Modeling Coupled Multifield Processes

Abstract

10.1 Introduction In many applications, multifield models arise from ad escription of thermo-chemical reactions occurringi nd eformable multiphase solids (Figure 10.1). Relevante xamples include certain problems of environmental mechanics con-cerned with the detrimental chemical attack on solids by volatile gases or liquid solutes whichc ome in contactw ith structural surfaces and then dif-fuse into the subsurface.T he subsequentr eactions lead to loss of structural integrity. 1 In this chapter, ar elatively general multifield model is developed whichd escribes the diffusion of ad ilute solute into ah eterogeneous solid ma-terial, the subsequentr eactions, the productiono fh eat, the changes in the stress fieldsa nd the evolution of material changes andi nelastic strains within the solid. The modelinga nd solutiona lgorithms are general enough to be ap-plicable to aw ide range of long-term thermo-chemo-mechanical phenomena associated with damagei nm aterials with heterogeneousm icrostructure. For experimental and theoretical overviews, we refert he reader to the serieso f works by Huet and coworkers [90]-[100].F or general overviews in the area of heterogeneousm aterials seeN emat-Nasser and Hori [151]. Although the emphasis will be on thes imulation of long-term multifield phenomena, the analysis in this chapteri sa lso applicable to shorter time-scale problems in-volving thermo-chemical processing suchasself-propagating high-temperature synthesis (SHS), wherebyc hemical reactions arei nitiatedo nt he surface of a material to be processed. In the method, the substantial heat evolved by surface chemical reactions sustain and propagate thermo-chemical processes. This approach is ar elatively new economical way of manufacturing advanced materials. Forexample by initiatingahighly exothermicsurface thermalreac-tion between bonded titanium powder in anitrogen gasatmosphere, an initial amounto ft itanium-nitride, Ti(s)+1/ 2 N 2 (g)=TiN (s), whichi sad esirable product,isproduced. Thisprocess releasesasubstantial amountofheat, which 1 This chapter followsf rom work found in Zohdi [250] and [251].