Capturing shrinkage and neck growth with phase field simulations of the solid state sintering

The suitability of the phase field method for the simulation of the evolution of the microstructure during sintering, which has been assumed for more than a decade, receives new impetus from the progress described in this paper. A zero force formulation for the calculation of the rigid body motion of powder particles is adapted to diffuse interface model of Cahn–Hilliard and Allen–Cahn type. In this approach, the rigid body motion ensures the mechanical equilibrium in the powder compound. For this aim, the derivative of the free energy with respect to the additional degree of freedom of rigid body motion was approximated by a force in the grain boundary caused by concentration differences there. The potential of the model is demonstrated by first 2D simulations. These are compared with 2D simulations results generated with a model, which previously showed good agreement with experimentally obtained sintering data in the 3D case. In this comparison good agreements are observed qualitatively as well as quantitatively, showing the plausibility of the new approach. (paper)