Effects of Geometric Constraint on Phase Selection and Segregation in Cast TiAl
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Effects of Geometric Constraint on Phase Selection and Segregation in Cast TiAl Sailei Zhang, David R. Johnson, Matthew J.M. Krane School of Materials Engineering, Purdue University, West Lafayette, IN 47906, U.S.A. ABSTRACT Simulations of directional solidification of binary peritectic TiAl alloys through ceramic preforms consisting of narrow straight channels with spacings on the order of the dendritic tip radius were performed with a modified cellular automaton coupled to a finite volume calculation of solute diffusion. Depending upon the channel spacing, the microstructure may be refined after dendritic growth through the preform. As the channel width decreases, the lateral solute diffusion in the liquid is more constrained, changing the morphology of the primary phase from dendritic to cellular. In narrow channels, the liquid concentration gradient ahead of the solid/liquid interface decreases resulted in lower growth velocities and higher undercoolings. For hypoperitectic TiAl alloys, growth conditions that lead to growth of β dendrites can result in α nucleation and growth in narrow channels due to the geometric constraint on solute diffusion. INTRODUCTION Constraint of liquid diffusion for solidification through narrow channels and preforms can alter the microstructure and phase selection when compared to unconstrained growth. For example, Shao et al [1,2] found that single crystal growth of a nickel base superalloy (CMSX-4) through ceramic preforms resulted a lower fraction of eutectic within the preforms than outside them [1]. This phenomenon is caused by the interference of the sides of the narrow channels with the diffusion field in the liquid ahead of dendrite tips, especially as the channel size approaches the size of the dendrite tip radius. In addition to metal matrix composites, phenomena associated with constrained solidification may be important in thin sections of investment cast turbine blades. For TiAl, a wide variety of microstructures is possible due to the peritectic cascade during solidification and subsequent solid-solid phase transformations. In this paper, the constrained growth of TiAl with compositions near the peritectic liquidus (Ti-49 at%Al) and hypo-peritectic composition (Ti-47 at%Al) will be presented. DESCRIPTION OF MODELING ALGORITHMS Solidification microstructures were simulated using a solid-liquid interface tracking model combined with a finite volume treatment of the mass diffusion as described previously [2,3]. The model was modified here to simulate the growth of both β-dendrites of cubic symmetry and α-dendrites of hexagonal symmetry as commonly found in TiAl alloys. In this model, the solid fraction change of each cell at the solid/liquid interface is determined from the local composition and the composition of the neighboring cells. The temperature of the solid/liquid interface is then given by:
T * = Tm − [(CL* − C0 ) ⋅ mL − Γ ⋅ κ ]
eq. 1
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where Tm is the melting temperature of the alloy, C0 is the initial alloy composition, mL is the slope of liqidus, ț is th
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