
Local changes in principal curvature radii at grain free surfaces and grain boundaries induce an extra stress upon the
outer boundaries of the grains. The latter are regarded as single crystals, of elastic constitutive law. Navier-Lamé equations
resolution in the bulk of each grain gives the 3D-displacement field and hence the density of the elastic mechanical energy.
Resulting Gibbs free energy variations along the grain interfaces (free surfaces and grain boundaries) induce surface and
grain boundary mass transport (Fick’s first law). Since matter is almost incompressible, locally accumulated matter on
grain surfaces makes the surface move (second Fick’s law). This results in an irreversible shape evolution.
A 3D-software has been designed. At each time step the Navier-Lamé equations are solved using a finite element method
and Fick’s second law is treated by a finite volume-like method enabling boundary nodes to move in an irreversible way.
Continuous media mechanics is taken as the origin of grains evolution although the granular nature of matter remains the
core of the model. The software has been developed for the simplified case of a chemically homogeneous material. Results
referring to the evolution of two initial spherical grains of the same size are checked against Coble’s works extended by
Coblenz in the case of grain boundary and surface diffusion. A second simulation is compared to Coble’s model for grain
boundary and volume diffusion. Discrepancies appear to be mainly attributed to the fineness of the mesh which accounts
for the real curvature in the vicinity of the grain boundary.