.
33
THE USE OF COMPUTERIZED THERMODYNAMIC
DATABASES
FOR SOLIDIFICATION
MODELING OF FUSION WELDS
IN MULTI-COMPONENT
ALLOYS
(2
#~~
=m
‘=0
d<
J.N. DuPont 1, B.D. Newbury 1, C.V. Robino 2, and G.A. Knorovsky
2
-!ifi
ABSTRACT
Most engineering alloys contain numerous alloying elements and their solidification behavior
can not typically be modeled with existing binary and ternary phase diagrams. There has recently
been considerable progress in the development of thermodynamic
software programs for
calculating solidification parameters and phase diagrams of multi-component
systems. These
routines can potentially provide usefid input data that are needed in multi-component
solidification models. However, these thermodynamic routines require validation before they can
be confidently applied to simulations of alloys over a wide range of composition. In this article, a
preliminary assessment of the accuracy of the Thermo-Calc NiFe Superalloy database is
presented. The database validation is conducted by comparing calculated phase diagram
quantities to experimental measurements available in the literature. Comparisons are provided in
terms of calculated and measured liquidus and solidus temperatures and slopes, equilibrium
distribution coefficients, and multi-component
phase diagrams. Reasonable
agreement is
observed among the comparisons made to date. Examples are provided which illustrate how the
database can be used to approximate the solidification sequence and final segregation patterns in
multi-component alloys. An additional example of the coupling of calculated phase diagrams to
solute redistribution computations in a commercial eight component Ni base superalloy is also
presented.
1.
Lehigh University,
2.
Sandia National Laboratories,
Bethlehem,
PA
Albuquerque,
NM
m
0
DISCLAIMER
This report was prepared as an account of work sponsored
by an agency of the United States Government. Neither the
United States Government nor any agency thereof, nor any
of their employees, make any warranty, express or implied,
or assumes any legal liability or responsibility for the
accuracy, completeness, or usefulness of any information,
apparatus, product, or process disclosed, or represents that
its use would not infringe privately owned rights. Reference
herein to any specific commercial product, process, or
manufacturer,
or
service by trade name, trademark,
otherwise does not necessarily constitute or imply its
endorsement, recommendation, or favoring by the United
States Government or any agency thereof. The views and
opinions of authors expressed herein do not necessarily
state or reflect those of the United States Government or
any agency thereof.
~
DISCLAIMER
Portions of this document may be illegible
in electronic image products.
Images are
produced from the best available original
document.
INTRODUCTION
The microstructure of fision welds in engineering alloys is dependent on the redistribution of
solute (microsegregation)
during solidification as well as the form of the phase diagram.
Previous studies conducted to fimdamentally quanti~ the relation between alloy composition,
microsegregation, and weld microstructure often utilized binary alloy systems (Refs. 1,2). This
approach is convenient because the alloy parameters required for microsegregation ,c.alculations
(e.g., liquidus temperature, distribution coefficient, eutectic temperature and composltlon) can be
determined directly from the binary phase diagram. However, many alloys of engineering
significance contain numerous solute additions, and can undergo one or more eutectic-type
reactions over a broad” temperature and composition range, In this case, microsegregation
calculations require the knowledge of multi-component phase diagmms and the distribution
coefficients for all solutes which significantly affect development of the final microstructure. In
addition, when a eutectic-type reaction occurs over an appreciable temperature and composition
range, it then becomes necessary to know two distribution coefficients for each important solute;
one which describes solute partitioning between the liquid and primary solid phase, and a second
which describes partitioning between the liquid and secondary solid phase within the eutectic
constituent. The lack of such information restricts solute redistribution modeling of multicomponent alloys.
In recent years there has been considerable progress in the development of thermodynamic
software programs for calculating solidification parameters and phase diagrams of multicomponent systems (Ref. 3). This progress is likely to lead to more frequent use of solute
redistribution models and their application to alloy systems containing many elements. In view
of this fact, it is useful to consider how such thermodynamic databases can be integrated into
modeling efforts directed at understanding weldability phenomenon. In this article, preliminary
results of an assessment of the accuracy of the Thermo-Calc thermodynamic
routine for
modeling solidification of nickel base superalloys will be presented. An example on the
integration of thermodynamic calculations and solute redistribution models for the purpose of
modeling microstructural evolution in alloy IN718 will also be provided.
APPROACH
Some of the nickel base alloys of primary interest in this work are summarized in Table 1 along
with their chemical composition. The table also includes references to previous work which
investigated the solidification behavior of these alloys through differential thermal analysis
(DTA) and microstructural characterization techniques. DTA has been used to determine the
Iiquidus and solidus temperatures as well as the temperatures of eutectic-like reactions which
occur near the end of solidification. Phase identification of secondary constituents has been
conducted using electron microscopy. The combination of DTA data with microscopy results has
been used to experimentally determine the solidification reaction sequences and the details of the
procedures can be found within the references cited. In the current study the Thermo-Calc
routine was used in conjunction with the Nil?e Superalloy database (Ref. 4) to estimate various
phase diagram quantities and solidification
reaction sequences for comparison
to the
experimental data. This database has been shown to provide accurate descriptions of solid-solid
phase equilibria in multi-component Ni base alloys (Ref. 4), but an assessment
solidification reactions has not yet been reported.
for modeling
Table 1. Concentration
weight percent.
All values in
of major elements of some of the alloys under investigation.
Alloy
Fe
3.17
5.44
18.2
2.4
11-45
C-22
C-276
IN718
IN 625
Experimental
Ni
Bal
Bal
Bal
Bal
Bal
Composition
Other
Cr
~ Mo
21.22 ~ 13.43
, 3.29 W
3.93W
15.83 I 15.56
18.2
3.1
5.2 Nb-O.04C
22.7
9.6
Range of Nb,Si, and C
19.0
Range of Nb,Si, and C
--
RESULTS
Reaction Temperatures
Ref.
5
5
6
7
8
AND DISCUSSION
and Phase Diagrams
Liquidus and solidus slopes are important for solidification modeling as they can be used to
provide values for the equilibrium distribution coefficients. Experimental measurement of these
quantities can be accomplished by measuring the liquidus and solidus temperatures with DTA on
single phase alloys with systematic variations in composition (Refs. 7,9).
homogeneous,
Although this approach is effective, it is also quite time consuming. Direct calculation of liquidus
and solidus temperatures through thermodynamic
databases would thus provide a useful
technique for minimizing the extent of experimental measurements. Figure 1 compares the
measured and calculated liquidus and solidus temperatures for the alloys listed in Table 1 in
addition to data on other alloys reported in the literature, and the agreement is reasonable. These
1500
X Ref. 16
Z Ref. 5
A Ref. 7
O Ref. 8
+Ref.17
A Ref. 18
0 Ref. 6
■
X Ref.
g
x
A
A Ref. 7
$j 1400-
0 Ref. 8
+ Ref. 17
A Ref. 18
$
=
d
6
.-
g i300 ~
5
.! 1200- A
!%’
~
w
1320
1360
ThermoCalc
1400
.
1440
values (Celcius]
b
1100Y
1100
1200
ThermoCalc
1300
1400
3500
values (Celcius)
Figure 1. Comparison of calculated and measured liquidus (a) and solidus (b) temperatures.
calculations can easily be extended to determine the liquidus and solidus temperatures over a
range of composition for a particular alloying element, and an example is shown in Figure 2 for a five component alloy @Ii-l lFe-19Cr-O.02C-XNb).
The liquidus and solidus slopes with respect
to Nb in this system have been measured to be –8.3 and –17.9°C/wt% Nb, respectively. The
calculated slopes are in reasonable agreement with these values (–11 and –24°C/wtO/0). The
equilibrium distribution coefficient for Nb, which is given by the ratio of liquidus to solidus
slope, has also been measured for this system and is 0.46. This is in excellent agreement with the
value of 0.46 obtained from the slopes given in Figure 2.
1500
Ni-llFe-19Cr-O.02C
SIOpe = -24 UwtO/ONb
1150
t
0.0
2.0
10.0
12.0
;&ght &!rcen! ‘8b
Figure 2. Calculated variation in liquidus and solidus temperature
Ni-1 lFe- 19Cr-O.02C-XNb alloys.
as a function of Nb content for
Phase diagrams are needed in order to follow the progression of reactions over the eritire
solidification range. Various experimental measurements of multi-component
equilibria have
been reported, and these are usually portrayed by using simplified binary or ternary-like
diagrams. These experimentally derived diagrams are useful for database validation. Knorovsky
et al. presented a binary-like phase diagram for IN 718. This alloy exhibits a three step
solidification reaction according 1: L -> y, 2: L -> (y+ NbC), 3: L -> (y+ Laves). The L -> (y+
NbC) reaction occurs over a relatively wide temperature range and forms a small amount of the
y/NbC eutectic-type constituent. The L -> (y + Laves) reaction occurs over a small temperature
interval and the y/Laves accounts for most of the eutectic-type constituent in the as-solidified
microstructure. Neglecting the small amount of y/NbC that forms, Knorovsky et al. developed a
binary-like eutectic phase diagram at solidification temperatures that includes the primary L ->
y and eutectic-type L -> (y+ Laves) reactions. Key temperature/composition
points on the
diagram were determined by a combination of DTA and electron microscopy. Their diagram is
compared to a calculated diagram for IN 718 in Figure 3. The calculated liquidus line and L ->
(Y+ Laves) reaction composition are in reasonable agreement with experimental values. The
calculated solidus line is 75-100 “C below the experimental line, and the calculated eutectic
temperature is approximately 50 “C below the measured value. The difference in solidus values
could, in part, be attributed to the sample used in the DTA measurements. These samples
contained a combination of NbC and austenite. The presence of NbC depletes the austenite of Nb
and C relative to the bulk composition of the alloy. Since the solidus slopes for Nb and C are
negative (Refs. 7,9), this reduction in Nb and C would increase the effective solidus temperature
of the austenite. Additional comparisons are, however, needed to confirm this effect.
1500
1400
u
:“1300
3
21200
1000 1,,/,
,,,
,,,
900
0.0
5.0
10.0
15.0
25.0
20.0
WeightPercentNb
Figure 3. Comparison of measured and calculated binary-like phase diagram forIN718.
0.6
0.5
:04
+
experimental
Y
o
,
0
10
Liquid Composition
Figure 4. Comparison
Nb-Si-C alloys.
20
Nb @
of measured and calculated ternary-like
30
YO
Iiquidus projection for Fe-Ni-Cr-
The small amount of y/NbC which forms in the IN 718 investigated by Knorovsky et al. can be
attributed to it’s low carbon content (- 0.04 wtYo).
However, it has been shown (Refs. 7,9) that
the amount of y/NbC constituent that forms in Nb bearing superalloy will increase significantly
with relatively minor increases in carbon content. In this case, binary-like diagrams that account
for only one eutectic-type reaction must be replaced by ternary-like liquidus surfaces. A y-Nb-C
liquidus surface has recently been reported for Fe-Ni-Cr-Nb-Si-C
alloys and is reproduced in
Figure 4 along with a calculated version for the same alloy system. The general shape of this
diagram is very similar to that reported for the simple Ni-Nb-C ternary system (Ref. 10), except
that the Ni3Nb phase is replaced by the Laves phase (because of the presence of Fe and Cr).
Ternary solute redistribution models (Refs. 11,12) require a priori knowledge of the slope of the
two fold saturation line and the liquid composition at which the L -> (y+ NbC) reaction is
replaced by the L -> (y + Laves) reaction. Reference to Figure 4 indicates these values are in
reasonable agreement, indicating that the calculated liquidus surface should provide sufficiently
accurate input values for solidification models. This will be assessed in more detail under the
section on “Coupling of Solidification Models and Calculated Phase Diagrams”.
Reaction Sequences and Elemental Partitioning
The sequence of solidification reactions and final microsegregation patterns depend on both the
shape of the phase diagram and the solute redistribution behavior. For example, a binary alloy
that is below the maximum solid volubility and solidifying under equilibrium conditions exhibits
only a primary solidification reaction, since the liquid is consumed before the eutectic
composition is reached. Immediately after solidification the alloy is single phase with uniform
composition. However, under “Scheil-type” conditions (Ref. 13), where the diffusivity of solute
in the solid is negligible, the liquid will become progressively enriched in solute until the eutectic
composition
is reached, thus initiating a eutectic reaction as solidification
terminates
isothermally (for a simple binary system). In this case, the as-solidified microshwcture contains
cored primary dendrites and interdendritic eutectic. In many alloys of engineering importance,
however, some solid state redistribution is possible. Thus, in the general case, the reaction
sequence and distribution of alloying elements cannot be accurately estimated until both the
kinetic and thermodynamic considerations are understood. For these situations, calculated phase
diagrams must be integrated with more complex solute redistribution models. An example of this
integration for multi-component
aIloys exhibiting both Scheil-type
and more complex
solidification behavior are given below.
Considering Scheil-type solidification first, it has been shown that microstructural evolution
during solidification in many nickel based alloys is controlled by substitutional alloying elements
which exhibit negligible diffision in the primary austenite constituent @ef 5). For these alloys,
a simple Scheil simulation can be easily coupled to phase equilibria calculations to approximate
the sequence of solidification reactions and final segregation patterns. Computationally,
this
coupling is accomplished sequentially by using the Scheil equation and re-setting the nominal
alloy composition to that of the liquid composition from the previous temperature step. This
ensures the liquid composition will always reach a local minimum on the liquidus surface, as
expected from the Scheil equation. The corresponding fi-action liquid is determined by the
product of the fraction liquid from the previous and current temperature steps. Under the
assumptions of negligible diflisivity, this approach can be used to compute the fractions and
.
compositions
Thermo-Calc
of solid and liquid during solidification without the need for any kinetic data. The
application contains a module for making these calculations.
‘1400
1400
1380
—
Gamma
-----
Gamma + Sigma
—
1380
\
Gamma
----
Gamma +
P
1391
~ 1360
“$’ 1340
(u
~
1309
E 1320
$
1300
C-276
2
1300
,299
A:
b
1280
1280
o
1
0.5
1.5
0
0.5
Weight Fraction Solid
Figure 5. Scheil simulations
‘
1
1.5
Weight Fraction Solid
for alloys C-22 and C-276,
a
!
I
o
0.4
0.2
0.6
0.8
1
Weight Fraction Gamma
b
60
iz 50
w
Q
= 40
UJ
a 30
i’==
g 20
G
3
lo
o
~
i
Ni
–
–
–
UC
ID
Cr
-
0
–
I
Mo
I
I
t
I
I
I
01234567
I
I
8
9
10
POSITIC?hI (MICRONS)
Figure 6. Comparison
in alloy C-22.
of calculated (a) and measured (b) segregation patterns for Ni, Cr, and Mo
Microstructural evolution of fusion welds in Hastelloy alloys C-22 and C-276 has been shown to
be governed primarily by partitioning of Mo and Cr (Ref. 5). These substitutional elements
exhibit negligible solid state diffusion during the time fi-ames associated with the cooling rates of
conventional arc welds (Ref. 5,8). The final segregation pattern of Mo is of particular interest
since welds in these alloys are known to be susceptible to localized corrosion attack at the Modepleted dendrite cores (Ref. 14). Figure 5 shows a Scheil simulation for these alloys. For
Hastelloy C-22, the simulations predict a two step solidification reaction consisting of L -> y
followed by L -> (y+ G) which initiates at 1310 “C. For the C-276 alloy, a reaction sequence of
L -> y followed by L -> (y+ P) initiating at 1309 “C is predicted. These solidification sequences
are”in agreement to those experimentally observed by Cieslak et al, with the exception that the
final reactions occur at 1285 ‘C in each alloy. Figure 6a shows the calculated concentrations of
Ni, Cr, and Mo in austenite as a function of ii-action solid in Hastelloy C-22. Since solid state
diffusion is assumed to be negligible, these results are analogous to the final distribution of
solute that should exist across the dendritic substructure, where the fraction solid (fraction
gamma in the figure) is equal to zero at the dendrite core and equal to one at the center of two
neighboring dendrites. Figure 6b shows the experimentally measured segregation patterns of Ni,
Cr, and Mo across the dendritic substructure in Hastelloy C-22 (Ref. 5). The segregation profiles
in Figures 6a and 6b are comparable in terms of both segregation direction and magnitudes
(assuming constant density across the range of compositions estimated). Similar results were
obtained for the C-276 alloy.
Coupling of Solidification
Models and Calculated Phase Diagrams
As indicated above, conditions exist where the solidification behavior can not be estimated with
a simple Scheil-type analysis because one or more of the important solutes do not obey the
assumption of negligible solid state diffusion. In these cases, the solidification path must be
calculated with a more complex solute redistribution model and combined with the pertinent
liquidus surface to understand the solidification behavior. The binary-like diagram presented for
alloy IN 718 in Figure 3 is useful for alloy compositions (heats) with low carbon contents that
form negligible quantities of y/NbC. In higher carbon alloys, the L -> (y+ NbC) reaction will
occur over an appreciably larger temperature range, and y/NbC will account for a large fraction
of the total eutectic-type constituent present in the final microstructure. The binary-like diagram
can not account for this additional reaction, and higher order diagrams are needed to represent
the multiple eutectic reactions. In this final section, an example is presented where a calculated
ternary-like liquidus projection is combined with a solute redistribution model to understand the
influence of composition on the solidification behavior of alloy IN718.
Table 2 lists the chemical composition of five heats of IN 718 that contain variations in the Nb
and C concentrations. Figure 7 shows typical DTA cooling curves for Heats 1 and 5, where the
three step L -> y, L -> (y+ NbC), L -> (y+ Laves) reaction sequence is displayed for each alloy.
However, note that a seemingly small change in carbon content from 0.04 to 0.09 wt’%0 increases
the L -> (y+ NbC) start temperature by an average of 36 “C. These experimentally determined
reaction start temperatures are summarized in Table 2. In agreement with previous results (Ref.
6), the L -> (y + Laves) reaction occurs near 1200 “C over a relatively small temperature interval.
Figure 8 shows a calculated ternary-like Iiquidus projection for IN 718. This diagram was
computed by determining the position of the lines of two-fold saturation which separate the y,
,
.
●
NbC, and Laves primary phase fields. Although the diagram is displayed in ternary-like fkshion,
it accounts for the presence of eight elements (Ni-Fe-Cr-Mo-Al-Ti-Nb-C)
by approximating “y”
as an elemental constituent. The liquid composition at which the L -> (y+ NbC) reaction is
replaced by L -> (y+ Laves) is calculated at 19.1 WtO/O
Nb and 0.03 wtO/OC. These values are in
excellent agreement with those previously reported as 19.1 WtO/ONb (Ref. 6) and 0.04 WtO/OC
(Ref. 8). Superimposed on the diagram are the primary solidification paths, which were
computed with the solute redistribution model described in Ref. 11. This model assumes
negligible diffusion of Nb in austenite (which has been experimentally validated – Ref. 8), but
permits C to diffuse infinitely fast. Based on previous results (Ref. 15), this latter assumption is
expected to be valid. The intersection of the primary solidification path with the line of two fold
saturation separating the y and NbC phase fields provides a predicted value for the start
temperature of the L -> (y+ NbC) reaction. These predicted values are summarized in Table 2,
and good agreement is observed between the calculated and measured reaction temperatures.
This provides a positive, preliminary indication on the usefulness of calculated phase diagrams
for solidification modeling in this alloy system, Work is in progress to assess the validity of this
approach over a wider range of alloy compositions.
Table 2. Summary of alloy compositions and measured and calculated L -> (y+ NbC) reaction
start temperatures. Compositions in’weight percent, temperatures in ‘C.
Element
Ni
Al
Cr
Fe
Mo
Nb
Ti
c
Measured
L -> (y + NbC)
Temperature (°C)
Calculated
L -> (y + NbC)
Temperature (°C)
Heat 1
Bal.
0.46
17.65
19.36
2.90
5.17
0.90
0.04
Heat 2
Bal,
0.41
17.15
20.56
2.92
5.02
0.87
0.02
Heat 3
Bal.
0.28
17.68
19.47
2.87
2.97
0.84
0.05
Heat 4
Bal.
0.46
17.32
19.49
2.88
6.38
0.88
0.06
Heat 5
Bal.
0.42
17.19
19.19
2.86
5.07
0.90
0.09
1260
+/- 12
Not
Detected
1290
+/- 9
1283
‘+/- 9
1296
+/- 9
1260
1237
1297
1264
1294 ~
.
o
-0.02,
a
b
-0.04-
-0.02
H-l
~ -0.06
Heat 1
1268
i
1195
5
s
g -0.08
z
5
.0. I
07
1202
i=
n -0.12L.>
L ->7 + Laves
-0.14
J
L.>y
1170
1220
1270
Temperature
1320
~
g
I
1100
1370
L.>y
L->1’+1-aves
1
.0.16
-0.12
1120
1367
351
Y+NC
-0.1
1150
1250
I zm
1300
1350
1400
Temperature [C)
~C)
Figure 7. DTA cooling curves for Heat 1 (a) and Heat 5 (b).
Calculated
L -> y + NbC
Start Temperatures
\
NbC
‘/
Y
/’
/’
o
5
10
15
20
25
Liquid Composition, W. % Nb
Figure 8. Calculated
heats of alloyIN718.
ternary-like
liquidus projection
and solidification
paths for five different
SUMMARY
A preliminary assessment on the applicability of the Thermo-Calc NiFe Superalloy database to
solidification problems in complex multi-component alloys has been conducted. To this point,
the validation has been conducted by comparing calculated phase diagram quantities to
experimental measurements avaiIable in the literature, The comparisons indicate the database
provides useful estimates of phase equilibrium information that is needed as inputs for
solidification models. Work is in progress to extend the validation study to a wider range of alloy
compositions and to couple the calculated thermodynamic information to more realistic solute
redistribution models.
!!
b
ACKNOWLEDGEMENTS
This work was performed at Lehigh University under contract to Sandia National Laboratories,
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin
Company, for the United States Department of Energy under Contract No. DE-AC0495 AL85000.
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.
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