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Personne# Amin Rostamian

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thumb|Du bronze liquide versé dans des moules.
En métallurgie, un alliage est un mélange de plusieurs éléments chimiques, dont le principal constituant est un métal, et dont les caractéristiques sont

In materials science, lamellar structures or microstructures are composed of fine, alternating layers of different materials in the form of lamellae. They are often observed in cases where a phase

vignette|Microstructure d'origine organique : celle d'un œuf, mise en évidence par une source lumineuse.
Le concept de microstructure peut se définir indépendamment des matériaux considérés (métaux,

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Gamma titanium aluminide (γ-TiAl) based alloys are very interesting materials for structural applications at elevated temperatures owing to the combination of high specific strength, good oxidation, creep and fatigue resistance. However, their relatively poor ductility and fracture toughness remain important obstacles for their industrial applications in engineering components. The mechanical properties of these alloys, namely the poor room temperature ductility, as well as the yield stress, creep and fracture resistance, can be significantly improved by controlling the microstructure. These alloys undergo solid state phase transformations upon cooling from the high temperature α phase, which results in formation of different types of microstructures depending on the cooling conditions and the alloy composition. Low and moderate cooling rates lead to the precipitation of the γ phase as parallel plates within the α matrix, followed by the α → α2 ordering reaction. As a result of this transformation, the characteristic lamellar structure of TiAl is produced. Rapid cooling leads to a massive transformation from α to γ. It has been shown that the massive microstructure can be used as a precursor to obtain a refined microstructure through a subsequent tempering in the α + γ phase field. However, obtaining a fully massive microstructure at all depths in a component can be difficult to achieve. Numerical simulation of microstructure formation can be used as a tool to anticipate the microstructure distribution in a component depending on the local chemistry and cooling conditions. The main objective of this work was to develop microstructure models describing the formation of the massive and lamellar microstructures. Two distinct modeling approaches have been used. The first approach is a deterministic model having for objective to predict the microstructure distribution in a cast and heat treated component. The model was designed to be integrated into a FEM or FDM heat flow solver in order to calculate microstructural quantities such as the proportion of phases and lamellar spacings at each nodal point of the mesh. The modeling approach is based on a combination of nucleation and growth laws which take into account the specific mechanisms of each phase transformation. Nucleation of massive and lamellar γ is described with classical nucleation theory, accounting for the fact that nuclei are formed predominantly at α/α grain boundaries. Growth of the massive γ grains is based on theory for interface-controlled reactions. A modified Zener model is used to calculate the thickening rate of the lamellar γ precipitates. The model incorporates the effect of particle impingement and coverage of the nucleation sites by the growing phases. The driving pressures of the phase transformations are obtained from Thermo-Calc based on the actual temperature and matrix composition. The deterministic approach was used to calculate CCT diagrams and lamellar spacings, which showed to be in good agreement with experimental data obtained from dedicated heat treatment experiments and from the literature. The model permitted investigating the influence of cooling rate, alloy chemistry and average α grain size upon the amount of massive γ and the average thickness and spacing of the lamellae. In particular, it indicated that the Al depletion of the α phase during lamellar precipitation seems to play an important role in the suppression of the massive transformation at moderate cooling rate and in the large lamellar spacings observed at low cooling rate. It was also found that Nb additions enhance the formation of massive γ by lowering the lamellar transformation temperature, increasing the T0 temperature and slowing down the lamellar growth due to the low diffusivity of Nb. The second approach was a cellular automaton (CA) model, which was used to describe the formation of the lamellar microstructure on the scale of a few microns. The objective of this approach was to make a direct description of the growth of a precipitate by an interfacial ledge mechanism, and then to evaluate whether the simplifications made in the deterministic model regarding this mechanism are appropriate. The modelling approach is based on the resolution of the diffusion equations in the α and γ phases. The ledge structure at the α/γ interface is described by introducing different types of cells in the CA grid. The CA model was used to describe the formation of the lamellar microstructure at isothermal conditions and at various cooling rates. The thickening kinetics of the lamellae, the lamellar spacings and the overall kinetics of the transformation were calculated with this approach and were compared with the results obtained with the deterministic model. It was found first that the thickening kinetics of the lamellae calculated with the deterministic model are slower than those calculated with the CA model. It was established that the method used in the deterministic model to account for the growth by a ledge mechanism always leads to a growth exponent of 0.5, which is characteristic of diffusion controlled reactions. In contrast, the CA approach yields growth exponents that are comprised between 0.5 and 1, as it is expected for growth in a mixed diffusion/interface controlled mode. The incorporation of a kinetic undercooling term into the deterministic model was found to be an appropriate correction. A good agreement was finally obtained in terms of lamellar spacings and overall kinetics. The underestimated thickening kinetics of the deterministic model was observed to be partly compensated by a higher nucleation rate at the beginning of the transformation. The overall kinetics of the lamellar transformation calculated with the deterministic model was found to be sufficiently accurate to correctly predict the competition between the lamellar and massive microstructures.

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A phenomenological modelling approach has been developed for the description of die massive and lamellar microstructures which form in gamma-TiAl alloys at high and moderate cooling rates, respectively. The nucleation of both massive and lamellar gamma is described by classical heterogeneous nucleation theory which takes into account that nuclei are formed predominantly at a grain boundaries. The thickening rate of the lamellae is described with a modified multicomponent Zener model of precipitation while the growth rate of massive gamma is calculated with an expression for interface-controlled reactions. The model, which is coupled with a thermodynamic database, permits to investigate the influence of the alloy composition and cooling rate on the proportion of massive and lamellar gamma. Calculted CCT diagrams showed good agreement with experimental data for binary alloys. The approach was also used to discuss the effect of Nb additions on the transformations kinetics and on the competition between lamellar and massive microstructures. The calculations illustrate how Nb additions tend to favour the massive microstructure by slowing down the growth of lamellar precipitates.

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A phenomenological modelling approach has been developed to describe the massive transformation and the formation of lamellar microstructures during cooling in binary gamma titanium aluminides. The modelling approach is based on a combination of nucleation and growth laws which take into account the specific mechanisms of each phase transformation. Nucleation of massive and lamellar gamma is described with classical nucleation theory, accounting for the fact that nuclei are formed predominantly at alpha/alpha grain boundaries. Growth of the massive gamma grains is based on theory for interface-controlled reactions. A modified Zener model is used to calculate the thickening rate of the gamma lamellar precipitates. The model incorporates the effect of particle impingement and coverage of the nucleation sites by the growing phase. The driving pressures of the phase transformations are obtained from Thermo-Calc based on the actual temperature and matrix composition. CCT diagrams and lamellar spacings calculated with the model are in good agreement with experimental data obtained from dedicated heat treatment experiments and from the literature. The model permitted investigating the influence of cooling rate, alloy chemistry and average alpha grain size upon the amount of massive gamma and the average thickness and spacing of the lamellae. In particular it indicates that the Al depletion of the alpha phase during lamellar precipitation seems to play an important role in the suppression of the massive transformation at moderate cooling rate and in the large lamellar spacings observed at low cooling rate. (C) 2008 Elsevier Ltd. All rights reserved.