A thermodynamically consistent phase‐field model for viscous sintering

Abstract

A thermodynamically consistent phase-field model for viscous sintering is proposed. It is based on an energetic variational formulation that allows the governing equations to be analytically derived from a defined energy law. The conservation of mass is satisfied through the incompressibility assumption and the assumption that mass density is uniform initially within the particle compact while the balance of linear momentum is formulated from an energy dissipation law. The morphological changes of particles are described by the temporal and spatial evolution of a phase-field variable governed by a modified Cahn-Hilliard equation, and the motion of viscous mass flow is controlled by the Stokes equation incorporating the surface tension effect. The application of the phase-field model is illustrated by examining the effect of particle shape, initial contact angle and rearrangement effects on viscous sintering.

Effect of rigid body motion in phase-field models of solid-state sintering

“…Note that the advection term does not have to be based on a rigid-body motion model, it could also originate from solving a momentum transport equation. Hence it would be interesting to verify whether phase-field models for liquid-phase and viscous sintering [22,23] naturally include the proper scaling with chain length. These models do not introduce additional parameters such as ρ gb or include external forces, but rather can be derived thermodynamically consistently as done by [23] which ensures that the free energy is indeed minimized.…”

Viscous coalescence of unequally sized spherical and cylindrical doublets

“…Balemans et al, 24 Martı ´nez-Herrera and Derby 64 and Yang et al, 67 show excellent agreement, in neck growth as a function of time, between their numerical simulations and Hopper's model for equal cylinders. However, in all three publications the initial half-neck width is 0.1a o .…”

Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V

“…E.g., in the work [16,54] the δ GB is taken of the order of 1 nm that corresponds to the boundary layer of atomically clean interface between metallic grains. On the other hand δ GB is often assumed to be of the order of the mesh size (i.e., ∼1 µm) [51,55] or to have intermediate value, e.g., 60 nm [25] The results of the MD simulations discussed in the previous section will be used to estimate the effective width of the boundary layer δ gb , which is shown to be of the order of 1 µm. This value was used in the phase-field calculations below.…”