Introducing long-range particle interactions into phase-field models of sintering using continuum mechanics principles

Abstract

This work presents a novel meso-scale phase-field model of solid-state sintering that couples the continuum thermodynamics and continuum mechanics governing the sintering process. The microstructure evolution is described by a system of equations consisting of one Cahn–Hilliard equation and a set of Allen–Cahn equations to distinguish neighboring particles. These equations are coupled with the balance of momentum of linear elasticity. The latter is defined by applying the Wang sintering forces as distributed body loads to compute advection velocities for the phase-field equations. This introduces long-range interaction mechanisms between particles. Our numerical implementation uses monolithic coupling and implicit time integration. It is based on the hpsint code, an efficient matrix-free finite element solver for phase-field simulations of many-particle sintering processes with advanced grain tracking capabilities and block preconditioning. With a simple academic test setup that analyzes a chain of identical particles we investigate in detail the problems of the original sintering model proposed by Wang around two decades ago and then clearly demonstrate how our new coupled approach resolves them. We then study a series of two- and three-dimensional benchmark problems to demonstrate the advantages of our novel model that clearly exhibits invariance of shrinkage regarding the model size (number of particles in the packing) and renders microstructures whose metrics agree well with estimates based on analytical and experimental studies.