Stabilization of thermosolutal convective instabilities in Ni-based single-crystal superalloys: Carbon additions and fre
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I. INTRODUCTION
NICKEL-BASED single crystals are critical to the continued development of high-performance turbine engines, including aircraft engines and power-generation turbines. As the levels of refractory alloying additions to these materials have increased to improve high-temperature mechanical properties, grain-defect formation during directional solidification has become an increasingly important problem. Typically, grain defects, such as freckles and misoriented grains, are caused by the onset of thermosolutal convective instabilities due to dendritic segregation in these multicomponent alloys.[1–8] Preventing these defects is a major challenge, particularly when solidifying physically large, high-refractory-content crystals under inherently low thermal-gradient conditions. Freckle formation has been a persistent problem in the solidification of single-crystal Ni-based superalloys since VerSnyder[9] pioneered the process in the 1960s. The presence of these undesirable grain defects, which lower the creep and fatigue properties, could potentially result in the premature failure of critical components. Early efforts taken to prevent these grain defects included the modification of gating designs and the application of high thermal gradients at the solidifying interface.[10] The onset of thermosolutal convection occurs when the buoyancy forces of the segregated solute in the interdendritic region exceed those of the surrounding viscous forces. Hence, by limiting the size of the channels in which solute can be accumulated through the adjustment of solidification parameters (the applied thermal gradient (G) and withdrawal rate (R)), the initiation of convective instabilities can be minimized.[1,3,11–15] Criteria for the development of convective instabilities have often been expressed in terms of dimensionless thermal and solutal Rayleigh numbers.[7,15] Making assumptions for the shape S. TIN, Graduate Research Associate, and T.M. POLLOCK, Professor, are with the Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109. W. MURPHY, Senior Engineer, is with General Electric Aircraft Engines, Cincinnati, OH 45215. Manuscript submitted June 27, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
of the dendrite tip and accounting for primary dendrite arm spacing (PDAS) measurements in terms of G and R, the solutal Rayleigh number can be written as[3] Rs ⫽
g K 9r 22mLD GR
冢 冣
[1]
where  is the solute volume-expansion coefficient, is the set of material parameters that relate to the PDAS selection, K is the permeability in a unidirectional temperature gradient, r is the dendrite tip radius, is the viscosity, and D is the diffusivity. This expression suggests that the tendency for convective fluid flow to develop is inversely related to the product of G and R. Using this and other relationships involving G and R, various macroscopic criteria were developed from experimental data and used to predict the formation of grain defects.[1,7,16,17] In addition, recent solidificat
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