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It is necessary to better understand the composition-processing-microstructure relationships that exist for materials produced by additive manufacturing. To this end, Laser Engineered Net Shaping (LENSä), a type of additive manufacturing, was used to produce a compositionally graded titanium binary model alloy system (Ti-xW specimen (0 £ x £ 30 wt pct), so that relationships could be made between composition, processing, and the prior beta grain size. Importantly, the thermophysical properties of the Ti-xW, specifically its supercooling parameter (P) and growth restriction factor (Q), are such that grain refinement is expected and was observed. The systematic, combinatorial study of this binary system provides an opportunity to assess the mechanisms by which grain refinement occurs in Ti-based alloys in general, and for additive manufacturing in particular. The operating mechanisms that govern the relationship between composition and grain size are interpreted using a model originally developed for aluminum and magnesium alloys and subsequently applied for titanium alloys. The prior beta grain factor observed and the interpretations of their correlations indicate that tungsten is a good grain refiner and such models are valid to explain the grain-refinement process. By extension, other binary elements or higher order alloy systems with similar thermophysical properties should exhibit similar grain refinement.

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Additive manufacturing (AM) processes have many benefits for the fabrication of alloy parts, including the potential for greater microstructural control and targeted properties than traditional metallurgy processes. To accelerate utilization of this process to produce such parts, an effective computational modeling approach to identify the relationships between material and process parameters, microstructure, and part properties is essential. Development of such a model requires accounting for the many factors in play during this process, including laser absorption, material addition and melting, fluid flow, various modes of heat transport, and solidification. In this paper, we start with a more modest goal, to create a multiscale model for a specific AM process, Laser Engineered Net Shaping (LENS™), which couples a continuumlevel description of a simplified beam melting problem (coupling heat absorption, heat transport, and fluid flow) with a Lattice Boltzmann-cellular automata (LB-CA) microscale model of combined fluid flow, solute transport, and solidification. We apply this model to a binary Ti-5.5 wt pct W alloy and compare calculated quantities, such as dendrite arm spacing, with experimental results reported in a companion paper.