Modeling freckle formation in three dimensions during solidification of multicomponent alloys

Abstract

The formation of macrosegregation defects known as ''freckles'' was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

“…For details of the volume-averaging procedure and the form of the macroscopic volume-averaged formulations, see Beckermann and Viskanata. 57) Further exploration of aspects of the volume-averaging procedure and assumptions were made by Ganesan, Poirier, and Voller et al 49,58) Following the pioneering works highlighted above, many studies used similar or modified versions of the same continuum equations to examine a number of different solidification phenomena, including channel formation in directionally-solidified alloys, [59][60][61][62][63][64] the effect of solidification shrinkage and pore formation, [63][64][65][66][67][68][69][70][71][72][73][74] and the effect of transformation-induced strains. [75][76][77] Many authors have also examined the particular formulations and assumptions of the original models.…”

“…It was later applied to freckle formation in Ni-based superalloys producing one of the earliest studies in three dimensions. [93][94][95][96][97][98] Other multicomponent approaches were presented by Vannier et al 32) and Krane and Incropera, 99,100) but have not been widely used.…”

“…31) To resolve channel segregates, mesh sizes need to be smaller than channel widths (usually of the order of a few millimetres) and need to be even less if results are to be mesh independent. 59,60,92,95,117,136) Introducing too many simplifications can also gravely impact a model's predictive power. Commercial software packages are often guilty of making significant simplifications in order to deliver sensible computing times in an industrial setting, and as a result neglect key macrosegregation phenomena, such as equiaxed grain sedimentation.…”

The multiphase physics of sea ice: a review for model developers

“…Much work has been performed in this area in the context of the solidification of binary metal alloys (e.g. Bennon and Incropera, 1987;Beckermann and Viskanta, 1988;Voller et al, 1989;Oldenburg and Spera, 1991;Felicelli et al, 1998;Jain et al, 2007;Katz and Worster, 2008). All assume an incompressible flow and use the Boussinesq approximation.…”

Modeling of Vacuum Arc Remelting of Alloy 718 Ingots

“…These criteria are essentially based on a critical mushy zone size and thus a maximum local solidification time beyond which freckling occurs in the ingot. Recently, criteria involving the Rayleigh number have been proposed based on the studies in the area of directional solidification [29][30][31]. The Rayleigh number (Ra), which is the ratio of buoyancy-to-viscous force is defined as:…”