Scale-bridging studies of the elastic contributions to initial microstructure formation in the eutectic system Ti-Fe
Mechanische Eigenschaften von metallischen Werkstoffen und ihre mikrostrukturellen Ursachen
Zusammenfassung der Projektergebnisse
The motivation for this project constitutes a key issue for the further development of the basic understanding of the microstructural evolution in Fe-Ti eutectic alloys at different cooling rates. Tibased alloys have been suggested for commercial applications with a great potential due to their high strength (~1000 MPa) and good corrosion resistance. In this joint project between the group of Prof. Dr. Eckert at IFW Dresden (IFW), Prof. Dr. Neugebauer at the MPIE at Düsseldorf and Prof. Dr. Emmerich at Bayreuth University (MPS) a quantitative and systematic understanding should be acquired on evaluating the effect of cooling rate on microstructure formation at the initial stages in a eutectic model system, i.e. Ti-Fe. To achieve this, experiments in the IFW were combined with phase-field simulations in MPS as well as with ab initio calculations of elastic constants at the MPIE. MPS Bayreuth: Within the project, the MPS developed a phase-field model for the eutectic solidification which incorporates the diffusion in the liquid phases as well as the energy contributions in the solids during solidification. The phase-field model described in was used to simulate the solidification of the real eutectic material system Ti70.5Fe29.5 and calibrated by several parameter studies and numerical simulations for the directional solidification of this eutectic alloy. The simulated solidification microstructure of the alloy system was then compared with those obtained from the experiments made IFW Dresden. As a result, the simulation with many grains in a large domain with optimized parameters results in a microstructure comparable to that of the experiments. Furthermore, the dependency of the lamellar spacing vs. the undercooling was estimated. It could be shown that, with time, lamellar spacing converges to the steady state value and decreases with increasing undercooling according to the theoretical prediction. However, at large undercooling deviations from the theoretical predictions were observed because of kinetic effects. Moreover, we refined the phase-field model by including the elastic free energy and the orientation free energy to simulate the influence of elastic misfit between different phases as well as different grain orientations occurring in the real material systems. This model was applied to first parameter studies to evaluate the effect of elastic misfits on the microstructure formation during directional solidification of a eutectic Ti70.5Fe29.5 alloy. For these simulations elastic data calculated at the MPIE Düsseldorf were introduced. The results show that the undercooling as well as the extreme value of λm increase with increasing elastic fields (εm) and that the lamellae are stable in larger spacing in the presence of misfit strain. In a further phase we implemented the multiple orientations of the nuclei into our elastic phasefield model by introducing a non-conserved orientation field and the orientation free energy, respectively. Using this extended model, the obtained microstructure is similar to those seen in the experiment but in the experimental micrograph the presence of directionality can been seen by the preferential growth direction of the lamella which could arise due to experimental conditions. In the simulation, this is absent and hence results in symmetric growth. IFW Dresden: During the project duration, moulding and casting of different TiFe phases (Ti100-xFex; x=15, 29.5 and 49.5 at.%) with different process techniques under non-equilibrium conditions was performed. The microstructure of the specimens was characterized in different directions by SEM, TEM, EDX, XRD and the elastic properties of the specimens were measured by ultrasonic measurements. Comparing the results with the ab initio calculations of the MPIE Düsseldorf shows a good agreement. The preparation of the eutectic TiFe alloy under non-equilibrium conditions in different solidification devices exhibits different ultrafine eutectic structures (β-Ti(Fe))+TiFe ss). After the microstructural investigations of the different prepared samples a correlation between lamellae spacing, colony size and lattice parameters were done. By measuring the eutectic lamella spacing of the directional solidified samples calculation of the cooling rate of the eutectic TiFe was done. With this findings an estimation of the cooling rate of the rapidly solidification devices (e.g. cold crucible device) was possible. To clarify the structural features of both eutectic phases more in detail, XRD analysis for the single phase - and eutectic material was done. The reflections of the different TiFe samples yield lattice parameters, which agree very well with the results of ab initio calculations (MPIE). Mechanical tests showed that the eutectic TiFe alloys exhibit compressive strengths between 2200 and 2700 MPa and plastic strains between 7 and 19% in compression. Further the compressive strength of both single-phase samples are about 1000 MPa lower compared to the eutectic material. The total strain of the β-Ti(Fe) is significantly higher than the total strain of the TiFe. This finding is consistent with the ab initio calculations from the MPIE of elastic constants of both phases which show that β-Ti(Fe) is significantly softer than FeTi. MPIE Düsseldorf: During the project duration, quantum-mechanical calculations of thermodynamic, structural and elastic properties of different Fe-Ti phases have been performed. Selected computed results were compared with experimental finding at the IFW Dresden in order to verify/estimate the accuracy of the theoretical results. After benchmarking the used computational approach, the ab initio calculations have been (i) employed to interpret experimental findings and (ii) further extended to phases from a broader range of Ti concentrations that are specifically important for early stages of microstructure formation but are not directly accessible experimentally due to their metastable nature. The computed compositional dependencies in formation energies and elastic parameters as well as calculated interface properties were then provided to the MPS Bayreuth for the phase-field simulations of the time evolution of microstructural patterns in Fe-Ti alloys that are computationally prohibitive for quantum-mechanical calculations at the IFW.
Projektbezogene Publikationen (Auswahl)
- Phase-Field Modeling of Elastic Effects in Eutectic Growth with Misfit Stresses, AICES Technical Reports, AICES-2010/07-1, (2010)
Z. Ebrahimi, J. L. Rezende, J. Kundin
- Anisotropic mechanical behavior of ultrafine eutectic TiFe cast under non-equilibrium conditions, Intermetallics 19, 327-335 (2011)
A. Schlieter, U. Kühn, J. Eckert, W. Löser, T. Gemming, M. Friák, and J. Neugebauer
- Methodological challenges in combining quantum-mechanical and continuum approaches for materials science applications, Eur. Phys. J. Plus 126, 101 (2011)
M. Friák, T. Hickel, B. Grabowski, L. Lymperakis, A. Udyansky, A. Dick, D. Ma, F. Roters, L.-F. Zhu, A. Schlieter, U. Kühn, Z. Ebrahimi, R. A. Lebensohn, D. Holec, J. Eckert, H. Emmerich, D. Raabe, and J. Neugebauer
- First-principles study of the thermodynamic and elastic properties of eutectic Fe–Ti alloys, Acta Materialia 60, 1594 (2012)
L.-F. Zhu, M. Friák, A. Dick, B. Grabowski, T. Hickel, F. Liot, D. Holec, A. Schlieter, U. Kühn, J. Eckert, Z. Ebrahimi, H. Emmerich, J. Neugebauer
(Siehe online unter https://doi.org/10.1016/j.actamat.2011.11.046)
