Modelling of Phase Transformations in Titanium Alloys with a Phase-field Model
We have used a phase field model devoted initially to solidification for studying some phase transformations in metastable β titanium alloys. First calculations have been carried out to determine if we can rely on the model to get quantitative information
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Introduction
Titanium alloys have more and more applications due to their desirable combination of properties. First, titanium alloys have low densities which provide very attractive strength to weight ratios allowing lighter structures. Secondly, they show superior corrosion and erosion resistance in many environments. Finally, they have a high temperature capability. Although titanium aJIoys are still considered as expensive materials, their cost can be justified on the basis of their versatile properties for many applications. Their good mechanical properties are achieved thanks to proper thermo- mechanical treatments, optimised to design the complex microstructures hierarchy. From a metaJIurgical point of view, the microstructure formation obtained by solid/solid phase transformations is easy to study by microscopy when considering ß metastable alloys. Indeed, for these alloys it is possible to freeze the microstructures during a transformation without subsequent occurence of any displacive transformation at low temperatures. During their thermo-mechanical treatments, most of the titanium alloys are deformed in the high temperature range where the most stable phase is ß (bcc) and further cooled to room temperature where the material is a mixture of ß and 0: (hcp) phases. Different morphologies of the 0: phase are observed depending on the cooling rate and the previous deformation conditions: - for smaJI departures from equllibrium conditions, 0: allotriomorph grains at the ß grain boundaries are first observed (Fig. la). H. Emmerich et al. (eds.), Interface and Transport Dynamics © Springer-Verlag Berlin Heidelberg 2003
Phase-field Modelling in Titanium Alloys
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- For greater departures from equilibrium conditions, a plates of widmanstätten have grown from or near the allotriomorph grains (Fig. 1b). - And finally, for the greatest departures from equilibrium conditions, acicular a grains nucleated on defects are observed inside the ß grains (Fig. lc). Furthermore, deforming the material prior to the cooling prornotes the apparition of the allotriomorphs together with the widmanstätten plates.
Fig. 1. Scanning electron microscopy (SEM) images of microstructures of a ß titanium alloy (a) isothermally treated at 790°C during 5min.j (b) isothermally treated at 790°C during 10min.j (c) isothermally treated at 700°C during 6min.. To explain these different morphologies, some mechanisms have been proposed ([1] and references therein) mainly from post-mortem observations with microscopy. However some features are unclear which could be explained thanks to 2D /3D numerical modelling.
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Which Model to Choose?
Among the different modelling techniques which can tackle this kind of problem, the phase field models have proved to be the best suited for the moment. This is in great extent because the interfaces of complex morphologies have not to be tracked explicitely. Another advantage of this kind of models, which is of great importance for solid state transformations, is the possibility to incorporate easily p
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