Transformation toughening in titanium aluminides - Free energy analysis based alloy design

Dispersed-phase transformation toughening is one of the most potent mechanisms for toughening and ductility enhancement in materials. The transformation volume change and the stability of the dispersed, transforming phase are the principal factors which determine the applicability of this mechanism in a material system. Design of the dispersed Ti-AI-V beta phase for the facilitation of this mechanism in a gamma titanium aluminide matrix in the presence of a crack, could be done using a thermodynamic analysis based approach involving: (i) the Gibbs Free Energy difference at room temperature between the parent and the transformed phase, (ii) the mechanical driving force due to the stress state (crack-tip) and (iii) the driving force for nucleation. This coupled with experimental information on the transfromation volume change and the relative stability of the transforming phase over a range of compositions in the Ti-AI-V system is used to develop an optimum compositon of the dispersed phase. Titanium-aluminide alloys based on TiAl have great potential as aerospace materials because of the wide range of properties that they possess. These include low density, high melting temperature, good retention of strength and modulus at elevated temperatures, excellent creep properties and high resistance to oxidation and hydrogen absorption. However, their application in a wide range of areas is inhibited by their limited ductility and toughness especially at temperatures below 600%. To overcome this limitation several approaches such as grain size refinement, introduction of whiskers, fibers and dispersoids, use of ternary and quarternary alloy additions, are currently being pursued. Another very promising approach is the introduction of fine-scale, dispersed, metastable phases which lead to toughening on transformation. This method of dispersed phase transformation toughening, yielded record ductility and fracture toughness levels in high-strength steels and ceramics. '12 There have been, however, few reports on the possible application of this mechanism in titanium aluminides. This paper seeks to explore the potential of deformation-induced martensitic transformation of the dispersed Ti-AI-V beta phase as a toughening mechanism for gamma TiAl-base matrix alloys. The mechanism of transformation toughening involves the transformation of certain metastable dispersed phases within a brittle matrix as a mechanism for creating a plastic zone and increasing the ductility and toughness of the material. The phase transformation could occur, not only due to cooling to the transformation temperature, but also due to the stress (or deformation) activation . The transformation is accompanied by transformation shear as well as volume change of the transforming particles. It is well-established that dispersed-phase transformation toughening is controlled by the stability of the metastable dispersion and the t rans fo rmat ion vo lume change.3 Microstructural aspects as average particle size and chemical composition of the dispersion affect the optimum stability required for maximum transformation toughening. The volume change accompanying the transformation should be positive and maximum so as to facilitate the formation of an effective plastic zone. Stress-assisted martensitic transformation in Ti-A1 base alloys consists of the transformation of the parent beta phase, P, which has a BCC structure to a martensitic product phase, a", having an orthorhombic structure (or hexagonal depending on the stability of the parent beta phase). Detailed thermodynamic analysis backed by Copyr ight o American Insti tute o f Aeronautics and Astronautics. Inc.. 199 1 . A l l r i gh t s reserved. experimental information pertaining to the above transformation reaction with specific reference to the stability and volume change aspects form the basis of this work. THERMODYNAMIC ANALYSE Deformation induced transformation could be visualized as being governed by an interplay of three 'free-energy changes, AGs ' .~ These are illustrated schematically in Figure 1. transformation induced plasticity are examined here. The kinetics of stress-assisted transformation can be determined by integrating the mechanical driving force component with the existing theory of spontaneous (stress-free) transformation.5 The former has been estimated by calculating the interaction work of the resolved stress acting through the shape strain of the most favorably oriented martensitic variant, as,6 Figure 1 : Schematic of Free Energy as function of Temperature for the a and the P phase^.^ aGch is a measure of the parent phase stability and is provided by the free-energy difference between the martensitic and beta phases at room temperature, When the To temperature (the temperature at which the $-parent phase and the amartensite have the same Gibbs free energies) is below room temperature, RT = T i in Figure 1, A G C ~ ( R T ) is a positive quantity. Conversely, when Tois above room temperature; RT = Tp, A G ~ ~ ( R T ) is negative. aGnucl is the effective driving force for martensitic nucleation (unassisted by stress), which is by convention always positive. aGrnech represents the mechanical driving force for transformation due to the applied stress. The physical significance of these quantities in the context of alloy design for where yo and EO are the shear and normal components of the invariant-plane shape strain, r and a n are the shear and normal components of the stress resolved along yo and E O . The Mohr's circle diagrams for the calculation of W for the most favorably oriented variant in a random polycrystal are shown in Figure 2 for the uniaxial compression, uniaxial tension, elastic crack tip and indentation stress state^.^^^ Uniaial cornpression Elastic crack-tip Indentation Uniaxial tension Figure 2: Mohr's Circle diagrams for stress states corresponding to uniaxial compression, tension, elastic crack-tip and indentation. Defining 8 as the angle between the martensitic habit plane normal and the axis of the maximum magnitude principal stress 01, and expressing the applied stress in terms of the maximum and minimum principal stress, the mechanical driving force can be expressed as: where Vm is the molar volume of the parent (beta) phase. Expressing stress in terms of the Von Mises equivalent tensile stress, a, the driving force contribution of stress, G ~ ~ m e c h l G 8 , for: a given stress state can be calculated. This shall be demonstrated for the crack tip stress state. Setting d ~ ~ m e C h / d e = 0 in the above equation (3), the habit orientation for maximum A G ~ ~ C ~ is given by tan28=y01e0. For the crack tip stress state, it can be seen from the relevant Mohr's circle: Expressing in terms of Von Mises equivalent stress, From (3), (4) and (5). For .the shape strain of a"-martensite in Ti-AI-V alloys, under consideration here, Y ~ = O . O ~ . ~ eo which is a measure of the transformation volume change is calculated from the lattice paramaters of the beta and martensite phases determined experimentally for different compositions in the Ti-AI-V system. EXPERIMENTAL INFORMATION The isothermal section of the Ti-AI-V ternary phase diagram at 1073OK as proposed by Hashimoto et a19 is shown in Fiaure 3. v Since we are specifically interested in a metastable dispersion of the beta phase in a gamma TiAl matrix, different compositions along the $/(P+v) boundary are chosen so as to ensure chemical compatibility between the two phases. The compositions of the alloys studied is shown in Table 1. The alloys were prepared from the elemental powders by the process of arc-melting in an inert argon atmosphere. The alloys were remelted ten times to ensure macroscopic homogeniety and were then encapsulated in quartz tubes, again, under 20kPa (150 torr) of ultra-high purity argon gas. The encapsulated specimens were homogenized to remove microscopic inhomogenities at 1 200°C for two hours, following which they were water quenched after soaking at 800°C for an hour. X-ray diffraction studies were conducted to identify the phases and determine their lattice parameters. It has been reported in the case of Ti-V alloys containing ternary additions of Al that the lattice parameters of orthorhombic martensite are strongly composition d e ~ e n d e n t . ~ However, the molar volume is only a weak function of the alloy composition. Nevertheless, the alloy composition does have an effect on the lattice parameter a ~ , and hence the volume, of the p phase. To determine the relative stabilites of the and the aWphases, two samples of each alloy are prepared one, as quenched from 800°C as mentioned above, and the other quenched further down to liquid nitrogen temperature. A partially transfromed alloy at room temperature would thus be provided with further activation energy for martensitic transformation when cooled to the liquid nitrogen temperature. The relative amounts of the two phases present at room temperature and liquid nitrogen temperature in each alloy, is a measure of the stability of the beta phase of that composition. results of the X-Ray Diffraction analysis is shown in Table 1. The volume of the two phases is determined from the respective lattice parameters. The volume change per atom is determined by the formula: