Étude des macroségrégations induites par le retrait et la déformation thermomécanique lors de la solidification de la peau des produits sidérurgiques

Abstract : Mathematical expressions of segregation rates occurring during solidification with spongy deformation of an alloyed mushy zone have been derived from classical mass balance analyses [LesO3]. The boundaries of the domain considered for the mass balances deform with the same velocity as the solid phase: the reference frame is attached to the solid phase. The three variables needed to fully describe segregation within this "Lagrangian" approach are the mass of solid in the domain, the volume of the domain and the relative velocity of the liquid with respect to the solid. The main result is a mathematical expression for the local macrosegregation rate. The analysis is further extended to produce an expression for the local microsegregation rate that can be compared with a previously proposed expression [Fle67]. It appears that an additional term is found to enter into our expression. This term is proportional to the local strain rate multiplied by the ratio of the volume fraction of solid over the volume fraction of liquid. It is expected to become dominant when the mushy zone is fully developed (large value of the ratio) and when the strain can be transmitted through a coherent solid skeleton that deforms like a sponge. Still, the origin of the deformation remains arbitrary and the derived expressions could be used to quantify segregation due to the thermal contraction of the solid and liquid phases, the shrinkage associated with the phase transformations, and/or the mechanical deformation of the domain. The mathematical expression for the local macrosegregation rate is combined with a numerical one dimensional model of the heat flow previously developed for the study of directional solidification of an undercooled mushy zone using an Eulerian frame of reference [GanOO]. The local strain rate is first deduced from a simple thermomechanical analysis. It gives access to the velocity of the solid phase in a region of the mushy zone located below a given temperature, known as temperature of coherence. The value of the latter is arbitrarily fIXed. The velocity of the solid phase then enters the total mass balance for the determination of the liquid flow due to shrinkage and contraction of both the solid and liquid phases. Finally, the fields for the temperature, velocities of the solid and liquid phases, and average composition are deduced using a fully coupled iterative scheme. ln addition to inverse segregation close to the mold and negative segregation at the ingot end due to porosity formation [Rou95], segregation induced by deformation and growth undercooling of the columnar growth front are predicted. Application to the solidification of the skin of steel cast products agree qualitatively weil with experimental observations.
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http://docnum.univ-lorraine.fr/prive/INPL_T_2004_NGADIA_TAHA_N.pdf
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Submitted on : Thursday, March 29, 2018 - 12:36:42 PM
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Ngadia Tahane Niane. Étude des macroségrégations induites par le retrait et la déformation thermomécanique lors de la solidification de la peau des produits sidérurgiques. Autre [cond-mat.other]. Institut National Polytechnique de Lorraine, 2004. Français. ⟨NNT : 2004INPL088N⟩. ⟨tel-01750052⟩

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