The development of solidification microstructures in the presence of lateral constraints
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INTRODUCTION
THE ability to define processing conditions to obtain an optimum microstructure in the solidified material is the key aspect of the design of many technologically important processes, including casting, welding, single crystal preparation, and rapid solidification techniques. Our fundamental understanding of the correlation between the processing conditions and the microstructural development has primarily come from theoretical models ~1-~~ and critical experimental studies r~~-20~carried out under well-characterized solidification conditions. For directional solidification, the microstructure evolution is studied under fixed conditions of temperature gradient at the interface, G, the externally imposed velocity, V, and the alloy composition, Co. It is also often assumed that the interface is growing under steady-state conditions so that its velocity is precisely the same as the externally imposed velocity. Also, the cross section of the solidifying material is assumed to be constant. If the solidification technique is to be used successfully to process advanced engineering components, it is important that we extend our understanding of microstructure formation to more complex conditions. Many engineering components do not have a uniform cross section. For example, the turbine blades made by the directional solidification technique have varying cross sections which will influence the final microstructure that forms in the finished product; [zl,22'231 a discontinuous
L.M. FABIETrI, Graduate Research Assistant, and R. TRIVEDI, Senior Scientist and Professor of Materials Science and Engineering, are with Ames Laboratory, United States Department of Energy, Iowa State University, Ames, IA 50011. V. SEETHARAMAN, formerly with Ames Laboratory, is Senior Scientist with Universal Energy Systems, Dayton, OH 45432. Manuscript submitted April 24, 1989. METALLURGICAL TRANSACTIONS A
change in cross section exists when an alloy is solidified in the presence of discontinuous fibers, t24-271and the ability to produce shaped single crystals of varying cross-sectional areas has important applications in device technology and instrumentation, t28,29j Two important effects arise due to the change in cross section that will influence the microstructure of the solidified alloy. First, the heat flow may not be unidirectional so that one needs to investigate the thermal field in a complex geometry. Detailed numerical studies of such thermal fields have indeed been carded out. [22'23] Second is the change in solute field ahead of the interface as the interface approaches the region where the cross section changes significantly. This aspect has not been studied in detail, and it is the purpose of this paper to report critical experimental studies which elucidate the effect of discontinuities in the cross section on the morphology of the interface. When an interface that is moving under steady-state conditions encounters a change in cross section, the interface velocity changes significantly from the externally imposed ve
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