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Simulation and Experiments on Plasticity and Recrystallization in SX
Superalloys by Investment Casting
LI Zhonglin1, a, XU Qingyan1, b, XIONG Jichun2, c, LI Jiarong2, d, LIU Baicheng1, e
1School of Materials Science and Engineering, Key Laboratory for Advanced Materials Processing
Technology, Ministry of Education, Tsinghua University, Beijing 100084, China
2National Key Laboratory of Advanced High Temperature Structural Materials, Beijing Institute of
Aeronautical Materials, Beijing, 100095, China
[email protected] , [email protected] , [email protected] , [email protected] , [email protected]
Keywords: recrystallization, directional solidification, single crystal, superalloys
Abstract. Recrystallization (RX) can occur during the manufacture of turbine blades from single
crystal nickel-based superalloys by investment casting, which is potentially detrimental to
mechanical performance due to the introduction of grain boundaries. In this work, modeling and
targeted experimentation on the rod casting with ceramic core are used to quantify the plasticity,
which can cause recrystallization during the subsequent solution heat treatment, as a result of the
different thermal contractions of the metal, ceramic shell and core during directional solidification.
For the modeling, the thermal-elastic-plastic analysis is carried out with the high-temperature
plasticity assumed to be rate independent, considering the orthotropic characteristics of single
crystal nickel-based superalloys. The calculation results indicate that the plasticity occurs mainly
during two stages: during the initial solidification stages (around solidus) owing to its low
immediate yield strength, and the later solidification stage (below 800℃) as a result of tensile or
compressive strain. The influential factors, such as wall and shell thickness, flanges etc., are
analyzed in the modeling. Experimentally, recrystallization takes place in the thin-walled areas due
to broken or buckled cores, which agrees satisfactorily with the plasticity calculations. The model
provides the foundation for a systems-based approach predicting recrystallization and reference for
the casting process design.
Introduction
For gas turbine engineers, considerable emphasis is always put on pursuing higher inlet gas
temperature, which can provide improved efficiencies, less pollution and more reliability[1]. This
presents great challenges to turbine blade manufacturers. Single crystal superalloys, which
eliminate grain boundaries, are contributing to this, as are the thermal barrier coating that has been
adopted widely. In addition, the external and internal geometries of turbine blades are becoming
increasingly complicated to promote aerodynamic performance and guide cooler air into and
through the blades during operation for weight savings and greater cooling efficiency. A
disadvantage, however, is that the blades from single crystal superalloys become very more difficult
to cast, and great cares should be taken to prevent defects such as freckles, recrystallization etc[2,
3].
During the manufacture of single crystal components, recrystallization can easily occur on
both internal and external surfaces, which introduces high-angle grain boundaries and degrades the
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creep and fatigue properties significantly[4, 5]. Its occurrence is intolerant and can be ascribed to
the plastic deformation during solidification and grit blasting, which leads to recrystallization
during subsequent heat treatment[6-8]. The root cause of plasticity during casting is considered to
be differential thermal contraction of the metal, mould and core, arising from their different thermal
expansion coefficients[7, 9]. Recrystallization will appear where the plastic strain exceeds a critical
limit[1]. The probability of recrystallization depends upon the alloys, the shell and core systems as
well as the processing details of casting and annealing conditions. Precious work on
recrystallization of single crystal superalloys by other researchers focus on annealing conditions and
microstructural features rather than the processing details[10, 11].
Traditionally, recrystallization of SX nickel-base superalloy has been avoided with an
empirical way, with reliance placed on existing casting practice, experience or else rules of thumb.
This paper is concerned with the mathematical modeling of the investment casting of single-crystal
superalloys with particular emphasis on thermal-mechanical effects, allowing to anticipate the
plasticity causing recrystallization. Obviously, it’s more advantageous. The aim of this research is
to elucidate the characteristics of plasticity during investment casting and the amount of plastic
strain needed for recrystallization to occur.
Validation of Orthotropy in Single Crystal Superalloy
For orthotropic materials displaying cubic structure (bcc or fcc), three principal orientations
(here denoted 1, 2, 3 respectively) are orthotropic at arbitrary points. In addition, the properties in
three principal orientations are identical Elastic constitutive equation can be expressed as
follows[12]:
m mm
S (1)
Where:
1/ / / 0 0 0
/ 1/ / 0 0 0
/ / 1/ 0 0 0[ ]
0 0 0 1/ 0 0
0 0 0 0 1/ 0
0 0 0 0 0 1/
m
E E E
E E E
E E ES
G
G
G
(2)
with Sij denoting the elastic compliance constants, which measure the strain necessary to
maintain a given stress. E, μ , G are Young’s modulus, poisson ratio and shear modulus
respectively in three principal orientations. There are only 3 independent constants in [S]m.
Through the spatial geometry transformation, the Young’s modulus in any crystallographic
orientation can be obtained as follows[13, 14]:
2 2 2 2 2 2
11 11 11 12 441/ ' ' (2 2 )( )E S S S S S l m l n m n (3)
Where l , m and n represent the direction cosines relative to the 1, 2, 3 axes.
In this work, the nickel-based single crystal superalloy DD6 was used. The orthotropy of DD6
can be inferred, though nickel-based single crystal superalloys are just acknowledged as
engineering SX. The rest of this section will validate the elastic orthotropic characteristics of DD6
through comparing the experiment data with the theory.
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First, Eq. 7 to Eq. 10 are reconsidered. Since l2m2+l2n2+m2n2=1/3 in the orientation [111], Eq.
10 will take the following form:
111
1 3 1 2
G E E
(4)
In this way, the relationship between E, E110, E111, G and μ can be obtained as follows:
110
1 4 2 2
G E E
(5)
110 111
1 4 10
3 3E E E (6)
Experimentally, it is relatively easy to measure E, E110, E111 andμ shown in Fig. 1(a) whose
data is from the literature. By making use of Eq. 14 and Eq. 15, the shear modulus G can be
obtained respectively, denoted G1 and G2. For the modeling of this work, G takes the average of G1
and G2:
G=(G1+G2)/2 (7)
By applying calculated G and experimental E, μ to Eq. 11, the compliance constants S11, S12
and S44 can be calculated. And Young’s modulus in all orientations can be calculated, as shown in
Fig. 1(b). From Table 1, it’s acceptable that the orthotropic mechanical properties of this alloy can
be employed in the following modelling.
（a） (b)
Fig. 1 (a) Variation of E100, E110, E111 andμin DD6 superalloy with the temperature (b) Young’s
Modulus of DD6 in all orientations at 25℃
Table 1 Variation of calculation error with different temperatures
Temperature/℃ 25 700 760 850 980 1070 1100
Calculation Error of E110 1.51% -3.69% -7.73% 9.16% 2.69% 0.85% 2.07%
Calculation Error of E111 -2.57% 7.5% 19.2% -10.9% -4.51% -1.53% -3.40%
Plastic Behavior of SX Superalloy
For the anisotropic materials, the Hill yield criterion, a simple extension of the von Mises
criterion, was usually employed.
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In general, Hill’s potential function can be expressed in terms of rectangular Cartesian stress
components as
2 2 2 2 2 2
22 33 33 11 11 22 23 31 12( ) ( ) ( ) 2 2 2f F G H L M N (8)
Where F, G, H, L, M and N are independent constants obtained by tests of the material in
different orientations. When 0( )f , the material will yield. 0 is the user-defined reference
yield stress specified for the metal plasticity definition, usually using the yield stress in one
principal orientation[15-17]. In this article, 0 [001]S , where S[001] indicate the yield strength in
[001]. The mechanical properties are identical in the three principal orientations [001], [010] and
[100] of FCC crystal. Therefore, ( )f can be expressed as:
2 2 2 2 2 2
22 33 33 11 11 22 23 31 12
1( ) ( ) ( ) 2 ( )
2f K (9)
Where K=L/F denotes anisotropic parameter. Theoretically, the yield stresses S[001], S[011] and
S[111] obtained by uniaxial tests have the following relations:
1/2
[111] [001]
1/2
[011] [001]
( / 3)
1(1 )
2
S K S
S K S
(10)
From the equation, K can be calculated using S[001] and S[111]. For the SX superalloy DD6, the
prediction of S[011] and ultimate tensile strength (UTS[011]) using calculated K were compared with
the experimental results as shown in Table 2. It reveals that the calculated yield strength and
ultimate tensile strength in [011] have a fair accuracy at the temperature 850℃ and 980℃. The
Hill’s yield criterion is acceptable in modelling above 700℃, which is the most concerned
temperature range in this modelling.
Table 2 Variation of calculation error of S[011] and UTS[011] with different temperatures
Temperature/℃ 25 700 760 850 980 1070 1100
Calculation Error of
S[011]
34.2% - - - -2.4% -13.2% -10.7%
Calculation Error of
UTS[011]
26.3% 11.1% 13.6% -1.5% -5.9% -9.6% 5.3%
Case Description
In this research, the following influential factors on the plasticity of SX superalloy during
investment casting were investigated: wall thickness and flanges. For these purposes, three cases
(shown in Fig. 2) were designed to model, with one compared with experimental results.
For the modelling of temperature field, calculations were carried out using both the finite
difference method and the finite element method. Thermal-elastic-plastic analysis was carried out
considering the orthotropic property of SX superalloy, with the high-temperature plasticity assumed
to be rate independent. Temperature-dependent material parameters were assumed. The stresses,
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plastic stored energy and strains, especially the plastic strains, are of primary interest here.For shell
and core, purely isotropic elastic properties are assumed.
(a) (b)
Fig. 2 Geometry in three cases: (a)Case A (b)Case C
Case A: Cored Rod
Thermo-mechanical modelling of cored rods with different wall thickness was carried out to
investigate the influence of casting thickness on the final plasticity. The geometry used in this case
is shown in Fig. 3(a). It was assumed that the superalloy and core keep the same temperature and
interact without friction during solidification and subsequent cooling to 500℃. The axis of the test
rod parallels with the orientation [001] of single crystal superalloy. Without regard for high
temperature creep strain, the static equilibrium condition is assumed during the calculation of stress
field, giving rise to the ignorance of cooling rate. It proved sufficient to model a quarter section of
the cored rod for the mechanical part of the calculation.
Case B: Rod with Section Mutation
In this case, modelling and experiments of cored rods with section mutation were implemented
to represent an analogue of a turbine blade. An industrial-scale Bridgman facility in Beijing
Institute of Aeronautical Materials was employed. The SX alloy with <001> orientation was
directionally solidified. A withdrawal rate of 5mm/min was used. The core system used the
alumina-based material, while the shell system employed alumina-silica-based one. The interaction
of casting with cores and shells is assumed to be free of friction. It is supposed that cores and shells
are tied. Subsequent standard heat treatment was applied after casting.
Results and Discussion
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In this modelling, great care was taken to ensure that the mesh is sufficiently fine for the
results to be independent of element size. The results quoted in this article correspond to the
integration points because of their high accuracy in stress and strain.
Case A:
In this case, it’s interesting to find that the distribution of stress and strain on the circumference
of the rod is non-uniform and the maximum values are in the orientation [011]. It can be explained
by the fact that the maximum Young’s and shear modulus on the circumference lies in the
orientation [011].
Fig. 3 shows the modelling results of maximum strain, plastic energy and potential function in
the situation of wall thickness 0.4mm. It can be seen from Fig. 3(a) that plastic deformation occurs
mainly during two stages: above 1300℃ (or around solidus temperature) and below 800℃.
Between the solidus and 800℃ is the elastic region. During the first plastic occurring stage, the
immediate yield strength is very low, giving rise to plastic deformation easily. On the other hand,
the predicted effective plastic strain (PEEQ) is so low that there is almost no increase in the plastic
energy, due to very low Young’s modulus and shear modulus at that elevated temperature. When
the temperature falls below 800℃, there is a dramatic increase in plastic strain, and the elastic strain
declines continuously. The reason can be understood by Fig. 3(b), which illustrates the variation of
calculated potential function and yield strength with temperature. Above 1300℃, the predicted
potential function is slightly higher than the experimental 0.2% proof strength, but falls below it at
lower temperature. During the cooling stage from solidus to 850℃, the yield strength of the
material increases continuously to as high as 1030MPa, then go to a platform after a small decline.
At the same time, the potential function rises rapidly, just a little smaller than the yield strength
before 800℃. Therefore, the material will yield when the temperature falls below 800℃. From Fig.
(a), high PEEQ will be predicted clearly without consideration of the fracture of the core. Plastic
strain energy density was also calculated so as to find the level of the driving force of
recrystallization by the plastic deformation, which is illustrated in Fig. 4(a).
In what follows in this case, the influence of wall thickness from 5mm to 0.4mm was studied,
as shown in Fig. 4. It’s obvious that the maximum plastic energy density increases with wall
thickness decreasing, especially when it falls below 1.0mm. However, most of the plastic strain is
introduced below 800℃, which is more difficult to produce recrystallization than the same induced
at above 1000℃[1].
（a） (b)
Fig. 3 Variation of PEEQ, THE, EE, Potential Function and plastic energy with the temperature
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Fig. 4 Variation of PEEQ with wall thickness
Case B:
For the purpose of model validation, the geometry was fabricated from DD6 single-crystal
superalloy by investment casting in this case. The design of the geometry, more close to the reality,
combines the ideas of case A and case B. The calculated temperature field is shown in Fig. 5.
Fig. 5 The temperature field of test rod in Case B
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It was found that the core often broke or buckled during the casting process, giving rise to the
non-uniform wall thickness or core penetrating the wall. Recrystallization often occurs in this
situation. Fig. 7(a) shows the geometry of the casting in which the core buckles and passes through
the wall. The calculated PEEQ result of this model was illustrated in Fig. 7(b), compared with the
real rod in Fig. 8(c). It is discovered that the zone below the hole instead of the circumference is
prone to recrystallize in the experiment, which is consistent with the predicted PEEQ. Furthermore,
high PEEQ is also found in the section mutational zone located on the top of the hole, where there is
no recrystallized grain discovered. This is possibly related to the initial set-up in the modelling,
which should be dealt with later.
(a)
(b) (c)
Fig. 6 Model of one test rod with core penetrating the wall, and its PEEQ distribution and real test
piece with recrystallized grains
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Summary and Conclusions
A model for predicting the processing-induced plasticity during investment casting of single
crystal superalloys has been raised in this article. The following conclusions can be drawn from this
work:
1. By comparing the literature data with the theory, the mechanical properties of SX superalloy
are practically orthotropic. Temperature-dependent orthotropic parameters are obtained for SX
superalloy DD6.
2. It is the first attempt to calculate the thermal-mechanical effect during investment casting,
considering the orthotropy of SX superalloy.
3. The plasticity of SX superalloys during investment casting occurs mainly in two stages: around
solidus due to its low immediate yield strength and below 800℃ owing to high thermal
contraction stress.
4. The effective plastic strain and energy of SX superalloy during investment casting increase
with the decreasing wall thickness.
5. The zone below the hole of casting with core penetrating through the wall will be prone to
recrystallize instead of the circumference of the hole.
Acknowledgements
This research is funded by National Basic Research Program of China (No. 2011CB706801)
and National Natural Science Foundation of China (No. 51171089).
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