MICRO-MACRO RELATIONSHIPS FROM DISCRETE ELEMENT SIMULATIONS OF SINTERING

A two-scale modeling framework for sintering processes has been presented. Formulation of the micromechanical model of sintering developed in the discrete element method and basic relationships in the macroscopic model of sintering have been briefly reviewed. The methodology to determine macroscopic quantities-stress, strains, and constitutive viscous properties-from the discrete element simulations has been presented. This methodology has been applied to modeling of NiAl sintering. First, the discrete element model (DEM) has been calibrated by fitting the numerical densification curve to the experimental data. The DEM model with calibrated parameters has been used in simulations specially conceived to give macroscopic viscous moduli of the sintered material. Using the averaging procedures macroscopic stresses and strains have been calculated. Strain rates have been obtained differentiating the strain curves with respect to time. Finally, the viscous constitutive properties of the sintered material have been determined. The dependence of the shear and volumetric viscous moduli on the relative density (or equivalently) on the porosity has been obtained. It has been found that the numerical simulations predict a similar dependence as that assumed in the phenomenological macroscopic models. Thus, the validity of the micro-macro relationships obtained from the discrete element simulations of powder sintering has been confirmed. The proposed methodology allows us to use the discrete element model in the framework of multiscale modeling of sintering.