A numerical model for the description of the lamellar and massive phase transformations in Ti-Al-Nb alloys

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.

Numerical simulation of solid state phase transformations in gamma-TiAl alloys

Amin Rostamian

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.

EPFL2009

A numerical model for the description of the lamellar and massive phase transformations in TiAl alloys

Alain Jacot, Amin Rostamian

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.

Elsevier2008

Modelling oriented investigations of primary radiation damage in ultra high purity Fe and FeCr alloys

Anna Prokhodtseva

In the quest of the structural materials for the future fusion reactor, it has been shown that ferritic/martensitic (F/M) steels are very promising candidates, with a good radiation resistance in terms of damage accumulation in the microstructure relative to for example austenitic steels. However, our ability to predict their response to irradiation in such harsh conditions is still not satisfactory. In this view, there is a critical need for information on the primary damage occuring in this materials class, as input to the multiscale modelling of the irradiation effects, including the impact of He and H. Despite numerous studies in the last 50 years, there is still lack of knowledge in many areas of the irradiation response of the microstructure of ferritic steels. This is due to the complexity of these materials, for they contain numerous alloying elements, grains boundaries and precipitates. The strategy nowadays to identify basic mechanisms of primary damage is to investigate so-called model alloys of those, which allows parametric studies in simplified structures. In this work ultra high purity Fe and Fe(Cr) model alloys were investigated in a transmission electron microscope (TEM) under ion irradiation in an attempt to better understand the fundamental mechanisms of radiation damage starting from the lowest doses, and the dependence on Cr content. Attention is also paid to the effects of He and H. Radiation induced dislocation loops and cavities were quantified. This study provides data for validation of the modelling efforts. Single, dual and triple beam ion irradiations were performed in JANNuS facility located on two sites, in Orsay and in Saclay in France. In Orsay, electron transparent thin foils of UHP Fe, Fe -5, -10 and -14Cr were irradiated in situ in TEM as a single beam experiment with 500 keV Fe+ ions and as a dual beam experiment with 500 keV Fe+ and 10 keV He+ ion beams, to a dose of 1 dpa with and without 1000 appm/dpa He at room and liquid nitrogen temperatures in order to observe the very first defects, desirably before their thermal evolution. Effects of dose rate on the produced damage were assessed in UHP Fe. The impact of He and Cr on defect accumulation was scrutinized in terms of the number density, size and Burgers vector of the visible defects. Special care was taken in the analysis of the TEM micrographs, for which new techniques were developed, with a particular one to determine the Burgers vector of a dense dispersion of fine nanometric defects. Emphasis was put on the identification of the loops Burgers vector, which is considered to be either a0〈100〉 or 1/2 a0〈111〉 in ferritic materials. 2 In order to study the effect of the free surfaces of the electron transparent thin specimens on the irradiation induced microstructure, the results obtained for TEM thin foils were compared to bulk samples that were irradiated ex situ in Saclay in single beam experiments with 24 MeV Fe8+ ions, and dual beam ones with 24 MeV Fe8+ to 1 dpa and 2 MeV He+ ions 1000 appm/dpa He at RT. To study synergistic effects of He and H a triple beam bulk irradiation with 24 MeV Fe8+, 2 MeV He+ and 0.6 MeV H+ ions, to 1 dpa, 1000 appm/dpa He and 4000 appm/dpa H at room temperature was preformed. From the bulk specimens thin lamellae were extracted by focused ion beam, which allowed the TEM observation of the damage through the whole implanted range of about 3.5 μm. In this way, the effect of irradiation with and without He and synergistic effects of simultaneous He and H implantation on the produced defects were assessed. In addition, radiation induced hardening was assessed by nano-indentation and related to the radiation induced microstructure. The analysis shows that in thin foils of UHP Fe the defect population is dominated by a0〈100〉 defects, while in presence of He it is dominated by 1/2 a0〈111〉 loops after irradiation to 1 dpa. It indicates that helium stabilizes mobile 1/2 a0〈111〉 loops, which in thin foils otherwise escape to 2 the free surfaces. Irradiation to the lowest dose of 0.05 dpa resulted in the production of either increased ratio of 1/2 a0〈111〉 loops, compared to the highest dose, or in the entire population of 2 1/2 a0〈111〉 loops in all materials in single and dual beam. In bulk UHP Fe and Fr(Cr) samples 2 after single and dual beam irradiation mainly 1/2 a0〈111〉 loops and few a0〈100〉 loops were 2 observed, but of smaller size than in thin foils, emphasizing the effects of free surfaces on the type of produced loops. It is thus inferred that 1/2 a0〈111〉 loops dominate the early loop 2 2 population and visible a0〈100〉 loops observed in UHP Fe and Fe(Cr) thin foils stem from addition and/or absorption reactions between 1/2 a0〈111〉 loops. It follows that these reactions 2 are reduced by the presence of He, which may eventually impede the formation of a0〈100〉 loops, leaving a loop population dominated by 1/2 a0〈111〉 loops. The same type of reactions 2 are valid for Fe(Cr) alloys, but the reduction in mobility of 1/2 a0〈111〉 loops by Cr in the single 2 beam case and the synergistic effects of He and Cr after dual beam irradiation result in a mixed population of 1/2 a0〈111〉 and a0〈100〉 type loops. This confirms the idea that the formation of 2 visible a0〈100〉 loops is promoted by the presence of free surfaces. Irradiation of UHP Fe thin foil at liquid nitrogen temperature confirmed the assumption of initial 1/2 a0〈111〉 loops. These then escape to the free surfaces after warming to RT, the more so 2 in the thinnest regions of the sample leaving a loop population dominated by a0〈100〉 loops. In single beam irradiated UHP Fe no dependence of the total density of defects or their Burgers vector on the rate of irradiation was observed. However, in the presence of He, only 1/2 a0〈111〉 2 loops formed under higher dose/implantation rates, while at the lowest dose rate results were similar to the single beam. This observation is attributed to the local increase of the effective He/defect ratio in the case of the high dose rate due to the increased temporal overlap of displacement cascades. Regarding mechanical properties, it appears that hardness of the as received materials increases with increasing Cr content. Following irradiation there is a significant hardening, which is not monotonous with Cr content, and which increases for all materials when irradiated together with He, and the more so when irradiated simultaneously with He and H. Hardening relates well to the observed microstructure and is the largest for Fe-5Cr.