PROCEEDINGS OF THE 2003 INTERNATIONAL SYMPOSIUM ON LIQUID METALS JOURNAL OF MATERIALS SCIENCE 39 (2 0 0 4 ) 7213 – 7219 Prediction of macrosegregation during the solidification involving a peritectic transformation for multicomponent steels L. THUINET, H. COMBEAU Laboratoire de Science et G ´ enie des Mat ´ eriaux M ´ etalliques, Ecole des Mines, Parc de Saurupt, 54042 NANCY Cedex, France E-mail: combeau@mines.inpl-nancy.fr Micro-macro segregation models are based on the multi-scale approach of the segregation, i.e., on the coupling of a macrosegregation model, which describes transport phenomena at the ingot scale, with a microsegregation model, which describes solidification at the scale of the primary or secondary dendrite arm spacing. The goal of this work is to illustrate the influence of the microsegregation phenomena on the macrosegregation. A microsegregation model for multicomponent steel alloys has been developed which takes into account solutal diffusion in solid and liquid phases, a correct description of the multicomponent phase diagram, and the variation of the local average solute concentration (open system). The peritectic transformation has been tackled and specific attention has been drawn on the accurate determination of the δ /γ and γ /liquid interface movements during solidification. Examples of micro-macro calculations obtained with this microsegregation model on ingot cases are presented and original results which illustrate specific effects of the peritectic transformation on macrosegregation are discussed. C  2004 Kluwer Academic Publishers Nomenclature Latin symbols w mass fraction (component) (%wt) k partition coefficient ¯ w average mass fraction of the calculation domain (component) (%wt) ¯ h average specific enthalpy of the domain calculation (J/kg) f mass fraction (phase) g volume fraction (phase) h specific enthalpy (J/kg) D diffusion coefficient (m 2 /s) r spatial variable (m) T temperature ( ◦ C) T liq liquidus temperature ( ◦ C) m ϕ1ϕ2 i local slope of the equilibrium surface ϕ1/ϕ2 for the solute element i ( ◦ C/%wt) K permeability (m 2 ) k c Kozeny constant t tortuosity Greek symbols ϕ phase δ ferrite γ austenite λ characteristic diffusion length (m) λ 1 primary dendrite arm spacing (m) λ 2 secondary dendrite arm spacing (m) ρ density (kg/m 3 ) β T thermal expansion coefficient (K −1 ) β i w solutal expansion coefficient of solute i (wt% −1 ) μ dynamic viscosity (Pa·s) Superscripts l liquid s solid 0 initial ϕ1/ϕ2 at the ϕ1/ϕ2 interface, where ϕ1, ϕ2 = δ, γ or liquid Subscripts i component 1. Introduction In an ingot, composition variations in alloy element can be observed at different scales: macrosegregation develops at the scale of the whole product, whereas microsegregation designs the segregation observed at the scale of dendrites. Several fundamental origins of macrosegregation have been identified and recently re- viewed [1], among them the liquid flow induced by thermal and solutal gradients which develop during so- lidification: liquid density is not uniform in the ingot, which causes thermo-solutal convection. A part of these gradients are due to microsegregation, since it induces at the dendrite scale heterogeneities in solute which can 0022–2461 C  2004 Kluwer Academic Publishers 7213