study on segregation behavior of alloying elements …
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STUDY ON SEGREGATION BEHAVIOR OF ALLOYING ELEMENTS IN TITANIUM ALLOYS DURING SOLIDIFICATION
A K I R A K A W A K A M I
B.E., Kyushu University (Japan), 1987 M.E., Kyushu University (Japan), 1989
A THESIS SUBMITTED IN PARTIAL FULFUFILMENT 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
May 2002
© Akira Kawakami, 2002
In presenting this thesis in partial fulfilment of the requirements for an advanced
degree at the University of British Columbia, 1 agree that the Library shall make it
freely available for reference and study. I further agree that permission for extensive
copying of this thesis for scholarly purposes may be granted by the head of my
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Department of
The University of British Columbia Vancouver, Canada
Date 0T/Z2. /OZ.
DE-6 (2/88)
ABSTRACT
A fundamental study was conducted on segregation behavior of alloying elements in
titanium alloys to clarify the formation mechanism of "beta-flecks", melt-related defects
enriched in beta stabilizing elements, which can cause a decrease in mechanical
performance. Commercial titanium alloys, which are prone to the beta-fleck formation,
such as 10-2-3 (Ti-10%V-2%Fe-3%Al), Ti-17(Ti-5%Al-2%Sn-2%Zr-4%Mo-4%Cr) and 6242
(Ti-6%Al-2%Sn-4%Zr-2%Mo) were used. Solidification parameters, such as dendrite arm
spacing, distribution coefficients and densities of solid/liquid phase during solidification,
were investigated in these alloys.
Electron Probe Micro Analysis (EPMA) revealed that periodicity in distribution profiles
of alloying elements corresponded to the primary or secondary dendrite arm spacing both
in laboratory melted 10-2-3 ingots and in production 10-2-3 and Ti-17 ingots. This result
indicates that EPMA is an effective method to clarify the dimensions of dendrite
structures in titanium alloys(no good etching technique has been demonstrated that
resolves the original dendritic structure). Distribution coefficients of alloying elements in
10-2-3, Ti-17 and 6242 were experimentally obtained using a zone-melting furnace.
Distribution coefficients for iron in 10-2-3, zirconium and molybdenum in 6242 were
deviated from the equilibrium distribution coefficients calculated from the binary phase
diagrams. The fraction solidified (fs) at the initiation of beta-flecks was estimated to be 0.9
in 10-2-3 and Ti-17 using the Scheil equation, in which experimentally obtained
distribution coefficients were used. The density of liquid and solid metal at around the
melting point was estimated with the calculation software "METALS" and it was clarified
that solid metal is heavier than liquid enriched with iron in 10-2-3 and that enriched with
ii
chromium in Ti-17.
The Rayleigh number was calculated to exceed 1 when the periodicity of chromium
observed in a Ti-17 production ingot was assumed to be primary dendrite arm spacing.
This fact suggests that the density-driven downward flow of liquid metal can occur. This
in turn could cause channels perpendicular to the solidification direction and lead to the
formation of beta-flecks, and supports the proposed mechanism. However, there are still
some questions about the mechanism, such as the possibility of fluid flow at the final stage
of solidification and the validity of considering the periodicity as primary dendrite arm
spacing.
iii
Table of Contents
Abstract ii
Table of Contents iv
L i s t of Tables vi
L i s t of F igures vii
L i s t of Symbols ix
Acknowledgements xi
1. I N T R O D U C T I O N 1
2. L I T E R A T U R E R E V I E W 3
2.1 SEGREGATION BEHAVIOR OF ALLOYING ELEMENTS IN TITANIUM ALLOYS(GENERAL) 3
Solidification microstructures in titanium alloys 3 Dendrite arm spacing 4 Solidification parameters 6 Distribution coefficients 6 Solidus and liquidus temperature 8 Solid state diffusion 8
2.2 BETA-FLECKS IN TITANIUM ALLOYS 10 Features of beta-flecks 10 Effects of beta-flecks on mechanical properties 13 Features of freckles 15 Formation mechanisms of freckles and beta-flecks 17 Freckle criterion and its application to beta-flecks 19
2.3 SUMMARY OF LITERATURE REVIEW 22
3. R E S E A R C H O B J E C T I V E S 34
4. E X P E R I M E N T A L M E T H O D O L O G Y 36
4.1 CHOICE OF ALLOYS 36
4.2 EXPERIMENTAL METHODS 37 Segregation behavior of iron in 10-2-3 small ingots melted and cast in an argon arc melting furnace 37
Segregation behavior of alloying elements in production ingots 38 Segregation behavior of alloying elements in laboratory melted small ingots using a zone melting furnace 39
iv
5. EXPERIMENTAL RESULTS 43
5.1 SEGREGATION BEHAVIOR OF ALLOYING ELEMENTS IN TITANIUM ALLOY INGOTS SOLIDIFIED IN DENDRITIC MANNER 43
Segregation behavior of iron in laboratory melted 10-2-3 ingots using an argon arc furnace 43 Segregation behavior of alloying elements in production ingots 45
5.2 SEGREGATION BEHAVIOR OF ALLOYING ELEMENTS IN ZONE MELTED TITANIUM ALLOY INGOTS 48
5.3 DENSITY OF BETA-FLECK AND LIQUID METAL CALCULATED USING "METALS" FOR 10-2-3 AND Ti-17 ALLOYS 54
6. DISCUSSION 74
6.1 DETERMINATION OF DENDRITE ARM SPACING BY EPMA 74 The relationship between dendrite arm spacing and solidification conditions in laboratory-melted ingots using argon an arc furnace 74 Dendrite arm spacing in production ingots 75
6.2 SEGREGATION COEFFICIENTS OF ALLOYING ELEMENTS IN COMMERCIAL TITANIUM ALLOYS AND ESTIMATION OF THE FRACTION SOLIDIFIED AT THE INITIATION OF BETA-FLECKS 77 Segregation coefficients of alloying elements in zone-melted commercial titanium alloys 77
Estimation of the fraction solidified at the initiation of beta-flecks 79 Estimation of distribution coefficients and fraction solidified at the initiation
of beta-flecks with "pseudo-binary phase approach" 80
6.3 FORMATION MECHANISM OF BETA-FLECKS 82 Possibility of downward flow of liquid metal during solidification 82 Problems in the proposed formation mechanism of beta-flecks 84
7. CONCLUSIONS AND FUTURE WORKS 88
7.1 CONCLUSIONS 88
7.2 RECOMMENDATIONS FOR FUTURE WORKS 90
REFERENCES 92
APPENDIX A: MATHEMATICAL MODEL"METALS" 99
v
List of Tables
Table 1 Distribution coefficients of alloying elements in titanium alloys 7,20-23 7 Table 2 Liquidus and solidus temperatures in titanium alloys !3,23,24 g Table 3 Melting experiment results with an argon arc furnace. 43 Table 4 Composition variations and distribution coefficients (k) in a zone melted
10-2-3 ingot. 53 Table 5 Composition variations and distribution coefficients (k) in a zone melted
Ti-17 ingot. 53 Table 6 Composition variations and distribution coefficients (k) in a zone melted
6242 ingot. 53 Table 7 Composition variations and distribution coefficients (k) for oxygen and
nitrogen in a zone melted 10-2-3 ingot 4 7 . 53 Table 8 Parameters and values used for pseudo-binary phase approach for Ti-17. 81 Table 9 Parameters and values used for pseudo-binary phase approach for 10-2-3. 81
vi
List of Figures
Figure 1 Solidification maps for (a) Ti-6-4 and (b) Ti-17 alloys 1 4 . 24 Figure 2 Dendrite arm spacing in Ti-17 1 3 . 24 Figure 3 Residual segregation index vs. homogenization parameter for
chromium in steel19. 25 Figure 4 Macrostructure of cross-section of a 10-2-3 ingot27. 25 Figure 5 Optical micrograph and scanning fractograph of fractured 10-2-3 5 . 26 Figure 6 Effect of beta-fleck area on LCF fife of 10-2-3 5 . 26 Figure 7 Typical microstructure of Ti-6-6-2 with beta flecks 2 8 . 27 Figure 8 Various appearances of freckles in industrial castings 3 0 . 28-29 Figure 9 Schematic diagram of directional solidification and associated thermal
(pT), solutal (pc) and thermosolutal (pT+c) density profiles illustrating the density inversion theory 3 0 . 29
Figure 10 Schematic illustration depicting freckle formation and associated fluid flow pattern 2 9 . 30
Figure 11 The mechanism of freckle formation showing the sequence of the density-driven downward-forming channel to form a freckle 3 6 . 30
Figure 12 Schematic illustration of typical curved growth front found in ingot 2 9 . 31 Figure 13 Modified Rayleigh number vs growth front angle for alloy (a)CMSX-HB,
(b)RENE88, (c)NIM80A, (d)IN718-Si, (e)WASPALOY and (f)MAR-M247 2 9 . 32 Figure 14 Calculated Rayleigh numbers for the directionally solidification
experiments for the SX-1 superalloy as a function of the thermal parameter G-1/2»R-1/4 4 2 . 33
Figure 15 Photograph of an argon arc melting furnace in AMPEL. 41 Figure 16 Schematic diagram of an argon arc melting furnace in AMPEL. 42 Figure 17 Macrographs of 10-2-3 ingots melted by an argon arc furnace.
(a)No.l (b)No.2 (c) No.3 (d) No.5 (e) No.7 56,57 Figure 18 Distribution of iron concentration in the horizontal direction in a
10-2-3 lboratory-melted ingot. 58 Figure 19 Distribution of iron concentration in the direction inclined to the
horizontal direction by 30 ° in a 10-2-3 laboratory-melted ingot. 58 Figure 20 Distribution of iron concentration in the direction inclined to the
horizontal direction by 45 ° in a 10-2-3 laboratory-melted ingot. 59 Figure 21 Distribution of iron concentration in the direction inclined to the
horizontal direction by 60 ° in a 10-2-3 laboratory-melted ingot. 59 Figure 22 Evolution of temperature with time during solidification in
Commercially Pure Titanium melted in an argon arc furnace. 60 Figure 23 Macrograph of a Ti-17 production ingot (as-received). 61 Figure 24 Microstructure of a Ti-17 production ingot. 61 Figure 25 Distribution of chromium concentration in a Ti-17 production ingot. 62 Figure 26 Estimated distribution of chromium concentration in a Ti-17 production
ingot just after solidification. 62 Figure 27 Macrograph of a 10-2-3 production ingot (as-received). 63 Figure 28 Distribution of iron concentration in the direction inclined to the
horizontal direction by 60 ° in a 10-2-3 production ingot. 63 Figure 29 Distribution of iron concentration in a 10-2-3 production ingot. 64 Figure 30 Macrographs of zone melted samples (as received). 65 Figure 31 Cross-sectional macrographs of a zone melted 10-2-3 ingot. 66
vii
Figure 32 Cross-sectional macrographs of a zone melted Ti-17 ingot. 67 Figure 33 Cross-sectional macrographs of a zone melted 6242 ingot. 68 Figure 34 Concentration distribution of alloying elements in the longitudinal
direction of a zone melted 10-2-3 ingot. 69 Figure 35 Concentration distribution of alloying elements in the longitudinal
direction of a zone melted Ti-17 ingot. 69 Figure 36 Concentration distribution of alloying elements in the longitudinal
direction of a zone melted 6242 ingot. 70 Figure 37 Concentration distribution of alloying elements in the longitudinal
direction of a zone melted 10-2-3 ingot (original data). 70 Figure 38 Distribution of oxygen concentration in the longitudinal direction of a
zone melted 10-2-3 ingot 4 7 . 71 Figure 39 Distribution of nitrogen concentration in the longitudinal direction of a
zone melted 10-2-3 ingot 4 7 . 71 Figure 40 Effect of iron concentration on density of the liquid and solid phase at
around melting temperature (1905 K) in the 10-2-3 alloy. 72 Figure 41 Effect of temperature on density of the liquid and solid phase in the
10-2-3 alloy. 72 Figure 42 Effect of chromium concentration on density of the liquid and solid
phase at around melting temperature (1914 K) in the Ti-17 alloy. 73 Figure 43 Effect of temperature on density of the liquid and solid phase in the
Ti-17 alloy. 73 Figure 44 Effect of primary dendrite arm spacing on the Rayleigh number in a
Ti-17 production ingot. 87 Figure 45 Effect of primary dendrite arm spacing on the Rayleigh number in a
10-2-3 production ingot. 87
viii
List of Symbols
Symbols C Solute Concentration (wt.%) Co Equilibrium Solute Concentration (wt.%) CM Maximum Solute Concentration of Component i at Time th(wt.%) Cm Minimum Solute Concentration of Component i at Time th(wt.%) C°M Maximum Initial Solute Concentration of Component i (wt.%) C°m Minimum Initial Solute Concentration of Component i (wt.%) Cave Average Concentration of Alloying Element in the Matrix (wt.%) Cmax Maximum Concentration of Alloying Element Detected by EDX (wt.%) Cmin Minimum Concentration of Alloying Element Detected by EDX (wt.%) CL1,CL2 Liquid Composition in a Phase Diagram (wt.%) D s Interdiffusion Coeficient in the Solid State (m2/s) DT Thermal Diffusivity (m2/s) fs Fraction Solidified g Gravitational Acceleration (m/s2) G Thermal Gradient (K/m) G F V Vertical Temperature Gradient (K/m) GL Temperature Gradient of the Liquidus (K/m) h Characteristic Linear Dimension (m) hm Height of the Mushy Zone (m) k Distribution Coefficient keq Equilibrium Distribution Coefficient K Permeability in the Vertical Direction (m2) Km Mean Permeability (m2) K y Permeability Parallel to the Primary Dendrite Trunks (m2) L Half of the Dendrite Arm Spacing (m) Nf Cycle Number R Solidification Rate (K/s) Ra, RaT/s Rayleigh Number Racrit Critical Rayleigh Number Ra* Modified Rayleigh Number t Time (s) t s Total Solidification Time (s) T Temperature (K) Tl,T2 Temperature in a Phase Diagram (K) Tbuik Bulk Alloy Transformation Temperature (K) TL Liquidus temperature (K) Ts Solidus Temperature (K) V Withdrawal Rate (m/s)
ix
Greek Symbols a Thermal Diffusivity of the Melt (m2/s) Si Residual Segregation Index • Inclination Angle (degree)
Dynamic Viscosity of Liquid (kg/m/s) Xi Primary Dendrite Arm Spacing (m)
Secondary Dendrite Arm Spacing (m) Up Columnar Growth Coefficient for Primary Dendrite Arm Spacing
(m1.25. s0.25.K-0.5)
Columnar Growth Coefficient for Secondary Dendrite Arm Spacing ( m > s 0 . 3 3 )
P Density (kg/m3) po Reference Density (kg/m3) pc Solutal Density (kg/m3) PT Thermal Density (kg/m3) pC+T Thermosolutal Density (kg/m3) Pmatrix Density of Matrix (kg/m3) pfreckle Density of Freckle (kg/m3) A p Density Difference (kg/m3)
Abbreviations AMPEL Advanced Materials and Process Engineering Laboratory EBR Electron Beam Remelting EDX Energy Dispersion Spectrometer EPMA Electron Probe Micro-Analysis ESR Electro-Slag Remelting HCF High Cycle Fatigue HDI High Density Inclusion LCF Low Cycle Fatigue LDI Low Density Inclusion N/A Not Applicable NIR Near-Infra Red PDAS Primary Dendrite Arm Spacing SDAS Secondary Dendrite Arm Spacing SEM Scanning Electron Microscope SX Single Crystal TC Thermocouple VAR Vacuum Arc Remelting UBC University of British Columbia
Acknowledgement
I would like to thank first and foremost my supervisor, Dr. Alec Mitchell, for his
invaluable guidance throughout this Master thesis. I would also like to thank my co-
supervisor, Dr. Steve L Cockcroft, for his useful suggestions. I appreciate Mr. Rudy
Cardeno and Ms. Mary Mager for their direct support through my experimental works.
All the support staff in the- department of Metals & Materials Engineering at the
University of British Columbia (UBC, Vancouver, Canada) were also helpful. I am very
grateful for Timet Corporation and RMI Titanium Company to supply the materials and
for the Wright Patterson Air Force Laboratory to conduct floating zone melting
experiments. I really appreciate our company, Nippon Steel Corporation (Japan), for their
support for everything I needed to make a living in Canada and to study at UBC. Finally,
I would like to thank my wife who supports me every time and my family in Japan who
encourages me.
xi
1. I N T R O D U C T I O N
Titanium and its alloys are promising structural materials for industrial use because
of their high strength, low density and superior corrosion resistance1-2. Since the price of
titanium is higher than that of other conventional metals, such as steels, the titanium
market is still small. However, the demand for titanium is projected to increase when
titanium products are more generally recognized to have much longer life than other
conventional metals since this leads to lifetime cost reduction. Titanium demand will also
increase as the production costs are lowered.
In titanium alloys, melting and casting problems are important issues3, which can
cause an increase in the production cost and also lower the quality of the products. The
formation of Low Density Inclusions (LDI's), High Density Inclusions (HDI's) and beta-
flecks, caused by inhomogeneities in the cast ingot, have detrimental effects on the
mechanical performances of titanium and its alloys4"7. LDI's and HDI's are exogenous
inclusions. The former originates from low quality raw materials, which contain locally
high concentrations of nitrogen, oxygen or carbon, while the latter consists of heavy metal
elements, like tantalum, cobalt or tungsten, from machine tool tips or heavy metal scrap3.
It has been shown to date that these exogenous inclusions can be reduced by the strict
selection of raw materials or by applying hearth or skull melting processes3-8-9.
In contrast, beta-flecks, indigenous inclusions, are defined as localized areas rich in
beta stabilizing elements3. Beta-flecks are known to form through the segregation of beta
stabilizing elements during solidification and have deleterious effects on mechanical
properties, particularly on the fatigue life of titanium alloy components5"7.
Homogenization heat treatment, which results in the redistribution of beta-stabilizing
elements in products, is lengthy and causes an oxidizing problem on the surface of the
products3-10. The formation of beta-flecks during solidification or casting should be
suppressed; however, the formation mechanism of beta-fleck has not yet been clarified and
no effective manufacturing procedure for its elimination has been established.
The present research study is focused on the segregation behavior of beta stabilizing
elements in titanium alloys in order to clarify the formation mechanism of beta flecks.
Chapter 2 contains the literature review on related topics. It summarizes segregation
parameters of titanium alloys and describes the main features of beta flecks. The
formation mechanism of freckles (melt-related defects in superalloys, arising due to fluid
flow of the liquid metal in interdendritic region) is also discussed. The goal of the research
study is presented in Chapter 3. Experimental procedures, conducted in the research
study, are shown in Chapter 4. Results and discussions are presented in Chapter 5 and
Chapter 6, respectively, followed by conclusions with recommendations for future works
presented in the final chapter.
2
2. L I T E R A T U R E R E V I E W
2.1 S E G R E G A T I O N B E H A V I O R O F A L L O Y I N G E L E M E N T S IN
T I T A N I U M A L L O Y S
Solidification microstructures in titanium alloys
Prior to a discussion of beta-flecks in titanium alloys, it is important to review
segregation behavior in titanium alloys. In the production of large VAR (Vacuum Arc
Remelting) ingots, the solidifying interface is in a cellular mode in CP (Commercially Pure)
titanium and in a cellular or dendritic mode in the 6-4 (Ti-6%A1-4%V) alloy7'11-49. In fact,
both dendritic14 and non-dendritic11-49 microstructures have been reported for the
solidification microstructure of 6-4 VAR ingots, which might be because the chemical
composition of 6-4 corresponds to a transition area from a cellular to a dendritic
solidification manner. In contrast, solidification proceeds in a columnar/equiaxed dendritic
mode in beta alloy VAR ingots7'11-49. This assumption has been clarified recently by
observing the surface of the solidification interface in CP and beta alloys11 and the
dendritic morphology of surfaces of shrinkage cavities12-13 in beta alloys. A wider
temperature range between the liquidus and the solidus line in beta alloys than in CP and
6-4 is considered as a reason for a change in the solidification manner. Therefore,
microscopic segregation of alloying elements has to be mainly taken into account in beta
alloys, while macroscopic segregation might be recognized in CP and the 6-4 alloy in most
cases.
Nastac et al 1 4 proposed solidification maps for the 6-4 alloy and Ti-17(Ti-5%Al-2%Sn-
2%Zr-4%Mo-4%Cr) by using a software modified from SIMCAST, as shown in Figure 1.
According to the results, typical cooling conditions of a production ingot (Calculated with
3
VAR model (Ingot Dia.=762 mm, Ingot Length=635 mm, Melting Rate=273 kg/hr): G=5-10
K/cm=5xl02-lxl03 K/m, V=40 um/s=4xl05 m/s, R=G»V=2-4xlO"2 K/s) produce a mixed
microstructure of columnar/equiaxed grains. Solidification maps are very useful in
predicting microstructures under certain solidification conditions and some maps have
been developed for stainless steels15. It is important to produce solidification maps for
titanium alloys, although the practical problems of experimental verification are
considerable.
Dendrite arm spacing
Dendrite arm spacing is an important morphological parameter when attempting to
model beta-fleck formation11-13. However, no effective solution has been developed for
etching titanium alloys, which offers direct and clear observation of dendrite structures11.
This is due to the transformation from beta to alpha phase that occurs during cooling,
which makes it difficult to identify the prior dendrite structures. Dendrite arm spacing
has been evaluated indirectly from the spacing between concentration peaks of alloying
elements obtained from Electron Probe Micro-Analysis (EPMA), however; only a few
results have been reported16-17.
The relationship between dendrite arm spacing and cooling conditions in binary
titanium alloy ingots is shown in Figure 213-16. Primary dendrite arm spacing (PDAS) and
secondary dendrite arm spacing (SDAS) are assumed to be between 2500-4000 um and
1500-2000 um, respectively, at R=G»V=2-4xl0"2 K/s, which is a typical cooling condition for
production ingots. Ichihashi et al 4 9 demonstrated 800-1000 um for SDAS in 660mm dia.
beta alloy ingots. Aleksandrov et al 1 7 reported 3000-5000 urn for PDAS in 430mm dia.
BT3-l(Ti-6.5%Al-2.5%Mo-1.5%Cr-0.5%Fe-0.3%Si) production ingots.
4
Dendrite arm spacing was calculated on the basis of the following equations by
Nastac 1 4 and the results are shown in his solidification maps (See Figure 1).
Xi = uP«V-0-25.G-«-5 (Eq.l)
X2 = Us»t s-°-33 (Eq.2)
where Xi is the PDAS(m), \xP is the columnar growth coefficient(=1.924xl0-3 m 1 - 2 5 ^ 0 - 2 5 *!^- 0 - 5
in Ti-17), V is the withdrawal rate(m/s), G is the thermal gradient(K/m), is the
SDAS(m), \xs is the columnar growth coefficient^LGSSxlO- 5 m « s 0 - 3 3 in Ti-17) and t s is the
local solidification time(s)
The above equations are formulated on a basic theory that the primary arm spacing
depends on the cooling rate during solidification and the secondary arm spacing is
controlled by the local solidification time 1 5. Equations 1 and 2 yield 1000-2000 jam for
PDAS and 200-400 (a,m for SDAS for a Ti-17 production ingot. These values are smaller
compared to the experimental values and the difference between them is presumed to be
caused by the limited number of data on dendrite arm spacing in titanium alloys. In this
case, experimental values are considered to be more reliable, although the number of the
data is limited.
A comparison of the dendrite arm spacings in titanium alloys with those in superalloys
and steels was also attempted. McLean's morphology map of superalloy structures 1 8,
which was established by a large number of data, can be used as a guideline. From the
morphology map, at V»G=2-4x lO- 2 K/s , SDAS is estimated as 180-240 |j.m, which is smaller
than that reported on titanium alloys. Under similar solidification conditions, PDAS and
SDAS were 1000-1500 nm and 200-400 \im in Fe-26%Ni alloy 1 9, which are also smaller
than those observed in titanium alloys. In conclusion, under conditions for casting large
5
production ingots, the dendrite arm spacing is smaller in titanium alloys than in
superalloys or steels.
Solidification parameters
The solidification parameters related to the segregation behavior of alloying elements
in titanium alloys, k(distribution coefficient), TiXliquidus temperature) and Ts(solidus
temperature) are critical. In particular, the distribution coefficient of the alloying element
is essential, since the volume fraction of the solid phase in the liquid/solid interface can be
estimated by applying the distribution coefficient to the Scheil equation, shown as the
following (Eq.3).
C s=k.Co»(l-f s) k- 1 - (Eq.3)
where C s is the concentration of solute in the solid, Co is the average concentration of
solute in the solid, k is the distribution coefficient and fs is the fraction solidified
Distribution Coefficients
Distribution coefficients or partition coefficients, k, have been reported in some
studies7'20"23. Under equilibrium conditions, k is the ratio of a slope of liquidus line to that
of the solidus line in binary phase diagrams at a given composition20. Tin, zirconium,
vanadium, chromium and iron have k<1.0, while aluminum, molybdenum, oxygen,
nitrogen and carbon show k>1.0. This indicates that the former five elements tend to be
depleted in the initial part of solidification and to be enriched in the final part, while the
latter five behave in the opposite way. Distribution coefficients obtained from
experiments7-21'22 and calculation23 are listed in Table 1. Different alloys were used in
each reference (See Table 1). In all the studies, the k value for tin deviated from those
6
obtained from the b inary phase diagram, whereas i n ref(7), the k values for c h r o m i u m and
iron a l l deviated from those obtained from the b inary phase diagram. In contrast,
a l u m i n u m and v a n a d i u m show distribution coefficients close to those obtained from the
equi l ibr ium phase diagrams. T i n is neutral i n stabil izing phases i n t i tan ium alloys, which
might be the cause for the variat ion i n the distribution coefficients. However, the cause of
variat ion i n iron and chromium i n ref(7) from equi l ibr ium data is not clear. These results
suggest that i n m a n y cases the binary equi l ibr ium phase d iagram can be used to obtain
pract ical phase conditions but there are some exceptions l ike iron, chromium, etc.
Therefore, it is important to measure distribution coefficients of al loying elements i n
commercial t i t an ium alloys with multi-component system.
Table 1 Distribution coefficients of alloying elements in titanium alloys7-20-23
Al Sn Zr Mo V Cr Fe O N C note 1.05 0.92 0.90 1.50 0.95 0.70 0.60 1.60 1.58 0.50 Binary phase diagram:
ref(20)
1.01-1.05
1.06-1.51
0.95-1.01
0.87-1.03
BT3-1: ref(7)
1.00-1.06
1.03-1.14
0.77-0.84
1.14-1.18
0.90 0.77 0.59 679, 6-6-2, Ti-Mo-Cr: ref(21)
1.02-1.08
1.09-1.13
0.89-0.95
0.79 0.61-0.71
6-4, 6-6-2, 15-3 : ref(22)
1.05 0.83 0.92 1.06 0.65 Ti-17: ref(23) BT3-1: Ti-6.5Al-2.5Mo-l.5Cr-0.5Fe-0.3Si, 679 : Ti-2.25Al-llSn-5Zr-lMo-0.22Si 6-6-2 : Ti-6Al-6V-2Sn, 6-4 : Ti-6A1-4V, 15-3 : Ti-15V-3Al-3Cr-3Sn Ti-17 : Ti-5Al-2Sn-2Zr-4Mo-4Cr
7
Solidus and Liquidus Temperature
Auburtin13 presented experimental data on Ti-6242(Ti-6%Al-2%Sn-40/oZr-2%Mo), Ti-17
and 10-2-3(Ti-10%V-2%Fe-3%Al) obtained from thermo-couple measurements (TC data)
and from pyrometer measurements (NIR data), as shown in Table 2. Table 2 includes the
calculation results on Ti-17 reported by Nastac23, including values obtained from Metals
Handbook24. The liquidus temperatures obtained as NIR data are lower than the TC data.
The measurements by pyrometer are subject to calibration errors in emissivity values and
temperatures obtained from thermocouple measurements are possibly more accurate. TC
data on the liquidus and solidus temperatures listed in the table, therefore, are considered
to be more reliable.
Table 2 Liquidus and solidus temperatures for titanium alloys 1 3 2 3- 2 4
Alloy T l i q(°C) T s oi(°C) notes Ti-6242 166815 1634110 TCdata ref(13) Ti-6242 1675 1595 Metals Handbook data ref(24) Ti-6242 1590 N/A NIR data ref(13) Ti-17 164115 1632110 TCdata ref(13) Ti-17 1590 N/A NIR data ref(13) Ti-17 1649.3 1591.1 PAM ingot model ref(23) Ti-17 1649.3 1503.1 Scheil model ref(23) Ti-17 1649.3 1625.0 Lever rule model ref(23) Ti-10-2-3 163215 1595110 TCdata ref(13)
Solid State Diffusion
When partition or segregation coefficients are considered, the diffusion behavior of
solute atoms immediately after solidification has to be considered as the back diffusion
effect of the solute atoms cannot be ignored19-25-26. Shamblen10 calculated the
interdiffusion coefficient (Ds) of chromium in the solid state of Ti-17 on the basis of
experimental data. This is shown as (Eq.4), which was estimated from the relationship
8
between diffusion coefficients and temperatures in the literature.
D s= -1.93xl0- 4x(l/T(°C))+1.55xl0- 7 (cm2^-1) (Eq.4)
where D s is the interdiffusion coefficient of chromium in Ti-17(cm 2«s- 1) and T is the
temperature(°C). It is possible to estimate the concentration of chromium just after
solidification in Ti-17 from the relationship between residual segregation index(8i), shown
as (Eq.5) and D s »th/L 2 , as presented in Figure 31 9, where D s is the interdiffusion coefficient
of solid state (m 2«s- 1), th is the local solidification time (s) and L is the half of the dendrite
arm spacing (m).
5i = (CM-Cm)/(Com-CoM) (Eq.5)
where 5i is the residual segregation index, C M is the maximum solute concentration of
component i at time th (s), Cm is the minimum solute concentration of component i at time
th (s), C°m is the maximum initial concentration of component i (wt.%) and C ° M is the
minimum initial concentration of component i (wt.%).
The above equations were applied for estimating the redistribution of segregated
alloying element during the homogenizing process which consists of 1 to 100 hours of heat
treatment. Moreover, it is clear from (Eq.4) that slow diffusion rates make
homogenization of defects quite difficult. Holding time in the homogenizing process is
considered to be much longer than the corresponding holding time during solidification but
the effect of solute redistribution during solidification should be taken into consideration.
9
2.2 B E T A - F L E C K S I N T I T A N I U M A L L O Y S
Features of beta-flecks
Beta-flecks are localized defects, which contain a higher content of beta stabilizing
elements than in the bulk. Beta-flecks have been found frequently in BT3-1, BT-22 (Ti-
5%Al-4.5%Mo-4.5%V-l%Cr-l%Fe), Ti-17, 10-2-3 and other aUoys: aU of which contain iron
and/or chromium. Iron and chromium are strongly rejected at the solid/liquid interface
with effective segregation coefficients of 0.6-0.8 in most titanium alloys13, causing
macrosegregation and microsegregation. The former occurs under a high temperature
gradient and the latter takes place when the interface is dendritic3. Therefore,
microsegregation should be considered in production scale ingots, while macrosegregation
might take place under quite special solidification conditions, such as an uni-directional
solidifying condition with a high thermal gradient and a slow cooling rate using a floating
zone melting furnace.
Since there has been no clear criteria established for the amount of segregation
responsible for beta-flecks, the chemical compositions of areas corresponding to beta-flecks
are reported to be different depending on the observer. In 10-2-3 ingots, Brooks found
beta-flecks formed with an enrichment of 0.4wt.% iron and lwt.% vanadium27. Zhou found
that beta-flecks contained at least 2.72wt.% iron and 10.6wt.% vanadium6. The largest
difference in iron content observed was 0.5% by Chen4. Shamblen10 demonstrated that a
typical beta-fleck might show increases of 1.0-1.5wt.% chromium and 0.5wt.% zirconium
along with decreases of 0.5wt.% molybdenum and 0.2wt.% aluminum in Ti-17. Tetyukin7
presented increases of 0.25wt.% chromium and 0.lwt.% iron and a decrease of 0.5wt.%
molybdenum were found in "strings"(beta-flecks) in BT3-1. In fact, these results were
obtained from chemical analysis conducted on the locations showing beta-fleck
10
microstructures, which were identified by each observer. Observed microstructures,
including beta-flecks, might have appeared differently even if the chemical compositions
were the same, depending on the etching procedures or techniques. This might have
caused different chemical compositions of beta-flecks, depending on the observers. The
appropriate definition for beta-flecks has to be established to identify beta-flecks.
With respect to heat treatment/forging practice, practical criteria to define the
chemical compositions of beta-flecks have been proposed13. In heat treatment/forging
operations, problems arise from beta-flecks due to differences in the transformation
temperature between beta-flecks and the matrix, caused by a difference in chemical
composition. A heat treatment just below/above transformation temperature is often
required in titanium alloys, where a difference in the transformation temperature in the
beta-fleck and in the matrix can give rise to a decrease in mechanical properties.
Therefore, most product specifications for titanium alloys specify a permissible range of
heat treatment temperature relative to the bulk alloy transformation temperature, e.g.
(Tbuik-15 °C) and the industrial experience of the occurrence of beta-flecks is related to this
interval in practice13. For example, in BT3, the bulk composition contains a chromium
level of 1.5 wt.%, and a typical beta-fleck area will contain 1.7-1.8 wt.% chromium. In 10-
2-3, the bulk composition is 2.0 wt.% iron and the beta-fleck area will contain 3.1 wt.%
iron. In Ti-17, the bulk is 4 wt.% chromium and the beta-fleck will contain 5.5 wt.%
chromium3. This definition is quite reasonable and can easily be applied to identify beta-
flecks.
From these chemical compositions, the fraction solidified can be estimated at the point
when beta-flecks are formed. For instance, if these alloys are assumed to solidify under
conditions obeying the Scheil equation, with distribution coefficients of 0.60 for iron and
11
0.70 for chromium, temperatures at which beta-fiecks initiated are calculated to be
consistent with the fraction solidified, is, of 0.91 for iron and 0.89 for chromium. This high
fraction solidified suggests that beta-flecks were initiated at the final stage of
solidification.
Morphologically, beta-flecks observed in large ingots appear as string or pencil like
structures and V-shaped distributions near the center of the ingots7-27. Tetyukin7
demonstrated bright and string-shaped streaks in the equiaxed/columnar dendritic region
around the center of a 750 mm dia. BT3-1 ingot by radiographic observation. This result
suggested that the density of the beta-fleck might be quite different from that of the bulk,
although the detailed conditions of the radiographic method were not mentioned. Brooks27
reported V-shape distributions of beta-flecks both with iron distribution mapping analyzed
by X-ray spectroscopy and with optical microscopy. It was found that beta-flecks, in which
iron was enriched compared with the matrix, corresponded to the termination of magnetic
stirring during the melting process and that the V-shape represented the bottom shape of
molten pool. A clear microstructure of beta-flecks in an as-cast ingot was obtained, which
appears as dark-colored pencil-like contrasts, as indicated in Figure 4, after a "beta-fleck
heat treatment" (800 °C for lhour and water quenched), projecting to obtain a clearer
microstructure of beta-flecks. The noticeable feature in this figure is that beta-flecks run
through the beta grains. This result suggests that the beta grains might have
recrystallized irrespective of segregation of beta stabilizing elements during the "beta-
fleck" heat treatment.
Also, it has been reported that a beta-fleck consists of a prior-beta grain or some grains
and the grain size was larger than that in the matrix in forged and heat-treated products,
as shown in Figure 55 During the solution heat treatment, beta grains must have
12
recrystallized and the grain boundaries should have formed just at the interface between
the original beta-flecks and the prior matrix. Larger grains in the beta-fleck area might
have formed because of a higher growth rate in the recrystallized grains due to a lower
transformation temperature in the beta-fleck area than that of the matrix. However, the
reasons for this behavior are not clear. Further detailed studies on the microstructural
evolution of beta-flecks during and after heat treatment are necessary to clarify the effect
of beta-flecks on mechanical performances, which will be discussed below.
Effects of beta-flecks on mechanical properties
The effects of beta-flecks on mechanical properties of titanium alloy products have
been studied and in most cases the detrimental effects have been demonstrated4-7-28,
particularly, on Low Cycle Fatigue (LCF) life5-7-28 and fracture toughness4-5. All of the
authors used forged and heat-treated final products, which means that beta-flecks
survived even after the forging process to reduce final mechanical properties.
Chen4 found that yield strength increased from 1176 to 1306 MPa and the total
elongation decreased from 6 to 1 % due to the existence of beta-flecks in 10-2-3. Since
Kevex microprobe analysis revealed a high peak concentration of iron in beta-fleck area,
solid solution hardening should have occurred in the area. However, no detailed
discussion on microstructures was given. Zhou5 reported a detrimental effect of beta-
flecks on LCF life, considering both the volume fraction and the maximum size of beta-
fleck in 10-2-3, as shown in Figure 6. A decrease in LCF life could be found in specimens
containing even a small volume fraction of beta-flecks, which did not affect the tensile
properties in the whole specimen. In the specimens, cracks were initiated from the beta-
fleck, leading to a decrease in LCF life. In general, a particle, which is harder than the
13
matrix, could be a stress raiser and may cause cracks at the interface between the particle
and the matrix due to a stress concentration57. This finding supports Tetyukin's results on
BT3-16, in which LCF life decreased in the region containing beta-flecks, although the
tensile strength of the region was almost the same as that of beta-fleck free region.
According to detailed observations of microstructures, Funkenbusch7 demonstrated that
beta-flecks were crack initiation sites in Ti-17, which caused a shorter LCF life.
In contrast, Rudringer28 showed that beta-flecks did not affect the LCF and High Cycle
Fatigue (HCF) life in Ti-6-6-2 (Ti-6%Al-6%V-2%Sn). Actually, no clear difference could be
found in LCF and HCF life between samples containing beta-flecks and samples free from
beta-flecks. This might be because the author used 6-6-2, which contains vanadium as a
beta-stabilizing element. As shown in Table 2, the distribution coefficient of vanadium is
0.9-0.95 and the segregation ratio of vanadium in 6-6-2 is assumed to be much lower than
that of iron in 10-2-3 or that of chromium in Ti-17. The degree of solid solution hardening
might be much less in 6-6-2 than in 10-2-3 or Ti-17. However, microstructures appeared
differently near the center area compared with those in other locations in 6-6-2 ingots,
which might have been affected by beta-flecks, as presented in Figure 728. This result
shows that there are two types of beta-flecks: one being harmful and the other being
harmless to mechanical properties.
A difference in alloy type of the bulk materials could have caused different effects in
mechanical properties of titanium alloys containing beta-flecks: 6-6-2 is an alpha-beta
alloy, while 10-2-3 and Ti-17 are beta-alloys. Solid solution hardening in the beta phase
might have more deleterious effect on mechanical properties in beta alloys than in alpha-
beta alloys. In this case, however, the effect of alloy type must be lower than that of
alloying elements because LCF life was reduced by beta-flecks in BT3-1, which is an
14
alpha-beta alloy containing chromium and iron.
In conclusion, beta-flecks in general tend to reduce the mechanical properties in
titanium alloys which contain chromium and/or iron. Beta-flecks cause a decrease in
tensile elongation if the volume fraction is high or a decrease in LCF life if the size is
considerably large. However, detailed analysis has not yet been carried out and the
quantitative effects, such as volume fraction, size and hardness of beta-flecks. Formation
of beta-flecks is one of the most important issues for titanium alloys. Detailed and
systematic research work is considered to be necessary.
Features of freckles
Freckles (channel segregates or 'A'-segregates) are melt-related defects in nickel-based
superalloy or specialty steel castings, which appear as a long trails of the equiaxed grains
with a composition shift consistent with alloy segregation29-30. Freckles are also highly
undesirable in critical applications because of their deleterious effect on mechanical
performances. Because of their obvious similarity to beta-flecks, it is worth while to
review the literature on freckle formation. Features of freckles, together with comparison
with those of beta-flecks, are given below:
(1) Freckles show various appearances depending on a difference in solidification procedure
and alloying system. (See Figure 830)
For example, in VAR/ESR(Electro-Slag Remelted) ingots, freckles are usually located in
the center to mid-radius of the billet31 and in directionally solidified superalloy castings
(DS or SX), freckle lines are normally located on the exterior surface of the castings32.
In killed steel ingots, freckles ('A'-segregates) usually form in the middle of the
solidification zone, which grows perpendicularly to the sidewalls33 and in IN718
15
containing small amounts of silicon (Ni-0.5%Al-0.2%Co-18%Cr-3%Mo-5%Nb-55%Ni-
l%Ti-Fe, Si<0.3%), the freckles distributed parallel to the liquidus line30.
(2) Freckles are found to be enriched in the normally segregating elements and depleted of
the inversely elements.
(3) The freckle initiation temperature is assumed to be consistent with a fraction solidified
fs=0.529.
(4) Freckling can be significantly reduced and even avoided by operating at larger thermal
gradients and faster solidification rates30.
The location and the shape of freckles is influenced by the mushy zone and its shape34,
which indicates appearance of freckles changes depending on the casting procedures and
alloying systems. Geometric distribution of beta-flecks is in most cases V-shape in the
center of ingots7-27, which appears similar to that observed in IN718 containing low Si.
The fact that freckles are enriched in normally segregating elements indicates that
freckles are shifted toward the eutectic composition35. This behavior supports the fact that
superalloys, which contain high titanium (segregating normally) or tungsten (segregating
inversely), are reported to be more freckle prone35. The frecle initiation temperature is
consistent with fs=0.5, which is quite different from fs=0.8-0.9 for beta-flecks13.
It would appear that the geometric distribution and the initiation temperature are
quite different in freckles and in beta-flecks.
16
Formation mechanisms of freckles and beta-flecks, It is now generally agreed that freckles arise due to channels associated with
"thermosolutal" or "double diffusive" convection in the mushy zone, which is caused by a
density inversion in the mushy zone, as shown in Figure 930. In this figure, the alloy is
solidifying vertically upward, while the heat flow is vertically 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. The density of a liquid alloy is dependent on its
temperature and solute concentration, whose profiles are also indicated in the figure (in
this case, rejected solute is lighter than the solvent). 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 dendrite tip. This is a case of density inversion at the growth
front. This system is unstable, and can lead to fluid convection in order to reduce the
potential energy. This phenomenon is known as "thermosolutal" or "double diffusive"
convection and is considered to be the cause of freckling and the formation mechanism of
freckles is schematically shown in Figure 1029. 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 direction and is established over one or more
primary dendrite spacings. The freckle channels eventually freeze, as the thermal profile
passes through the region. This mechanism can explain freckles formed in the direction
parallel to the growth direction.
The segregation channels corresponding to an array of freckles were formed parallel to
the liquidus line in IN718 containing low silicon, in which density inversion during
solidification was not obtained, based on calculations by Auburtin35. The author also
17
computed interdendritic liquid density profiles by "METALS" and clarified that freckles in
this alloy are heavier than the surrounding.bulk metal (pmatrix= 7490 kg/m3(Tnq=1336 °C),
pfreckie= 7570 kg/m3(Tuq=1336 °C), pfreckie= 7640 kg/m3(TSoi= 1260 °C)). VanDenAvyle36
has schematically described this mechanism of freckle formation, as shown in Figure 11.
When a liquid of composition CL2 is increased in temperature from T l to T2, 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 interdendritic
liquid flowing into a higher temperature field, is the basis of the mechanism by which the
channel defects form and propagate. From optical microscopic observation and microprobe
analysis, it appeared that these defects formed fairly deep in the mushy zone30. It is quite
interesting that even in the same alloy system, in this case in nickel-base superalloys,
completely different phenomena can occur depending on the relationships between the
density of liquid and that of solid. It is therefore important to take the effect of the density
into consideration during solidification.
Brooks proposed a density-driven downward-forming channel for the formation
mechanism of beta-fleck in large ingots, as shown in Figure 11, which was used for
freckles in IN718 containing low silicon27. A requirement for this type of channel to form
is that the density of the interdendritic liquid increases during solidification process. This
phenomenon is possible because chromium and iron tend to concentrate in the liquid and
are heavier elements than titanium. Auburtin13 calculated densities of beta-flecks and
that of bulk liquid at 1605 °C in 10-2-3 by "METALS" and obtained 4243 and 4184 kg/m3,
respectively. The data obtained by Zhou5 were used as chemical compositions of beta-
flecks and bulk liquid(Fe; 3.10 wt.°/o(beta), 2.03 wt.%(bulk), Al; 2.25 wt.%(beta), 3.05 wt.%
(bulk), V; 11.00 wt.%(beta), 10.23 wt.%(bulk)]. This calculated result is considered to
18
support Brooks' mechanism, although the density gradient is very small.
Freckle Criterion and its application to beta-flecks
The development of a numerical criterion, which provides quantitative insight on the
conditions of freckle/beta-fleck formation, is considered as a major factor toward the
successful manufacture of large diameter ingots. There have been some approaches, which
have attempted to clarify the criteria of freckle formation recently.
Auburtin29 has first adopted the basic Rayleigh number suggested by Sarrazin and
Hellawell37. The basic Rayleigh number represents the ratio of driving force for flow to
resistance against flow and may be employed to characterize the onset of fluid flow in
unstable systems38. He attempted to calculate the basic Rayleigh number by putting the
growth front angle of freckles to the horizontal direction as a geometrical factor but could
not obtain a single value for the Rayleigh number, above which no freckling occurs.
In practice, the mushy zone is curved against the growth front angle in most cases and
the direction of permeation relative to that of gravity should be considered. Permeability
of liquid metal was considered in a typical mushy zone arising in VAR processed ingots, as
shown in Figure 12. Considering the relationship between permeability and
primary/secondary dendrite arm spacing geometrically39"41 together with the relationship
between dendrite arm spacing and temperature gradient, Auburtin finally obtained the
modified Rayleigh number, Ra*. For each experimental casting, Ra* was plotted against
growth front angle, as presented in Figure 13. The freckled and freckle-free regions were
clearly divided by a horizontal line and a critical threshold Ra* value was achieved for
each alloy. For example, Ra*(CMSX-llB)=0.88, Ra*(IN718-Si)=0.65, etc.
Auburtin's approach is simple and the obtained threshold value is considered to be
19
accurate and reliable. However, experiments are necessary to determine the threshold
value for every alloy system because the value might be different depending on alloy
systems.
Beckermann42 proposed the critical Rayleigh number, which can be applied to any
solidification conditions, any alloying systems and so on. Beckermann's approach adopted
a characteristic linear dimension that is different from Auburtin et al 2 9. The proposed
Rayleigh number has a maximum value for 10-15vol.% of fraction solidified. Once the
maximum Rayleigh number is found, it needs to be compared to some critical value(RaCrit)
to judge the stability to freckling. Here, the critical Rayleigh number is defined such that
freckles will not form if
Ra<RaCrit (Eq.6)
where Ra is the Rayleigh number, Racrit is the critical Rayleigh number.
The relationship between Ra and G-1 / 2«R_ 1 / 4 is shown in Figure 14, which was originally
obtained by Pollock43. Beckermann proposed Racrit = 0.25 as a criterion for freckling,
considering a more conservative value than G-1/2»R-1/4 < 0.95 proposed by Pollock, which
corresponds to Racrit = 0.4.
This critical value should be the same for all superalloys, assuming a minimal
variation with other system parameters. Beckermann evaluated the critical Rayleigh
number from numerical simulations as well, which predicted the possibility of channeling
leading to freckle formation. He also observed the effect of inclination angle to the critical
Rayleigh number and clarified the relationship as the following:
Racrit = 0.125 -0.00144 for 10 °< <(><45 ° (Eq.7)
where <() is the inclination angle (degrees).
Beckermann's approach is also simple and universal to all the superalloy products,
20
irrespective of alloy systems and casting procedures. However, in some cases, the critical
value might be too conservative, which restricts the production and processes too much.
These two different approaches give us important information on criteria for freckling and
they also have their own advantages and disadvantages.
There has been no report on criteria for the formation of beta-flecks in titanium alloys
yet. Only Auburtin13 tried to estimate the dendrite arm spacing, which causes the density-
driven liquid flow in Ti-10-2-3, according to the basic Rayleigh number, Ra, shown as
(Eq.8). The following parameters were used to calculate Ra, in which A,i ,primary dendrite
arm spacing (PDAS), was substituted for h.
Ra-r/s = g«dp/dz/(r|«DT/h4) (Eq.8)
where g is the gravitational acceleration(m/s2) (= 9.81 m/s2), DT is the thermal diffusivity
(m2/s) (= 9x10-6 m2/s), r\ is the dynamic viscousity of liquid titanium(kg/m/s) (= 0.004
kg/m/s), h is the characeristic linear dimension(m) and dp/dz is the density gradient (kg/m)
(calculated from VAR model58).
When Ra<l, density driven fluid flow is unlikely; when Ra>l, density driven fluid flow
is more likely to occur37. The above equation takes into account permeability due to
dendrite arm spacing and is sensitive to X. Using a calculated liquid density gradient, the
primary dendrite arm spacing should be between 1000 and 1500 um before density driven
fluid flow would occur, according to the Rayleigh criterion.
21
2.3 S U M M A R Y O F L I T E R A T U R E R E V I E W
Studies on segregation of beta stabilizing elements in titanium alloys during
solidification were reviewed and can be summarized as :
(1) In large scale ingots, the solidification mode in CP is either planar or cellular and that
in 6-4(Ti-6%Al-4%V) is either cellular or dendritic, while solidification proceeds in a
columnar/equiaxed dendritic mode in beta alloys.
(2) Dendrite arm spacing in titanium alloys is in the same order of those reported on
steels or copper alloys. Data on titanium alloys is limited and some of them might
not be reliable.
(3) Experimental distribution coefficients are close to those obtained from the equilibrium
binary phase diagram. However, some alloying elements, like iron or chromium, have
different distribution coefficients in different alloy systems.
(4) By using the Scheil equation, temperatures at which beta-fleck initiated were
estimated to be consistent with the fraction solidified of 0.8-0.9.
(5) Beta-flecks in as-cast ingots appear irrespective of the etched microstructures, while
those after heat treatment contain a prior-beta grain or some prior-beta grains.
(6) Beta-flecks have detrimental effects on LCF (Low Cycle Fatigue) life in alloys
containing chromium and/or iron. There have beenno detailed studies on
relationship between mechanical properties and microstructures.
(7) Differences in features of freckles and those of beta-flecks are :
i) Geometrical distribution in large ingots or billets
Freckles : along the longitudinal direction in the center to mid-radius of the billet
Beta-flecks : V-shape distribution in the center of the ingot
22
However, in low Si-IN718, freckles are distributed parallel to the liquidus line,
ii) The initiation temperature
Freckles : fs(fraction solidified) = 0.5
Beta-flecks : fs = 0.8-0.9
(8) The density-driven upward "thermosolutal channel" is proposed as the formation
mechanism of freckles in superalloys except for low-Si IN718.
In low-Si IN718, the density-driven downward channeling is proposed for the freckle
formation mechanism.
The formation mechanism of beta-flecks is estimated to be similar to the latter.
(8) For some superalloys, criteria for freckle formation are clarified on the basis of the
modified Rayleigh number. For titanium, no criterion has been made clear for
formation of beta-flecks yet. Only secondary dendrite spacing, which cause density
driven fluid flow, was estimated according to the basic Rayleigh number.
2 3
Range of VAR ingot values for Ti alloys
at 10000
1000
100
£ i
c
a. to
c
0.001 0.01 0.1 10 100 1000
Cooling Rate (G x R) °C/see
Figure 2 Dendrite arm spacing in T i - 1 7 1 3 .
24
Figure 3 Residual segregation index vs. homogenization parameter for chromium steel 1 9.
(a) Longitudinal direction (b) Radial direction Figure 4 Macrostructure of cross-section of a 10-2-3 production ingot 2 7.
25
Figure 5 Optical micrograph and scanning fractograph of fractured 10-2-3 5
(Forged + 760Cx2hr WQ + 520Cx8hr AC)
o •
Ti-10%V-2%Fe-3%AI alloy
760Cx2HR W Q + 520Cx8HR AC
Low Cycle Fatigue Test
Constant amplitude longitudinal pull-pull cyclic stress Stress Ratio : R-0.1
The Cyclic Frequency: f=15Hz
o maximum beta-fleck area
• volume fraction of beta-fleck
beta-fleck area
=31.22%
6
beta-fleck area (%)
10 12
Figure 6 Effect of beta-fleck area on L C F life of 10-2-3 5 .
26
Figure 7 Typical microstructures of Ti-6-6-2 with beta flecks28.
27
concentrates under hot-top segregation
bands
A-segregates
V- segregates
cone of negative segregation
a) "A" segregate in a large killed steel ingot
b) Centre to mid-radius freckles in VAR IN718 (quarter of a cross-section)
Figure 8 Various appearances of freckles in industrial castings 3 0 (continued).
28
c) Surface freckles in the root portion of a large SX IGT Mar-M247 blade
Figure 8 Various appearances of freckles in industrial castings 3 0.
Figure 9 Schematic diagram of directional solidification and associated thermal(pT), solutal(pc) and thermosolutal(pT+c) density profiles illustrating the density inversion theory 3 0.
29
Liquid Melt
FreckJe Plume
A A Heavier Non-
_Segregatecj Liquid
Lighter « Segregated ' uquicl
Equiaxed
I and/or I jEutectk-; j Enriched j I Material • i (l-2m«i) f
Figure 10 Schematic illustration depicting freckle formation and associated fluid flow pattern 2 9.
T , <;Y-
c L
X r / " '"\
Sy
% Nb
a) An alloy 718 niobium pseudo-binary phase diagram. When liquid of CL2 is increased from T 2 to T i , C Sr-Csi and C L 2 -C L 1 ,
b) Increased density of interdendritic liquid results in a downward flow,
c) Channel defects form by a d) The channel consists of a high-dissolution mechanism, solute dendritic fragmented region.
Figure 11 The mechanism of freckle formation showing the sequence of the density-driven downward-forming channel to form a freckle 3 6.
30
31
2.5
E
op
T3 <U
s '•3 o
1.5
1 i
• Freckles o No Freckles I
Ra*
[CMSX-11B \
0.5 V~ (No Freckles)
10 20 30
Growth front angle (deg.)
(a)
40
2.5
1.5
Bi •a
o S 0.5
! • Freckles i
i o No Freckles j j Ra* !
[Nim80A )
(Freckles |
(No Freckles )
10 20 30
Growth front angle (deg.)
( C )
40
2.5
e 3
Z
OS -a
1.5
o 2 0.5
j . • Freckles j j o No Freckles; ! i
Ra*
(Waspaloy \
(No Freckles \ I
10 20 30 Growth Front Angle (deg.)
(e)
40
2.5
3
z 1.5 T
I 0.5
• Freckles
o No Freckles
Ra*
(Rene88 1
[No Freckles]
10 20 30 Growth front angle (deg.)
40
•5 1.5
i 1
-g 0.5
• Freckles ! * No Freckles
Ra*
(lN718-Si )
(Freckles )
(No Freckles )
10 20 30
Growth Front Angle (deg.)
id)
40
S 3
z 00
3.5
3
2.5
2
1.5
1
0.5
0
• Freckles j
o No Freckles: Ra* I
|Mar-M247 )
t Freckles
[No Freckles]
10 20 30
Growth Front Angle (deg.)
if)
40
Figure 13 Modified Rayleigh number vs. growth front angle for alloy (a)CMSX-llB, (b)RENE88, (c)NI80A, (d)IN718-Si, (e)WASPALOY and (f)MAR-M24729.
32
100
10
<» No Grain Defects x Freckles and/or Grains
s | 1
Z •5 I 0.1 <2
o.oi 4
o.ooi o.i
critical value proposed by Pollock and Murphy (1996)
10 G - , / J R - w [ c m , V V w ]
Figure 14 Calculated Rayleigh numbers for the directionally solidification experiments for the SX-1 superalloy as a function of the thermal parameter G-1/2»R~1/4 4 2 ' 4 3 .
33
3. R E S E A R C H O B J E C T I V E S
A literature review revealed that some solidification parameters, such as dendrite arm
spacing, have been investigated in titanium alloys and that a formation mechanism of beta
fleck has been proposed. However, the proposed mechanism is not convincing since no
systematic study has been conducted to verify the mechanism and there has been little
data reported on the parameters, which is necessary to validate the mechanism. As liquid
metal flow at the liquid/solid interface, which might lead to the formation of beta-fleck, is
taken into consideration, permeability of the liquid metal through dendrite structure has
to be discussed. Therefore, dendrite arm spacing is a critical parameter and may be used
in criteria to determine if density-driven flow of liquid metal occurs during solidification by
way of the basic Rayleigh number, as shown in (Eq.8). Particularly, it is critical to clarify
the dendrite arm spacing in segregation sensitive titanium alloys, in which no effective
etching method has been developed to make dendrite structure visible. A method to obtain
dimensional and morphological information on dendrite structures, except for a
conventional etching method, should be established in order to determine dendrite arm
spacing in these titanium alloys.
Densities of liquid and solid metal at the interface and the fraction solidified at the
initiation of beta flecks should be clarified in considering the formation mechanism of beta-
fleck. Liquid and solid metal density can be estimated from the chemical composition of
beta-flecks with the calculation software, "Metals". The volume fraction of solid at the
liquid/solid interface can be calculated by putting distribution coefficients into the Scheil
equation, shown in (Eq.3). However, distribution coefficients of alloying elements in
practical alloys containing multi-components have not been clarified yet. It is considered
34
to be difficult to assess the accurate volume fraction in these alloys by distribution
coefficients obtained from the binary equilibrium phase diagrams.
Therefore, the present study is focused on the following items as the research
objectives :
(1) To experimentally determine the dendrite arm spacing in segregation sensitive
titanium alloys.
The experimental methodology to obtain dimensions of dendrite arm spacing will be
established by applying EPMA and the relationship between dendrite arm spacing and
solidification conditions is planned to be clarified.
(2) To determine distribution coefficients in practical titanium alloys consisting of multi-
component system.
The segregation behavior of alloying elements in practical alloys has to be investigated
under solidification conditions close to the equilibrium state.
(3) To establish the formation mechanism of beta fleck by applying parameters obtained
from (1) and (2).
Finally, the validity of the proposed model must be examined by applying dendrite arm
spacing and distribution coefficients, which are experimentally obtained, to the
Rayleigh number.
35
4. E X P E R I M E N T A L M E T H O D O L O G Y
4.1 C H O I C E O F A L L O Y S
The following three alloys have been selected for this experimental investigation.
1. 10-2-3 (Ti-10%V-2%Fe-3%Al)
2. Ti-17 (Ti-5%Al-2%Sn-2%Zr-4%Mo-4%Cr)
3. 6242 (Ti-6%Al-2%Sn-4%Zr-2%Mo)
All three of these alloys are industrially used titanium alloys. 10-2-3 and Ti-17 are beta
titanium alloys, both of which are used as component materials in airplanes, especially
landing gear, etc1-44. 10-2-3 and Ti-17 contain a large amount of beta stabilizing elements,
such as 10 wt.% of vanadium and 2 wt.% of iron in the former and 2 wt.% of zirconium, 4
wt.% of molybdenum and 4 wt.% of chromium in the latter in order to stabilize beta phase
at room temperature. In practice, however, beta phase is metastable at room temperature
and alpha phase precipitates during cooling from the beta phase region with a slow cooling
rate. It is expected that iron may segregate heavily in 10-2-3, while severe segregation of
chromium would occur in Ti-17 during solidification.
On the other hand, 6242 is an alpha+beta alloy, more precisely a near-alpha alloy,
which is mainly used for high temperature services, such as compressor section's
components of aircraft gas turbine engines1-44. 6242 contains a higher concentration of
aluminum and lower concentrations of beta stabilizing elements to stabilize both alpha
and beta phase from room temperature to operating temperature. In this alloy,
molybdenum is assumed to segregate heavily during solidification.
Considering each alloying element in these alloys, aluminum is an alloying element
36
common to all three alloys; molybdenum and zirconium are contained in Ti-17 and 6242.
Therefore, a difference in segregation behavior of the above alloying elements can be
examined in different alloying systems as well as that depending on a difference between
binary system and multi-component system.
4.2 E X P E R I M E N T A L M E T H O D S
Segregation behavior of iron in 10-2-3 small ingots melted and cast in an argon arc
melting furnace
In order to clarify the relationship between the solidification conditions and the
segregation behavior of iron together with microstructures, 10-2-3 was melted using an
argon arc melting furnace in the Advanced Materials and Process Engineering Laboratory
(AMPEL) at The University of British Columbia(UBC). A picture of the furnace and its
schematic layout are shown in Figures 14 and 15, respectively. During melting
experiments, the chamber was kept in an argon gas atmosphere with a pressure of 35kPa
in order to protect the molten metal from air. Typical operation conditions during melting
were 10-15 volts and 1100-1500 amperes. The shape of molten metal pool was monitored
through sight glasses during the experiments. Molten metal was superheated for 2-5
minutes, while the graphite crucible was preheated with an induction coil. After the
molten metal was superheated, the water-cooled copper bottom plate was pulled out and
molten metal was poured into the mold. Dimensions of crucible were 20 mm in inner
diameter and 60 mm in length, if the crucible was filled with molten metal. Ingots were
cut in half in the longitudinal direction and the transversal surfaces were polished to 1
diamond and finally etched for optical microscopic observation with an acid solution
containing HF:HN03:H20(15 ml:50 ml:535 ml). Microstructures were observed with an
37
optical microscope.
The segregation behavior of iron was analyzed by Electron Probe Micro Analysis
(EPMA) attached to a Hitachi S-570 Scanning Electron Microscope (SEM) in the
Department of Metals and Materials Engineering at UBC. The acceleration voltage of
electron beam was 20kV and the analysis was carried out under a vacuum of lxlCHPa.
Segregation behavior of iron was examined in the directions inclined from the horizontal
line by 0, 30, 45 and 60 ° in a cut plane to clarify the direction of dendrite arm. The
intensity of Fe-Ka were counted and calibrated to weight per cent.
Time evolution of temperature in the ingots during solidification was monitored in the
argon arc furnace casts. Type-C thermocouples (tungsten-5wt.%rhenium vs. tungsten-
26wt.%rhenium) with wire thicknesses of 10/1000"(0.25 mm), inserted into alumina tubes
for protection, were set in the vertical direction at 25 mm and 15 mm in height from the
bottom of the crucible. Thermocouples were connected to a laptop computer by way of the
temperature acquisition system "instruNET'. Temperature was read and recorded by the
"instruNET' software installed on the computer. The frequency for reading temperatures
(voltage) was 5Hz.
Segregation behavior of alloying elements in production ingots
In order to establish a method to determine dendrite arm spacing in production
titanium alloy ingots, chemical analysis of alloying elements was carried out on specimens
cut from a Ti-17 ingot and a 10-2-3 ingot with EPMA. The Ti-17 ingot was supplied by
Timet Corporation and had dimensions of 450 mm in width and 430 mm in thickness. A
160 mm x 350 mm x 20 mm plate cut from a 10-2-3 ingot was supplied by RMI Company,
which had initial dimensions of 760 mm in diameter and 2164 mm in length27>. Specimens
38
with a cross-section of 10 mm x 10 mm were cut from the sample materials and the
transversal surfaces were polished to 6 |̂ m diamond.
The segregation behavior of chromium in Ti-17 and that of iron in 10-2-3 were
analyzed by EPMA attached to a Hitachi S-570 SEM as mentioned above. The
acceleration voltage of electron beam was 20 kV and analysis was carried out under a
vacuum of lxlO"4 Pa. Analysis was conducted in the direction assumed to be perpendicular
to the solidification direction, to investigate the distribution of chromium in Ti-17 and that
of iron in 10-2-3. The intensities of Cr-Ka and Fe-Ka peaks were counted and calibrated
to wt.%.
Segregation behavior of alloying elements in laboratory melted small ingots using a
zone melting furnace
10-2-3, Ti-17 and 6242 (Ti-6%Al-2%Sn-4%Zr-2%Mo) were melted and cast in a uni
directional induction levitation furnace at the Wright Patterson Air Force Laboratory in
Ohio. Bar samples were heated and melted with a 30 mm long induction coil moving along
the longitudinal direction. The coil moving speed was 4 mm/hr (l.llxlO-6 m/sec) and the
maximum temperature during melting was held at TL+20-30 K (TL: the liquidus
temperature), which corresponds to a temperature gradient of 5.5-5.7xl04 K/m. During the
experiments, samples were shrouded with argon gas which not only protected the system
from oxidation, but also minimized elemental loss due to evaporation. Evaporation is a
particular problem in the alloy systems chosen and for example negated the choice of
levitation electron beam zone refining as a possible method for this experiment.
Dimensions of the samples were 0.5"(12.7 mm) in diameter and 5"(127 mm) in length. The
samples were cut in half in the longitudinal direction initially and then cut into three
39
specimens containing the start, the middle and the finish of melting. The specimens were
polished to 1 um diamond and finally etched for optical microscopic observation. As an
etchant, an acid solution containing HF:HN03:H20(15 ml:50 ml: 435 ml) was used for 6242
and Ti-17, while that consisting of HF:HN03:H20(15 ml:50 ml: 535 ml) was used for 10-2-
3. After microstructural observation, specimens were re-polished to 6pm diamond before
chemical analysis.
The segregation behavior of the alloying elements was analyzed using an energy
dispersion spectrometer (EDX) microprobe (KEVEX detector and a Quartz Xone analyzer)
attached to a Hitachi S-570 SEM at UBC. Acceleration voltage of the electron beam was
20 kV and the analysis was carried out under a vacuum of lxlO - 4 Pa in the longitudinal
direction of each sample. The intensity of Al-Ka, V-Ka, Cr-Ka, Zr-Ka, Mo-La and Sn-La
peaks was measured in each alloy and calibrated into wt.%.
40
Figure 15 Argon arc melting furnace in A M P E L , U B C .
41
Movable tungsten
electrode
Tubes for cooling
water
Argon gas
c * c
c c
IH coil
Alumina container
Graphite crucible
Tubes for
Cooling water
Molten
metal
I
Arc
Sight glass
0
3 Pressure
Gauge
Removable copper
bottom plate
Tubes for cooling
Water
Thermocouples
Connected to
a PC
Figure 16 Schematic diagram of the argon arc melting furnace in AMPEL.
42
5. E X P E R I M E N T A L R E S U L T S
5.1 S E G R E G A T I O N B E H A V I O R O F A L L O Y I N G E L E M E N T S I N T I T A N I U M
A L L O Y I N G O T S S O L I D I F I E D I N D E N D R I T I C M A N N E R
Segregation behavior of iron in laboratory melted 10-2-3 ingots using an argon arc
furnace
The melting experiments were conducted in an electrode arc furnace using an argon
atmosphere. A total of six charges were made and four ingots were obtained. In one of the
cases, an ingot was not obtained because of excessive oxidation during the experiment due
to a shortage of argon gas supply and in another case, an ingot was not obtained due to
failure of the electrode during melting. The results for each charge, including the two
failed attempts, are summarized in Table 3.
Table 3 Mel t ing experiment results with the argon arc furnace
Cast Ingot Holding time before Microstructure Notes no length pouring the molten metal 1 50mm 1 minute Equiaxed Initial conditions 2 45mm 2 minutes Partially elongated More superheat than No.l 3 Failed N/A N/A Excessive oxidation in molten metal 4 50mm 3 minutes Mostly elongated More superheat than No.2 5 Failed N/A N/A Electrode dropped during melting 6 50mm 5 minutes Equiaxed More superheat than No.4
Micrographs of the etched ingot samples 1,2,4 and 6 are shown in Figure 17(a)-(d),
respectively. The microstructures listed in Table 3 were categorized from the results in
the shape of the prior-beta grains, as shown in the figures. The equiaxed prior-beta grains
were observed mainly in samples 1,2 and 6, while elongated grains along the longitudinal
direction of the ingot could be seen in sample 4(Figure 17(c)). In general, dendritic
43
columnar growth is promoted under solidification conditions with a higher temperature
gradient and a lower solidification velocity5, etc. More superheat in the molten metal and
more preheat into the crucible was applied by increasing the holding time before pouring
the molten metal into the mold in sample 4 than in sample 1 or 2. This might have caused
the elongated prior-beta grains. The holding time was prolonged to 5 minutes in sample 6,
2 minutes longer than in sample 4. The microstructure of sample 6, however, consisted of
the equiaxed prior-beta grains, which were distributed uniformly.
The iron concentration distribution in the directions inclined from the horizontal line
by 0,30,45 and 60 0 on a cut surface in sample 4 ingot are shown in Figures 18-21. Both of
the average of iron concentration and the statistical error of the data were deviated
depending on the analyzed direction: from 1.589 to 1.780 wt.% in the former and from
0.083 to 0.113 in the latter. In the figures, error max shows a summation of the average
concentration and statistical error, while error min shows a subtraction from the average
concentration by statistical error. Among the figures, the concentration curve obtained
from the horizontal direction showed the clearest peaks and periodicity in the curve,
presenting almost the same spacing of 47 um between the peaks. In other figures, in the
directions inclined from the horizontal line by 30-60 °, a difference between the peak and
bottom concentration decreased but showed periodicity and a spacing of 42-48 um between
the peaks.
Evolution of temperature with time at the height of 25 mm and 15 mm from the bottom
of a CP titanium ingot is shown in Figure 22. There were not enough raw materials of 10-
2-3 and CP titanium was used in these experiments, whose thermal conductivity is close to
that of 10-2-3. In this experiment, the holding time before pouring molten metal into the
mold was 3 minutes and the induction heating system was switched off just prior to
44
pouring. This condition was very close to that applied for melting sample 4 ingot. In the
figure, temperature rapidly increased at 7 seconds after slowly decreasing from 1323 K
(1050 °C) for the 25mm location and from 1123 K (850 °C) for the 15 mm location, which
indicates that the molten metal filled the crucible and touched the thermocouples at 7
seconds. Faster response in a temperature curve at 15 mm than that at 25 mm shows that
molten metal piled up steadily from the bottom of the crucible, indicating that
temperatures were monitored satisfactorily. Cooling rates were different depending on the
location of thermocouples and the extent of solidification. From 1923 K (1700 °C) to 1873
K (1650 °C), the cooling rates were 13.2 K/s at 25 mm and 47.0 K/s at 15 mm, respectively.
A clear change in cooling rate at around the melting point was not observed at either
location.
Segregation behavior of alloying elements in production ingots
A photograph showing the transverse cross section of a Ti-17 ingot and the location of
specimens taken for chemical analysis with EPMA is shown in Figure 23. Since no
effective etching technique has been developed for titanium alloys, which allows us to
identify the dendritic structure directly, the degree of the columnar growth of dendrites
can only be estimated from the shape of the prior-beta grains. Microstructure of the cross
section of the ingot consisted of elongated prior-beta grains originated mainly from the
edges toward the center, which might be the traces of the growth direction of the
dendrites. Specimen No.4, the closest to the center of the ingot as shown in Figure 23, was
eventually used for the analysis and consisted mainly of the equiaxed prior-beta grains.
An optical micrograph of Specimen No.4 is shown in Figure 24. The microstructure
consisted of the equiaxed prior-beta grains and finely distributed platelet alpha and beta
45
grains in each grain.
Chemical analysis with EPMA on chromium content was carried out in the two
diagonal directions of the sample, which are assumed to correspond to the directions
perpendicular and parallel to the elongated direction of the prior-beta grains, respectively.
The distribution of chromium concentration obtained by EPMA in the direction
perpendicular to the elongated direction of the prior-beta grains is presented in Figure 25.
It is to be noted that the ingot used was an experimental one and did not have the
conventional Ti-17 composition45-46 of 4 wt.% and the average chromium concentration was
2.295wt.%. Error max and error min in the figure were obtained from calculation between
the average concentration of chromium and a statistical error in chromium concentrations.
As can be seen in Figure 25, the distribution of chromium concentration has periodicity
consisting of 3 peaks, 2.66, 2.59 and 2.62 wt.% of chromium contents and shows the
spacing of 1062 and 1593 um between the peaks. These three concentration values at
peaks correspond to 1.13-1.16 times as high as that of the average and much higher than
the maximum error value of 2.42 wt.%. It is therefore clear that concentration of
chromium fluctuated periodically in the direction perpendicular to that of solidification.
Diffusion of solute chromium atoms in the solid state after solidification was taken into
consideration according to (Eq.4) and (Eq.5)19-25 in the production Ti-17 ingot. Calibrated
chromium concentrations are shown in Figure 26. A solid line indicates the chromium
concentrations measured by EPMA, while a broken line shows the chromium
concentrations just after the solidification, which was estimated from considering the
effect of diffusion of chromium atoms in the solid state. Diffusion of solute chromium
atoms in the solid state had little effect on a change in concentration, which caused an
increase of only 0.02 wt.% (from 2.67 to 2.69 wt.%).
46
The segregation behavior of iron in a 10-2-3 production ingot was investigated. Figure
27 shows a macrograph of an as-received 10-2-3 plate material. A 30" diameter ingot was
cut into 1" thick plate material in the longitudinal direction of the ingot27 and one surface
of the material was polished and etched. The microstructure consisted of the equiaxed
prior-beta grains, with grain diameters varying from 5 to 15 mm, distributed uniformly
throughout the material. Block samples (sample No. RIO 1-104) were cut from the marked
locations in Figure 27. The distribution of iron concentration obtained in the direction
inclined to the horizontal direction by 60 ° in the R102 sample is shown in Figure 28. In
the analyzed area, three sharp peaks can be observed with spacing of 1062 and 1151 um
between the peaks, indicating periodicity as seen in a Ti-17 production ingot. Clear peaks
and periodicity of concentration profiles could not be seen in any other directions.
In order to clarify if beta-flecks exist in this area, EPMA analysis for iron concentration
was conducted on each of these four samples. The distribution of iron concentration is
shown in Figure 29, in which the numbers indicate iron concentration in weight percent in
each section. The maximum iron concentration measured was 1.89 wt.%. This value is
not so different from the average concentration of 1.67 wt.%, showing that beta-flecks did
not exist in this region.
47
5.2 S E G R E G A T I O N B E H A V I O R O F A L L O Y I N G E L E M E N T S I N Z O N E
M E L T E D T I T A N I U M A L L O Y I N G O T S
Photographs of as-received specimens cast with a zone-melting furnace are shown in
Figure 30(a)-(c). The 6242 specimen consisted of one full-length bar but the Ti-17 and 10-
2-3 specimens were separated into two parts. The full length of the specimens was about
200 mm and that of the melted part was 70-80 mm. A step-like expanded shape could be
seen at the start point of melting, where the diameter was 1-2 mm larger than that of the
unmelted part. It may have arisen because melting was started at a more downward
location than the middle of the specimen, corresponding to 70 mm from the bottom end,
and it proceeded upward in the vertical direction. The final point of melting resulted in a
necked shape, where the Ti-17 and 10-2-3 specimens were separated into two parts.
However, the shape of the fractured surface was quite different for the Ti-17 and 10-2-3
specimens. A fibrous and zigzag surface was seen in the Ti-17 specimen, showing the
typical ductile fractured surface, which might have occurred at around room temperature.
It is considered that the specimen was separated into two parts after solidification had
been completed. In contrast, a smooth surface and spherical shape was seen on the
separated end in the 10-2-3 specimen, which shows that the fractured section remelted. In
analyzing the chemical composition of the 10-2-3 specimen, this effect has to be taken into
consideration.
The cross-sectional macrographs of the Ti-17, 10-2-3 and 6242 specimens are shown in
Figures 31-33. In all the samples, the unmelted parts consisted of fine equiaxed grains
close to both ends, which is the initial microstructure of the materials. At locations closer
to the start or finish point of melting from each end, the grain diameter becomes coarser,
48
showing grain growth occurred by the heat input during the melting experiment. At the
middle section, no clear grain boundary was identified and the structure appeared a single
crystal until the melting section terminated. There were subtle differences in the
microstructures in each specimen. In the Ti-17 and 10-2-3 specimens, some localized areas
around the tip of the final melting location was difficult to etch, indicating the chemical
compositions of these areas may be considerably different from those of the other parts
(Figures 31 and 32). In the middle part of melting in the 10-2-3 specimen, unclear lines
streaked in the longitudinal directions, which might be subgrains (Figure 32). Two
different etched colors or patterns can be seen in the middle part of the 6242 specimen but
no obvious grain boundaries were found between the different patterns. Detailed
observation revealed that these different etched patterns depended on the degree of
etching and they consisted of an acicular microstructure with the same configuration and
direction of laths. t
The distribution of alloying elements analyzed with EDX in the longitudinal direction
of the 10-2-3, Ti-17 and 6242 specimens are shown in Figures 34-36. These figures were
obtained by combining data from three specimens cut in the longitudinal direction for each
alloy. The concentration distribution of each alloying element showed a reasonably
smooth shape. However, the actual concentration profile obtained for the 10-2-3 specimen
was not smooth, as shown in Figure 37. For example, around the final melting point, two
irregular peaks were seen for the iron concentration profile in the figure, comparing with a
smooth curve with a peak for chromium in Ti-17 or for zirconium in 6242. It is thought
that this resulted from the redistribution of alloying elements due to remelting after the
sample had been separated. Therefore, paying attention to the similar concentration
profiles of alloying elements at the x-axis at 71-73 mm and at 82-84 mm, concentration
49
data at 73-82 mm were rejected. The final results are presented in Figure 34. The
concentration profiles should have been the one shown in Figure 34, if the samples had not
remelted.
Figures 34-36 show similar segregation behavior of other segregating elements: iron in
10-2-3, chromium and zirconium in Ti-17 and zirconium in 6242, all of which decreased as
melting started and increased rapidly near the finishing point. The maximum content of
iron close to the end of melting in 10-2-3 reached to 4.56 wt.%, which corresponded to 2.73
times the average iron content of the parent metal, 1.67 wt%. Brooks et al7 reported that
beta-flecks formed in regions containing higher than 2.4 wt.% of iron and it is surmised
that beta fleck formed close to the final melting point in this sample. In Ti-17, a large
increase in chromium content was identified at the final melting point, the increase of
which was 1.83 times higher than the average.
Concentrations of elements other than iron, chromium and zirconium indicated reverse
profiles, showing an increase at the start and a decrease near the finish. The molybdenum
content showed curious behavior, a much higher decrease in Ti-17 than in 10-2-3 at the
final melting point. It shows that even the same alloying element can have different
concentration profiles in different alloying systems. The broken lines in Figures 34-36
represent the concentration vs. is (fraction solidified) curves obtained using the Scheil
equation (Eq.(3)) for iron in 10-2-3, chromium in Ti-17 and zirconium in 6242, respectively.
fs was calculated as a ratio between the distance from the initial melting point and the
distance of the melted section. The actual concentration profiles obtained from
experiments have a steeper shape than the curves determined by the Scheil equation. In
reference, concentrations of oxygen and nitrogen in a 10-2-3 ingot produced in the same
zone-melting furnace are presented in Figures 38 and 39. These measurements were
50
obtained from LECO analysis conducted by TIMET Corporation47. The concentration
profiles of oxygen and nitrogen show an increase at the start point and a decrease at the
finish point, such as molybdenum, aluminum, etc.
The concentration data of each alloying element obtained from the zone-melted 10-2-3,
Ti-17 and 6242 alloy ingots is summarized in Tables 4-7. Each table contains the
average (Cave), maximum(Cmax) and minimum(Cmin) concentrations, the ratio between the
maximum and minimum concentration(Cmax/Cmin) and the segregation coefficient(k) for
each alloying element. The average concentration corresponds to the average value of
concentrations obtained in the unmelted parts, which is supposed to be the initial
composition (Co) of each alloying element. The segregation coefficient was calculated on
the basis that the concentration of each element at the start of melting (CL) equals the
product of the segregation coefficient and the average concentration (k»Co)48. As can be
seen in Figures 34-36, the concentration at melting start point corresponded to the
maximum concentration for aluminum, molybdenum and tin, and the minimum
concentration for iron, vanadium, chromium and zirconium. Therefore, the segregation
coefficients of the former three elements were obtained from the ratio of Cmax/Cave, while
those of the latter four elements were given by the ratio of Cmin/Cave.
Equilibrium distribution coefficients (keq) of each alloying element, calculated from the
binary phase diagrams20, are included in the tables.
In Table 4, Cmax/Cmin of iron is very high, 7.23, which shows that iron segregates
heavily in 10-2-3. C max/Cmin ratios of tin, zirconium, molybdenum and chromium in Ti-17
and that of zirconium in 6242 are higher than 2, indicating these elements also segregate
heavily in each alloy. On the other hand, aluminum in all the alloys, vanadium, oxygen
and nitrogen in 10-2-3 and tin and molybdenum in Ti-17 show C max/Cmin ratios smaller
51
than 2, indicating that they do not segregate heavily in these alloys. Tin shows interesting
behavior; it shows segregation increased in Ti-17 with a Cmax/Cmin ratio of 2.06 versus 1.30
in 6242. This result indicates that the same alloying element can show differences in the
degree of segregation in different alloying systems. 4
<
The segregation coefficients of some alloying elements are different depending on
alloying systems. For instance, k of aluminum fluctuates from 1.02 in 6242 to 1.13 in 10-2-
3, while that of tin varies from 1.08 to 1.15, etc, although the difference between them is
not so large. A large difference between k and k e q can be seen in iron in 10-2-3, tin,
zirconium, molybdenum and chromium in Ti-17 and tin and zirconium in 6242. In
particular, k is much less than k e q for iron in 10-2-3.
52
Table 4 Composition variations and segregation coefficients(k) of alloying
elements in a zone melted 10-2-3 ingot
Alloying Element
Cave wt.%
Cmax wt.%
Cmin wt.%
Cmax /Cmin
k keq(ref(20))
Al 2.76 3.11 2.35 1.32 1.13 1.05 V 9.92 10.53 9.15 1.15 0.95 0.95 Fe 1.67 4.56 0.63 7.23 0.38 0.60
Table 5 Composition variations and segregation coefficients(k) of alloying
elements in a zone melted Ti-17 ingot
Alloying Element
Cave W t . %
Cmax wt.%
Cmin wt.%
Cmax /Cmin
k keq(ref(20))
Al 5.55 5.86 4.80 1.22 1.06 1.05 Sn 1.52 1.75 0.85 2.06 1.15 0.92 Zr 1.39 2.53 1.07 2.36 0.77 0.90 Mo 2.75 3.16 1.30 2.43 1.15 1.50 Cr 5.50 10.04 4.06 2.47 0.74 0.70
Table 6 Composition variations and segregation coefficients(k) of alloying
elements in a zone melted 6242 ingot
Alloying Element
Cave W t . %
Cmax W t . %
Cmin W t . %
Cmax /Cmin
k keq(ref(20))
Al 5.83 5.94 5.66 1.05 1.02 1.05 Sn 1.50 1.62 1.25 1.30 1.08 0.92 Zr 2.63 4.49 1.90 2.36 0.72 0.90 Mo 1.34 1.46 1.03 1.42 1.09 1.50
Table 7 Composition variations and segregation coefficients(k) of oxygen and
nitrogen in a zone melted 10-2-3 ingot(ref(47))
Alloying Element
Cave wt.%
Cmax wt.%
Cmin wt.%
Cmax /Cmin
k keq(ref(20))
0 0.137 0.182 0.118 1.54 1.33 1.60 N 0.011 0.016 0.009 1.78 1.45 1.58
53
5.3 D E N S I T Y O F B E T A - F L E C K A N D L I Q U I D M E T A L C A L C U L A T E D U S I N G
" M E T A L S " F O R 10-2-3 A N D Ti-17 A L L O Y S
The density of beta-fleck and liquid metal was obtained by calculation using
"METALS", the principles of which are shown in Appendix A. Examples of the calculated
results are presented in Figures 40-43. In Figure 40, the density of solid phase was
calculated in an iron concentration range from 0.5 to 2 wt.% at 1900 K, while that of the
liquid phase was calculated in a range from 2 to 5 wt.% at 1905 K(the melting
temperature). These ranges were determined on the basis of the zone-melting experiment
results, where the minimum iron concentration was 0.63 wt.% and the maximum iron
concentration was 4.56 wt.%. There is a wide gap between the density of solid and liquid
phases, with the liquid showing lower density than the solid for the same composition at a
similar temperature. For instance, the density of the solid phase containing 2 % iron is
4497.8 kg/m3 at 1900 K, while that of the liquid phase containing 2 % iron is 4164.8 kg/m3
at 1905 K. The density increases with iron concentration, however; even though the liquid
phase contained 5 % iron, it is still lighter than solid phase consisting of 0.5 % iron. The
density of liquid, which might form beta-flecks in 10-2-3, is estimated to be higher than
4171.6 kg/m3 at the melting temperature since the iron concentration at beta-fleck is at
least 3.1 %.
The effect of temperature on density of the liquid(beta-flecks) and solid phase is shown
in Figure 41, where the calculation was conducted for liquid containing 3.1 % iron and the
solid containing 2.0 % iron. It is clear from Figure 41 that the density increases rapidly as
the alloy solidifies. The density increases with a decrease in temperature in the solid and
liquid phase but the slope is steeper in liquid than in solid.
54
Calculated results obtained for Ti-17 are shown in Figures 42 and 43. The density of
liquid metal containing 5.5 % chromium, which is known as a composition of beta-flecks in
Ti-1713, was higher than 4167.9 kg/m3 at melting temperature (1914 K), while that of solid
phase containing 4% chromium was 4503.4 kg/m3. In Ti-17, the density of the solid is
heavier than that of the liquid, which is the same trend as observed in 10-2-3.
55
(a) Sample 1
(b) Sample 2
Figure 17 Macrographs of 10-2-3 ingots melted by the argon arc furnace (continued).
56
(c) Sample 4
(d) Sample 6
Figure 17 Macrographs of 10-2-3 ingots melted by the argon arc furnace.
57
3
2.5
Ti-10%V-2%Fe-3%AI cast ingot Ingot diameter: 20mm, length : 50mm Analyrert hy FPMA (Fe-Kry)
Ingot bottom
Accelerated Voltage : 20kV Fe(ave)=1.780wt.%, cr=0.113
r/2 ddeg
t/3!
-* -p i tch=14.2# m
- • - error max
- a - error min
Ingot Top -*-p i tch=14.2# m
- • - error max
- a - error min
200 300 400 500
distance from the start point ( n m )
600 700
Figure 18 Distribution of iron concentration in the horizontal direction in a 10-2-3 laboratory-melted ingot.
200 400 600 800
distance from the start point (u m)
1000 1200
ure 19 Distribution of iron concentration distribution in the direction inclined to the horizontal direction by 30 in a 10-2-3 laboratory-melted ingot.
58
0.5
Ti-10%V-2%Fe-3%AI cast ingot Ingot diameter: 20mm, length : 50mm Analyzed by EPMA (Fe-Ka)
200
Ingot bottom
-pi tch=14.2j / m
- error max
- error min
400 600 800
distance from the start point (u m)
Itigot top
1000 1200
Figure 20 Distribution of iron concentration in the direction inclined to the horizontal direction by 45 in a laboratory-melted 10-2-3 ingot.
2.5
0.5
Ti-10%V-2%Fe-3%AI cast ingot Ingot diameter: 20mm, length : 50mm Analyzed by EPMA (Fe-KoQ
Accelerated Voltage: 20kV Fe(ave)=1.594wt.%, a =0.083
-pi tch=14.2# m
- error max
- error min
Ingot bottom
Ingot top
100 200 300 400 500 600 700
distance from the start point (u m)
800 900 1000
Figure 21 Distribution of iron concentration in the direction inclined to the horizontal direction by 60 in a 10-2-3 laboratory-melted ingot.
59
20 25
time (sec)
Figure 22 Evolut ion of temperature with time dur ing solidification in Commercial ly Pure Titanium melted in an argon arc furnace.
60
500Lim
Figure 24 Microstructure of a Ti-17 production ingot.
61
3.2
2.8
1.8
1.6
Ti-17 (Ti-5%AI-2%Sn-2%Zr-4%Mo-4%Cr) as cast slab Slab width: 450mm, thickness: 430mm Analyzed by EPMA (Cr-Ka) Accelerated Voltage = 20kV Cr(ave)=2.295wt.%, CT=0.120
1062U m 1593 u m
-chromium concentration
- error max
-error min
500 1000 1500 2000 2500
distance from the sample edge (u m)
3000 3500 4000
Figure 25 Distribution of chromium concentration in a Ti-17 production ingot.
3.2
2.8
2.6
8 2.4
2.2
1.8
1.6
Ti-17 (Ti-5%AI-2%Sn-2%Zr-4%Mo-4%Cr) production ingot Slab width: 450mm, thickness: 430mm Analyzed by EPMA (Cr-Ka) Accelerated Voltage = 20kV Cr(ave)=2.295wt.%, <r=0.120
- measured chromium concentration
• just after solidification
500 1000 1500 2000 2500
distance from the sample edge (u m)
3000 3500
Figure 26 Estimated distribution of chromium concentration in a Ti-17 production in£ just after solidification.
62
1 2 3 4 5 6 7 8 9
: j r IH11, t h j If I r 11111 j 1111.; 11. j l i! 11 s f 11 i tl I; • IL :̂ . 11 •, f 111 i r 11 f ? • f. h: j l; 111, r! I' 11 r I! t r;: i; n 11 i 11 |i 111
11 12 13 14 15 16 17 18 19 © 21
im
Figure 27 Macrograph of as-received Ti-10-2-3 production ingot.
2.5
2.25
Ti-10-2-3 (Ti-10%V-2%Fe-3%AI) production ingot Ingot diameter:760mm, length:2413 mm Analyzed by EPMA (Fe-Kar)
-Accelerated Voltage = 20kv
Cr(ave)=1.665wt.%, a =0.087
1062jim 1150.5^m + *•< •
1.25 - measured data
- error max
- error min
1000 2000 3000 4000 5000
distance from the sample edge (u m)
6000 7000
Figure 28 Distribution of iron concentration in the direction inclined to horizontal direction by 60° in a 10-2-3 production ingot.
G3
Sample No iron concentration (wt%)
RM101 1.67 1.59 1.61 1.47 1.63 1.71 1.80 1.85 1.55 1.86 1.51 1.73 1.59 1.70 1.66 1.43
RM102 1.65 1.75 1.64 1.78 1.56 1.83 1.76 1.54 1.74 1.65 1.74 1.61 1.76 1.88 1.50 1.66
RM103 1.57 1.77 1.59 1.45 1.88 1.71 1.61 1.55 1.63 1.65 1.52 1.89 1.58 1.57 1.65 1.56
RM104 1.69 1.66 1.77 1.68 1.69 1.84 1.53 1.62
•1.84 1.82 1.86 1.50 1.59 1.68 1.50 1.58
Figure 29 Distribution of iron concentration in a 10-2-3 production ingot.
64
Direction of solidification <
9 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 9 I!) ® 2 1 2 2 2 3 2 4 2 5 2 6 _ (a) 10-2-3
5 6 7 8 | (TJ 1 1 1 2 1 3 H 1 5 ' 8 " 1 8
1 9 ® 2 1 2 2 2 3 2 4 2 5 2 6
(b) Ti-17
, j . m - r -
5 6 7 8 » ® 1 1 1 2 1 3 1 * 1 5 1 6 1 7 , 8 . 9 0 2 1 2 2 2 3 2 4 2 5
ii I I I • i M i a i i ^ i M i i n t i r t n T i f t I : I.Ij | iilWlBM#!.T
(c) 6242 Figure 30 Macrographs of zone melted samples (as-received).
65
Direction of solidification Figure 31 Cross-sectional macrographs of a zone melted 10-2-3 ingot.
66
Direction of solidification Figure 32 Cross-sectional macrographs of a zone melted Ti-17 ingot.
67
14
12
10
£ 6
Ti-10-2-3 (Ti-10%V-2%Fe-3%AI) zone melted ingot Sample size : 12.7 mm in diameter and 127 mm in length Analyzed by SEM-EDX, Acceleration Voltage : 20 kV Analyzed Area : 55 nm x 68 nm
40 60 80
distance from the sample edge (mm)
— i — 100 120
Figure 34 Concentration distribution of alloying elements in the longitudinal direction of a zone melted 10-2-3 ingot.
12 Ti-17 (Ti-5%AI-2%Sn-2%Zr-4%Mo-4%Cr) zone melted ingot Sample size : 12.7 mm in diameter and 127 mm in length Analyzed by SEM-EDX, Acceleration Voltage : 20 kV Analyzed Araa : 55 i
samples were separate ^ at this point
20 40 60 80
distance from the sample edge (mm)
100 120 140
Figure 35 Concentration distribution of alloying elements in the longitudinal direction of a zone melted 10-2-3 ingot.
69
8
=° 6
s (0 c 5 E 5 <u cn 4
o 2
Ti-6242 (Ti-6%AI-2%Sn-4%Zr-2%Mo) zone melted ingot Sample size : 12.7 mm in diameter and 127 mm in length Analyzed by SEM-EDX, Acceleration Voltage : 20 kV Analyzed Area : 55 nm x 68 nm
melting start point
melting finish point
- • — M o
- ^ A l
— H — S n
- - Zr(cal)
20 40 60 80
distance from the sample edge (mm)
100 120 140
Figure 36 Concentration distribution of alloying elements in the longitudinal direction of a zone melted 6242 ingot.
14
12
10
= 6
Ti-10-2-3(Ti-10%V-2%Fe-3%AI)zone melted ingot Ingot size : 12.7 mm in diameter and 127 mm in length Analyzed by SEM-EDX, Acceleration Voltage : 20 kV Analyzed Area : 55 nm x 68 nm
- F e
-A l
- V
40 60 80
distance from the sample edge (mm)
100 120
Figure 37 Concentration distribution of alloying elements in the longitudinal direction of a zone melted 10-2-3 ingot (original data).
70
2000
1900
1800
1" 1700
| 1600
*jr 1500
1400
O 1300
1200
1100
1000
D
Remnant of
First f i r s t m e l t ?
Melted B * p
B i i n a
" a a • • a a
E Last i
i L Unmelted
Melted Rod
200 400 600 800 1000
Distance Along Rod (mils)
1200 1400 1600 j
Figure 38 Concentration distribution of oxygen in the longitudinal direction of a zone melted 10-2-3 ingot47.
180
160
E a a c D)
140
120
100
80
First Melted
Remnant of first melt? •4 •
Last B Melted
Unmelted Rod
200 400 600 800 1000
Distance Along Rod (mils)
1200 1400 1600
Figure 39 Concentration distribution of nitrogen in the longitudinal direction of a zone melted 10-2-3 ingot47.
7 1
4800
4700
4600
4500
' 4400
4300
4200
4100
4000
Ti-10-2-3 (Ti-10%V-2%Fe-3%AI) alloy Calculated by "METALS"
-solid phase at 1900K
-liquid phase at 1905K
-Beta-fIeck(>3.-1-%F-e)-
2 3 4
iron concentration (wt.%)
Figure 40 Effect of iron concentration on density of the liquid and solid phase at around melting point (1905 K) in the 10-2-3 alloy.
4800 •
4600 •
„— 4400 • E
•o 4200
Ti-10%V-2%Fe-3%AI alloy Calculated by "METALS"
4000
-2%Fe, solid phase
-3.1%Fe, liquid phase
melting point 1905K (=1632C)
3800 -! : ; i : • !
1200 1400 1600 1800 2000 2200 2400
temperature (K)
Figure 41 Effect of temperature on density of the liquid and solid phase in the 10-2-3 alloy.
72
4800
4700
4600
4500
' 4400
4300
4200
4100
4000
_Ti-17JTi-5%AI-2%Sn-2%Zr-4%Mo-4%Cr) alloy ~Calculate^~r5y',rv1ETACS''
-O-solid phase at 1900K
-0-l iquid phase at 1914K
Beta-fleck _(Cr>5.5wt.%)_
3 4 5
chromium concentration (wt.%)
Figure 42 Effect of chromium concentration on density of the liquid and solid phase at around melting point (1914 K) in the Ti-17 alloy.
4600
4500
4400
E 4300
f, 4200
4100
4000
3900
Ti-17 (Ti-5%AI-2%Sn-2%Zr-4Mo-4%Cr) alloy
-CalculatecTby"META1:S"~
1200
-4%Cr, solid phase
-5.5%Cr, liquid phase
melting point 1914K(=1641C)
1400 1600 1800 2000
temperature (C)
2200 2400
Figure 43 Effect of temperature on density of the liquid and solid phase in the Ti-17 alloy.
73
6. DISCUSSION
6.1 D E T E R M I N A T I O N O F D E N D R I T E A R M S P A C I N G B Y E P M A
The relationship between dendrite arm spacing and solidification conditions in
laboratory melted ingots using an argon arc furnace
In the 10-2-3 ingots melted and cast in the laboratory arc furnace, microstructures
changed by altering the holding time before pouring the molten metal into the crucible.
The holding time of sample 4, which mainly consisted of the elongated prior-beta grains,
was longer than that of samples 1 and 2, which consisted mainly of the equiaxed prior-beta
grains. The longer holding time in sample 4 led to more superheat in the molten metal
and more preheat in the crucible, which decreased the cooling rate during solidification
and may have caused a transition from the equiaxed to the columnar/dendritic
solidification manner. However, the microstructure of sample 6, which was held longer
than sample 4, showed only equiaxed prior-beta grains. More superheat may not have
increased thermal gradient in sample 6 than in sample 4. In contrast, solidification
velocity may have been lowered in sample 4 compared to sample 6, which is considered to
have caused the transition from columnar growth to equiaxed growth of dendrites.
EPMA, conducted in various directions in a section consisting of elongated grains from
sample 4, revealed the periodicity in the distribution of iron concentration with spacings of
40-50 um between peaks. It is possible that these values correspond to either the primary
or the secondary dendrite arm spacing and that peak locations may represent the center of
interdendritic locations at the liquid/solid interface during solidification.
From the temperature history results, the cooling rate at the location where EPMA
was conducted is assumed to be about 20-30 K/s. At this cooling rate, SDAS is estimated
74
to be 10-20 um from Figures 1(b) and 2 and the PDAS is assumed to be 40-50 um in Ti-17.
The periodicity of iron distribution obtained by EPMA is very close to this PDAS.
According to a solidification morphology map by McLean18, SDAS and PDAS are estimated
to be 10-15 um and 40-50 um, respectively, at the same cooling rate in superalloys.
Flemings19 reported that PDAS was 55 um at 10 K/s in Fe-26%Ni alloy. These data
strongly support the estimation of the PDAS at about 50 um in sample 4. The fact that the
spacing was the clearest in the direction perpendicular to that of solidification (horizontal
direction of the ingot) also suggests that the spacing indicates a trace of the PDAS directly.
In contrast, unclear periodicity observed in iron distribution profiles in the directions
inclined to the horizontal line by 30-60 ° may have been caused by fluctuation of iron
concentration affected by SDAS, etc.
Dendrite arm spacing in production ingots
Distribution of chromium concentration in the direction perpendicular to the elongated
direction of beta grains in a Ti-17 production ingot, shown in Figure 25, revealed
consistent periodicity with spacing of 1000-1600 um between peaks. The periodicity in a
production 10-2-3 ingot was about 1000 um, as can be seen in Figure 28. According to
some researchers13'17-49, the former spacing of 1000-1500, um is considered to correspond to
the SDAS. PDAS of 2500-4000 um and SDAS of 1500-2000 um have been demonstrated
under solidification conditions consisting of 5xl02-lxl03 K/m for G and 4xl05 m/sec13-17-49
for R. However, Nastac et al reported less than half of these values for the PDAS and
SDAS in titanium alloy production ingots by calculation: 1000-2000 um for PDAS and 300-
800 um for SDAS14. Considering the direction of the periodicity obtained in concentration
distribution curves, it appears more reasonable to think that the periodicity indicates
75
PDAS directly. However, judging from the values of the periodicity, it is also possible that
the periodicity is SDAS. It is possible to conclude that the spacings, ranging from 1000 to
1500 um, are either the PDAS or SDAS. Peak locations in the chromium/iron
concentration values would occur in the middle of the interdendric spaces, where the last
liquid to solid occurs, even if it was either the PDAS or SDAS.
In a Ti-17 production ingot, the effect of solute chromium atom diffusion in the solid
state was taken into consideration. However, the contribution of chromium diffusion in
the solid state was found to be extremely small; it amounted to an increase in chromium
concentration of only 0.02 wt.%. This shows that the redistribution of solute chromium
atoms by diffusion is limited in the solid state after solidification.
In conclusion, in production ingots, the distribution profiles of iron concentration in 10-
2-3 and the distribution of chromium concentration in Ti-17 showed periodicity, which may
indicate either the primary dendrite arm spacing or the secondary dendrite arm spacing
directly.
76
6.2 S E G R E G A T I O N C O E F F I C I E N T S O F A L L O Y I N G E L E M E N T S I N
C O M M E R C I A L T I T A N I U M A L L O Y S
Segregation coefficients of alloying elements in zone melted commercial
titanium alloys
Figures 34-36 show similar segregation behavior for some beta stabilizing elements
with k<l, such as iron and vanadium in 10-2-3, chromium and zirconium in Ti-17 and
zirconium in 6242. Concentrations of all these elements decreased as melting started and
increased near the finishing point. A large increase in iron concentration in 10-2-3,
chromium concentration in Ti-17 and zirconium concentration in 6242 was found at the
final melt point, which shows that these elements are likely to segregate heavily at the
bottom of titanium alloy ingots. Molybdenum,-a beta stabilizing element with k>l, and
alpha stabilizing elements, such as aluminum, oxygen and nitrogen in Figures 38 and 39,
showed a reverse segregation behavior. Tin is known to have an equal stabilizing effect on
both alpha and beta phase and this may be a reason that distribution coefficients of tin
fluctuate around 1. In our experiments, tin concentration increased at the melting start
point and decreased at the finish point slightly in Ti-17 and 6242 and the segregation
coefficient of tin was calculated as k>l.
Broken lines in Figures 34-36 represent the iron, chromium and zirconium
concentration profiles estimated from the Scheil equation(Eq(3)), in which the start melt
point and final melt point was assumed to be a location with fk=0 and with fa=1.0,
respectively. Compared with the Scheil curves, the actual concentration profiles have a
steeper slope just prior to the final melt point and show a more uniform concentration
during the middle part. This suggests that the solidification conditions, under which the
zone melting experiments were conducted, were close to the equilibrium state.
77
The segregation coefficient, k, of each alloying element for three alloys presented in
Tables 4-7 indicated the following characteristics :
(1) k deviated from k e q for iron and oxygen in 10-2-3, for tin, zirconium and molybdenum
in Ti-17 and tin, zirconium and molybdenum in 6242.
(2) k was almost the same as k e q for aluminum in all the alloys, for vanadium and
nitrogen in 10-2-3 and for chromium in Ti-17.
(3) k showed slightly different values for aluminum, tin, zirconium and molybdenum in
different alloying systems
It is considered that each of the alloying elements, such as iron, oxygen, tin zirconium
or molybdenum, was strongly affected by interaction between itself and elements other
than titanium and itself, which may account for the big difference between k and keq in
these elements. However, it has to be noted that the cases for iron, oxygen, tin and
zirconium are different from that for molybdenum. In the former four elements, k
deviated from keq and from the unity, 1, while in molybdenum, k fluctuated from keq but
approached 1. This indicates that the segregation of iron, oxygen, tin and zirconium in the
commercial alloys is heavier than that predicted from the phase diagram, while that of
molybdenum might be lighter than the prediction. This might be because the interaction
between alloying elements in 10-2-3 affected k of iron to get lower value than keq and those
between alloying elements in Ti-17 and those in 6242 caused k of molybdenum to get
closer to 1. With its k close to 1, molybdenum is considered as one of the most idealistic
beta-stabilizing elements which promote lighter segregation during solidification.
A change in alloying system led to a small difference in k for aluminum, tin, zirconium
and molybdenum. The difference might have been caused by a change in the strength of
interaction between itself and other alloying element(s) depending on the difference in
78
combination of alloying elements. This suggests that the segregation behavior of an
alloying element can be altered by changing the combination of other alloying elements. It
may be possible that the k of iron, which was much lower in 10-2-3 than the equilibrium
distribution coefficient, k e q, can have values closer to k e q or even 1 by selecting other
alloying elements. From this point of view, it is important to clarify k for each alloying
element, which is likely to segregate heavily. It is necessary to conduct the same
experiments on other titanium alloys with a zone melting furnace.
Estimation of fraction solidified at the initiation of beta-flecks
The fraction solidified at the initiation of beta-flecks in 10-2-3 and Ti-17 production
ingots was estimated using the distribution coefficients obtained from zone-melting
experiments. In the estimation, iron concentrations of the matrix and that of beta-flecks
in 10-2-3 were assumed to be 2.0 and 3.1 wt.%, respectively, while chromium
concentrations in Ti-17 were 4.0 wt.% in the matrix and 5.5 wt.% in beta-flecks. It was
assumed that solidification proceeded according to the Scheil equation, presented as
(Eq.3), in 10-2-3 and Ti-17 production ingots.
Using k=0.38 for iron in 10-2-3 and k=0.74 for chromium in Ti-17 as the distribution
coefficient, the fraction solidified at the initiation of beta-flecks was estimated as fs=0.896
in 10-2-3 and fs=0.908 in Ti-17. These values are close to the range 0.80-90 reported by
Auburtin13) for f s . However, these are more accurate since they were obtained from
calculation by using experimental distribution coefficients. From these results, it is
estimated that beta-flecks initiated when almost 90% of molten metal had solidified at the
interface between liquid and solid both in 10-2-3 and in Ti-17. At this moment, the
downward flow of molten metal must have commenced to drive and finally lead to form
79
beta-flecks.
Estimation of distribution coefficients and fraction solidified at the initiation of beta-
flecks with "pseudo-binary phase approach"
"Pseudo-binary phase approach" has been used in calculating degree of solutal
undercooling at dendrite tips as an extension of the Kurtz, Giovanola and Trivedi model
(KGT model) to multi-component alloys59'60. In calculating the degree of undercooling in
multi-component system, effective binary interface liquid concentrations (c), slope of the
liquids (m) and distribution coefficients (k) are expressed as follows.
c = S C L / (Eq.9)
m = Zmi»CL,i* (Eq.10)
k = £ (mi»CL,i*»ki/(m»c)) (Eq.ll)
where CL,I* is a chemical composition of alloying element i, mi is a slope of the liquidus line
of alloying element i in binary phase diagram and ki is a distribution coefficient of alloying
element i.
Chemical compositions of beta-flecks in 10-2-3 and Ti-17 reported by Auburtin et al1 3,
which were used for estimating distribution coefficients by pseudo-binary phase approach,
are as follows (in wt.%) :
Ti-17 : Al 4.8 (bulk 5.0), Cr 5.5 (bulk 4.0), Mo 3.5 (bulk 4.0), Zr 2.5 (bulk 2.0),
Sn 2.0 (bulk 2.0)
10-2-3 : Al 2.25 (bulk 3.05), Fe 3.10 (bulk 2.03), V 11.0 (bulk 10.0)
In estimating distribution coefficients by pseudo-binary phase approach, only alloying
elements with k<l, which segregate normally in used titanium alloys, were taken into
consideration. It was because the calculated distribution coefficients were not reasonable
80
when alloying elements with k>l, which tend to segregate reversely, were included in the
calculation. In this way, experimentally obtained distribution coefficients of chromium
and zirconium were taken into consideration in Ti-17, while those of iron and vanadium
were considered in 10-2-3. Parameters and values used for the estimation are listed in
Tables 8 and 9.
Table 8 Parameters and values used for pseudo-binary phase approach for Ti-17
Alloying Cbeta Co ki mi Element wt.% wt.% K/wt.%
Cr 5.5 4.0 0.74 -7.95K/wt% Zr 2.5 2.0 0.77 -2.5K/wt%
Cbeta = 8.0 Wt.%, C = 6.0 W t . %
Table 9 Parameters and values used for pseudo-binary phase approach for
10-2-3
Alloying Cbeta Co ki mi Element W t . % wt.% K/wt.%
V 11.0 10.0 0.95 -2.0K/wt% Fe 3.1 2.03 0.38 -15.6K/wt%
Cbeta = 14.1 wt.%, C = 12.03 wt.%
From (Eq.ll), 0.744 and 0.562 were obtained for k in Ti-17and 10-2-3, respectively.
Using these distribution coefficients, fraction solidified at the initiation of beta-flecks can
be calculated from the following equation, which is based on Scheil equation.
Cbeta = k.C.(l-f s)^ (Eq.12)
As a result of the calculation, 0.898 and 0.811 could be obtained for fraction solidified
at the initiation of beta-flecks in Ti-17 and 10-2-3, respectively. The fraction solidified
estimated in Ti-17, is almost the same as that estimated from the experimental
distribution coefficient. This is considered to be due to a similarity of distribution
coefficients in both cases. The fraction solidified estimated in 10-2-3, is smaller than 0.89,
81
which was obtained from the calculation using the experimental distribution coefficient of
iron, 0.38. However, there is no significant difference between the two values and this
result obtaining using the binary and pseudo-binary phase approaches are similar. In
both cases, fs in the range of 0.8 to 0.9 are needed in the Scheil equation to calculate
components consistent with beta-fleck formation.
6.3 FORMATION MECHANISM OF BETA-FLECKS
Possibility of downward flow of liquid metal during solidification
By calculating the Rayleigh number, presented in (Eq.8), the possibility of downward
flow, which may lead to the formation of beta-flecks, can be estimated. In this section, the
Rayleigh number was calculated and the validity of density-driven flow model is discussed.
RaT/s = g»dp/dz/(r)«DT/h4) (Eq.8)
where g is gravitational acceleration (= 9.81 m/s2), DT is thermal diffusivity (m2/s), r\ is i
dynamic viscousity of liquid titanium (kg/m/s), h is characteristic linear dimension (m) and
dp/dz is density gradient (kg/m).
For a Ti-17 production ingot, DT and r\ are estimated to be 9X10"6 m2/s and 0.004
kg/m/s, respectively13. Here, the density gradient, dp/dz, can be rewritten as
(dp/dT)»(dT/dz). It is estimated that dp/dT equals 0.656 kg/m3/K, which was obtained from
the gradient of the temperature-density line of liquid phase containing 5.5 wt.% chromium
in Figure 38. The temperature gradient, dT/dz, is assumed to be 103 K/m from the general
information on the similar size ingot68. Values used for the characteristic linear dimension
must be considered carefully: in this case, PDAS, Xi, was used. The Rayleigh number,
RaT/s, for PDAS varying from 0 to 0.0020 m (2000 um), are shown as a solid line in Figure
44. As can be seen from the line, RaT/s rapidly increases as A,i increases. Here, two
82
possibilities must be considered for the calculation of RaT/s: one is a case where the
periodicity obtained from the distribution of chromium concentration indicates the P D A S
and the other where the periodicity indicates the SDAS. In the latter, the P D A S is
assumed to be three times of the periodicity, according to some literatures13-18, and 3186
and 4779 um are assumed to be P D A S in this case. Closed square marks represent RaT/s
for P D A S of 3186 and 4779 um, indicating RaT/s equal to 18.15 (3186 um) and 91.87 (4779
um). These values are much greater than 1, which is the critical value for the onset of
unstable flow according to the Rayleigh criterion. In contrast, if the periodicity is assumed
to indicate P D A S directly, RaT/s are calculated to be 0.22 (1062 um) and 1.13 (1593 um),
which are presented as open circle marks. These values are more reasonable in
magnitude, which would appear to indicate that, from the standpoint of use of the RaT/s
criteria, the compositional periodicity is more consistent with a PDAS.
Calculated results on RaT/s in a 10-2-3 production ingot are shown in Figure 45. In the
calculation, the same numbers were used for DT, r| and dT/dz as were used for Ti-17, while
0.647 kg/m3/K was used as dp/dT, which was calculated from the gradient of the liquid
phase line containing 3.1 wt.% iron in Figure 39. The open circle marks in the figure were
calculated under the assumption that the periodicity indicates PDAS. This assumption
lead to Rayleigh numbers of 0.22 (1062 um) and 0.31 (1151 um). Both of these numbers
are smaller than 1, which suggests that the downward flow is unlikely to occur. In fact,
the formation of beta-flecks was not observed in these areas in the as-received sample, as
can be considered from the iron concentrations indicated in Figure 29. However, the
formation of beta-flecks was reported in different locations in the same ingot27. RaT / s
increases rapidly in the range of ̂ ,=0.001-00018 m and it might be possble that A. exceeded
0.0015 m at different locations depending on a difference in solidification conditions
83
locally. Therefore, solidification conditions, under which Ti-17 and 10-2-3 production
ingots were manufactured, might have existed in the critical condition to form beta-flecks.
In conclusion, it is possible to consider that downward density-driven flow occurs in
large production Ti-17 and 10-2-3 ingots, which causes channels and finally leads to the
formation of beta-flecks, according to the calculation results on the Rayleigh number. In
this case, periodicity identified in the concentration distribution curves in these ingots
would need to be the PDAS.
Problems in the proposed formation mechanism of beta-flecks
The Rayleigh number calculation revealed that density-driven downward flow of liquid
metal possibly may cause channeling and finally form beta-flecks, since the PDAS is more
than 0.0015m (1500 um) both in 10-2-3 and in Ti-17. However, there are some questions,
which make the proposed mechanism still controversial. In this section, problems in the
proposed formation mechanism of beta-flecks are mentioned.
The following four questions are still questionable in dealing with the proposed model.
Two of them are related to the model itself and the other two deals with the accuracy of
calculation.
(1) Is it still possible to commence the liquid flow driven due to a density difference in such
small volume fraction(10-20%) of liquid?
(2) Is it unnecessary to consider the effect of inclination?
(3) Does the periodicity of concentration distribution curves really indicate PDAS?
(4) Are physical parameters used for calculating the Rayleigh number accurate?
84
In both 10-2-3 and Ti-17, beta-flecks initiate at temperatures corresponding to fs=0.8-
0.9, which means only 10-20% volume fraction of liquid exists when beta-flecks begin to
form. Under this situation, the distribution of the remaining liquid is quite questionable:
if it is too narrow, the liquid layer might not be thick enough to cause density-driven flow,
and if it is too wide, channeling in the direction perpendicular to the solidification
direction appears difficult to occur. The most critical problem in considering the
mechanism is the shape of the remaining liquid layer. The model might be modified to
give full interpretation on this problem.
In considering a model which gives good interpretation to beta-fleck formation, the V-
shape of beta-flecks should not be ignored. The V-shape trace of beta-flecks shows that
beta-flecks form along the bottom of the liquid pool during melting. In this case, the effect
of the gravity by inclination might be necessary to be considered. It is assumed that
inclination makes density-driven flow easier to occur, as reported in superalloys29'30.
The evaluation of periodicity of concentration profiles obtained from EPMA may also be
a problem. If the periodicity obtained in production ingots is assumed to be the PDAS, the
calculated Rayleigh numbers are reasonable to validate the proposed mechanism.
Periodicity obtained from EPMA in this study, 1000-1500 urn, was close to the value
reported for the PDAS by Nastac et al 1 4 but also close to the SDAS reported by some
authors13'17'49. From the calculated results of RaT/s, it is more probable to think that the
periodicity indicates the PDAS but it is still possible to consider that the periodicity is the
SDAS. It is necessary to confirm the reproductivity of periodicity data to clarify that the
periodicity indicates either the PDAS or SDAS.
Finally, it is possible that physical parameters used in the calculation of RaT/s, such as
thermal diffusivity, dynamic viscosity and density gradient, are not accurate. There might
85
not be a large difference between the calculated values and the real values in the former
two parameters. However, the density gradient may deviate from the actual value since it
was calculated from the data obtained from a calculation software "METALS", which
calculates densities based on a simple summation of the effects of each alloying element.
The validity of these parameters should be taken into consideration in calculating the
Rayleigh number in the next step.
86
0.0005 0.001 0.0045 ' 0.005
H 1 1 1 1—
0.0015 0.002 0.0025 0.003 0.0035 0.004
primary dendrite arm spacing (PDAS or X,: m)
Figure 44 Effect of primary dendrite arm spacing on the Rayleigh number a Ti-17 production ingot.
4.5
3.5
2.5
1.5
0.5
10-2-3 (Ti-10%V-2%Fe-3%AI) production ingot Ra T , s=18.15
The Rayleigh number (PDAS=0.0032m) — rn i=^grdp7dT)(dT/dz)»^ iTD= 1
Ra T r a =25.04
(PDAS=0.0035m)
Ra T / s >1
"RaiS^T
Ra T ) s =0.22
(PDAS=0.0011m)
— calculated curve
O periodicity=PDAS
• periodicity=SDAS
:a^i=Q:31
(PDAS=0.0012m)
0.0005 0.001 0.0015 0.002 0.0025 0.003
primary dendrite arm spacing (PDAS or X, : m) 0.0035 0.004
Figure 45 Effect of primary dendrite arm spacing on the Rayleigh number a 10-2-3 production ingot.
87
7. CONCLUSIONS AND FUTURE WORKS
7.1 C O N C L U S I O N S
A fundamental study was conducted on the solidification behavior of alloying elements
in titanium alloys. In particular, critical parameters, such as dendrite arm spacing,
distribution coefficients and densities of solid/liquid during solidification, were obtained in
segregation sensitive titanium alloys. Finally, the formation mechanism of beta-fleck was
discussed on the basis of the obtained parameters. Results obtained in this research study
are summarized as the following.
1. A 10-2-3 (Ti-10%V-2%Fe-3°/oAl) ingot containing the elongated beta grains in the
solidification direction was obtained by argon arc melting.
Periodicity of the iron concentration was identified in the horizontal direction of the
ingot. Spacing between peak concentration of iron was close to that of the primary
dendrite arm spacing(PDAS) estimated from the cooling rate measured in an ingot
during solidification. The spacing determined in this work demonstrates that titanium
alloys follow the same general relationships between spacing and cooling rate as would
be found in other high temperature systems.
2. Chromium concentration in a production Ti-17(Ti-5%Al-2%Sn-2%Zr-4%Mo-4%Cr) ingot
and iron concentration in a production 10-2-3(Ti-10%V-2%Fe-3%Al) ingot was found to
distribute periodically. Spacing between peaks with 1000-1500 um was obtained in both
alloys.
88
3. Zone melted Ti-17, 10-2-3 and 6242 (Ti-6%Al-2%Sn-4%Zr-2%Mo) ingots appeared to be
single crystal. A large increase in the concentration of chromium in Ti-17 and that of
iron in 10-2-3 was found close to the final melt point, as anticipated from the Scheil
analysis of the planar front solidification mode.
4. Distribution coefficients of alloying elements in commercial titanium alloys were
obtained from the zone melted ingots. Aluminum, iron, nitrogen and oxygen in 10-2-3,
zirconium, tin and molybdenum in 6242 showed distribution coefficients that deviated
from the equilibrium distribution coefficients, while all the other alloying elements in
10-2-3, Ti-17 and 6242 indicated similar values.
Aluminum, tin, zirconium and molybdenum had different distribution coefficients,
depending on alloying systems.
5. Using the assumption that the solidification proceeds under Scheil condition, the
fraction solidified (fs) at the initiation of beta-fleck was estimated as fs=0.90 for both
10-2-3 and Ti-17 by the binary phase approach, while £=0.90 and 0.81 were obtained for
10-2-3 and Ti-17, respectively, by the "pseudo binary phase approach". In both cases,
experimentally obtained distribution coefficients were used with compositions for beta-
fleck formation of 3.1 wt.% iron in 10-2-3 and 5.5 wt.% chromium in Ti-17.
6. Densities of solid and liquid metal during solidification were estimated by calculation
software "METALS". It was clarified that the solid metal was heavier than the liquid
enriched in iron in 10-2-3 and that enriched in chromium in Ti-17 at the melting point.
Thermal density gradient (dp/dT) of the liquid metal containing the composition
corresponding to that of beta-flecks was estimated as 0.656 kg/m3/K for Ti-17 and as
0.647 kg/m3/K for 10-2-3.
7. The Rayleigh numbers exceeded 1, if 1593 um, a peak spacing obtained in chromium
89
concentration distribution curve, was used as the PDAS in Ti-17. In this case, density-
driven downward flow of liquid metal can occur.
7.2 R E C O M M E N D A T I O N S F O R F U T U R E W O R K S
1. One data point could be obtained for the relationship between cooling rate and dendrite
arm spacing in this study. More temperature monitoring experiments with an argon arc
furnace should be conducted to clarify the relationship in a formula.
In particular, in the next experiment, higher heat input during solidification with
higher power input should be introduced in an induction coil to get a lower cooling rate.
2. The solidification direction was not clear in the samples cut from production ingots,
in which the periodicity of distribution profile was either the PDAS or SDAS. In
future, EPMA should be carried out for other samples cut from production ingots, in
which solidification direction is known.
3. Through a literature review, it was clarified that a detailed microstructural study on
beta-flecks has not been conducted. Microstructural features of beta-flecks should be
made clearer by more detailed microstructural observations.
4. Zone melting experiments should be conducted on different commercial alloys to clarify
the actual distribution coefficients of alloying elements: in particular, on LCB (Ti-
1.5%Al-6.8%Mo-4.5%Fe), SP-700 (Ti-4.5%Al-3%V-2%Fe-2%Mo) and Super-TIX (Ti-
1.5%Fe-0.5%O-0.05%N), all of which contain iron that is likely to segregate heavily.
LCB is a beta alloy developed by TIMET Corporation, featuring application of ferro-
molybdenum, which is generally used for steel making and is cheap, as a master
alloy50'51. LCB is promising as a material for suspension springs in automobiles50.
90
SP-700 is a near-beta alloy developed by Nihon Kokan Corporation, featured with lower
Superplastic Forming (SPF) temperature than the 6-4 alloy, which is conventionally
used for component material in airplanes52-53. Super-TIX (Ti-1.5%Fe-0.5%O-0.05%N) is
a near-alpha alloy developed by Nippon Steel Corporation54-55. This alloy contains a
combination of iron, oxygen and nitrogen, all of which are cheap alloying elements, but
has the same level of mechanical properties as 6-4 at around room temperature. It
may be interesting to compare the k value of each alloying element, including iron, in all
these three alloys with those obtained in this study.
5. Applicability of calculated phase diagrams using "Thermo-Calc"56 should be examined in
estimating segregation coefficients of alloying elements in commercial titanium alloys.
If the calculated phase diagrams are proved to be applicable, there is no need for
obtaining segregation coefficients experimentally. Otherwise, experimental k values
should be added to a data base of "Thermo-Calc".
91
R E F E R E N C E S
1) I.J.Polmear ; "Light Alloys", 2 n d edition, pp.211, Pergamon Press, London, (1986).
2) H.Kusamichi, Y.Murakami, K.Kimura and O.Izumi; "Titanium and Its Application", (in Japanese), Nikkan-kogyo-simbunsha, Tokyo, pp.3(1992).
3) A.Mitchell; "Melting, Casting and Forging Problems in Titanium Alloys", Materials Science and Engineering, A243, pp.257(1998).
4) C.C.Chen and R.R.Boyer ; "Practical Considerations for Manufacturing High-
Strength Ti-10V-2Fe-3Al Alloy Forgings", Journal of Metals, pp.33(1979).
5) Y.G.Zhou, J.L.Tang, H.Q.Yu and W.D.Zeng ; "On Effects of Beta Flecks on the
Properties of Ti-10V-2Fe-3Al Alloy", "Titanium'92" Science and Technology, Edited
by F.H.Froes and I.Caplan, The Minerals, Metals & Materials Society, pp.513(1992).
6) A.F.Funkenbusch and L.F.Coffin ; "Low-Cycle Crack Nucleation and Growth in Ti-17", Metallurgical Transactions Vol.9A, pp. 1159(1978).
7) V.V.Tetyukin, V.N.Kurapov and Yu.P.Denisov ; "Segregation and Phase Heterogeneity in Titanium Ingots and Semifinished Products", "Titanium'80", edited by H.Kimura and O.Izumi, Met. Soc. AIME, New York, pp.2117(1980).
8) C.E.Shamblen and G.B.Hunter ; "Titanium Base Alloys Clean Melt Process
Development", Proceedings of the 1989 Vacuum Metallurgy Conference on the
Melting and Processing of Specialty Materials, Edited by L.W.Lherbier and
J.T.Corby, Pittsuburgh, PA, American Vacuum Society, pp.3(1989).
92
9) A.Mitchell and D.W.Tripp ; "HID and HDI Dissolution during Titanium Melting
Process", "Titanium'92" Science and Technology, Edited by F.H.Froes and I.Caplan,
The Minerals, Metals & Materials Society, pp.2257(1992).
10) C.E.Shamblen ; "Minimizing Beta Flecks in the Ti-17 Alloy", Metallurgical and Materials Transactions, Vol.28B, pp.899(1997).
1 l)A.Mitchell; "The Influence of Titanium Alloy Composition and Application on Melting and Casting Practices", Metallurgy and Technology of Practical Titanium Alloys, Edited by S.Fujishiro, D.Eylon and T.Kishi, The Minerals, Metals and Materials Society, pp.201(1994).
12) H.Hayakawa, N.Fukada, T.Udagawa, M.Koizumi, H.G.Suzuki and T.Fukuyama ;
"Solidification Structure and Segregation in Cast Ingots of Titanium Alloy Produced
by Vacuum Arc Consumable Electrode Method", Iron and Steel Institute Japan
International, Vol.31, pp.775(1991).
13) P.Auburtin, C.Edie, B.Foster, I.Mackenzie, A.Mitchell and A.Schmalz ;
"Solidification and Segregation Properties of Some Titanium Alloys and their
Relation to the "Beta-Fleck" Defect", Proceedings of the 1997 International
Symposium on Liquid Metal Processing and Casting, Edited by A.Mitchell and
P.Auburtin, American Vacuum Society, Santa Fe N M , pp.60(1997).
14) L.Nastac, C.Wang, H.Dong and Y.Pang ; "Solidification Structure in Ti-5Al-2Sn-2Zr-4Mo-4Cr Ingots Processed through Plasma Arc Cold Hearth Melting", Proceedings of the 2001 International Symposium on Liquid Metal Processing and Casting, Edited by A.Mitchell and J.V.D.Avyle, American Vacuum Society, Santa Fe N M , pp.288(2001).
15) W.Kurtz ; "Solidification Microstructure-Processing Maps: Theory and Application",
Advanced Engineering Materials 2001, Vol.3, No.7, pp.443(2001).
93
16) J.I.Nurimen ; "Solidification Structure and Segregation in Binary Titanium Base
Alloys", U.M.I. Dissertation Information Services, Ph.D Thesis (1972).
17) V.K.Aleksandrov, N.F.Anoshkin, A.F.Bepov, S.G.Glasinov, V.N.Dobatkin,
B.A.Kopayev, V.A.Livanov, G.G.Maslov and R.E.Shchalin ; "Melting and Casting of
Titanium and its Alloys", Moscow, pp.81(-1994).
18) M.McLean ; "Directionally Solidified Materials for High Temperature Service", The Metals Society, London, pp.26(1982).
19) M.C.Flemings, D.R.Poirier, R.V.Barone and H.D.Brody ; "Microsegregation in Iron-
base Alloys", Journal of the Iron and Steel Institute, Vol.208, pp.371(1970).
20) T.B.Massalski, J.L.Murray, L.H.Bennett, H.Baker and L.Kacprzak ; "Binary Alloy
Phase Diagram", 2nd Edition, ASM, Ohio (1990).
21) H.W.Rosenberg and KS.Snow ; "Microsegregation in Titanium Alloys", TMS Paper
Selection, Paper No.A73-31, AIME, pp.439(1973).
22) H.Inoue and T.Ogawa ; "Weld Cracking and Solidification Behavior of Titanium
Alloys", Welding Journal, 74-1, pp.21(1995).
23) L.Nastac, J.S.Chen and Y.Pang ; "Assessment of Solidification-kinetics Parameters
for Titanium-base Alloys", Proceedings of the 1999 International Symposium on
Liquid Metal Processing and Casting, Edited by A.Mitchell, L.Ridgeway and
M.Baldwin, American Vacuum Society, Santa Fe NM, pp.207(1999).
24) Metals Handbook, 9th Edition, 3, pp.372(1980).
25) T.F.Bower, H.D.Brody and M.C.Flemings ; "Solute Distribution in Dendritic
Solidification", Transactions of the Metallurgical Society of AIME, Vol.236,
pp.624(1966).
94
26) D.J.Allen and J.D.Hunt; "Melting during Solidification", Metallurgical Transations Vol.7A, pp.767(1976).
27) J.A.Brooks, J.S.Krafcik, J.A.Schneider and J.A.VanDenAvyle ; "Fe Segregation in
Ti-10V-2Fe-3Al 30 Inch VAR Ingot, Beta-Fleck Formation", Proceedings of the 1999
International Symposium on Liquid Metal Processing and Casting, Edited by
A.Mitchell, L.Ridgeway and M.Baldwin, American Vacuum Society, Santa Fe NM,
pp. 130(1999).
28) K.Rudinger and D.Fischer ; "Effect of Beta-Flecks on the Fatigue Behavior of Ti-6Al-6V-2Sn", "Titanium'80", edited by H.Kimura and O.Izumi, Met. Soc. AIME, New York, pp. 1907(1980).
29) P.Auburtin, T.Wang, S.L.Cockroft and A.Mitchell; "Freckle Formation and Freckle
Criterion in Superalloy Castings", Metallurgical and Materials Transactions,
Vol.31B, pp.801(2000).
30) T.Wang ; "The Freckling Mechanism of Superalloys", M.A.Sc. Thesis, The University of British Columbia (1999).
31) K.O.Yu, J.A.Domingue, G.E.Maurer and H.D.Flanders ; "Microsegregation in ESR
and VAR Processes", Journal of Metals, pp.46(1986).
32) A.F.Giamei and B.H.Kear ; "On the Nature of Freckles in Nickel Base Superalloys",
Metallurgical Transactions, Vol.1 pp.2185(1970).
33) K.Suzuki and T.Miyamoto ; "Study on the Formation of A Segregation in Steel
Ingots", Transactions of ISIJ, Vol.l8(2), pp.80(1978).
34) S.M.Copley, A.F.Giamei, S.M.Johnson and M.F.Hornbecker ; "The Origin of Freckles
in Unidirectionally Solidified Castings", Metallurgical Transactions, Vol.1,
pp.2193(1970).
95
35) P.Auburtin ; "Determination of the Influence of Interdendritic Segregation during the Solidification of Freckle-Prone Alloys", M.A.Sc. Thesis, The University of British Columbia (1995).
36) A.James, J.A.VanDenAvyle, J.A.Brooks and A.C.Powell; "Reducing Defects in
Remelting Process for High-Performance Alloys", Journal of Metals, Vol.50, No.3,
pp.22(1998).
37) J.R.Sarrazin and A.Hellawell; "Channel Flow in Partly Solidified Alloy Systems", Advances in Phase Transition, pp. 101(1987).
38) W.Kurz and D.J.Fisher ; "Fundamentals of Solidification", TransTech Publications,
Aedermannsdorf, Switzerland, pp.86(1992).
39) D.R. Poirier ; "Permeability for Flow of Interdendritic Liquid in Columnar-Dendritic
Alloys", Metallurgical Transactions, V0I.I8B, pp.245(1987).
40) M.S.Bhat, D.R.Poirier and J.D.Heinrich ; "Permeability for Cross Flow through
Columnar-Dendritic Alloys", Metallurgical and Materials Transactions, Vol.26B,
pp. 1049(1995).
41) A.E.Scheidegger ; "The Physics of Flow through Porous Media", 3rd edition,
University of Tronto Press, Toronto, ON, Canada, pp.78(1974).
42) C.Beckermann, J.P.Gu and W.J.Boettinger ; "Development of a Freckle Predictor via
Rayleigh-Number Method for Single-Crystal Nickel-Based Superalloy Castings",
Metallurgical and Materials Transactions A, Vol.31A, pp.1(2000).
43) T.M.Pollock and W.H.Murphy ; "The Breakdown of Single-Crystal Solidification in
High Refractory Nickel-Base Alloys", Metallurgical and Materials Transactions A,
Vol.27A, pp. 1081(1996).
96
44) R.R.Boyer ; "An Overview on The Use of Titanium in The Aerospace Industry",
Materials Science and Engineering, A213, pp.103(1996).
45) D.W.Tripp ; "Raw Material Chemical Analysis Report", issued by TIMET company, pp.1 (2001).
46) D.W.Tripp ; private notes
47) "Maximum Concentration of Oxygen During Solidification of Titanium Alloys", pp.1, (2000).
48) M.C.Flemings ; "Solidification Processing", McGraw Hill Series in Material Science and
Engineering, McGraw Hill Book Company, New York, US, pp.46(1974).
49) H.Ichihashi and A.Yamanaka ; "Segregation in Titanium Alloy VAR Ingots", (in
Japanese), Kinzoku, Vol.65, No.4, pp.339(1995).
50) Y.Kosaka and S.P.Fox ; "Recent Developments in the Manufacturing of Low Cost
Titanium Alloys", High Performance Metallic Materials for Cost Sensitive
Applications, Edited by F.H.Froes, E.Chen, R.R.Boyer, E.M.Taleff, L.Lu, D.L.Zhang,
C.M.Ward-Close and D.Elizer, The Minerals, Metals & Materials Society, pp.35(2002).
51) P.J.Bania, A.J.Hutt, R.EAdams and W.M.Paris ; "A New Low Cost Titanium Alloy",
Titanium'92 Science and Technology, Edited by F.H.Froes and I.J.Caplan, The
Minerals, Metals & Materials Society, pp.2787(1993).
52) M.Ishikawa, O.Kuboyama, M.Niikura and C.Ouchi ; "Microstructure and Mechanical
Properties Relationship of Beta-rich Alpha-Beta Titanium Alloy; SP-700",
"Titanium'92" Science and Technology, Edited by F.H.Froes and I.Caplan,
The Minerals, Metals & Materials Society, pp. 141(1993).
97
53) C.Ouchi ; "Development and Application of New Titanium Alloy SP-700", Metallurgy
and Technology of Practical Titanium Alloys, Edited by S.Fujishiro, D.Eylon and
T.Kishi, The Minerals, Metals and Materials Society, pp.37(1994).
54) H.Fujii, S.Soeda, M.Hanaki and H.Okano ; "Development of High Performance, Low Alloy Ti-Fe-O-N Series", Proceedings on the 8th World Conference on Titanium, Birmingham, UK, pp.2309(1995).
55) H.Fujii, KTakahashi, S.Soeda and M.Hanaki; "Development of High Strength Ti-Fe-
O-N Alloy Series"(in Japanese), CAMP-ISIJ, Vol.8, pp.642(1995).
56) N.Saunders and A.P.Miodownik ; "CALPHAD (calculation of phase diagrams) : a
comprehensive guide", pp.1, Pergamon materials series vol.1, Oxford, UK (1998).
57) R.W.Herzberg ; "Deformation and Fracture Mechanics of Engineering Materials" 4th
Edition, pp.1, John Wiley & Sons, Inc. (1996).
58) "Numerical Analysis Results on Temperature Distribution in Vacuum Arc Remelted Ingot", pp.1, (1987).'
59) M.Rappaz, S.A.David, J.M.Vitek and L.A.Boatner ; "Analysis of Solidification
Microstructures in Fe-Ni-Cr Single-Crystal Welds", Metallurgical Transactions A,
Vol.21A, pp. 1767(1990).
60) M.Bobadilla, J.Lacaze and G .Lesoult; "Influence des Conditions de Solidification sur
Le Deroulement de La Solidification des Aciers Inoxydables Austenitiques", Journal of
Crystal Growth, 89, pp.531(1988).
98
APPENDIX A
MATHEMATICAL MODEL "METALS"
Densities of liquid metal and solid at the solid/liquid interface at the initiation of beta
flecks are calculated using a mathematical model "METALS" to examine a proposed model
of beta fleck formation. 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, viscousities, thermal conductivities and diffusivities). This
approximation is now a widely accepted approach). The basic equations in these models
are presented below.
The molar volume in solid phase MVL
S of each pure element i is given by:
MV's (T) = MV*S (25°C)»(l+ai
s»(T-25)) (Eq.Al)
for temperatures (T) below the liquidus temperature Tuq. At the temperature T (in°C), the
molar volume in the liquid phase MVl
8 of each pure element i (of melting point T^mp) is
given by a similar equation:
MV'L (T) = MV>L (TuqWl+aiL'iT-Tiig)) (Eq.A2)
with
MV'L (TlJg) = MVL {Tmp)»(l+rfL*(T-'Pmp)) (Eq.A3)
for a given total weight W of an alloy of known composition, the number of mole * 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 the following:
ps(T) = W/[Y.(ai*MV>8 (7))]™.:.... (Eq.A4)
and ps(T) = W/[Z(ai*MV>L (T))] (Eq.A5)
99
This model is accurate to about 5% according NPL. It was tested in ref(35) 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 interdendeitic liquid is at the local liquidus temperature.
As indicated in ref(35), this model is not a good approximation in the case of interstitial
elements, such as carbon in nickel base superalloys. For instance, addition of carbon may
increase the total weight of a superalloy 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, "METALS" calculations involving elements such as
carbon should probably be regarded as qualitative approximations.
100