Sintering is a decisive step in the manufacture of ceramic materials since it defines the quality of the final product, thus defining its applications. The sintering or consolidation of a green body occurs by heating the material at temperatures below its melting point, but high enough so that diffusion is promoted. Here, the main driving force is the minimization of the free surface energy of a powdered compact through the reduction of the internal surface area associated with the pores. This leads to changes on the microstructure due to densification and grain growth. Even though sintering has existed for thousands of years, the sintering cycles to obtain ceramic products are still defined by previous work carried out under very specific sets of conditions or through trial and error approaches. These procedures can lead to a misuse of raw material and additives, and are time and energy consuming, thus they are economically expensive. Hence, modeling and simulation that aid define suitable sintering conditions to obtain the desired microstructure can significantly reduce planning costs. Several models have been developed to theoretically describe the effects of process variables over the properties of sintered materials, such as two-sphere models and the Master Sintering Curve (MSC). The latter is a combined-stage model widely used to design sintering cycles for solid-state and liquid-phase sintering. This approach allows the determination of the densification evolution over temperature and time, but it presents some limitations since important model parameters must be retrieved from experimental setups, hence they are valid only for specific sets of conditions. In addition, it fails to describe shrinkage and changes on the microstructure, which are essential to predict the properties of the product. Models based on the Discrete Element Method (DEM) provide a great opportunity to accurately forecast the evolution of the microstructure and the volumetric changes that occur during sintering. Besides from the densification evolution, sintering contact models coupled to DEM equations can also showcase effects due to particle rearrangement and flattening of particle contacts. So far, this methodology has been successfully applied for solid-state sintering, but the efforts regarding liquid-phase sintering (Figure 1) are scarce.

The simulation of sintering using a DEM approach has been investigated at the SPE in the past. Recently, the Thermo-mechanics coupled with Sintering (TMS) model has been developed within MUSEN to simulate non-isothermal solid-state sintering of alumina. This model allows the study of sintering starting from room temperature since it integrates heat transfer equations to evaluate the temperature evolution inside the particle packing. In the meantime, particle-particle interactions are calculated using a modified Hertz-Mindlin model that considers the viscoelastic nature of particles below sintering temperature, and a sintering contact model based on Parhami and McMeeking is activated when a minimum temperature is reached. Finally, the sintering model is stopped to avoid unrealistic results by overdensification. In this work, the TMS model will be further extended to simulate liquid-phase sintering of an alumina-borosilicate glass mixture, and will be validated based on experiments. The influence of liquid-forming phase fraction, heating and cooling rates, temperature and holding times will be assessed to determine their effect over the microstructure of the final product. This includes the evaluation of the kinetics of grain growth, and the determination of the porosity morphology depending on processing conditions. For the experimental validation of the model, the final properties of the sintered product will be assessed, namely density, grain size, and bending strength.