Phase-field simulation of sintering and related phenomena

烧结,相场法模拟

Phase-field simulation of sintering and related phenomena –A

vacancy diffusion approach

Klara Asp *,John A

˚gren Division of Physical Metallurgy,Department of Materials Science and Engineering,Royal Institute of Technology (KTH),SE-10044Stockholm,Sweden

Received 15September 2005;received in revised form 28October 2005;accepted 1November 2005

Available online 27December 2005

Abstract

A phase-field model of sintering and related phenomena in a two-phase system and in a multi-phase system is presented.We consider diffusion of vacancies as the atomic mechanism for redistribution of material and we will use the familiar model of thermal vacancies in a crystal as our energy formulation.The solid material will thus be characterized by a low vacancy content and the surroundings by a very high vacancy content and a very low content of atoms.The surface of the solid body will be characterized by a continuous variation in vacancy content.The temporal development of particles during solid state sintering with effects such as wetting is shown in various simulations.

Ó2005Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

Keywords:Sintering;Phase-field models;Surface energy;Dihedral angle

1.Introduction

Sintering is a surface-energy driven process of consider-able technical importance.It is the basis for powder metal-lurgy,i.e.,materials that are difficult to produce with conventional casting may be produced by compacting a powder and sintering it to a solid body.Cemented carbides,cermets and ceramics are technologically important exam-ples.The decrease in total interfacial energy yields a driving force for various diffusion processes that lead to a lowering of porosity and a densification of the material.Many other processes of technological importance are governed by the same physics,e.g.,coarsening of particles,grain-boundary etching,etc.

The purpose of the present work is to consider a simple but physically realistic model and apply the phase-field approach to simulate sintering of a pure substance.The model will also,in a later stage,be extended to multicom-ponent alloys.To some extent sintering has already been analyzed by means of the phase-field method by other

authors,see for example Refs.[1,2].However,we feel that the previous approaches are less suitable for extension to multicomponent systems.For a pure component sintering involves an interfacial-energy driven redistribution of material.In principle this may be achieved by convective flow or by diffusion.Here we shall consider vacancy diffu-sion as the atomic mechanism for redistribution of mate-rial.In the first section we will summarize the vacancy model and then describe its phase-field formulation.We will then present the results of a number of simulations.The vacancy model is only capable of representing redistri-bution of material,i.e.,changes in density,but not orienta-tion differences between different http://www.360docs.net/doc/info-884a07f57c1cfad6195fa7a3.html ually,grains with different orientations are involved and sintering will then involve grain-boundary diffusion and grain-boundary migration.Moreover,different phases are usually of inter-est.It is thus necessary to include additional variables in the simulations.This will be discussed in Section 4.2.The vacancy model

The present work will be derived from the familiar model of thermal vacancies in a crystal.The solid material

1359-6454/$30.00Ó2005Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

doi:10.1016/j.actamat.2005.11.005

*

Corresponding author.Tel.:+4687909131;fax:+468207681.

E-mail address:john@mse.kth.se (K.Asp,J.A

˚gren).

Phase-field simulation of sintering and related phenomena

Phase-field simulation of sintering and related phenomena

Phase-field simulation of sintering and related phenomena

http://www.360docs.net/doc/info-884a07f57c1cfad6195fa7a3.html

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