[Paper Review] Phase-field modeling of non-isothermal grain coalescence in the unconventional sintering techniques

Yangyiwei Yang, Min Yi+2 more|arXiv (Cornell University)|Jun 7, 2018

Solidification and crystal growth phenomenaMaterials Science38 references4 citations

TL;DR

This paper presents a thermodynamically consistent phase-field model for simulating non-isothermal grain coalescence during unconventional sintering processes such as spark plasma sintering and selective laser sintering. By coupling temperature-dependent free energy, order parameters for grain orientation and interfaces, and heat transfer kinetics, the model captures asymmetric morphologies and curved grain boundaries due to local temperature gradients, demonstrating accurate prediction of neck growth, porosity evolution, and grain shrinkage/growth in multi-particle systems.

ABSTRACT

A thermodynamically consistent phase-field model is developed to study the non-isothermal grain coalescence during the sintering process, with a potential application to the simulation in unconventional sintering techniques, e.g. spark plasma sintering, field-assisted sintering, and selective laser sintering, where non-equilibrium and high temperature gradient exist. In the model, order parameters are adopted to represent the bulk and atmosphere/pore region, as well as the crystallographic orientations. Based on the entropy analysis, the temperature-dependent free energy density is developed, which includes contributions from the internal energy (induced by the change of temperature and order parameters) and the order parameter related configurational entropy. The temperature-dependent model parameters are determined by using the experimental data of surface and grain boundary energies and interface width. From laws of thermodynamics, the kinetics for the order parameters and the order-parameter-coupled heat transfer are derived. The model is numerically implemented by the finite element method. Grain coalescence from two identical particles shows that non-isothermal condition leads to the unsymmetric morphology and curved grain boundary due to the gradients of on-site surface and grain-boundary energies induced by the local temperature inhomogeneity. More simulations on the non-isothermal grain coalescence from two non-identical and multiple particles present the temporal evolution of grain shrinkage/growth, neck growth, and porosity, demonstrating the capability and versatility of the model. It is anticipated that the work could provide a contribution to the research community of unconventional sintering techniques that can be used to model the non-isothermal related microstructural features.

Motivation & Objective

• To develop a thermodynamically consistent phase-field model for non-isothermal grain coalescence in sintering processes.
• To address limitations of classical models that assume isothermal and equilibrium conditions.
• To simulate realistic microstructural evolution in multi-particle systems with complex geometries and thermal gradients.
• To enable accurate modeling of unconventional sintering techniques involving high temperature gradients and non-equilibrium conditions.
• To incorporate temperature-dependent free energy, surface and grain boundary energies, and interface width from experimental data.

Proposed method

• A phase-field model is formulated using order parameters to represent bulk, pore, and crystallographic orientations.
• Temperature-dependent free energy density is derived from entropy analysis, including internal energy and configurational entropy contributions.
• Model parameters are calibrated using experimental data for surface and grain boundary energies and interface width.
• Kinetic equations for order parameters and heat transfer are derived from thermodynamic laws, ensuring consistency with energy conservation.
• The model is numerically implemented using the finite element method with weak forms of governing equations.
• The system of equations includes coupled evolution for order parameters, temperature, and heat flux, with variational formulations for stability and accuracy.

Experimental results

Research questions

• RQ1 How does local temperature inhomogeneity affect grain boundary curvature and morphological asymmetry during sintering?
• RQ2 What is the role of temperature gradients in inducing non-uniform neck growth and porosity evolution in multi-particle systems?
• RQ3 How do temperature-dependent surface and grain boundary energies influence grain coalescence dynamics under non-isothermal conditions?
• RQ4 Can the phase-field model accurately simulate grain shrinkage and growth in non-identical particle systems with thermal gradients?
• RQ5 To what extent can the model predict microstructural evolution in unconventional sintering techniques such as SPS and selective laser sintering?

Key findings

• Non-isothermal conditions lead to asymmetric grain morphologies and curved grain boundaries due to spatially varying surface and grain boundary energies induced by local temperature gradients.
• Simulations of two identical particles show that temperature inhomogeneity causes neck formation with asymmetric shape and non-uniform curvature.
• In multi-particle systems, the model successfully captures temporal evolution of grain shrinkage, neck growth, and porosity reduction.
• The model predicts realistic microstructural features such as pore elimination and grain boundary migration under non-equilibrium thermal conditions.
• The inclusion of temperature-dependent free energy and heat transfer kinetics enables accurate simulation of complex sintering dynamics in powder-based systems.
• The finite element implementation ensures robustness and accuracy in handling complex geometries and heterogeneous thermal fields.