Modelling sintering at particle scale using variational and molecular dynamic methods

Sintering is the thermal process that uses powders to form a new dense product by increasing temperature but holding it under the melting point of the material in use. Modelling the sintering process is important for fundamental understanding the behaviour of the particles during the sintering process instead of through empirical experimental work. In the first part of this thesis, a simplified method is developed to model the solid state sintering process which depends on the coupling between grain boundary and surface diffusion. A curve fitting method was developed to create a new relationship that relates the chemical potential at the junction of the grain-boundary and free surface to the neck size and the ratio of grain-boundary diffusivity over surface diffusivity. This relationship enables the de-coupling between the two diffusional processes when modelling the sintering process. The sintering process can, therefore, be separately modelled from the surface diffusion process, which greatly simplified the model for problems involving many particles such as those in a discrete element model. The results of the curve fitting method were first compared with the analytical Coblenz equations to allow for the validation and proofing of the new method in terms of modelling the sintering process; thereafter, comparisons were made with the full finite difference model using two parameters, namely diffusion coefficient ratio and applied stress. The curve fitting model matched well with the full finite difference model for the two parameters. In the second part of this thesis, two stages were undertaken: firstly, the new method was used in a variational model to simulate the two copper particles, and was compared with a new curve fitting-finite difference method for two sintering ratios. The variational model results were in good agreement with the new curve fitting-finite difference method. Secondly, multiple particles of copper were used in a variational model to simulate selective laser sintering for 27 copper particles. Laser scan speed, laser power, and particle temperature were collected from the COMSOL model, after which the particle temperature was used in the variational model to calculate the neck growth and shrinkage ratios between particles for different particle sizes. In the third part of this thesis, a molecular dynamics simulation code, LAMMPS, was used to investigate and understand the behaviour of nano-copper in the sintering process. Firstly, the melting temperature of nano-copper for different nanoparticle sizes was calculated and compared to four analytical models, after which neck size and shrinkage ratios were determined and compared with different diffusion mechanisms. The melting temperature numerical results matched well with the analytical nano-copper model. The hollow nano-copper improved the sintering process compared to solid nano-copper. Nanoparticle sintering has different behaviours comparing to micro-particle sintering. The nanoparticle sintering process is faster than for microparticle sintering; moreover, the melting temperature of the nanoparticles changed depending on size, when compared with microparticles where the melting point was constant.