Theory of sintering in presence of pressure and torque
Experiments like the sintering of single crystal spheres on a single crystal plate, the sintering of particle rows or 2D arrangements of powder particles as well as recent experiments by in-situ Synchrotron Computer Tomography show movements of entire particles beyond the particle center approach described by the well-known two particle model. Several attempts exist to describe these cooperative material transport processes by an analytical model of the sintering of two wires by grain-boundary diffusion. The described mechanisms are either rotations caused by asymmetric sintering necks or the application of a torque or changes of the rate of sintering by a normal stress in the sintering neck. To develop a more comprehensive model of sintering, volume diffusion was included in addition to grain-boundary diffusion and all driving forces mentioned above are used. As a result, the influence of normal stress, torque, and ratio of the sintering neck curvatures on the stress along the contact grain boundary, the diffusion current and the rate of removal along the sintering neck are shown. The contribution of volume diffusion and grain-boundary diffusion to sintering was also investigated, confirming that a large sintering neck and high sintering temperatures result in a dominating influence of volume diffusion. The shrinkage rate and the rate of rotation provided by this model were used in a subsequent numerical simulation. For several stages of sintering, the influence of particle radius and sintering temperature on the rolling angle of sintering particles was analyzed in 2D. Furthermore, the impact of external normal stresses on the rolling angle is shown. The simulation model gives a surprising result: The speed of wire rolling shows the same behavior as sintering kinetics-a high speed for small particles, small sintering neck diameter and high temperature, but the cumulated rolling angle for small particles is low compared to that for larger particles. Finally, a new approach for simulating particle rotation and rolling caused by torques due to grain-boundary anisotropy in 3D is presented, which is based on an existing Discrete Element Method sintering model. This model is applied to a row of particles confirming previous observations from the 2D sintering simulations.