Elsevier

Intermetallics

Volume 18, Issue 4, April 2010, Pages 509-517
Intermetallics

Study of nanometer-scaled lamellar microstructure in a Ti–45Al–7.5Nb alloy – Experiments and modeling

https://doi.org/10.1016/j.intermet.2009.09.012Get rights and content

Abstract

Quenching of Ti–45 at%Al–7.5 at%Nb from the single α-phase region to room temperature followed by aging below the eutectoid temperature leads to the precipitation of ultra-fine γ-TiAl lamellae. In addition to an extensive experimental program, reported by Cha et al. in Intermetallics 16 (2008) 868–875, in this work a micromechanical and thermodynamical model is presented for the formation of γ-TiAl lamellae within the α2-Ti3Al parent phase. A global transformation condition allows to predict a thickness to length ratio in accordance with experimental observations. Furthermore, a local transformation condition offers the basis for a kinetic law. The modeling concept can be applied to similar problems of combined diffusive and displacive phase transformations.

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   + γ)Lamellar  2 + 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  2 + 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, Δg=gα2gγ. ThermoCalc (http://www.thermocalc.com) calculations by

Transformation conditions

Generally, one distinguishes between a Global Transformation Condition (GTC) and a Local Transformation Condition (LTC).

  • 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 F¯mech 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 = , 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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