Study of nanometer-scaled lamellar microstructure in a Ti–45Al–7.5Nb alloy – Experiments and modeling
Introduction
Intermetallic titanium aluminides are innovative materials for application in aero-engines and combustion-engines [3], [4]. In two-phase γ-TiAl based alloys the mechanical properties are often determined by the presence of a lamellar microstructure which can be substantially varied by modifying the length scale between the internal γ-TiAl/α2-Ti3Al heterophase as well as γ-TiAl/γ-TiAl homophase boundaries [5]. In γ-TiAl based alloys, a lamellar microstructure can be obtained from the disordered α-phase or the ordered α2-phase by different routes. Route I is a slowly cooling from the single α-phase field region, i.e. the following reactions are taking place: α → (α + γ)Lamellar → (α2 + γ)Lamellar The lamellar spacing can be controlled by the applied cooling rate through the (α + γ)-phase field. Depending on the cooling rate an average lamellar spacing in the range of 0.1–1 μm can be adjusted [6]. For further information we refer to recent papers, dealing also with the kinetics of the microstructure, by Hazotte and co-workers [7], [8], [9], [10], and the preceding papers [11], [12]. In order to produce ultra-fine lamellar structures alloys with average lamellar spacing well below 100 nm a different route has to be applied. To this end route II uses the transformation from α → α2 → (α2 + γ)Lamellar by rapid cooling from the α-phase field region and subsequent aging below the eutectoid temperature, see [13] and references therein. With such a heat-treatment ultra-thin γ-lamellae, exhibiting an average thickness below 10 nm, are formed in supersaturated α2-grains, for details see chapter 2 and [13]. The goal of the present paper is to develop a model being able to predict both the dimension of such a lamella and its kinetics. The model employs continuum micromechanics and thermodynamics and starts with a transformation condition, see e.g. [14], and later also applied to twinning, see e.g. [15]. We would like to mention that we avoid any phenomenological (or rather heuristical) description as used e.g. in [16], where curvature-driven thermodynamic forces are applied to describe the longitudinal extension of lamellae.
Section snippets
Experimental and results
The experimental detail as well as a comprehensive description of the results were the content of a previous paper in this journal [13]. However, to give the reader a better introduction to following theoretical approach, the most important results are recapitulated and supplemented by recent results. For the investigation a high Nb containing Ti–45Al–7.5Nb (composition in atomic percent) alloy was used, which was produced via a powder metallurgical approach [1]. A two-step heat treatment,
Material properties
We consider a starting temperature Ts of ∼750 °C for the formation of ultra-fine lamella in the supersaturated α2-grains. This temperature was determined by means of in-situ heating experiments using high energy X-ray diffraction (HEXRD) [unpublished results by H. Clemens and T. Schmoelzer (2008)]. The thermodynamical driving force for the lamella formation is provided by the difference of chemical energies for α2 and γ, . ThermoCalc (http://www.thermocalc.com) calculations by
Transformation conditions
Generally, one distinguishes between a Global Transformation Condition (GTC) and a Local Transformation Condition (LTC).
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The GTC is applied to compare the energetical situation of a microregion, such as a martensitic plate, lath, precipitate, and a single γ-TiAl lamella of given thickness and length embedded in the surrounding matter, consisting of the parent phase. The energy balance between the parent and the product phase (i.e. the microregion) includes also the energy dissipated during a
An example
We apply the finite element method to calculate Fmech and for a specific lamella with “optimal” thickness h = 5 nm. The length of the modelled lamella is selected as m-times the thickness h. Since we need the detailed stress and strain state at the terminating edges, defined by 0 ≤ η ≤ h at ξ = 0 and ξ = ℓ, we concentrate our interest to regions adjacent to the edges. Therefore, we need not to model the whole lamella and select the factor m = 8, ensuring a constant strain and stress state in a safe
Conclusions
A micromechanical and thermodynamic concept is introduced, which allows formulating a local and a global transformation condition. Both, the driving and the dragging forces are calculated and discussed in detail. The global transformation condition can be considered as a somewhat “necessary” condition for the appearance of a γ-lamella in the α2-phase. However, the local transformation condition allows for a kinetic equation, if the mobility of the moving interface is known. The estimated
Acknowledgement
The authors appreciate the funding by Austrian FWF under the project “Massive Transformation – Experiments and Simulations”, Project number P20709-N20. The HRTEM experiments were performed at the Max-Planck-Institute for Metals Research, Stuttgart, and were supported by the IP3 project ESTEEM of the European Commission (contract number 0260019a). T.W. acknowledges the support by the research project “Bulk Nanostructured Materials” within the research focus “Materials Science” of the University
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