Grain Selection in Spiral Selectors During Investment Casting of Single-Crystal Components: Part II. Numerical Modeling
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IN single-crystal (SX) casting, a grain selector consists of a starter block and a spiral selector. The starter block optimizes grain orientation and the spiral selector selects a single grain, ensuring that only one grain can grow into the SX component. In the spiral selector, a ‘‘geometry blocking’’ mechanism was proposed in our prior study[1–3] to explain the grain selection during solidification. The prior experimental study showed that the efficiency of grain selection can be improved by reducing the spiral take-off angle. However, there is no systematic data available to quantify the effect of spiral geometry on grain selection. Moreover, owing to high experimental cost and time consumption, only limited experiments were carried out. Alternatively, numerical models were attempted to study the grain structure evolution.[4–9] In 2000, Carter et al.[10] used a threedimensional (3-D) processing model to predict the grain orientation selection in the starter block. In 2004, Esaka et al.[11] developed an analytical model to study the effect of starter block geometry and spiral take-off angle on grain selection. However, the developed analytical model is not sufficient to investigate grain selection in 3D spirals. In 2009, Seo et al.[7] employed a 3-D cellular automaton finite element (CAFE) model to simulate the grain texture in an angular selector. Their simulated results showed good agreement with experimental measurements, but the effect of spiral geometry on grain selection was not studied in a systematic manner. H.J. DAI, Recently Graduated PhD Student and Visiting Researcher, and H.B. DONG, Reader, are with the Department of Engineering, University of Leicester, Leicester LE1 7RH, United Kingdom. Contact e-mail: [email protected] N. D’SOUZA, Casting Specialist, is with Precision Casting Facility (PCF), Rolls-Royce plc, Derby DE24 8BJ, United Kingdom. J.-C. GEBELIN, Technical Director, and R.C. REED, Chair and Director, are with Metallurgy and Materials, PRISM2, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom. Manuscript submitted October 20, 2010. Article published online June 15, 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A
In this study, a systematic investigation of the effect of spiral geometry on grain selection is conducted using numerical modeling. A macroscale thermal model (PROCAST*) and a mesoscale cellular automaton *PROCAST is a trademark of ESI Group, Paris.
model were employed to study the grain selection in the spiral selector. The thermal predictions were validated against experimental data, and the simulated results of grain structure and orientation in spiral selectors were compared with the previous experimental observations. Then, the effects of geometry and dimensions of the spiral selector on grain selection were investigated systematically, based on which recommendations for designing spiral geometry are provided.
II. QUANTITATIVE DESCRIPTION OF SPIRAL GEOMETRY AND CRITERIA FOR ASSESSING GRAIN SELECTION A. Quantitative Description of Spiral Geometry As shown in Figure
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