An improved grand-potential phase-field model of solid-state sintering for many particles

Abstract

Understanding the microstuctural evolution during the sintering process is of high relevance as it is a key part in many industrial manufacturing processes. Simulations are one avenue to achieve this understanding, especially field-resolved methods such as the phase-field method. Recent papers have shown several weaknesses in the most common phase-field model of sintering, which the present paper aims to ameliorate. The observed weaknesses are shortly recounted, followed by presenting model variations aiming to remove these deficiencies. The models are tested in the classical two-particle geometry, with the most promising model being run on large-scale three-dimensional packings to determine representative volume elements. A densification that is strongly dependent on the packing size is observed, which suggests that the model requires further improvement.

Revealing process and material parameter effects on densification via phase-field studies

“…The model employed in this paper is based on the recent works 11 , 17 , 19 . In the Supplementary Material a derivation of the model is given together with the necessary assumptions.…”

“…The concentration can be interpreted to be the vacancy concentration, which is low in the solid and high in the surrounding vapor. The meanings of the remaining terms are described in detail in Hötzer et al 11 and Seiz et al 17 . On all fields no-flux conditions are employed as boundary conditions.…”

“…This depends on the simulation state S in order to account for the Gibbs-Thomson effect. It is approximated via the concentration of a bulk grain at its average surface chemical potential 17 . Finally, the displacement jumps are connected to individual grain displacements u in a matrix equation 19 .…”

“…The parameters of the simulations are given in Table 1 , with more details on the choices being given in Seiz et al 17 , 19 . The diffusion and interfacial energy values approximate copper at 700 K, with the choice of inverse mobility being such that diffusion-controlled growth is achieved for all simulations.…”

“…In the past two decades, the phase-field method has been used by many researchers 7 – 15 to investigate the sintering process. More recent works have pointed out several weaknesses of these models 16 – 18 , which were rectified subsequently 17 – 19 . Based on these works, the present paper aims to elucidate several factors of interest in the solid-state sintering process: external pressure is often applied to speed up densification: capillary pressure acts as a driving force for sintering and applying external pressure enhances this.…”