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The freckling mechanism of superalloys Wang, Tao 1999

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T H E  F R E C K L I N G  M E C H A N I S M  O F  S U P E R A L L O Y S  by  TAO WANG B.E., Chongqing University (P. R. China), 1989  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA March 1999 ©TaoWang, 1999  In  presenting  degree freely  at  this  the  available  copying  of  department publication  of  in  partial  fulfilment  of  the  University  of  British  Columbia,  I  agree  for  this or  thesis  reference  thesis by  this  for  his thesis  and  study.  scholarly  or for  her  I further  purposes  financial  gain  shall  It  be  not  of  Meld* tmJ.  T h e U n i v e r s i t y o f British Vancouver, Canada  DE-6  (2/88)  tfaJfAialt  Columbia  ZWrneefU  that  the  Library  by  understood be  for  an  allowed  advanced  shall  permission  granted  is  permission.  Department  that  agree  may  representatives.  requirements  the that  without  for head  make  it  extensive of  my  copying  or  my  written  ABSTRACT  Freckles are macro-segregation defects which are usually found in nickel-base superalloys or specialty steels and which occur during solidification. They are presently one of the major defects encountered in advanced casting technology of superalloys. Two modified Rayleigh criteria have been suggested which seem best adapted to freckling prediction. However only three superalloys have been previously tested for the application of the modified Rayleigh numbers and fAirther experiments on industrial alloys and in casting conditions similar to actual industry conditions are therefore needed. There are* conflicting reports as to the cause of freckling in IN718 alloy. One possible explanation is that freckling is caused by a downward interdendritic flow along the slope of solidification front, another possible explanation is that freckle may be caused by the density inversion between the interdendritic liquid and bulk liquid in the same way as in other superalloys. The Si content is believed play a critical role in influencing the freckle formation in IN718, without however any confirming experiment data. A vacuum induction furnace was built so as to directionally solidify superalloys at various angles to the vertical under typical industrial conditions (thermal gradients ranging from 500 to 4000°C/m (5 to 40°C/cm) and growth rates ranging from 1.6 x 10" to 10 x 10" m/s (1 to 6 5  5  mm/min). A comprehensive thermal modeling of this furnace was carried out with the F E M package ProCAST in order to accurately evaluate the solidification conditions (G and R) for each casting. Totally 10 alloys were tested and the modified Rayleigh criteria are shown to be able to predict freckling in all these alloys under different casting conditions and different growth front angles. Si content is shown to influence the density of the interdendritic liquid and hence the freckling mechanism in IN718.  ii  Table of Contents  Table of Contents  Ill  List of Figures  VII  List of Symbols  VIII  Acknowledgments  1. INTRODUCTION  X  ,  .1  2 LITERATURE REVIEW  4  2.1 T H E N A T U R E OF F R E C K L E S  4  2.2 MECHANISMS OF F R E C K L E F O R M A T I O N  7  2.2.1 The density inversion theory  7  ' 2.2.2 Freckling in LN718 — the influence of Si  11  2.3 T H E F R E C K L I N G CRITERIA— R A Y L E I G H CRITERION.  15  2.3.1 Thefrecklingcriteria for the density-driven downward convection mechanism 2.3.2 The Rayleigh criterion and its limitations 2.3.3 Influence of the angle of the growth front on freckle initiation 2.3.4 Anisotropic permeability of mushy zone 2.4 T H E MODIFIED R A Y L E I G H N U M B E R  :  2.4.1 The first theory 2.4.2 The second theory 2.4.3 Range and sensitivity of the parameters 2.4.4 Numerical evaluation of the Rayleigh number 2.4.5 Application of the modified Rayleigh number criteria to three superalloys (Waspaloy, Mar-M247, UBC1) 2..4.5 Direct application of the modified Rayleigh criterion to industrial situations 2.5 S U M M A R Y OF L I T E R A T U R E REVIEW  16 17 20 23 26 26 28 29 33 34 ....39 40  3. R E S E A R C H OBJECTIVES  41  3.1 R E S E A R C H FOCUS  41  3.2 OBJECTIVES  •  4. M E T H O D O L O G Y  42 43  4.1 CHOICE OF A L L O Y S  43  iii  4.2 E X P E R I M E N T A L APPARATUS  44  4.2.1 Tiltable Bridgman furnace 4.2.2 Experiment schedule and typical experiment 4.2.3 Sample analysis 4.3 N U M E R I C A L M O D E L I N G  44 47 50 51  4.3.1 Numerical Modeling of the furnace  52  4.3.2 Mathematical Model " M E T A L S "  56  5. R E S U L T S  58  5.1 E X P E R I M E N T A L RESULTS  58  5.2 F U R N A C E M O D E L I N G RESULTS  62  5.3 APPLICATION OF T H E MODIFIED R A Y L E I G H CRITERIA  69  5.3.1 Application of the first theory of Auburtin et al  69  5.3.2. Application of the second theory of Auburtin et al  71  5.4 LIQUID DENSITY C A L C U L A T E D F R O M " M E T A L S " FOR SOME A L L O Y S  6 DISCUSSION  72  74  6.1 V A L I D A T I O N OF T H E M E A S U R E M E N T S A N D EXPERIMENT RESULTS  74  6.1.1 Uniform composition of IN718HiSi casting samples 6.1.2 Freckle composition  74 75  6.1.3 Fraction liquid  76  6.2 E F F E C T OF SI C O N T E N T O N T H E F O R M A T I O N OF F R E C K L E IN IN718 A N D VARIATIONS  76  6.3 T H E APPLICATION OF MODIFIED R A Y L E I G H N U M B E R  78  6.3.1 Application of the first theory  78  6.3.2 Application of the second theory 79 6.3.3 Application of modified Rayleigh criteria to downward freckling phenomenon 79 6.3.4 Applicability of the modified Rayleigh criteria to freckling prediction and process optimization 80  7. C O N C L U S I O N S A N D F U T U R E W O R K  83  7.1 CONCLUSIONS....  83  7.2 RECOMMENDATIONS FOR F U T U R E WORK  84  iv  REFERENCE  86  APPENDIX A: CALCULATION OF T H E DESIGNED THICKNESS OF GRAPHITE SUSCEPTOR.  90  APPENDIX B: TYPICAL OUTPUTS OF PROCAST.  91  v  List of Tables  Table I Table II  Table HI: Table TV Table V Table VI Table V H Table Vm Table DC Table X Table XI Table XII Table XUI Table XTV Table X V Table X V I  Freckle and surrounding matrix calculated densities 14 Liquid density, viscosity and thermal diffusivity for the four superalloys investigated in this thesis at their liquidus temperature and 100°C above their liquidus temperature 30 Compositions (in wt%) and melting range of chosen alloys in this thesis 44 Casting conditions 49 Ratio of charged silicon to bulk IN718 when making IN718 variation samples ...50 Initial conditions of the materials at the start of the numerical simulation 55 Chemical analysis (measured by microprobe) of the matrix and freckles from some of the experimental samples. (wt%)...„ 60 Summary of the directional solidification experiments carried out on the tiltable Bridgman furnace 61 Calculated modified Rayleigh number Ral and Ra2 70 Threshold value Ral * of various alloys 71 Threshold value Ra2* of various alloys 72 Liquid densities of freckles and surrounding matrix of alloys CMSX-1 IB, IN718, IN718-0.4Si and IN718HiSi 73 Composition of matrix at the top and bottom of a sample of IN718HiSi 74 Comparison of the composition of freckle and matrix in IN718 detected in the present work and the literature (wt%) 75 Ranking of propensity of upward freckling alloys (the higher the number the higher the freckle-propensity) 82 Ranking of propensity of downward freckling alloys (the higher the number the higher the freckle-propensity) 82  vi  List of Figures  Figure 1 Figure 2  Figure 3 Figure 4  Figure 5 Figure 6  Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure Figure Figure Figure  14 15 16 17  Figure 18 Figure 19  Figure 20  Figure 21 Figure 22  Various appearance of freckles in industrial castings.(4) 6 Schematic diagram of directional solidification and associated thermal (pj), solutal (pc) and thermosolutal (pi+c) density profiles illustrating the density inversion theory. (4) 8 Freckle formation and associated fluid flow pattern 10 A numerical simulation of thermosolutal channel by J. Rappaz. The traces left behind by these channels in the final solidified product are called freckles (21) 10 Interdendritic liquid density profiles computed by "METALS" for 5 DSQ alloys....12 The upper left corner of a longitudinal section through the center of a 52 cm diameter ingot, at low magnification, the defects are nearly aligned with the pool surface (12) 13 The mechanism of freckle formation showing the sequence of the densitydriven downward-forming channel to form a freckle (12) 13 Schematic description of experiments with curved mushy zones(4, 6) 20 Freckle flow path and growth front angle in various industrial castings (4) 21 Schematic geometry for an angled growth front 27 Typical liquidfractionprofile along the mushy zone of. 32 The original Rayleigh number Ra (a), modified Rayleigh number Ral (b) and modified Rayleigh number Ra2 (c) versus growth front angle for alloy Waspaloy ..38 Original and modified Rayleigh criteria profiles along the radius of V A R IN718 (melt rate : 260kg/hr) (4) 39 Schematic diagram of the Bridgman-type furnace used in this study 45 Tiltable directional solidification furnace 46 Axisymetric mesh geometry used in ProCAST to model the furnace 54 Schematic heat flow diagram in the ProCAST model of the experimental tiltable furnace 55 Appearance of freckles on the surface of castings (castings diameter: 25 mm) :• 59 Typical thermal profiles in the casting during solidification (ProCAST simulation), (alloy: CMSX-1 IB; control temperature: 1500°C , withdrawal speed: 6 mnVmin) 63 Typical thermal profiles in the casting during solidification (ProCAST simulation), (alloy: CMSX-1 IB; control temperature: 1465°C; withdrawal speed: 1 mnVmin) 64 The direction of calculated temperature gradient in samples solidified with an inclined angle a by ProCAST • • • 65 Temperature gradient vector calculated by ProCAST model (GFreckie, alloy: IN718HiSi, T ckie = 1200°C, R = 1 mm/min, Tcontroi = 1465°C) 66 Fre  vii  L i s t of Symbols Symbols  C Co  D  SI U n i t wt% wt% m /s % variable  Meaning Solute concentration Reference solute concentration Thermal diffusivity Liquid fraction  N/m m/s  Driving force for freckle formation  2  T  fi F F  Threshold value for variousfrecklingcriteria  4  Gravitational acceleration (=9.81 m/s ) 2  2  g G, G Guquidus Gsolidus GFreckle s~t Vertical ^Freckle  h k K K Keffective K K M 0  x  Thermal gradient Thermal gradient at the liquidus temperature of the alloy Thermal gradient at the solidus temperature of the alloy Thermal gradient at the temperature of freckle initiation Vertical thermal gradient at TFreckie Characteristic linear dimension Partition coefficient Permeability Reference permeability Effective permeability  °C/m °C/m °C/m °C/m °C/m m m m m m m  2  2  2  2  2  2  kg/mol J/m s Lmol'-K2  q R R, R Ra Ral Ra2 Ra Ra Ra* t T  m/s  Solidification rate Rayleigh number Modified Rayleigh number (first theory) Modified Rayleigh number (second theory) Rayleigh number along the x axis Rayleigh number along the z axis Critical Rayleigh number (threshold value for freckling)  s °C °C  Time Temperature Reference temperature Liquidus temperature of the alloy Solidus temperature of the alloy Freckle initiation temperature of the alloy  x  z  To Tuquidust Tu °c Tsolidus, Tsol°c °c Tfreckle m/s V, V m x, x' m x m y q  z,z'  1  Permeability perpendicular to the primary dendrites Permeability parallel to the primary dendrites Molar weight Heat flux Gas constant (=8.3144 J/mol.K)  m  Fluid flow velocity First horizontal coordinate coordinate perpendicular to dendrite trunk Second horizontal coordinate Vertical coordinate  viii  Greek Symbols  SI Unit  Meaning  a  deg.  P  l/wt%  Y  1/°C °C/s kg.nf'.s m m kg/m  Angle with the vertical direction Solutal expansion coefficient Thermal expansion coefficient Cooling rate  s  P Po Ap X  0 r  Abbreviations CFD DS DSQ ESR EDX FEM HTC IGT LST N/A PDAS SEM SDAS SX TC VAR UBC WD  3  kg/m kg/m  3  3  _  Dynamic viscosity Primary dendrite arm spacing Secondary dendrite arm spacing Density Reference density Density difference Tortuosity factor Alloy chemistry function Casting condition function  Meaning Computational Fluid Dynamics Directionally Solidified Directional Solidification and Quench Electro-Slag Remelting Energy Dispersion Spectrometry Finite Elements Modeling Heat Transfer Coefficient Industrial Gas Turbine Local Solidification Time Not Applicable Primary Dendrite Arm Spacing Scanning Electron Microscope Secondary Dendrite Arm Spacing Single Crystal Thermocouple Vacuum Arc Remelting University of British Columbia Withdrawal  Note : Throughout this thesis, thermal gradients will be expressed mainly in ° C/cm units, more commonly used in the industry, rather than in °C/m SI units.  ix  Acknowledgments  The author would like to thank first and foremost his supervisor, Dr. A . Mitchell, for his invaluable guidance and encouragement throughout this Master thesis. Discussions with Dr. S.L. Cockcroft were greatly appreciated. Many thanks to Dr. P.B.L. Auburtin for all his help during the work. A l l the support staff in the department of Metals & Materials Engineering at the University of British Columbia (UBC) (Vancouver, Canada) were also most helpful. The contributions at various levels from the following companies were very much appreciated : Consarc Corporation, Special Metals Corporation, Canon-Muskegon, General Electric Corporation, Inco Alloys International, National Physical Laboratories (UK). Finally, this thesis is dedicated to the memory of my grandparents, who both passed away in 1998 when I was studying in a country far away from China.  1. INTRODUCTION Freckles are trails of macrosegregation defects enriched in the normally segregated elements and depleted of the inversely segregated elements. Freckles have been observed and studied in unidirectionally solidified castings, Vacuum Arc Remelted (VAR) and Electro-Slag Remelted (ESR) ingots, as well as static castings and ingots of nickel-based superalloys and specialty steels. Freckles are highly undesirable in any type of casting because they are unremovable by thermo-mechanical treatments. Since the 1960's, when they were linked to the failure of several military engines, freckles have been considered to be unacceptable defects in industrial aerospace castings. It is now well known that freckles are the product of thermosolutal convection, originating in the interdendritic liquid during solidification. As suggested in the classic freckling theory, this flow is driven by a density inversion occurring in the mushy zone as a result of the combination of cooling and interdendritic segregation. The occurrence of the freckling phenomenon has been correlated with casting geometry, solidification conditions and alloy composition. Presently available data suggests that a positive density gradient in the mushy zone (e.g. a heavier interdendritic liquid than bulk liquid) can form during the solidification of alloy EM718, in which freckles have been observed in V A R / E S R ingots for a long time. A density-driven downward-forming channel has been proposed as an alternative mechanism of freckling in IN718. Minor elements such as Si, (which will increase in concentration in the industrial alloy due to the contamination of steels in scrap turnings from machining), are estimated to play a critical role on variation of the density  1  of interdendritic liquid and hence the freckle formation mechanism in the EM718 ingots containing scrap recycled from machining chips. Freckle formation in ingots of superalloy has been avoided by keeping ingot diameters and melting rates below critical values; freckling in DS and SX castings has been minimized by maintaining a high thermal gradient at the solidification front. However, the development of large land-based industrial gas turbines (IGT) for power generation and larger aircraft engines requires a considerable scale-up of the diameter of turbine disks and the size of SX blades. Freckling becomes a major problem for this scaling-up and current rejection rates due to this defect are unacceptably high. Moreover, non-destructive testing technology is not yet capable of detecting internal freckles. As a result, the commercial production of larger castings has become highly risky because of the potential for catastrophic failure due to the presence of freckles and the resulting high liability costs involved, as well as the production costs incurred. Therefore, insight, knowledge and precise parameter control are required in the superalloy industry rather than relying on empirical knowledge and empirically determined casting parameters. To date, the modified Rayleigh criteria that combine the complete factors influencing freckle formation, seem to be the most promising criteria providing sufficient insight regarding the actions to be taken to minimize freckling, especially for those freckles formed by a density inversion (the classic condition). The literature review of this thesis (Chapter 2) first summarizes the main features of freckle formation; then reviews the research on the influence of interdendritic segregation during solidification of LN718; finally a brief description of the modified Rayleigh number criterion is given. The goal of this research program is described in  2  Chapter 3. In Chapter 4 (methodology), a set of experiments are suggested to test and apply the modified Rayleigh criterion theory to some superalloys, and to determine the influence of Si in freckle formation in DM718 castings. The modeling of the experimental apparatus and a mathematical model for density calculation are also presented in Chapter 4. Chapters 5, 6 gather and discuss the main results of the experiments and models. Chapter 7 summarizes the conclusions of this research program, as well as suggestions for future work.  3  2 LITERATURE REVIEW 2.1 THE NATURE OF FRECKLES  Freckles, also known as "channel segregates" or "A segregates", may be described as extended trails of macrosegregation. The name "freckles" is suggested by the spotted appearance of these trails when macroetched which is due to the presence of excess eutectic material, second phase particles, porosity and small randomly oriented grains in the local area. Freckles can potentially develop in any casting process involving directional (as opposed to equiaxed) solidification. They have been found in a variety of industrial castings such as V A R and ESR superalloy billets (1), DS and SX superalloy castings (2), and large killed steel ingots (3), (see Figure 1). In the case of V A R / E S R ingots, freckles are usually located in the center to mid-radius of the billet. In directional solidified superalloy castings (DS and SX), freckle lines are normally located on the exterior surface of the casting. In killed steel ingots, freckles ('A' segregates) usually form in the middle of the solidification zone which grows perpendicularly to the side walls. It has been reported that freckle specimens showed poor ductility and a reduction of about 30% in yield strength (1). Moreover, they cannot be removed by subsequent thermomechanical treatments. For the ingots, the combination of slow solid-state diffusion rates and relatively large freckle size requires prohibitively long homogenization heat treatment times. Moreover, the high levels of microporosity and primary precipitates (eutectic, primary carbides, etc.) cannot be significantly reduced. For blade castings, misoriented grains in freckle trails cannot be eliminated, and require the  4  scrapping of any affected DS/SX casting(4, 5). Freckles have been found to be enriched in the normally segregating elements and depleted of the inversely elements. Freckles are, therefore, shifted toward the eutectic composition (2, 4). The occurrence of freckling phenomenon has been correlated with part geometry, solidification conditions and alloy composition. 1) Geometry: In direct observation of the unidirectional solidification of the lowtemperature analogue, 3 O N H 4 C I - H 2 O , the location of freckles was found to be influenced by mushy zone orientation and shape (6). In the case of remelted superalloys ingots, ESR ingots have been observed to be more prone to freckling than V A R ingots. This observation has been related  concentrates  under hot-top segregation  bands  v_^~  om of negative .segregation  c  a) "A" segregate in a large killed steel ingot  Figure 1 Various appearance of freckles in industrial castings (4).  5  b) Centre to mid-radius freckles in V A R M 7 1 8 (quarter of a cross-section)  c) Surface freckles in the root portion of a large SX IGT Mar-M247 blade  Figure 1 Various appearance of freckles in industrial castings.(4) (continued)  6  to the V-shaped pool and mushy zone profile in ESR, as opposed to a U shaped profile in V A R (1), (7). The fact that freckles occur only on the surface of DS and SX investment castings only has been suggested to be a result of the angle of growth front with respect to the direction of gravity (4). 2) Alloy composition: It is well known that freckling is highly dependent on alloy composition (8, 9, 10, 11). Experiments involving binary alloys showed that, below a certain alloying limit, no freckles develop, above this limit, the number of freckles seems to increase with the solute concentration. The nature of the alloying elements is also important. Superalloys with high titanium (segregating normally) or tungsten (segregating inversely) are reported to be more freckle prone (2). 3) Solidification parameters and operating conditions: It is often suggested that freckling can be significantly reduced and even avoided by operating at larger thermal gradients and faster solidification rates (l).Heat transfer limits the application of this idea to larger sections of both ingots and castings.  2.2 MECHANISMS OF FRECKLE FORMATION  2.2A The density inversion theory  Except for the suggestion of a freckling mechanism of a density-driven downward-forming channel (such as suggested by James A. Van Den Avyle et al (12) in  7  1998 and Flemings et al in the 1970's (47)), almost all the other researches reveal that freckling is related to a phenomenon called "thermosolutal" or "double diffusive" convection in the mushy zone, which is caused by a density inversion in the solidification growth front. Figure 2 shows schematically the vertical upward directional solidification of an alloy.  F i g u r e 2 Schematic d i a g r a m o f directional solidification a n d associated t h e r m a l  (px),  solutal  (pc)  a n d thermosolutal  (px+c) d e n s i t y  profiles illustrating the density  i n v e r s i o n t h e o r y . (4)  The heat flow is vertical downward, creating a vertical thermal gradient along the casting. In addition to a thermal gradient, there also exists a variable solute concentration gradient in the liquid between the bottom of the mushy zone and the top of the casting. As  8  is well established, the density, p, of a liquid alloy can be considered to be dependent on its temperature and its solute concentration and usually, p can be expressed in the following form (6, 13, 14,15, 16, 17),  P = Po  X  i-Z^x(c/-ci)- x(r-r ) 7  0  Eq. 1  7=1  with  C  PodC! _J_dp  7  ~ Po ^  In the case of most metallic alloys and analog systems, y is positive (i.e. an increasing temperature always decreases the density). However, P can be either positive or negative, usually depending on the relative densities of the solute and solvent in binary alloys, and on the segregation sign. In the cases where the rejected solute is lighter than the solvent, p becomes positive. The combined influence of the temperature and concentration profiles in the liquid and mushy zone can lead to a density profile as shown schematically in Figure 2. Given such a density profile, it can be seen that the interdendritic liquid lower in the mushy zone (enriched in solute) is less dense than the liquid at the dendrites tip. This is a case of density inversion at the growth front. This system is inherently unstable, which can lead to fluid convection in order to reduce the potential energy (13). This phenomenon is known as "thermosolutal" or "double diffusive" convection, since it arises from the influence of both thermal and solute concentration gradients. It is now widely agreed that thermosolutal convection is the cause of freckling (13, 15, 18,19,20).  9  Liquid Melt Freckle Plume  A A  Heavier Non_ -Segregate^ Liquid  idus  1 IfLj  . Segregate^ dquid  Dendrite TsoKdus  Solid Casting  j Equiaxed :_Grains \ and/or Eutecvu.; Enriched : Material : (l-2mm) H *-  Figure 3 Freckle formation and associated fluid flow pattern.  Figure 4 A numerical simulation of thermosolutal channel by J. Rappaz. The traces left behind by these channels in the final solidified product are called freckles (21)  The rising plume has a steady-state lifetime during which it collects interdendritic liquid by fluid movement in a direction approximately at right angles to the growth  10  direction, and is established over one or more primary dendrite spacing, the freckle channels eventually freeze, as the thermal profile passes through the region. Figure 3 shows schematically the complete pattern associated with freckling. A numerical simulation of the thermosolutal channel by J. Rappaz is given in Figure 4 (web site: http://dmawww.epfl.ch/~rappaz/).  2.2.2 Freckling in IN718 — the influence of Si  The interdendritic segregation along the mushy zone of some directionally solidified superalloys has been measured by Auburtin (19) and the concentration data have been translated into liquid density profiles by a numerical model. Density inversions were observed on some freckle prone alloys such as M A R - M 002 as shown in Figure5. However, in the case of IN718, which was reportedlyfreckle-prone,no density inversion was observed (Figure 5). It is probable that the silicon content of the alloy is responsible for the reported "freckles" observations, since although carbon segregates strongly, the formation of solid NbC precipitates greatly reduces its role in the liquid density scheme. IN718 formulations of 10 or 20 years ago contained much more silicon than is normally present in today's alloys (23). This high level of silicon would have been sufficient to produce the necessary density inversion during solidification and hence to create a stable freckle plume. Over time, the silicon level has been lowered, ostensibly to reduce Laves phase formation, but at the same time the "freckle" morphology has changed into one in which the segregation channels are approximately parallel to the liquidus line rather than parallel to the growth direction as shown in Figure 6. In these latter alloy ingots, the  11  Interdendritic liquid density variations along the mushy zone of various alloys 8.75  8.50  8.25  _ 8.00 n  •  IN718  •  MAR-M002 MAR-M247  • C-276  E  • T1  £7.75 » c  0)  ° 7.50 Slope 0.005(g/cm)/°C 3  7.25  7.00  6.75 1250  1300  1350  1400  Temperature (in °C)  Figure 6  Interdendritic liquid density profiles computed by "METALS" for 5 DSQ alloys (20).  12  1450  Figure 6 The upper left corner of a longitudinal section through the center of a 52cm diameter ingot at low magnification, the defects are nearly aligned with the pool surface (12).  a) An alloy 718 niobium pseudobinary phase diagram. When liquid of C 2 is increased from T to Ti, Cs2~ Csi and C - C i , L  b) Increased density of interdendritic liquid results in a downward flow,  2  L2  L  c) Channel defects form by a dissolution mechanism,  d) The channel consists of a highsolute dendritic fragmented region.  Figure 7 The mechanism of freckle formation showing the sequence of the densitydriven downward-forming channel to form a freckle (12).  13  segregation liquid flow appears to have been one of heavy liquid seeping through the dendrite network towards the center of the ingot. The flow results from a density change, but the mechanism is substantially different. James A . Van Den Avyle et al (12) have schematically described this mechanism of freckle formation in Figure 7. As shown schematically in Figure 7a, when a liquid of composition CL2 is increased from T2 to T l the composition of the liquid will tend to decrease to CL1 by remelting some of the surrounding solute-lean solid. This dissolution process, resulting from inter-dendritic liquid flowing into a higher temperature field, is the basis of the mechanism by which the channel defects form and propagate. From the high niobium composition and porosity associated with the freckles, it appears that they form fairly deep in the mushy zone. Microprobe analysis and density evaluation of freckles in recent V A R LN718 ingots, also indicate that freckles are heavier than the surrounding bulk metal as shown in Table I (20).  Table I Freckle and surrounding matrix calculated densities (after "METALS") (20).  Alloy  Area of interest  Liquid Density (in g/cm) Matrix (T =1336°C) 7.49 Freckle (T p1336°C) 7.57 Freckle (7 r1260°C) 7.64 3  Uq  IN718  U£  So  The potential effect of minor elements such as C and Si on the liquid density of IN718 has been estimated by Auburtin (20, 22). The results are shown below: Liquidus  composition with 0.03wt%C and 0.3wt%Si:  14  p ; (1336°C)=7.44g/cm X  g  3  1321°C  composition with 0.25wt%C and0.3wt%Si:  p ^1321°C)=7.46g/cm  1321°C  composition with 0.25wt%C and 0.6wt%Si:  p (1321 C)=7.42g/cm  3  1321°C  composition with 0.25wt%C and 1.0wt%Si:  p (1321°C)=7.36g/cm  3  3  L  0  i;9  L/?  Auburtin's calculation using the Rayleigh number as a criterion for freckling shows that freckles could result from density inversion gradients of the order of 0.01 (g/cm )/°C. Thus, it can be seen that segregation of carbon alone is insufficient to create J  density inversion, however, additional segregation of Si could result in a density inversion sufficient to form freckles. It has been foundfrecklingmore often to occur during the remelting of IN718 alloys recycled from machined chips than the normal IN718 alloys, the fairly increased Si content of the alloy due to contamination with steels during machining is therefore considered to play a critical role on this problem. However, in any event, more detailed analysis of the segregation of Si is required for further investigation. Moreover, in order to eliminate it, it is necessary to unambiguously distinguish which macrosegregation mechanism is at work.  2.3 THE FRECKLING CRITERIA— RAYLEIGH CRITERION  The evaluation of a numerical criterion able to provide quantitative insight on the conditions of freckle formation is now recognized as a major key toward the successful manufacture of large diameter V A R / E S R ingots and large DS/SX castings.  15  2.3.1 The freckling criteria for the density-driven downward convection mechanism  Flemings et al (47) provided the mathematical statement for the requirement of the density-driven downward-forming channel: V-VT e  <-l  Eq. 2  where V— interdendritic flow velocity; T - temperature; s = rate of temperature change (cooling rate). This equation simply states that the formation of a channel occurs when the interdendritic fluid velocity is greater than the solidification rate. This can be called the Flemings' criterion for density-driven downward-forming channel. Fas a function of position can be obtained by solving the following equations simultaneously,  Eq. 3  (VP + P g) L  •—  =  (P -Ps) l  dt  Eq.4  s  1^ e dt  Eq. 5  where V= velocity of the interdendritic liquid (ms" ); 1  // = viscosity of the interdendritic liquid (Nsm" ); 2  f = volume fraction of the interdendritic liquid; L  P = pressure (N-m" ); 2  16  PL = density of the interdendritic liquid (kgm" ); 3  ps = density of the solid (kgm" ); 3  g = gravitational acceleration (ms" ); 2  K = permeability (m ). 2  The solid density was assumed to be constant. pL is a function only of composition and hence of temperature, T, in the liquid-solid zone (this function can be obtained for a specific alloy by the experiment measurement of interdendritic liquid composition and the density calculation with software "METALS", as did by Auburtin (20)).The permeability for a two dimensional system is given by Eq. 7, 8 and 9. James A . Van Den Avyle et al (12) have developed freckle-potential criteria to include the thermal gradient, G, the local solidification time, LST, and incorporated them into mushy-zone solidification model predictions to establish quantitative predictions of the downward channel freckles for different melt conditions in alloy IN718, but no detail is available at present. Another choice for downward freckling criteria may be the modified Rayleigh numbers that will be discussed in the following chapters.  2.3.2 The Rayleigh criterion and its limitations  Several more or less successful criteria (based on various mathematical expressions involving the local thermal gradient G, local solidification rate R, and local solidification time (LST) have been reported. However, these criteria usually lack  17  precision. Moreover, they do not provide sufficient insight regarding the actions to be taken to minimize freckling. The most complete criterion available seems to be the Rayleigh criterion, which combines two of the three factors influencing freckle formation: alloy chemistry and casting conditions, but not casting geometry. The Rayleigh number, as reported by Sarrazin & Hellawell (24), can be written in the following manner: dp Ra =  rjD  T  h  4  showing that this Rayleigh criterion is based on the "thermal" Rayleigh number (expressed with the thermal diffusivity D rather than the solute diffusivity). The reason T  for this choice lies in the fact that the diffusion of heat is much faster (by a factor 10 ) 3  than the diffusion of solute in conventional metallic system, and therefore the diffusion of solute can be considered negligible during the evolution of freckle flow in the mushy zone. This is confirmed by the observation in analog systems that freckle plumes rising above the mushy zone are usually in thermal equilibrium with the surrounding bulk liquid, but still retain their high solute concentration (13). The parameter h has been linked to the dendritic array with the following 4  expressions: h = X 4  4  or h = K x A; . As well, dp/dz can also be written as dp/dz = G x 4  2  dp/dT in vertical gradients. The numerator corresponds to the driving force (due to density inversion) in the interdendritic liquid to produce freckling flow. The denominator represents the restriction opposed to this flow by viscosity and diffusivity of the melt, and permeability of the mushy zone. Sarrazin & Hellawell estimated that, considering h = 4  18  A\, then the critical threshold value for the Rayleigh criterion is Ra = I (i.e. freckling occurs when the driving force is greater than the restraining factors). Like most of the other criteria that have been suggested, the Rayleigh number describes the critical conditions for the initiation of freckle flow rather than its steady state. However, since freckling results from the breakdown of a metastable equilibrium state (heavier liquid atop a lighter one), it is assumed that freckle initiation will always produce fully grown freckles. The subsequent path of the resulting freckle is however not characterized by the criterion. However, there are at least two particularities infreckledcastings that do not seem to be accounted for by the factors in the Rayleigh number: •First, when several freckles appear in a given region of a casting, they are usually "equi-spaced". In other words, it is possible to attribute same-size crosssection areas to each freckle (6). This size is considered to be the minimum crosssection area necessary for the fluid flow pattern associated with freckling to develop. Thus it is believed that freckles should not develop in casting areas that are thinner than the minimum freckling area. This phenomenon is verified in blade casting, where freckles are usually found in the root rather than the airfoil section. This factor, however, is not currently included in the Rayleigh criterion. •Second, the Rayleigh criterion does not presently include any factor taking into account the fact that virtually all freckles found in DS and SX castings occur at a metal/ceramic interface (e.g. mold wall/surface of the casting) and at the mid-radius only in V A R / E S R ingots. Thus, several factors, such as the growth front curvature (i.e. its angle to the horizontal), or the potential increase of the  19  permeability at the non-wetting mold walls, need to be investigated and possibly included in the Rayleigh criterion.  2.3.3 Influence of the angle of the growth front on freckle initiation  (a) Flat front  (b) Convex front  (c) Concave front  Figure 8 Schematic description of experiments with curved mushy zones(4, 6)  Experiments on the transparent analog system ammonium-chloride/water (NH4CI/H2O) (6) yielded important observation on the influence of mushy zone curvature, which is depicted schematically below: 1) In straight forward vertical experiments (Figure 8a), the growth front was horizontal flat, and freckles seemed to be randomly distributed across the casting. 2) Some thermal insulation was then introduced at the bottom of the casting to artificially curve the growth front. When the center of the casting was colder than the edges (convex front) (Figure 8b), freckles appeared preferentially at  20  the center. Conversely, when the edges were colder than the center (concave front) (Figure 8c),freckles formed preferentially at the surface of the casting. This suggests that the segregated interdendritic liquid may first flow perpendicularly to the dendrites (path of higher permeability) at a certain depth in the mushy zone (probably along the iso-liquid fractionyl = 0.5 at which it initiates). It is then diverted upward, either by the mold wall (concave front case) or because the growth front angle diminished to zero and cannot sustain radial flow at the center (convex front case). It is therefore suggested that the angle of the growthfrontplays an important role on freckle formation and that some angles should favor freckling. Further more, this factor (which can be considered as a "casting geometry factor") provides a plausible explanation for the occurrence of surface-only or mid-radius only freckles. This mechanism is described schematically in Figure 9 by Auburtin.  Large DS/SX Casting (Freckles at the surface)  ESR/VAR Ingot (Freckles at mid-radius)  Large killed steel ingot ("A" segregates)  Figure 9 Freckle flow path and growth front angle in various industrial castings (4).  21  Freckle flow tends to follow the path of least resistance at first, which is perpendicular to the dendrites (it will be shown in the next chapter that the permeability perpendicular to the primary dendrite trunks is about 2 to 4 times greater than that parallel to the primary dendrite trunks). In the case of DS/SX castings, this flow will reach the edge of the casting and then develop vertically upward forming a surface freckle. Freckles can also develop at a certain angle to the vertical, even at the surface of the casting. The latter probably occurs when the growth front is angled in the third direction and offers greater sideways permeability. In the case of V A R / E S R ingots, as the flow gets farther from the centerline, the permeability of the mushy zone decreases, diverting the freckling flow upward at midradius. In the case of large killed-steel ingots, freckles develop on the side walls rather than the bottom of the ingot, also probably because of the higher permeability for flow perpendicular to the primary dendrites. Moreover, as the side-walls growth-front advances, permeability ahead of the freckle flow is reduced, progressively diverting the freckle flow towards the center of the ingot. The term "growth front angle" used here refers to the angle between the horizontal (perpendicular to the gravitational direction) and the temperature isotherm sXfi = 0.5 in the mushy zone (corresponding to the location of freckle flow initiation), rather than the actual dendrite tips (iso-liquid fraction of 1.0). This definition of the "growth front angle" is the one used in the remainder of this thesis. In the cases that undercooling can be neglected, the growth front angle will also refer to the angle between the horizontal and the Tpreckie isotherm.  22  2.3.4 Anisotropic permeability of mushy zone  From the above discussion., it can be seen that the permeability of mushy zone is a key factor to explain the influence of growth front angle on the initiation of freckling. Darcy's law is used to model the thermosolutal convection in mushy zone that is treated as a porous medium. When inertial effects are negligible, Darcy's law is written as Eq.3. It can be seen that permeability K is actually the Darcy's coefficient whose magnitude regulates the resistance exerted by the presence of porous medium in the distribution region. Most of the research published to date especially numerical simulations (25, 26, 27, 28) usually consider permeability as an isotropic parameter depending only on liquid fraction. One of the extensively used examples is the Blake-Kozeny model (28,29), also called the Kozeny-Carman equation (4)  Eq. 6  However, it is now accepted that the mushy zone in directionally solidified metallic systems is highly anisotropic (32). Poirier et al (29, 30, 31, 32) studied the permeability for fluid flow parallel and perpendicular to the primary dendrite trunks in a DS mushy zone. He also conducted empirical numerical simulations for perpendicular flow based on actual dendrites geometry. When only the influence of primary dendrite arm space Xj and liquidfractionfi on the permeability is considered, the permeability can be described as below (17):  23  For flow perpendicular to the dendritic array:  i.o9xio: /i 3  f  4.04 x l f T -6.49xl0  3 3 2  ^  A  2  < 0.65  N, 6.7336  y  6  0.65 <f <  0.75  L  + 5.43xl0  - 2  0.25 4  -2  0.75^/, <1  2  \-f .  Eq. 7  L  For flow parallel to the dendritic array:  f  3 . 7 5 X 1 0 - / L -A 4  2  2  L  < 0.65  \ 10.739  K, =  2.05 x I O  A2  -7  0.0741 l o g ( l - / J "  1  0.65 < f  L  -1.49 + 2 ( l - f ) - 0.5(1  A  L  2  < 0.75 0.75</ <l ;  Eq. 8 (Ai and  in m and K , K , K , in m ) 2  x  y  z  It is easy to calculate that, when fi = 0.5 which is the liquid fraction where freckle initiation takes place (20), KJK  Z  = 1.16. This means that flow perpendicular to the  direction of the dendrites should be easier than that parallel to the dendrites. However, while permeability of flow parallel to the primary dendrite arms is found slightly dependent on secondary dendrite arm space A2, the influence of X2 on permeability of flow normal to the primary dendrite arms can not be neglected (29,33). The permeability for flow perpendicular to the dendritic array as a function of A], A and liquid fraction f 2  L  can be best described as (4)  A^=3.62xl0V/ -4° 34  699  -^  27 3  (±30%)  (Ai and A2 in m and K in m ) x  24  (for 0.19 <f < 0.66) L  Eq. 9  Auburtin has examined the numerical values of the permeability for castings where freckles are usually encountered (4). In typical of both V A R / E S R ingots and small DS/SX castings, Xi = 0.35 mm (350pm), X = 0.12 mm (120pm), and assuming^ = 0.5, 2  yieldingK = l.lx z  10  -11  m and K = 2.7 x 10" m . 2  11  2  x  In the case of large DS/SX castings, the dendrite arm spacing increases to X\ - 0.5 mm (500pm) and X = 0.175 mm (175pm), yielding K = 2.3 x 10 2  -11  z  m and K = 9.8 x 2  x  10- m . n  2  It can be seen that the permeability for flow perpendicular to the direction of the dendrites is 2.5 to 4 times greater than that for the flow parallel to the dendrites. No data on the permeability in actual superalloy systems has been published to date. Nevertheless, because the mushy zone structure is relatively similar between analog and industrial systems, Eq. 8 and Eq. 9, the empirical formula based on the data of solid Pb-Sn and bomeal-paraffin columnar-alloys, have been chosen as the best available approximations. They are used in reference 4 and this thesis. These empirical expressions of permeability are probably quite sensitive to the details of dendrite geometry, particularly at large values of Xj and X . Moreover, 2  superalloy mushy zones may exhibit noticeable localized deviations from the average PDAS and SDAS values, possibly creating preferential paths of increased permeability and interdendritic fluid flow channeling (at the grain boundaries for example). Theoretical efforts to estimate the actual permeability in the mushy zone in real industrial conditions have been done (32, 34). However, although these methods have been validated in numerous configurations and comparisons with experimental studies and have been much simplified , they require solving of the momentum equation for flow  25  through a nonhomogenenous porous structure, and therefore are beyond the scope of this thesis.  2.4 THE MODIFIED RA YLEIGH NUMBER  Two possible modifications to the Rayleigh criterion have been suggested by Auburtin (4) to account for the effect of the growthfrontangle on freckle formation. The difference between these two theories lies on the assumption regarding the initial direction of the freckling flow: along the main axes of the mushy zone (parallel or perpendicular to the primary dendrites), or along the vertical direction. These two modified Rayleigh numbers have been applied to several superalloys and provided very good prediction of freckling in industrial situations (VAR/ESR ingots, DS/SX castings).  2.4.1 The first theory  In this theory the original Rayleigh criterion was extended to a 2D geometry. In a geometry shown below, the mushy zone (and the corresponding isotherms) are curved and form an angle a with the horizontal direction at the location of the freckle flow initiation.  26  C,, T,, p, C, T,p 2  2  2  Figure 10 Schematic geometry for an angled growth front (general casting conditions) In the local projection axes (x, z) (perpendicular and parallel to the primary dendrites), the two components of the driving force F for freckle formation are (F is based on the numerator of the Rayleigh number):  rp z  _  dp  _  dp  ^ "df 8  Vertical  ^Vertical F r e M e  '_/  \  „„„/„.  Eq. 10  \  Eq. 11  ()  -cos  a  Where G^.^ is the temperature gradient in the direction parallel to gravity vector at freckling temperature, because only the temperature gradient in this direction will contribute to the driving force F for freckle formation. Assuming that the initial flow due to density inversion and leading to freckling will be either parallel or perpendicular to the primary dendrites in the mushy zone, two separate Rayleigh numbers can be defined: For flow perpendicular to the dendrites:  27  Eq. 12  For flow parallel to the dendrites:  Eq.13  2  The term h in the original Ra expression is chosen as K 4  2  and K  2 Z  (h = 4K  is  indeed a characteristic linear dimension of the mushy zone linked to the average "pore" diameter). This choice is consistent with the fact that permeability is expressed in units of m. 2  The modified Rayleigh criterion for this theory is written as Freckling  occurs when: Ral = Max(Ra , Raj > Ral* x  Eq. 14  2.4.2 The second theory  Instead of considering that the flow associated with freckle formation will start either parallel or perpendicular to the dendritic direction, it is also possible to assume that this flow may always start vertically, following the direction of the density inversion driving force. Considering the same geometry of a tilted growth front already shown in Figure 10, the effective permeability of the mushy zone for fluid flow in the vertical direction is defined as (4, 35):  28  The characteristic linear dimension was considered to be h = y/~K similarly to the first theory, the corresponding Rayleigh number was defined as:  &  Ra = 2  irp  ^Freckle  ^ ~  Eq. 16  T]-D / T  /  effective  The modified Rayleigh criterion for this second theory can then be written: Freckling occurs when: Ra2>Ra2*  Eq. 17  2.4.3 Range and sensitivity of the parameters  Many variables in the Rayleigh number or modified Rayleigh number are either known or can numerically evaluated from literature data: 1. T and G are typical outputs of a casting model: in most casting processes, G is strongly dependent on the temperature at which it is measured or estimated (e.g. Gii dus and G ndus are quite different). This should influence greatly any qui  so  results given by a freckling criterion. Therefore care is taken to associate thermal gradients with their relevant temperature in this thesis. 2. Viscosity r/: measured values for the alloys of interest (and their composition variations due to segregation) are probably unavailable. However, TJ can be numerically evaluated for any alloy composition at any temperature through  29  the following expression published in references (36, 37) r/ = A e x p ( % )  (± 10%)  r  (in Kg/m-s)  Eq. 18  1.7xlO- .p^.^.M^ 7  Where A =  (in Kg/m-s) expl % .  and  5=2.65-7^  Eq. 19  T  Liquidus  (in J/mol)  Eq. 20  (with R = 8.3144 J/mol-K (gas constant), p in kg/m , Tand Tuquidus in K and M 3  in Kg/mol) Typical values of viscosity for nickel-based superalloys can found below in Table II.  Table II Liquid density, viscosity and thermal diffusivity for the four superalloys investigated in this thesis at their liquidus temperature and 100°C above their liquidus temperature. Superalloy  Temperature (°C) 1347  IN718 IN718 IN718LSi IN718LSi CMSX-11B  1447 1354 1454  Liquid density (xlO kg/m ) 7.44 3  3  7.35 7.44 7.34  Viscosity (xlO Kg/ms) 4.17 3.61 3  4.18  Thermal diffusivity (xlO' m /s) 7.69 7.75 7.73 6  3.61 4.10 3.54 4.16 3.60 4.10  7.79 8.68 CMSX-11B 1436 8.89 Rene 88 1355 7.95 Rene 88 1455 8.38 Nim80A 1379 8.57 Nim80A 1479 7.08 3.55 8.88 (p calculated by weighted average (38), TJ calculated with the formula in fEq. 18) and-Dr calculated by the 1336  7.26 7.16 7.34 7.25 7.17  software "Metals" (38). The nominal compositions of these superalloys can be found in Chapter 4.1.) 3. Thermal diffusivity Dr. as for rj, measured values of Dj are probably also unavailable. Nevertheless, DT can be estimated numerically with reasonable  30  2  precision (± 10%) as well, the values in Table II have been calculated by the program "Metals" developed by National Physical Laboratories (NPL, England) (37, 38). In view of the data in Table U, values of rj and DT are expected to be relatively constant within the range of alloy compositions, temperatures and segregation patterns usually involved in freckle formation in superalloys. 4. Primary dendrite arm spacing (PDAS) fa and secondary dendrite arm spacing (SPAS) A? can be evaluated from the thermal gradient G and the growth rate R (39, 40). The relationship can be translated to the following equations (4) 150x10^ 4=7TosT m \ Li uidus G  X  q  40 x I O G  Eq.21  -6  and 4 = 7 \ Liquidus  (±30%)  )  R  r^2~ X  (±  m  3 0 %  )  Eq-  2  2  )  R  (fa and fa in m, cooling rate Guquidm  x  R  m °C/s)  5. Liquidfractionfjj fj. is usually one of the parameters in a casting model, it governs the latent heat release on solidification. In the case of nickel based superalloys, liquidfractionprofiles are relatively independent of the alloy system considered as can be seen in Figure 11. It has been shown that freckles initiate at a liquidfractionbetween 0.4 and 0.6 in superalloys (20, 42). A value of 0.5 (± 20%) can therefore be considered a good approximation for most superalloys. Given the profile shown in Figure 1L/2  =  0.5 corresponds to a melting rangefractionof about 0.8, consequently,  31  Figure 11 Typical liquid fraction profile along the mushy zone of nickel base superalloys (4) it is possible to define the temperature for freckle initiation ^Freckle  1.  ^-^Solidus  =  7Freckle  as:  ^F  +  Eq, 23  Liquidus  Density inversion term dp/dT Based on Rayleigh number, it is possible to write  dp dp dz r/D 1 — -= — x — = Rax — rT" x — — dT  dz dT  Eq. 24  gX\ G  Assuming a critical Rayleigh number Ra* = 1 as reported in (24), and substituting numerical values (in SI units) provided by (24) and "METALS", and a vertical thermal gradient G = 10°C /mm (i.e. 10 K/m), yields: 4  In the case of Pb-10wt%Sn: dp ^ = d  T  2.5xlO"" -1.1x1 (T 1 = , ^ 7 n T 9.8-(3.0xl0" ) 10 3  l  x  5  X  4  32  0  -  3  0 3 5  OyanVC  Eq. 25  In the case of Pb-2wt%Sb: dp 3.0 x l O LOxlO - £ = lx — 9.8(3.0xl0~ ) - 3  d  T  -5  4  1 x — ^ 0.038 1  , (g/cm )/°C  Eq. 26  3  0  In the case of Ni-based alloys (numerical data for pure liquid nickel at 1500°C): dp 4.4 x l O -1.0x10 -£ = lx — 9.8-(3.5xl0" ) - 3  d  T  4  -5  1 x — ^ 0.030 10  3  g/cm /°C  Eq. 27  3  4  Confirmation of these numerical estimates was carried on for various alloy compositions (superalloys and tool steel) known to befreckle-prone,by Directional Solidification and Quench (DSQ) experiments (18, 19). By comparing the density inversions in Mar-M002 (freckle-prone) and Mar-M247 dp (freckle free), the density gradient —— necessary to produce freckles was dT found to be of the order of 0.01 (g/cm )/°C at the freckle initiation. 3  2.4.4 Numerical evaluation of the Rayleigh number  In any event, the Rayleigh number could be written: Ra = 0(77, D , dp/dr) x r(G, R, h, LST) T  Eq. 28  Thus, it can be seen that those coefficients with limited precision (77, DT, dp/dT) are used only in the proportionality factor ( 0 function) (which could also be named "alloy chemistry factor"). The same 0 would apply to different casting conditions, providing the  33  same alloy is used. Since this proportionality coefficient is not known with great precision, it may be necessary to recalibrate some of its terms to account for a given critical threshold value Ra*. Alternatively, it is also possible to calibrate Ra* instead. This calibration could be carried out by comparing freckle defect maps for actual castings to the numerical maps predicted by the criterion in a computer model. However, the more interesting factor is probably the second term, or "casting conditions factor" (/"function). Indeed, it is this factor which will provide some insight for a given alloy chemistry, about location and extent of freckling for various casting conditions and various casting procedures.  2.4.5 Application of the modified Rayleigh number criteria to three superalloys (Waspaloy, Mar-M247, UBC1)  Auburtin has cast directionally solidified cylindrical samples of three superalloys at various angles simulating a tilted mushy zone. The casting conditions in the samples were determined accurately by a complete thermal modeling of the furnace. The original and modified Rayleigh number have been applied to these alloys. This section will provide a brief critique of Auburtin's work. As discussed above, the viscosity 77, thermal diffusivity DT and density inversion term dp/dT can be considered independent of the casting conditions or of the alloy composition and to assume the values given below (referring to Table LI). g = 9.81  m/s  2  34  dp/dT= 30 (kg/m )/°C 3  77= 0.004 kg/ms D = 9 ' x 10- m /s 6  2  r  Permeability is calculated using the expressions previously presented in Chapter 2.3.4. K = 3.15 x l 0 - - f V 4  2  z  ^ where  L  = 3.62xl0 -f 3  3  34  L  ->  a699 w  a  m  2  m  2  273 2  fi = 0.5  and  15010"  A\ = /  6  m  \0.33  [Guquidus  X  R)  40-IO"  6  4  ~  /  \0.42  m  Thus the original Rayleigh number can be reduced to  Ra = 4.16 x IO" x G ™ x [G 6  Uquidus  fl)""  x  2  (± 15%)  Eq. 29  The modified Rayleigh number of the first theory can then be reduced to: Ra = 4.62 x 10~ x G j £ £ x [G 15  x  Ra = 3.64 x IO" x  x (G,,,,^ X R)'  14  U2  2  and  x R)' x 2  Liquidus  Ral = max(Ra , Ra ) x  sin(a)  ( ± 15%)  Eq. 30  X cos(a)  (± 15%)  Eq. 31  (±15%)  z  Eq. 32  The modified Rayleigh numbers of the second theory then reduces to f-i Vertical  Ra2 = -  ^  (l.48 x 10 • [G 7  x R)  38  Liquidus  —  • s i n ( « ) + 5.24 x 10 • (G 2  6  Liquidus  35  x R)  rj • cos («)J 2  (± 15%) ( Freckle G  ^  Eq. 33  °C /m, R in m/s)  The precision of the proportionality coefficients and of the Rayleigh calculations has been discussed by Auburtin (4). It is explained that the possible inaccuracies in the numerical values of the physical properties are all combined in the alloy chemistry factor (proportionality coefficient). This term may need to be refined for each alloy system considered. Instead of considering variable proportionality coefficients (based on specific alloy chemistry) and comparing Rayleigh numbers to a unique threshold value Ra* valid for all alloys, it is simpler and more practical to consider one given proportionality coefficient (valid for all alloys) and compare Rayleigh numbers to alloy dependent threshold values. Therefore an estimated proportionality coefficient is considered valid for all three superalloys studied in Auburtin's work and all these superalloys in this work. The actual uncertainty on the calculation of Rayleigh numbers then lies on the estimation of the solidification conditions. Given the range of variations of thermal gradients and solidification rates observed in the quasi steady-state section of each sample (see reference 4) (R varying from 2.8 x 10" m/s to 4.2 x 10" m/sabout its average value of 3.5 5  5  x TO m/s for example), the Rayleigh numbers can be calculated with a precision of about -5  (± 15%). The various casting conditions of the three superalloys were plotted in the form of the original and modified Rayleigh number Ral or Ra2 versus growth front angle (see Figure 12 taking Waspaloy as an example). It can be seen that it is possible to evaluate for each alloy a critical Ral * or Ra2* independent of growthfrontangle, below which freckling does not occur and above 36  1.4  (Waspaloy)  o No Freckles 1.2  1.0 • S3  "I 5  • Freckles - - Ra*  0.8  (Freckles)  (No Freckles)  •a  ;og> a  0.4 0.2 0.0  10  15 20 25 Growthfrontangle (degree)  30  35  40  (a)  2.0E-08  (Waspaloy)  o No Freckles • Freckles 1.5E-08  - - - Ra*  (Freckles)  13  •a  1.0E-08  • i-H  t <u  •3 o  (No Freckles)  5.0E-09  0.0E+00 10  15 20 25 30 Growthfrontangle (degree)  35  40  (b)  Figure 12 The original Rayleigh number Ra (a), modified Rayleigh number Ral (b) and modified Rayleigh number Ra2 (c) versus growth front angle for alloy Waspaloy (4).  37  1.2E-07  (Waspaloy)  o No Freckles • Freckles - - Ra*  3 S3  8.0E-08  C  •a tD  4.0E-08  o  (Freckles) (No Freckles) 0.0E+00 10  15 20 25 Growthfrontangle (degree)  30  35  40  (C)  Figure 12 The original Rayleigh number Ra (a), modified Rayleigh number Ral (b) and modified Rayleigh number Ra2 (c) versus growth front angle for alloy Waspaloy (4) (continued).  which freckling always occurs. Results are shown in Table VIU and LX. However it was failed to find such a critical Ra* of original Rayleigh number independent of growth front angle (as shown in Figure 12a). This indicates that the modifications of the original Rayleigh number to account for the angle of the growthfrontare successful at predicting freckling in experimental castings.)  38  2.A.5 Direct application of the modified Rayleigh criterion to industrial situations  The original, modified Ral and modified Ra2 Rayleigh numbers have been applied to some given casting conditions in V A R ingot which have been previously modeled (42). It was shown that Ral and Ra2 can indeed predict mid-radius only freckle whereas the original Rayleigh criterion cannot (see Figure 13) (4). It was shown by numerical modeling with ProCAST that, depending on the casting geometry and process operation conditions, growthfrontangles in DS/SX castings can range from 0° (flat horizontal front) up to 45° or more, thus demonstrating the potential applicability of the modified Rayleigh criteria to industrial situations (4).  Figure 13 Original and modified Rayleigh criteria profiles along the radius of VAR IN718 (melt rate : 260kg/hr) (4).  0  50  100  150  200  250  Radius (mm)  39  2.5 SUMMARY OF LITERATURE REVIEW  Freckles in superalloys have been considered as resulting from a thermosolutal convection driven by density inversion in the bulk liquid and mushy zone. The fact that the density of freckles is heavier than the density of matrix of the bulk alloys indicates that the "freckle" defects in IN718 have the similar morphology of classic freckles but a substantially different mechanism. The freckles in JJM718 may be caused by a densitydriven downward-forming channel, same as the mechanism of center macrosegregation defects. The segregation of Si in IN718 has been estimated sufficient to create density inversion and hence the formation of classical freckle (e.g. buoyancy driven upward flow freckling). Two modified Rayleigh numbers have been suggested as the freckle formation criteria, which combined the effect of solidification front angle relative to gravity vector into the original Rayleigh criterion, and therefore take account of all the three factors correlated with freckling phenomenon: casting geometry, solidification conditions and alloy composition. These modified Rayleigh criterion are easy to calculate, they have been applied to three superalloys under typical casting conditions and have been shown to describe the casting conditions leading to freckling with much better accuracy than the original Rayleigh number. These modified Rayleigh criteria have also been shown to be suitable to account for the occurrence of freckles only at the surface of DS/SX blade castings or only at mid-radius in E S R / V A R ingots.  40  3. RESEARCH OBJECTIVES 3.1 RESEARCH FOCUS  Two modified Rayleigh criteria were developed which incorporated all three factors influencing freckle formation (alloy chemistry, casting conditions, casting geometry) (4). More specifically, the angle of the growthfrontwith respect to the direction of gravity is taken into account in these criteria. The modified criteria were applied to typical superalloy castings and some superalloys and were shown to be suitable to account for the occurrence of freckles at DS/SX blade casting or in E S R / V A R ingots. One focus of this research is to apply these criteria to more superalloys, to evaluate the critical threshold values for the criteria to these alloys and finally to try to find threshold values for all the superalloys. It is now generally agreed that freckles are the product of specific fluid flow patterns, which is driven by a density inversion occurring in the mushy zone as a result of interdendritic segregation. However, in the research of Auburtin at al. (22) there is no density inversion was observed in IN718, a reportedfreckleprone alloy. Estimates of the concentration of some of the minor elements in the mushy zone showed that segregation of carbon and silicon in LN718 (with high Si) could produce sufficient density inversion for classical freckling (e.g. buoyancy driven upward flow freckling).  41  Another focus of this research is therefore to analyze the basic role of Si in freckling in LN718 by experiments and its relation to the modified Rayleigh criteria theory.  3.2 OBJECTIVES  The objectives of this research program are the following: 1. Apply the modified Rayleigh criterion to some superalloys and test these criteria on these alloys. 2. Estimate quantitatively the threshold values Ra* of the modified Rayleigh criterion for these alloys. 3. Demonstrate the influence of Si on freckle formation in LN718 alloy.  42  4. METHODOLOGY  A modified Bridgman-type furnace has been used to apply different casting conditions on six superalloys (CMSX-1 IB, Nim 80A, Rene 88, IN718 and variations). These casting conditions were accurately determined by numerical simulation using a commercial F E M package named ProCAST, calibrated with thermocouple measurements in the furnace.  4.1 CHOICE OF ALLOYS  Five alloys were selected for this experimental investigation: 1. CMSX-1 IB: a typical SX alloy; 2. Rene 88: a typical P M alloy used in disk applications in advanced engines; 3. Nim 80A: a typical wrought alloy; 4. IN718: a widely-used Ni-base superalloy; 5. I N 7 1 8 - l o w C , N , Si(IN718LSi):avariationofIN718. In addition, pure silicon was added to IN718 alloy to make five IN718 variations with different content of silicon, which are named as IN718-0.1Si, EN718-0.2Si, IN7180.3Si, LN718-0.4Si and IN718HiSi. The first four of the chosen five alloys are (or  43  reported as) nickel-base superalloys prone to freckle formation. The compositions and melting range of these alloys are presented in table HI.  Table HI: Compositions (in wt%) and melting range of chosen alloys in this thesis Alloy  Nominal Composition (wt%)  Tsoi-Tuq ( ° C ) 1275- 1336*  CMSX-11B  3.6A1, 7Co, 12.5Cr, 0.5Mo, O.lNb, 4.2Ti, 5W, 5Ta, 0.04Hf, Bal. N i  Rene 88 (2)  2.1A1, 0.03C, 13Co, 16Cr, 4Mo, 0.7Nb, 3.7Ti, 4W, 0.015B, Bal. N i  Nim80A  1.4A1, 0.03B, 0.06C , 19.5Cr, 0.3Mn, 76.0Ni, 0.3Si, 2.4Ti, 0.06Zr >  1313-1379*  IN718  0.46A1, 0.031C, 0.2Co, 18.12Cr, 2.96Mo, 5.27Nb, 53.46Ni, ITi, 0.08Si, 18.24Fe*  1253 - 1347*  IN718-LSi  0.5A1, 0.008C, O.OOICo, 18Cr, 3Mo, 5.0Nb, 54.03Ni, ITi, 0.007Si, Bal. Fe  <45)  (43)  (44  IN718-HiSi  1250 - 1355  (43)  1280-1354* 1175-1206*  *samples analyzed by the Special Metal Corporation. ** alloys provided by: Canon Muskegon Corp. (CMSX-1 IB); General Electric Corp. (Rene 88); Special Metal Corp. (IN718); Inco Alloys International (Nim 80A).  4.2 EXPERIMENTAL  APPARATUS  4.2.1 Tiltable Bridgman furnace  All the samples (25 mm diameter x 150 mm long or 1 in. diameter x 6 in. long) were melted and directionally solidified in a vacuum induction furnace. The basic design of this furnace is similar to that of the classical Bridgman furnace used in the industry, and a schematic diagram is presented in Figure 14. The induction coil is connected to a 50 kW (adjustable) /4.5kHz power supply. The top lid and walls of the graphite susceptor are 30 mm thick in order to absorb over 99% of the magnetic field and prevent any electromagnetic stirring of the melt (Appendix A). The melting chamber of the furnace is evacuated by a mechanpump only when the furnace is tilted, the vacuum level ranged from 80 um to 120 um; in other time the chamber is evacuated by a mechanic pump and a  44  diffusion pump, and the vacuum level was consistent at 20 urn. Vacuum was considered sufficiently good when cast samples would come out of the furnace without any scale or oxide "skin". The thermal model of this furnace, which will be described below, shows that except for transient zones at the start and the end of solidification (bottom and top of the  Ceramic Insulation—>. Graphite Susceptor •Alumina Mold  Metal Casting  Copper B a f f l e — • r ± ^ : Steel Spacer  Copper Chill Water Cooling  Withdrawal Direction i  F i g u r e 14 Schematic d i a g r a m o f the B r i d g m a n - t y p e furnace used i n this  study (4).  45  casting respectively), the solidification conditions in this experimental furnace are steadystate and constant throughout the sample. In the remainder of this thesis, all the results (such as the presence or absence of freckles) will pertain to this steady-state middle section of the casting, where gradients and solidification rates can be ascertained with reasonable precision. The thermal gradient at the growth front (Guquidus) can be adjusted from 5 to 40 °C /cm and depends essentially on the withdrawal speed and on the difference between the temperature of the susceptor (the "control temperature") and the liquidus temperature of the alloy. The solidification rate R in steady-state operation is determined by the withdrawal speed, which can be changed from 1.6 x 10 to 10 x 10" -5  m/s (1 and 6 mm/min).  Figurel5: Tiltable directional solidification furnace.  46  5  This furnace can be tilted from O°(conventional vertical operation) to 40°to the vertical. The whole chamber and all its contents are tilted together as shown in Figure 15. This presents the great advantage of allowing the study of the influence of the growth front angle on freckle formation, since the inside of the chamber is not modified. However the diffusion pump can not work under this condition because it is tilted with the furnace too.  4.2.2 Experiment schedule and typical experiment  The casting conditions of all the samples are given in Table TV. Following the results of experiments of the first alloy CMSX-1 IB which was tested under 12 different casting conditions, the remaining five alloys were cast under 5 different conditions, which are enough to reflect the effects of the variation of three control parameters (the furnace angle, the control temperature and the withdrawal speed) on the freckle formation during the solidification of the alloys. A typical experimental run follows the standard procedure outlined below: 1) The alumina crucible is filled with solid blocks of superalloy and raised in the top position inside the graphite susceptor; 2) The furnace chamber is closed, evaluated and tilted (when needed) to the desired angle;  47  3) The graphite susceptor is heated up to the desired operation temperature (= "control temperature") (about one hour), the power is then reduced to the proper level to maintain this control temperature constant throughout the remainder of the experiment. This control temperature is chosen to set the solidification gradient to a desired value (either a low thermal gradient or a high thermal gradient); 4) The casting is allowed to reach its equilibrium temperature for an additional 2000s before it is withdrawn. Calibration experiments with thermocouples inside the melt (4) showed that this period of 2000s is more than sufficient; 5) Withdrawal is started and is carried out at a constant speed for the entire length of the casting. During the entire experiment, the furnace operating conditions (susceptor temperature, temperature alongside the casting, chill position, withdrawal speed and vacuum) are continuously monitored and recorded by a computer data acquisition system. The readers are recommended to read reference (4) for more details of this furnace. The LN718 with high Si (IN718HiSi) samples were made by adding 3 g silicon to about 550 g LN718 alloy bulks as charge materials. After casting and solidification, the compositions of samples were analyzed at both the top and the bottom end of the sample in order to verify if a uniform composition has been obtained. Similarly the LN718-0.1 Si, LN718-0.2Si, LN718-0.3Si, LN718-0.4Si were made by adding different amount of silicon into LN718 bulk with the ratio shown in Table V .  48  Table IV Casting conditions. Alloy  CMSX-1 IB  Rene 88  Nim80A  IN718  IN718LSi  IN718HiSi  IN718-0.1 Si IN718-0.2Si IN718-0.3Si IN718-0.4Si  Sample  Angle  #001 #002 #007 #008  0 0 0 0  Control T (°C) 1435 1435 1500 1500  #006 #005 #012 #010  20 20 20 20  1435 1435 1500 1500  1 6 1 6  #004 #003 #011 #009 #101 #102 #103 #104 #105 #201 #202 #203 #205 #204 #301 #302 #303 #304 #305 #401 #402 #403 #404 #405 #501 #502 #503 #504 #505 #601 #701 #801 #901  35 35 35 35 35 35 20 20 0 35 35 20 20 0 35 35 20 20 0 35 35 20 20 0 35 35 20 20 0 35 35 35 35  1435 1435 1500 1500 1400 1465 1400 1465 1400 1435 1500 1435 1500 1435 1400 1465 1400 1465 1400 1435 1500 1435 1500 1435 1400 1465 1400 1465 1400 1465 1465 1465 1465  1 6 1 6 6 1 6 1 1 6 1 6 1 1 6 1 6 1 1 6 1 6 1 1 6 1 6 1 1 1 1 1 1  49  WD rate (mm/min) 1 6 1 6  Table V Ratio of charged silicon to bulk IN718 when making IN718 variation samples Alloys IN718-0.1 Si IN718-0.2Si IN718-0.3Si IN718-0.4Si IN718HiSi  Charged Silicon (gram) 0.6 1.1  Charged bulk LN718 (gram) 516.2 541.5 500.0 534.1 550.0  1.5 2.2 3.0  4.2.3 Sample analysis  The casting samples were etched with 20 ml H 0 + 40 ml HC1 to display the 2  2  grains and the freckles on the sample surface. Most of the samples were polished before etching because the rough surface makes it so difficult to reveal the freckles on the surface clearly. The casting of LN718 alloy and its variations must be etched twice to be observed clearly. At least one sample of each alloy was cut longitudinally along the centerline in order to find whether there were freckles inside the samples or not. The compositions of the matrix andfreckleswere analyzed by S E M / E D A X on the cross section of samples for each alloy. The location of the freckles was determined by optical observationfirst,then confirmed by the composition analysis.  50  D T A tests were applied to most of the alloys to obtain the correct data of liquidus and solidus, especially for new alloys (such as Rene 88) or modified alloys (such as IN718HiSi) for the special purpose of this research.  4.3 NUMERICAL MODELING  In order to estimate the actual solidification conditions (GLiquidus, GFreckie, R) at various locations inside the sample, a numerical model of the experimental furnace was developed. The goal of this model was to enable, after proper calibration, the desired translation from furnace operation parameters to actual solidification conditions in the casting, for each experiment. Because no physical measurement of the density was possible in the scope of this thesis's experiments, another mathematical model named " M E T A L S " was used to translate the measured chemical compositions into densities at a given temperature while investigating the effect of high Si in the density inversion in the liquid of alloy IN718. This model is a courtesy provided by National Physical Laboratories NPL (UK).  51  4.3.1 Numerical Modeling of the furnace  ProCAST is a general finite element heat transfer and fluid flow package developed by UES Inc., specially designed to simulate mold casting process. The information needed for ProCAST to develop the model is: the geometry of the problem as defined by the finite element mesh, the relevant material property data, and the relevant boundary and initial conditions. Several modules modeling fluid flow (mold filling and thermal convection), stress/strain analysis and/or electro-magnetic effects can be coupled to the main thermal conduction module. The method for calculating radiation view factors used by ProCAST made it feasible to recompute view factors which are changing with time, therefore the process of vacuum directional solidification during which a casting is slowly withdrawn from the hot zone of a furnace can be easily simulated: view factors are automatically updated by the model in order to accurately compute the radiation heat transfer, which depend on the relative positions of the various furnace parts. The enthalpy formulation employed in ProCAST can accurately model the phase transformation of any alloy to the extent that the fraction solidified function has been quantified, as is the case in the present work. Thus, in ProCAST, the release of latent heat on solidification is governed by the fraction solid profile in the melting range of the alloy, an example of which has been shown in Figure 11, rather than by a linear release between Tuqutdus and Ts ndus- ProCAST has a very accurate and efficient coincident node 0  methodology for modeling the interface heat transfer between the casting and the mold, which is a dominant rate controlling mechanism, time and/or temperature dependent  52  coefficients can be accommodated. In our case the local heat transfer coefficients (HTC) are governed by the local temperature of one of the two surfaces forming the interface. All these features make ProCAST a very suitable tool to simulate the directional solidification process of this research. More details of this technique and its applications are available in the ProCAST User's Manual (46). The mesh used to model the furnace was generated by the commercial code P A T R A N . The geometry is axisymetric and corresponds accurately to the geometry and dimensions of the furnace, as it has been presented in Figure 14. The axisymetric mesh of the whole furnace, as well as an enlargement of the hot zone, can be seen in Figure 16. Because most of the top part of the chamber is masked off by the baffle and susceptor assembly and will therefore play only a minimal role in the view factor calculation, it has not been included in the meshing of the radiation enclosure. The susceptor, baffle and furnace walls are considered to form a "radiation enclosure", which is divided into "bar 2" elements. Each of these elements is assigned a given emissivity and temperature. The copper chill, copper water cooling pipes, steel spacer, alumina crucible and superalloy casting are modeled as independent bulk materials and meshed with "quad 4" elements. Six interfaces have been defined: copper chill/water pipes, copper chill/steel spacer, copper chill/alumina crucible, steel spacer/alumina crucible, steel spacer/alumina crucible, steel spacer/alumina crucible, steel spacer/superalloy casting, and superalloy casting/alumina crucible.(Figure 17). The simulation begins with the furnace radiation enclosure already at its desired control temperature. The various modeled materials are initially set at the arbitrary temperatures given in Table VI. After the system reaches its steady-state equilibrium (i.e.  53  Hot Zone  Furnace chamber  100mm  •1 • • r i •1 • • l i •1 •III •1 ••11 •1 • • 1 9 •1 • B i •1 • • i i •1 • • I ! •1 •Ill •1 • • : : •1 HIS •1 • • •1 • i •1 • • i i •1 • • 11 •Hi II I I ! II H i l II •1 •III •I •1 •III •1 •III •1 •1 •III •III •I •1 • I •III III! • I Mil •• • • •III HIS •• •III • I •III • I •III •I Mil • • Mil •I • I •III • I H•III li i!  Legend  II  •1 M inl m ••in •1 Mill 20mm (a) Entire furnace.  (b) Detail of the hot zone.  Figure 16 Axisymetric mesh geometry used in ProCAST to model the furnace.  54  Casting Alumina tube Steel spacer Copper chill Water cooling pipes  Figure 17 Schematic heat flow diagram in the ProCAST model of the experimental tiltable furnace.  Table VI Initial conditions of the materials at the start of the numerical simulation.  Material  Initial temperature  Superalloy casting  TLiquidus of the superalloy  Alumina tube  Tuquidus  Steel spacer  600°C 20°C  Water cooled copper chill  of the superalloy  all the temperatures in the modeled materials are constant), similarly to an actual experiment, the casting/chill assembly is withdrawn from the hot zone at a predetermined speed and calculations are continued until solidification of the casting is complete.  55  The results from ProCAST can be displayed with the post-processing modules PostCAST and ViewCAST as temperature versus time curves or as isotherm evolution animation. Temperature gradient at different temperature (for example Guqutdus, GFreckie) and solidification rate R are also the typical outputs of the ProCAST model. Gravity was assumed to have no influence on these parameters, in other words, all these thermal parameters were assumed to be independent on the tilted angle of the castings. The model parameters have been calibrated with thermocouple measurements in the experimental furnace. The simulation shows relatively-little sensitivity to most of the parameters in the model which had to be estimated (emissivities, surface temperatures, heat transfer coefficients). More details are available in reference (4).  4.3.2 Mathematical Model "METALS"  This model is based on a weighted average of the molar volumes of each pure element forming the alloy (along the same principle, this model is also capable of calculating alloy enthalpies, viscosities, thermal conductivities and diffusivities). This approximation is now a widely accepted approach (20). The basic equations in these models are presented below: The molar volume in solid phase MVs of each pure element i is given by: MV'(T)=  MV (15°C)x(\ l  s  + a^ x(T-25))  Eq. 34  for temperatures (7) below the liquidus temperature T\ . At the temperature T(in °C), the iq  56  molar volume in the liquid phase MV[ of each pure element / (of melting point f )  is  mp  given by a similar equation: MV[(T)= MVliT^xil  + ai x(T-T ))  Eq. 35  Uq  with MV[{T )^ Uq  MV[(T )x(l mp  +  al x(T -Tl )) Liq  p  Eq. 36  for a given total weight f^of an alloy of known composition, the mumber of mole d of each element is also known. Thus the density of the alloy in the solid and liquid state, at any given temperature T, can be calculated as follow: Ps(T) = W/[£ (a'xMV^T))]  Eq.37  i  and  p (T)^W/[X(a'xMVi(T))]  Eq. 38  s  This model is accurate to about 5% according NPL. It was tested in reference (20) with good agreement. In the present case of directional solidification, interdendritic liquid at any depth is assumed to be in thermodynamic equilibrium with the solid/liquid interface. Thus, at any depth, the interdendritic liquid is at the local liquidus temperature. However, as indicated in reference (20), this model is not a good approximation in the case of interstitial elements, such as carbon. For instance, addition of carbon may increase the total weight without necessarily increasing the volume, thus, as carbon content increases, the density of the alloy could increase, instead of decreasing as predicted by "METALS". Therefore, " M E T A L S " calculations involving elements such as carbon should probably be regarded as qualitative approximations.  57  5. RESULTS  5.1 EXPERIMENTAL  RESULTS  As indicated in reference (4), the tilt angle of the whole furnace is indeed representative of the angle of the growth front in the casting with the gravity vector (despite any potential effects from the melt convection). The steady-state solidification zone is the middle section of each sample, which was visually inspected (as-cast and etched surface as well as etched cross-sections) in order to determine whether the corresponding set of casting conditions was subject to freckling or not. Similar to the observation of Auburtin, the freckles appear on the upside surface of inclined samples of alloys CMSX1 IB, Rene 88, Nim80A and IN718HiSi, however freckles were also found on the underside surface of the inclined samples of alloys IN718, IN718-0.1 Si, IN7180.2Si, IN718-0.3Si, IN718-0.4Si. All the freckles observed in this research were surface freckles. None was detected on the cross-sections etched to investigate the inside of the casting. This is comparable to the total absence of freckles inside larger industrial DS/SX castings. The typical appearance of freckles in a casting is shown in Figure 18. Microprobe analysis results of the observed freckles were shown in Table VJJ. Among the alloys of which freckles occurred on the upside surface of inclined casting samples, CMSX-1 IB and IN718HiSi have been chemical analyzed as typical examples; similarly LN718 and JJSf718-0.4Si among the alloys with freckles occurred on the underside surface of their inclined samples have been analyzed, IN718-0.4Si was selected  58  because it has the highest Si content among these alloys. As can be seen, the chemical composition of freckles is noticeably shifted toward the alloy's eutectic composition, confirming that they are indeed freckles. The numerical data relevant to all of the experimental results for tilted castings are gathered in Table VLTJ. For each experimental casting, the growthfrontangle and the casting conditions Guquidus, GFreckie and R (estimated with the ProCAST model from the furnace operating conditions)and the presence or absence of Freckles are reported.  a) Freckles on the upside surface of an inclined CMSX-11B sample (#004)  b) Freckles on the underside surface of an inclined IN718LSi sample  c) Freckles on the vertical surface of an IN718HiSi sample  Figure 18 Appearance of freckles on the surface of castings (castings diameter: 25 mm)  59  Table VII Chemical analysis (measured by microprdbe) of the matrix and freckles from some of the experimental samples. (wt%)  Al  IN718 Matrix Freckle 0.37 0.40  IN718-0.4Si Matrix Freckle  IN718HiSi Matrix Freckle  CMSX-11B Matrix Freckle  0.41  0.27  0.38  0.33  2.93  0.97 1.61  0.62 0.90  1.35 1.39  -  3.32 -  1.31  0.50 0.95  3.93  7.08  18.48  17.98  18.67  15.90  18.58  16.08  11.34  Fe  18.63  17.41  18.82  15.06  19.45  16.33  -  5.59 -  Ni  53.94  53.0  53.42  53.06  53.41  51.88  59.02  61.75  Nb  4.66  6.09  4.21  9.07  4.05  8.86  0.13  0.11  Mo  3.07  3.54  3.04  4.05  2.86  3.79  0.48  0.26  Co  '-  -  -  -  -  -  5.51  4.49  -  -  -  0.16  0.22  -  -  -  6.23  9.4  -  -  -  9.90  7.77  Si Ti  0.23 1.08  0.27  Cr  Hf  -  Ta  -  W  -  -  -  -  •  60  Table VIII Summary of the directional solidification experiments carried out on the tiltable Bridgman furnace. Alloy  Sample #001 #002 #007 #008  CMSX-11B  #006 #005 #012 #010  Control T Angle (°C) 1435 0 1435 0 1500 0 1500 0 1435 1435 1500 1500.  (°C/cm) 27 27 33 19  R (mm/min) 1 1 1 6  Freckling?*  (°C/cm) 23 23 30 7 23 7 30 7  27 18 33 19  1 6 1 6  yes no yes no  ^Liquidus  20 20 20 20  ^Freckle  no no no no  #004 1435 35 23 27 1 yes #003 1435 35 7 18 6 no #011 1500 35 30 33 1 yes #009 1500 35 7 19 6 no #101 1400 35 9 18 6 no #102 1465 35 26 32 1 yes Rene 88 #103 1400 20 9 18 6 no #104 1465 20 26 32 1 yes #105 1400 0 11 19 1 yes #201 1435 35 11 17 6 no #202 35 1500 26 • 30 1 yes Nim80A #203 1435 20 11 17 6 no #205 1500 20 26 30 1 yes #204 1435 0 15 21 1 yes #301 1400 35 10 16 6 no yes(underside) #302 1465 35 26 31 1 IN718 #303 1400 20 10 16 6 no yes(underside) #304 1465 20 26 31 1 #305 1400 0 14 20 1 yes #401 1435 35 15 22 6 no #402 1500 35 29 33 1 yes(underside) IN718LSi #403 1435 20 15 22 6 no #404 1500 20 29 33 T no #405 1435 0 20 25 1 no #501 1400 35 9 17 6 no #502 1465 35 35 38 1 yes IN718HiSi #503 1400 20 9 17 6 no #504 1465 20 35 38 1 yes #505 1400 0 31 35 1 yes yes(underside) IN718-0.1 Si #601 1465 35 1 yes(underside) IN718-0.2Si #701 1465 35 1 yes(underside) IN718-0.3Si #801 1465 35 1 yes(underside) IN718-0.4Si #901 1465 35 1 *: "yes" meansfrecklesoccur on the upside surface of an inclined sample or the surface of a vertical sample; "yes(underside)" meansfrecklesoccur on the underside surface of an inclined sample.  61  5.2 FURNACE MODELING RESULTS  A steady-state solidification was observed for all the alloys under various casting conditions, this steady-state solidification is characterized by the constant height of the mushy zone and a small amount change of the position of the growth front relative to the baffle lip during the solidification, as indicated in reference (4). The isotherm map within a CMSX-1 IB sample withdrawing in a control temperature of 1500°C and a withdrawal speed of 6 mm/min, and another one withdrawing in a control temperature of 1500°C and a withdrawal speed of 1 mm/min are shown in Figure 19 and Figure 20 respectively. From the above figures, as well as indicated in reference (4), the growth front is observed flat and perpendicular to the vertical axis of the casting and axis of withdrawal at low withdrawal speed (1 mm/min), and a small curvature of the isotherms occurs (from 0° at the center to about 7° to the horizontal at the edge of the casting) at withdrawal speed of 6 mm/min. Therefore, at low withdrawal speeds, the tilt angle of the furnace corresponds to the angle of the growth front with the direction of gravity: =  (  ± l  °)  '  E  q-  3 9  for high withdrawal rates, the actual growth front angle should be slightly adjusted as follows: «  /  r  o  n  (  =«^+4  0  (±3°)  Eq.40  The small difference between the actual growth front angle and the tilt angle of the furnace was considered negligible for both of the cases.  62  Figure 19 Typical thermal profiles in the casting during solidification (ProCAST simulation), (alloy: CMSX-1 IB; control temperature: 1500°C , withdrawal speed: 6 mm/min)  63  1500.00  1100.00  1360.00  ill ::!§|!|-  1337.00  1336.00  1325.00  1323.00  1277.00  1273.00  HI  1200.00  1000.00  800.00  600.00  100.00  200.00  15.00 TEMPERATURE STEP NUMBER - 850 TIME - 1.166000E+03 TIME STEP - 5.0O0O00E+00  F i g u r e 20 T y p i c a l thermal profiles i n the casting d u r i n g solidification ( P r o C A S T simulation), (alloy: C M S X - 1 1 B ; control temperature: 1465°C; w i t h d r a w a l speed: 1 mm/min)  64  Results from the model can be post-processed to produce maps of thermal gradients and of isotherm velocities. These values are calculated for each node in the casting when they reach a specific temperature, such as the alloy liquidus temperature or the freckle initiation temperature. In the present case, the global thermal gradient is defined as:  Eq. 41  Figure 21 The direction of calculated temperature gradient in samples solidified with an inclined angle a by ProCAST.  In the ProCAST model employed in this thesis, the z coordinate was parallel to the axis of the castings. Under the thermal condition of a DS furnace, the direction of temperature gradient at freckling temperature and liquidus temperature of the alloy is actually parallel to the casting axis, as shown in Figure 21, that is  65  TEMPERATURE GRADIENT GRADIENT COMPUTED AT TEMPERATURE = 1.200000E+03 MAGNITUDE OF THE TEMPERATURE GRADIENT  TEMPERATLeEJoRAmE^^  Figure 22 Temperature gradient vector calculated by ProCAST model (Grreckiw alloy: IN718HiSi, T eckie = 1200°C, R = 1 mm/min, T , = 1465°C). Fr  c o n t r o  66  This was confirmed by the results of gradient vector plot shown in Figure 22. However, only the component of GFreckle in the direction parallel to gravity vector (z'coordinate in Figure 21) will contribute to the driving force of freckling, as described in Figure 10, i.e. FrTkfe  G  = Freckle G  X  COS(«)  The solidification rate is evaluated in the following manner, as quoted in the ProCAST user's manual (46): "when each node reaches a specified temperature, a point is located along the temperature gradient some distance away, and the time that it takes for the isotherm to reach that point is determined. R is then calculated as that distance divided by the difference in time". In the case of this thesis, the direction oiR is parallel to the casting axis. The specific values of the thermal gradient and isotherm velocity are given in Table VIU. Details of the simulation maps are given in reference (4). It should be mentioned that the solidification rate is similar to the withdrawal rate throughout the casting (top and bottom transients excluded) and R is not dependent on the temperature(7i, ,rf or Ts ndus for example) at which it is evaluated, unlike the thermal ?u  liJ  0  gradient G. The precision of the measurements for the data in Table VHI is approximately the following (based on the ProCAST results): •  Thermal gradients Guquidus and GprecUe- ±15% (about ± 3 - 4 ° C / c m ) ;  67  Solidification rates R:  ±20% (about +0.42 mm/min).  68  5.3 APPLICATION OF THE MODIFIED RAYLEIGH CRITERIA  5.3.1 A p p l i c a t i o n o f t h e first t h e o r y o f A u b u r t i n e t a l .  The modified Rayleigh numbers of the first theory of Auburtin et al. can be calculated as: Ra = 4.62x1 Cf  13  x  X GFreckle  (GLiquidus  x  Ra = 3.64xl0'  xG ie  and  Ral = max(Ra , RaJ  14  z  x  R)'  2  x(G uidus xR)'  U2  Freck  Liq  ?5  x  Sirl(cc)X COS(CC)  xcos (a) 2  (±15%)  Eq. 42  (±15%)  Eq. 43  (±15%)  x  (GFreckie and G uidus hi °C/m, R in Liq  Eq. 44  m/s)  The modified Rayleigh numbers Ral for various casting conditions for all the superalloys considered in this study except IN718-0.1 Si, IN718-0.2Si, IN718-0.3Si, DSf718-0.4Si are calculated, the results were shown in Table LX. A critical threshold value Ral * independent of growth front angle, below which freckling does not occur and above which freckling always occurs, can be easily estimated without any exception, the results for each alloy are given in Table X . It is worth to note that, in his Ph.D. thesis, Auburtin (4) did not distinguish the difference between G Me Fre  calculated from ProCAST and  G ™lf v e F  e  as the driving force of  freckling, he simply treated G p™u as V  e  *-* Vertical _ s~t  ^Freckle  ^Freckle  this will give a larger modified Rayleigh number for the inclined samples, and hence a  69  larger threshold value than the results in this thesis for the same alloy. However, the results of Auburtin were still included in Table X and Table XI for reference. Table IX Calculated modified Rayleigh number R a l and Ra2.  Alloy  Sample  Freckling?  Ral (x IO" ) 7.28 7.28 6.27 2.31 31.5 4.01 18.5 4.23 46 5.86 27.1 6.18 2.94 38.9 2.01 26.6 13.6 1.6 36.5 1.09 •25 9.95 1.95 37.7 1.34 25.8 10.4 0.88 29.7 0.87 20.3 8.11 2.77 20.4 1.9 14 6.36 9  CMSX-11B  Rene 88  Nim80A  IN718  IN718LSi  IN718HiSi  #001 #002 #007 #008 #006 #005 #012 #010 #004 #003 #011 #009 #101 #102 #103 #104 #105 #201 #202 #203 #205 #204 #301 #302 #303 #304 #305 #401 #402 #403 #404 #405 #501 #502 #503 #504 #505  no no no no yes no yes no yes no yes no no yes no yes yes no yes no yes yes no yes(underside)  no yes(underside) yes(underside)  no yes(underside)  no no no no yes no yes yes  70  Ra2 (x IO" ) 7.28 7.28 6.27 2.32 8.18 2.37 6.94 2.51 10.3 2.75 8.47 2.9 1.85 1.02 1.67 8.2 13.6 1.26 9.56 1.19 7.68 9.96 1.39 9.88 1.28 7.94 10.4 0.97 8.92 0.98 7.27 8.11 1.75 7.71 1.58 6.46 6.37 9  Table X  Threshold value Ral * of various alloys  Ral*  Alloy  («) CMSX-11B  12.9 x IO"  Rene 88  8.3 x IO"  Nim 80A  5.8 x IO"  LN718  6.2 x 10"  JN718LC, N , Si  25.0 x IO"  IN718HiSi  4.6 x IO"  Waspaloy (4)  15.0 x 10"  9  9  9  9  9  9  9  Mar-M247) (4)  7.5 x IO  UBC1 (4)  10 x IO  -9  -9  5.3.2. Application of the second theory of Auburtin et al.  The modified Rayleigh number (second theory of Auburtin et al. (4)) can be written as: Ral =  G  .cos(a)  _  FreMe  (l.48 x 10 • [G  x Rf" • s i n ( « ) + 5.24 x 10 • (G  7  2  Liquidm  6  x R)° • c o s ( « ) J M  Liquidus  (+15%)  2  Eq. 45  (G eckie and Gu uidus in °C/m, R in m/s) Fr  q  Same procedures in chapter 5.3.1 were applied for each alloy. Results are given in Table LX and Table XI. A threshold value Ral* can be easily found for each alloy except CMSX-1 IB. As can be seen from Table X , for CMSX-1 IB the smallest Ra2 of freckled  71  samples is larger than the largest Ra2 of non-freckle samples, however, considering the error range of the calculation (±15%) a threshold value Ra2* can still be estimated for CMSX-11B. The result is shown in Table XI.  Table XI Threshold value Ra2* of various alloys Alloy  Ra2*  CMSX-1 IB  7.11 x 10"  Rene 88  5.0 x IO"  Nim 80A  4.5 x IO"  IN718  4.7 x IO"  IN718LC,N, Si  8.5 x IO"  IN718HiSi Waspaloy (4)  4.1 x IO" 7.80 x IO"  Mar-M247) (4)  6.7 x IO"  UBC1 (4)  5.40 x IO"  («) 9  9  9  9  9  9  9  9  9  5.4 LIQUID DENSITY CALCULATED FROM "METALS" FOR SOME ALLOYS  As typical examples for alloys that have upside surface freckles and underside surface freckles, the densities of the freckles and the surrounding matrix at liquidus temperatures of CMSX-1 IB, IN718, IN718-0.4Si and IN718HiSi have been calculated with " M E T A L S " from the measured compositions (Table VII). The results are presented in Table XII, it can be seen that freckles occurred on the upside surface of inclined samples always have a lighter density than the matrix surrounding them, and the freckles occurred on the underside surface of a inclined sample are heavier than the matrix.  72  Table XII Liquid densities of freckles and surrounding matrix of alloys CMSX-11B, IN718, IN718-0.4Si and IN718HiSi  Alloy Freckling Area PT=liquidus  CMSX-1 IB upward  IN718 downward  Matrix  Freckle  Matrix  Freckle  7.653  7.483  7.425  7.425  (g/cm ) 3  pT=Tfreckle  7.442  7.495  (g/cm ) 3  73  JN718-0.4Si downward  LN718HiSi upward  Freckle  Matrix  Freckle  7.400  7.408  7.499  7.452  (1328°C)  (1328°C)  Matrix  7.515  7.521  (1206°C)  (1206°C)  7.457  6 DISCUSSION  6.1 VALIDATION OF THE MEASUREMENTS  AND EXPERIMENT  RESULTS  6.1.1 Uniform composition of IN718HiSi casting samples  The compositions of TN718HiSi were analyzed at both the top and bottom end of mple, and the results are shown in Table XUI. It can been seen that the composition in  a sai  the sample is quite uniform, the method to make IN718 variation with different Si content by adding pure silicon as charge material in the casting is therefore be considered suitable.  Table XIII Composition of matrix at the top and bottom of a sample of IN718HiSi Elements  IN718HiSi Matrix Bottom Top  Al  0.38  0.35  Si  0.62  0.57  Ti  0.90  0.88  Cr  18.58  18.76  Fe  19.45  19.60  Ni  53.41  53.12  Nb  4.05  3.66  Mo  2.86  3.06  74  6.1.2 Freckle composition  The position of a freckle in LN718 and variations was located in S E M screen by marks on the polished cross section of samples made before E D X test, then it was further confirmed by their relatively high Nb content. The measured composition of freckle in LN718 in this research was compared with literature values, as shown below. They are in very good agreement. It was shown, Nb, Mo, Ti and Si are elements segregated to interdendritic liquid, Cr and Fe are elements segregated to dendrite area. Element A l detected in present work segregate a little bit to interdendritic area (Freckle), which is different from the results reported in the literature, but the composition difference between freckle and matrix is very small (0.03 wt%) and is among the error range of E D X . Moreover, in samples of both LN718-0.4Si and LN718HiSi, A l was observed to segregated positively (into the interdendritic liquid). Furthermore because the content of  Table XIV Comparison of the composition of freckle and matrix in IN718 detected in the present work and the literature (wt%). Matrix Al  Present 0.37  Ref.(20) 0.33  Ref.(7) 0.67  Si Ti  0.23 1.08  -  -  Cr  18.48  0.83 18.48  Fe  18.63 53.94 4.66 3.07 100  19.37  0.97 18.58 17.62  51.68 5.55 3.41  53.19 5.46 3.38  99.65  99.9  Ni Nb Mo Total  75  Present 0.40 0.27 1.31  Freckle Ref.(20) 0.14  Ref.(7) 0.43  -  -  1.20  1.33 17.36  17.98 17.41  16.93 16.80  53.0 6.09 3.54 100  50.16 10.11 4.15 99.5  15.23 52.55 9.43 3.51 99.9  A l in IN718 and variations is very small, the influence of the error about A l on the density calculation is negligible. All these confirmed the validity of the experimental procedure used in this thesis to measure freckle and surrounding matrix compositions.  6.1.3 Fraction liquid  The composition of freckle and surrounding matrix were used to back calculate the fraction liquid at which freckling initiates. According to Scheil equation  7^ = 7 T T  Eq.46  Nb in JN718 (k = 0.44 for Nb in IN718) (reference (20)), which behaved according to the 0  Scheil equation was selected for this calculation. The results i s ^ = 62%, which confirmed the assumption made in the beginning of this thesis based on the research of Auburtin (20), that is freckling will initiate at fraction liquid of 50% (40 ~ 60%).  6.2 EFFECT OF SI CONTENT ON THE FORMATION OF FRECKLE IN IN718 AND VARIATIONS.  As shown in Chapter 5.1, freckles occurred on the underside surface of the inclined samples of IN718, the composition analysis and consequently density calculation indicates that freckles in IN718 are heavier than the surrounding matrix. Therefore these freckles were induced by a downward interdendritic liquid convection. Freckles were  76  found on the underside surface of inclined samples until the Si content of JN718 bulk area variation increased to some point (~ 0.62 wt% in our case), where freckles occurred no longer on the underside surface of inclined samples but on the upside surface of inclined samples only. Density calculation based on composition measurement as shown in Table VLT reveals that the upside surface freckle has lighter density than the surrounding matrix, then it is believed that the formation of freckle is under the density inversion mechanism again. Based on a calculation using "METALS", Auburtin (20) has suggested that a density inversion susceptible to create freckles can be produced when Si segregate up to 0.6 ~ 1.0 wt%. The results of this research, however, is a little bit different, Si has to segregate to a higher content (about 1.35 wt% as in IN718HiSi) to produce freckles lighter than matrix. In the case of LN718-0.4Si, the Si content in freckle is 0.97% (Table VH) but freckles heavier than matrix still occurred on the underside surface of inclined samples. The reason for this difference between calculation hypothesis and real results from experiments may arise from the calculation methods used in software "METALS". As discussed before in chapter 4.3.2, this model is not a good approximation in the case of interstitial elements, such as carbon, it tends to give a density smaller than the real condition. Secondly, as indicated in reference (20), carbide precipitation tends to increase the density of the interdendritic liquid, especially when numerous large NbC carbides can be found in freckles in IN718, this effect, however, has not been combined in the software "METALS". Thirdly, Auburtin's (4) calculation didn't include the segregation of other elements in the alloy, elements such as Mo segregating positively during solidification can largely increase the density of interdendritic liquid, ignoring this effect  77  will give a lower estimation of the critical number of Si content at which freckles of the alloy begin to be lighter than the matrix. The assessment of minimum necessary density difference of 0.01 (g/cm )/°C for 3  freckling with a density inversion mechanism (20) seems not suitable to describe the freckling driven by a downward interdendritic convection. However, the density difference between the freckle and the surrounding matrix that is enough to induce the downward convection is much smaller (0.001 (g/cm )/°C in IN718, 0.006 g/cm in 3  3  IN718-0.4Si at 1206°C), as can be seen from Table VII. Once again this observation has to consider the error introduced by the calculation of "METALS". In sum, it was observed that Si content has a very important influence on freckling in IN718 and variations. The formation of a freckle in normal IN718 is believed to be a gravity driven downward interdendritic convection mechanism. When the Si content increases to a high enough point, freckles can be induced by a density inversion mechanism.  6.3 THE APPLICATION OF MODIFIED RAYLEIGH NUMBER 6.3.1 Application of the first theory  The modified Rayleigh number Ral in various casting conditions for those alloys with upside freckles (CMSX-1 IB, Rene 88, Nim80A and IN718HiSi) are calculated and the results are given in Table LX. A critical threshold value Ral * can be evaluated for all the four alloys, below which freckling does not occur and above which freckling always occurs. The estimates from the present experimental results as well as estimated values from reference are given in Table X .  78  6.3.2 Application of the second theory  The modified Rayleigh number Ra2 in various casting conditions for upward freckling alloys (CMSX-1 IB, Rene 88, Nim80A and LN718HiSi) are also calculated and given in Table DC. The critical threshold value Ra2*, below which freckling does not occur and above which freckling always occurs, can also be easily evaluated for all these four alloys. The estimated values are given in Table XI. As can be seen the critical threshold value Ra2* is independent of growthfrontangle. Therefore, so far we can say that the effort to develop a criterion including all three factors which influence the formation of freckle succeeded in accounting for both the upward freckling alloys used in this thesis and in the work of Auburtin (4).  6.3.3 Application of modified Rayleigh criteria to downward freckling phenomenon  Although the modified Rayleigh criteria were expanded from the density inversion theory, it is logical to try to use these criteria to describe thefrecklingphenomenon induced by a downward convection. The modified Rayleigh numbers Ra 1 and Ra2 are calculated and given in Table DC. The same critical threshold values Ral * and Ra2* can be easily evaluated for these two alloys and the estimated critical values are given in Table X and Table XI respectively. Furthermore, the modified Rayleigh numbers Ral and Ra2 have been applied to some given casting conditions in V A R ingots of alloy LN718 by  79  Auburtin (4), which is a downward freckling alloy as indicated both in this thesis and reference (12). Ral and Ra2 can successfully predict mid-radius only freckles whereas the original Rayleigh Criterion can not. Indeed, because both the downward and upward interdendritic convection in the mushy zone are driven by a density difference between layers of different isotherm, the Rayleigh number  Ra = —~ h  4  actually represents the ratio between gravity and viscosity effects, and therefore characterizes the onset of both the downward and upward convection. It has been observed in V A R ingots of alloy DST718 that freckle lines lie at an angle somewhat more horizontal than the microstructural bands outlining the pool surface (12), this indicates that the downward gravity driven convection is strongly influenced by the solidification front angle. Therefore the modified Rayleigh number, which combined the solidification front angle as the third factors influencing freckle formation, can predict the freckling in a downward flow mechanism better than the conventional Rayleigh number.  6.3.4 Applicability of the modified Rayleigh criteria to freckling prediction and process optimization.  It can be seen from Table X and Table XI that both the critical threshold value Ral * and Ral* are very similar for all the nine alloys. Ral * is of the order of 10" ~ 10" ,  80  and Ra2* is of the order of 10" . It is impossible to find a common critical threshold value 9  Ral * and Ra2* for all the alloys. However, given the fixed proportionality coefficients, the actual threshold values may be indicative of the relative propensity of each alloy to form freckles. A n alloy with the highest critical threshold value will be considered as the least freckle-prone alloy. The alloys are ranked in a sequence of increased freckle propensity (the higher ranking number the higherfreckle-propensity),as shown in Table X V and Table X V I for upward freckling and downward freckling alloys respectively. Ral * and Ra2* gave the same ranking for all the alloys. The difference between the results from Ral * and Ra2 * may be due to the fact that the estimation of Ral * and Ra2 * is based on limited data of the experiments that have been done so far, and the fact that one of the modified Rayleigh number is more accurate than the other. It is believed that comparison of actual freckle maps and numerically predicted maps for industrial castings is the ultimate validation of these modified criteria, and should enable selection of the most suitable criterion of the two. Knowing the critical threshold value Ra* for a given alloy, it is then possible to use generic graphs for the modified Rayleigh criteria in order to estimate the required process conditions which will lead to freckle-free castings. For example, by knowing two of the three parameters G, R and a, it is possible with the appropriate threshold value to estimate the range of values of the third parameter required to avoid freckling.  81  Table X V Ranking of propensity of upward freckling alloys (the higher the number the higher the freckle-propensity) Alloy CMSX-1 IB Rene 88 Nim 80A IN718HiSi  Rank based on Ral* 1 2 3 4  Rank based on Ra2* 1 2 3 4  Table XVI Ranking of propensity of downward freckling alloys (the higher the number the higher the freckle-propensity) Alloy LN718 LN718LC, N , Si  Rank based on Ral* 2 1  82  Rank based on Ra2* 2 1  7. CONCLUSIONS AND FUTURE WORK  7.1 CONCLUSIONS  There were confusions about the freckling mechanism in LN718 with two possible explanations for the cause of freckling: First, the formation of freckles in LN718 alloy may be caused by a downward interdendritic flow along the slope of solidification front, because the segregated interdendritic liquid is heavier than the surrounding bulk liquid. This mechanism is similar to the centerline macrosegregates forming mechanism. Second, the freckling in LN718 may be still caused by a density inversion occurring when the segregated interdendritic liquid becomes lighter than the surrounding bulk liquid due to the influence of some minor elements such as C and Si (freckling in this condition is termed as classical freckling in this thesis). Directionally solidified casting samples of LN718 and variations with different Si content were tested in a tiltable furnace to see whether the freckle in IN718 is induced by a upward flow or downward flow and what is the influence of Si content on freckling. Two modified Rayleigh criteria were applied to samples of various freckle-prone alloys, which are cast in the same tiltable furnace at different angle. These criteria were tested to describe freckling phenomena governed both by a downward flow mechanism and positive density inversion. The following conclusions can be drawn:  83  1) The formation of freckles in IN718 can be induced by downward flow of the interdendritic liquid along the slope of solidification front. Freckles in conventional EM718 have higher density than the surrounding matrix; 2) The increase of Si content can change the freckling mechanism of IN718. When Si content rises to a critical point (between 0.50 wt% and 0.62 wt%), freckles with a lower density than the bulk matrix occur, as described by the conventional density inversion mechanism; 3) The two modified Rayleigh criteria accounting for the growth front angle can describe the casting conditions leading to freckling under the density inversion mechanism with excellent accuracy; 4) The modified Rayleigh number may also be used to describe the freckling caused by a downward interdendritic flow.  7.2 RECOMMENDATIONS FOR FUTURE WORK  1) The consideration of influence of Si content on freckling in IN718 was triggered by the difficulty of recycling the Si contaminated IN718 machine chips. The real condition (such as Si content) of these IN718 chips should be investigated, and the potential freckling problem might then be analyzed during the remelting of recycled IN718, based on the research in this thesis. 2) Fluid flow of interdendritic liquid during the freckling with a downward flow mechanism can be investigated using the present experiment furnace and a  84  modified suitable model based on the thermal model built in this research. A freckling criteria based on the fluid flow research may be found to give insight into this freckling mechanism. The modified Rayleigh number used in the present work may provide a base for such work. 3) The critical threshold values for the modified Rayleigh criteria have been evaluated for a few superalloys. They may be applied to and tested in actual industrial conditions. 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A n effective depth of the current-carrying layers, known as the reference depth or skin depth, d, depends on the frequency of the alternating current through the coil and electrical resistivity and relative magnetic permeability of the workpiece. The definition of d is:  d = 5000^/p / pf (metric units)  where d is the reference depth, in centimeters; p is the resistivity of the workpiece, in ohm-centimeters; p is the relative magnetic permeability of the workpiece (dimensionless); and f is the frequency of the ac field of the work coil, in Hertz. The reference depth is the distance from the surface of the material to the depth where the induced field strength and current are reduced to 1/e, or 37% of their surface values. The power density at this point is 1/e , or 14% of its value at the surface . 2  (1)  For graphite p = 1828.8 p Q c m at 450 °C; u=l f= 4.5 x 10 Hertz 3  so d = 5000 x ^1828.8 x 10" /l x 4.5 x 10 6  3  =3.19 cm Therefore, if the thickness of graphite of susceptor is designed as 3 0mm  in a induction  furnace with a 4.5 KHz power supply, 99% of the magnetic field will be absorbed by the susceptor.  S. Z i n n , S.L. Semiatin, I.L. Harry and R.D. Jeffress, "Elements o f Induction Heating, Design, Control, and A p p l i c a t i o n s " , P P . 1 5 , 87  90  APPENDIX B: TYPICAL OUTPUTS OF PROCAST  GLiquidus (°C/cm) 2.30000E+01  Z.ZOOOOE+01  2.10000E+01  2.00000E+01  1.90000E+01  1.80000 E+01  1.70000E+01  1.G000OE+O1  1.50000E+01  1.10000 E+01  1 30000E+01  1.20000E+01  1.10000E+01  1.00000 E+01  g.oooooE+oo  8.00000E+00 T E M P E R A T U R E GRADIENT G R A D I E N T C O M P U T E D A T T E M P E R A T U R E - 1.347000E+03 MAGNITUDE O F THE T E M P E R A T U R E GRADIENT  Figure B - 1 Temperature gradient map calculated at liquidus temperature (T = 1347 °C) for alloy IN718 (Control temperature: 1400 °C, withdrawal rate: 1 mm/min) L  91  Figure B - 2 Temperature gradient map calculated at freckling temperature (T 1328 °C) for alloy IN718 (Control temperature: 1400 °C, withdrawal rate: 1 mm/min)  92  1100.00 C  1380.00  1360.00  1348.00  1329.00  1327.00  1253.00  1252.00  1200.00  1000.00  800.00  600.00  100.00  200.00  15.00 TEMPERATURE STEP NUMBER - 800 TIME - 3.926000E+03 TIME STEP - 5.000OOOE+OO  Figure B - 3 Temperature isotherm map calculated at a moment during the solidification of alloy IN718 (Control temperature: 1400 °C, withdrawal rate: 1 mm/min)  93  

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