Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions
Casting of a gas turbine blade from MAR-M247 nickel-base superalloy is followed by multiple carbide precipitates as a result of solidification. The microstructure of carbide was established with scanning electron microscopy and energy spectrum analysis. A finite element model simulating the blade wi...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2019
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| Назва видання: | Проблемы прочности |
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| Цитувати: | Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions / H. Lin, H.P. Geng, Y.Y. Zhang, H. Li, X.Y. Liu, X.F. Zhou, L. Yu // Проблеми міцності. — 2019. — № 1. — С. 115-126. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1883092023-02-23T01:27:28Z Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions Lin, H. Geng, H.P. Zhang, Y.Y. Li, H. Liu, X.Y. Zhou, X.F. Yu, L. Научно-технический раздел Casting of a gas turbine blade from MAR-M247 nickel-base superalloy is followed by multiple carbide precipitates as a result of solidification. The microstructure of carbide was established with scanning electron microscopy and energy spectrum analysis. A finite element model simulating the blade with a random carbide precipitate is constructed using ANSYS software, and stress-strain evaluation is performed. The blade operation conditions are realized in a vibratory-tensile combined test setup with stress measurements using strain gauges arranged on different parts of the blade. The respective von Mises equivalent stresses obtained in simulation and test measurements are found to be comparable and can be used to assess the blade fatigue life based on the available fatigue curves and Palmgren–Miner rule of damage accumulation. Simulation and experimental results are the basis for plotting the relationship between the volumetric ratio of precipitates in the blade and its fatigue life. The results obtained at room temperature can; be extrapolated to the elevated ones to provide more reliable prediction of the superalloy blade fatigue and creep-fatigue life values. Литье лопатки газовой турбины из суперсплава на никелевой основе MAR-M247 сопровождается образованием множественных карбидных выделений в результате затвердевания. Микроструктуру карбида изучали с помощью сканирующей электронной микроскопии и энергетического спектрального анализа. Построена конечноэлементная модель лопатки со случайным карбидным выделением на основе программного обеспечения ANSYS, выполнена оценка напряженно-деформированного состояния. Условия эксплуатации лопатки реализовали на экспериментальной установке для комплексного испытания на вибрацию и растяжение, напряжения измеряли с помощью тензодатчиков, размещаемых на различных участках лопатки. Проведено сравнение эквивалентных напряжений по Мизесу, полученных при моделировании и экспериментально. Установлено, что их можно использовать для оценки усталостной долговечности лопатки на основании полученных кривых усталости и закона накопления повреждений Палмгрена Майлера. Они служат также основой построения зависимости между объемным соотношением включений в лопатке и ее усталостной долговечностью. Данные, полученные при комнатной температуре, могут быть экстраполированы на повышенные, что обеспечивает более достоверный прогноз усталости и усталостной долговечности лопатки из суперсплава при ползучести. Лиття лопатки газової турбіни з суперсплавів на нікелевої основі MAR-M247 супроводжується утворенням множинних карбідних виділень в результаті затвердіння. Мікроструктуру карбіду вивчали за допомогою скануючої електронної мікроскопії та енергетичного спектрального аналізу. Побудована скінченноелементна модель лопатки з випадковим карбідним виділенням на основі програмного забезпечення ANSYS, виконана оцінка напружено-деформованого стану. Умови експлуатації лопатки реалізували на експериментальній установці для комплексного випробування на вібрацію і розтягнення, напруги вимірювали за допомогою тензодатчиків, що розміщуються на різних ділянках лопатки. Проведено порівняння еквівалентних напружень по Мізесу, отриманих при моделюванні і експериментально. Встановлено, що їх можна використовувати для оцінки втомної довговічності лопатки на підставі отриманих кривих втоми і закону накопичення ушкоджень Палмгрена-Майлера. Вони служать також основою побудови залежності між об'ємним співвідношенням включень в лопатці і її втомної довговічністю. Дані, отримані при кімнатній температурі, можуть бути екстрапольовані на підвищені, що забезпечує більш достовірний прогноз втоми і втомної довговічності лопатки з суперсплавів при повзучості. 2019 Article Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions / H. Lin, H.P. Geng, Y.Y. Zhang, H. Li, X.Y. Liu, X.F. Zhou, L. Yu // Проблеми міцності. — 2019. — № 1. — С. 115-126. — Бібліогр.: 17 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/188309 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Lin, H. Geng, H.P. Zhang, Y.Y. Li, H. Liu, X.Y. Zhou, X.F. Yu, L. Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions Проблемы прочности |
| description |
Casting of a gas turbine blade from MAR-M247 nickel-base superalloy is followed by multiple carbide precipitates as a result of solidification. The microstructure of carbide was established with scanning electron microscopy and energy spectrum analysis. A finite element model simulating the blade with a random carbide precipitate is constructed using ANSYS software, and stress-strain evaluation is performed. The blade operation conditions are realized in a vibratory-tensile combined test setup with stress measurements using strain gauges arranged on different parts of the blade. The respective von Mises equivalent stresses obtained in simulation and test measurements are found to be comparable and can be used to assess the blade fatigue life based on the available fatigue curves and Palmgren–Miner rule of damage accumulation. Simulation and experimental results are the basis for plotting the relationship between the volumetric ratio of precipitates in the blade and its fatigue life. The results obtained at room temperature can; be extrapolated to the elevated ones to provide more reliable prediction of the superalloy blade fatigue and creep-fatigue life values. |
| format |
Article |
| author |
Lin, H. Geng, H.P. Zhang, Y.Y. Li, H. Liu, X.Y. Zhou, X.F. Yu, L. |
| author_facet |
Lin, H. Geng, H.P. Zhang, Y.Y. Li, H. Liu, X.Y. Zhou, X.F. Yu, L. |
| author_sort |
Lin, H. |
| title |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions |
| title_short |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions |
| title_full |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions |
| title_fullStr |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions |
| title_full_unstemmed |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions |
| title_sort |
fatigue strength and life prediction of a mar-m247 nickel-base superalloy gas turbine blade with multiple carbide inclusions |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2019 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188309 |
| citation_txt |
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions / H. Lin, H.P. Geng, Y.Y. Zhang, H. Li, X.Y. Liu, X.F. Zhou, L. Yu // Проблеми міцності. — 2019. — № 1. — С. 115-126. — Бібліогр.: 17 назв. — англ. |
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Проблемы прочности |
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| fulltext |
UDC 539.4
Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy
Gas Turbine Blade with Multiple Carbide Inclusions
H. Lin,
a,b
H. P. Geng,
a,b,1
Y. Y. Zhang,
a,b
H. Li,
a,b
X. Y. Liu,
c
X. F. Zhou,
b
and L. Yu
a,b
a School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China
b State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong
University, Xi’an, Shaanxi, China
c Dongfang Turbine Co. Ltd., Deyang, Sichuan, China
1 haipenggeng@126.com
Casting of a gas turbine blade from MAR-M247 nickel-base superalloy is followed by multiple
carbide precipitates as a result of solidification. The microstructure of carbide was established with
scanning electron microscopy and energy spectrum analysis. A finite element model simulating the
blade with a random carbide precipitate is constructed using ANSYS software, and stress-strain
evaluation is performed. The blade operation conditions are realized in a vibratory-tensile combined
test setup with stress measurements using strain gauges arranged on different parts of the blade. The
respective von Mises equivalent stresses obtained in simulation and test measurements are found to
be comparable and can be used to assess the blade fatigue life based on the available fatigue curves
and Palmgren–Miner rule of damage accumulation. Simulation and experimental results are the
basis for plotting the relationship between the volumetric ratio of precipitates in the blade and its
fatigue life. The results obtained at room temperature can; be extrapolated to the elevated ones to
provide more reliable prediction of the superalloy blade fatigue and creep-fatigue life values.
Keywords: fatigue strength, MAR-M247 nickel-base superalloy, gas turbine blade, carbide
precipitates, fatigue life prediction.
Introduction. High-temperature blades in heavy-duty gas turbines are usually made
of various nickel-base alloys, including MAR-M247 nickel-base superalloy. The operation
conditions of gas turbine blades imply their failure via fatigue fracture mechanism [1, 2],
which is accompanied by creep, mechanical structure strength, thermomechanical effect,
etc. [3, 4].
In the process of nickel-base alloy casting solidification, a variety of defects is formed
in the blade material [5]. This study is mainly focused on carbide defects, which exist in
nickel-base superalloy, due to the reaction between elements of parent metal (M) and
carbon (C) during the casting solidification and formation of carbides (MC). The total
content of carbides is about one percent. These carbides are discrete and blocky precipitates
of unknown shapes and sizes. They are random in the quantity, shape, and position, and
unpredictable in the casting blade of the nickel-base superalloy. Therefore, carbide defects
may deteriorate the strength of nickel-base superalloy, and their effect on the blade fatigue
crack initiation and propagation cannot be ignored.
Nickel-base alloys are widely used as high-temperature materials. A complex airfoil
surface of the gas turbine blade is produced through casting, and internal carbide defects
appear simultaneously. However, the research results on the fatigue strength simulation
analysis involving carbide defects are quite scarce [6]. The experimental realization of the
blade operation conditions is quite problematic, since special experimental setups are required
for the full-scale blade testing [7–9]. The above-mentioned carbide defects are important
factors controlling the blade service performance and reliability and seriously degrading the
blade superalloy mechanical structure fatigue strength and service life. Given this, the
influence of carbide defects on the blade fatigue strength needs to be taken into account.
© H. LIN, H. P. GENG, Y. Y. ZHANG, H. LI, X. Y. LIU, X. F. ZHOU, L. YU, 2019
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 115
In this paper, carbide defects in MAR-M247 nickel-base superalloy are analyzed by
the scanning electron microscope and the energy spectrum analysis. A finite element model
simulating the blade model with a random carbide defect is elaborated via the finite element
simulation software, and stress-strain calculations are performed. The blade operation
conditions are experimentally realized via a vibration-tensile combined test setup with
stress measurements using strain gauges applied to different parts of the blade. The
respective von Mises equivalent stresses obtained via simulation and test measurements are
found to be consistent and used to assess the blade fatigue life using available fatigue
curves and the Palmgren–Miner rule of damage accumulation. Finally, based on the
simulation and experimental results, the relationship between the volumetric ratio of defects
in the blade and its fatigue life is proposed in the normal temperature state.
1. Microstructural Characterization of Carbide Defects in a Blade. The blade
under study is the fourth stage one of the heavy-duty gas turbine. The blade is produced by
casting from MAR-M247 nickel-base superalloy, which chemical composition (in wt.%) is
shown in Table 1.
Several carbides of MC type, such as TaC, WC, TiC, HfC, etc., were found to
precipitate in the above blade material during its casting process. Although their amount is
small, carbides exert a significant impact on the material properties and facilitate the crack
initiation and propagation, which leads to a reduced lifetime [10]. Therefore, the micro-
structural evaluation of the blade material and carbides is carried out in this study.
The nickel-base superalloy sample of a cubic shape (5 5 10� � mm) is subjected to the
scanning electron microscopy (SEM). The respective backscattered electron image obtained
via JEOL JSM-6390A, (Japan) is shown in Fig. 1a. In addition, an energy dispersive X-ray
spectrometer (EDS) is used to analyze the energy spectrum in the corresponding area in
Fig. 1b. Finally, the surface morphology, chemical composition, and the relative content are
obtained. The precipitation elements of the revealed carbides are also detected and shown
in Fig. 2.
Figure 1 depicts the metallographic photograph and shows the distribution of different
phases. The distribution of MC type carbide defects can be observed in Fig. 1a, where
H. Lin, H. P. Geng, Y. Y. Zhang, et al.
116 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
T a b l e 1
The Chemical Composition of MAR-M247 Nickel-Base Superalloy
C Cr Mo Al Co Ti Fe W Hf B Ta Zr Ni
0.16 8.6 0.8 5.6 10.0 1.0 0.2 10.0 1.5 0.02 3.0 0.06 Rest
a b
Fig. 1. The metallographic analysis results via SEM: (a) MC type carbide defect; (b) compositional
analysis of the identification zone.
irregular blocky carbide defects are observed in the nickel-base superalloy. Figure 1b
shows the energy spectrum area in the identification zone 1.
The carbide defect compositional analysis by EDS for the identification zone 1 is
depicted in Fig. 2. The energy spectrum results strongly indicate that available carbides are
based on such metals as Ta, W, Ti, and Hf, where the ratio of TaC carbide in zone 1 is the
highest (over 50% of the total amount of different carbides).
2. Finite Element Analysis. The blocky carbide defect in the nickel-base superalloy
is formed randomly during casting, so its shape is irregular, and its position inside the blade
is uncertain [11]. The number of blade defects is expressed by the defect ratio in the total
volume, which is a random value.
Due to the high cost of design and manufacture of heavy-duty gas turbine blades, it is
essential to ensure their sufficient, but not excessive fatigue strength [12]. In this respect,
the strength deterioration due to carbide defects has to be accurately estimated. The finite
element method (FEM) is used in this study to simulate the defect in the blade via the finite
element simulation software. The finite element model needs to reflect the shape irregularity,
quantity inconsistency, and distribution randomness of carbide defects in the blade.
Within the elastic approach, the relations between displacements and strains are
expressed by the following geometric deformation equations:
�
�
�x
u
x
� , �
�
�y
v
y
� , �
�
�z
w
z
� , �
�
�
�
�xy
u
y
v
x
� � , �
�
�
�
�yz
v
z
w
y
� � , �
�
�
�
�zx
u
z
w
x
� � , (1)
where u v w, , are displacements in three orthogonal directions, � � �x y z, , represent the
normal strain, and � � �xy yz zx, , represent the shear strain.
The stress-strain relation is expressed by the material physical equations:
� � � �x x y z
E
�
�
1
[ ( )], � � � �y y z x
E
�
�
1
[ ( )], � � � �z z x y
E
�
�
1
[ ( )],
�
�xy xy
E
�
�2 1( )
, �
�yz yz
E
�
�2 1( )
, �
�zx zx
E
�
�2 1( )
,
(2)
where E is elastic modulus, is Poisson’s ratio, while � � �x y z, , represent normal
stresses acting along the respective coordinate axes.
Fatigue Strength and Life Prediction ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 117
Fig. 2. Carbide defect compositional analysis by EDS.
The relation between the stress and the external force is expressed by the force
equilibrium equations:
��
�
��
�
��
�
x xy zx
x
x y z
P� � � � 0,
��
�
��
�
��
�
y yz xy
y
y z x
P� � � � 0,
��
�
��
�
��
�
z zx yz
z
z x y
P� � � � 0,
(3)
where � � �xy yz zx, , are shear stress, while P P Px y z, , represent forces acting along the
respective coordinate axes.
Under the gas turbine blade operation conditions, large stresses appear in the vicinity
of internal carbide defects, which act as stress raisers. Thus, the blade fatigue strength
depends on the maximum local stress and strain at the stress concentration area. The
calculated fatigue life corresponds to the crack initiation and propagation within a small
area of stress concentration, where the stress concentration factor K t is defined as follows:
K
S
t �
�
�
� max . (4)
When estimating the blade fatigue life, the following relation linking the maximum
local stress and strain ranges (�� max and �� max , respectively), nominal stress range �S ,
and elastic modulus E can be used
� �
�
� �max max
( )
.�
K S
E
t
2
(5)
Hence, the blade fatigue life N can be assessed via the following equation:
�� �
� max ( ) ( ) ,
2
2 20 0�
�
f
f
c
E
N N (6)
where
� f ,
� f , 0 , and c0 are the material constants, which are referred to as fatigue
strength factor, fatigue ductility factor, fatigue strength index, and fatigue ductility index,
respectively.
A finite element model of the complete blade is constructed in ANSYS using solid 3D
tetrahedron-shaped elements. Their material properties correspond to those of the nickel-
base superalloy under study. Then, the respective elements corresponding to carbide defects
are randomly assigned within the blade model, which number depends on the volumetric
ratio of carbides and which material properties correspond to those of the particular carbide.
The blade material density, elastic modulus, and Poisson’s ratio are 8.2 g/mm3, 200 GPa,
and 0.3, respectively, while those of the defect element are 0.5 g/mm3, 200 MPa, and 0.03.
The yield strength of MAR-M247 was experimentally defined at 883 MPa.
The blade finite element model with boundary and loading conditions is shown in
Fig. 3. The model consists of 1285,212 tetrahedron elements and 1890,929 nodes. In order
to simulate the blade contact state in the operation conditions, 80,929 surface nodes of the
blade shroud, joint, and flange are connected by spring elements of stiffness equal to 1 108� ,
1 1010� , and 1 105� , respectively. The angular velocity of 628 rad/s is applied in the direction
of the blade rotation, which corresponds to the rated speed (6000 rpm) under the actual
loading conditions of the gas turbine blade.
118 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
H. Lin, H. P. Geng, Y. Y. Zhang, et al.
The defect tetrahedron-shaped element in the tangent section of the blade is shown in
Fig. 4. The finite element model can not only simulate the carbide defect size, but also
reflect its irregularity and randomness in the cast nickel-base superalloy blade.
Because of the complex shape and variable thickness of the blade body, casting-
induced defects are likely to form at its airfoil and produce stress raisers, which make it
more prone to accelerated fatigue failure than other turbine parts. Therefore, carbide defects
are assumed to exist in the blade body.
Firstly, the volumetric ratio of 0.02% is preset for carbide defects in the FEM
calculation via ANSYS software. Figure 5 shows the calculation results for the blade
equivalent stress distribution in the pressure and suction surfaces. The positive stress values
are shown to grow from the blade bottom to its top, where the maximum value of 637 MPa
is reached.
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 119
Fatigue Strength and Life Prediction ...
Fig. 3. Turbine blade finite element model.
Fig. 4. The finite element model including the defect element.
Fig. 5. Von Mises stress distribution nephograms (in Pa).
Based on the above stress analysis results, the blade fatigue life can be estimated
using the available fatigue curve (S–N curve). As shown in Fig. 6, blade fatigue life
distribution nephograms of the pressure and suction surfaces represent the number of cycles
to failure (fatigue life) of different blade parts with assumed inherent carbide defects. The
shortest fatigue life in the blade body is assessed at 199 106. � cycles and corresponds to the
most stressed top of the blade, while that of the blade middle part is 1 107� cycles, which
implies that its stress level is nearly equal to the fatigue life limit.
3. Blade Strength Test and Dynamic Stress Measurements. For the heavy-duty gas
turbine blade, it is quite problematic to simulate its true operation conditions by fatigue
tests under laboratory conditions [13]. Therefore, as shown in Fig. 7, a special experimental
setup, which provided mechanical fatigue conditions simulating the blade operation one,
was elaborated in this study. The experimental setup comprises (i) adjusting devices for the
fixation of the blade shroud, joint, and flange; (ii) a high-frequency micro-amplitude
vibration bench for simulating the blade contact state in the operation conditions; (iii) a
tensile loading device, which is applied to the blade shroud to simulate the centrifugal force
action under the rated speed of 6000 rpm.
120 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
H. Lin, H. P. Geng, Y. Y. Zhang, et al.
Fig. 6. Fatigue life distribution nephograms (in 10n).
Fig. 7. Fatigue experimental setup for the blade.
The blade fatigue life is mainly determined by scattered defects located within a large
damage area. In this experiment, the top, middle and bottom parts of the blade body were
selected as measuring points, with placement of strain sensors. There were two measuring
points in the bottom, two measuring points in the middle, and four measuring points in the
top. The LMS data device was used to acquire the dynamic stress data of the blade in the
real time scale.
The experimental data obtained were processed with the elimination of interference
signals [14]. Eventually, the experimental stress values in measuring points were obtained
at the data sampling frequency of 20,480 Hz. Then, the experimental data obtained were
used to plot the stress–time history in the measuring points, which are depicted in Fig. 8.
According to the experimental results, the maximum stress values in the top, middle,
and bottom of the blade body were equal to 657, 382, and 545 MPa, respectively, which did
not exceed the blade yield strength of 883 MPa. As shown in Table 2, the maximum stress
area was observed in the top of the blade body, and the minimum one in its middle.
The estimation of fatigue life of a blade subjected to cyclic loading with a variable
stress amplitude is based on the damage accumulation principle. When the blade is
subjected to the stress below the fatigue strength limit, each stress cycle produces a certain
amount of damage. The damage is accumulated, and the failure occurs when the damage
achieves its critical value.
According to the Palmgren–Miner linear fatigue cumulative damage rule [15], the
material fatigue damage at each stress level is accumulated independently of previous or
next levels, and the total damage can be superimposed linearly [16]. The critical failure
value D is assumed to be
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Fatigue Strength and Life Prediction ...
Fig. 8. Experimental stress–time history.
T a b l e 2
Experimental Maximum Stress and Fatigue Life Values
Measuring point Top Middle Bottom
1 2 3 4 5 6 7 8
Maximum stress value (MPa) 657 636 550 503 337 382 519 545
Fatigue life (�106, cycles) 1.0 1.55 1.78 4.90 7.0 7.0 6.46 5.89
D
n
N
i
ii
l
� �
�
�
1
1. (7)
For the experimental measured stress amplitude of � l , the damage caused by n
cycles in the test loading sequence can be expressed as follows:
D
n
C
l
l
m
� �
�
, (8)
where C and m are the material constants controlling the regression line of the blade S–N
curve.
Suppose that fatigue failure is achieved when the superposition of the number of
cycles at the fatigue limit value � a adds up to N a � 107 cycles.
According to Eq. (7), the number of cycles corresponding to the particular measured
stress amplitude can be calculated by the following equation:
N
C
L
n
C
a a
m
l
m� �
� � , (9)
where L is a constant.
The fatigue life values of each measuring point calculated from the experimental data
are listed in Table 2. The minimum fatigue life values in the top, middle, and bottom of the
blade body were assessed as 117 106. � , 107 , and 589 106. � cycles, respectively. Thus, the life
of the total blade is limited by the shortest fatigue life of 117 106. � cycles of its top part.
4. Results and Discussion. The comparison of experimental data and simulation
results is illustrated by Fig. 9. The experimental curves comprise the experimental data of
eight measured points, while the simulation curves show the simulation distribution of
stress and fatigue life values.
122 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
H. Lin, H. P. Geng, Y. Y. Zhang, et al.
Fig. 9. Comparison of experiment and simulation results.
The comparative analysis of experimental data and simulation results in Fig. 9 reveals
their close fit for both stress and fatigue life values, including the general evolution trends
throughout the blade body. This implies a feasibility of the applied FEM approach. Insofar
as the simulation values are slightly larger than the experiment ones, this implies the blade
strength evaluation in this study is conservative, and the simulation results on the blade
fatigue life assessment are reliable.
The applied FEM approach made it possible to construct blade models with various
defect volumetric ratio, namely: 0.02, 0.05, 0.08, 0.1, 0.015, 0.2, and 0.5%. For each of
these cases, the finite element simulation yielded the maximum stress and minimum fatigue
life values. The respective curves of the maximum stress and minimum fatigue life values
corresponding to different defect ratios ranging from 0.02 to 0.5% are shown in Fig. 10.
From the calculation results, it can be seen that different defect ratios affect the
stress distribution over the blade body. The maximum stress value increases from 637 to
820 MPa, which is yet smaller than the yield strength of 883 MPa. When the defect ratio
drops below 0.01%, the maximum stress value is equal to that in a defect-free blade. Thus,
calculation results properly reflect the mechanical conditions of the actual blade defects.
With an increase in the defect ratio, the minimum fatigue life is reduced from 199 106. �
to 224 104. � cycles. When the defect ratio is below 0.01%, the shortest fatigue life is
equivalent to the fatigue life level of a defect-free blade. The results obtained show that the
proposed finite element model with different defect ratios is instrumental in the assessment
of the maximum stress and minimum fatigue life values.
From the above Fig. 10, the variation trend of predicted maximum stress and fatigue
life cycle number values can be observed, and the shape type of the trend can be
approximatively an L-shaped. The points of maximum stress and fatigue life cycle number
values are shown in Figs. 11 and 12. Through the distribution of value points estimated,
values can be fitted as different function types, such as sine function, Gauss function,
logistic function, etc.
The comparative analysis of different function fitting results reveals the fitting of the
logistic function model is the closest for both stress and fatigue life values.
The fitting function model of the predicted maximum stress value S is expressed by
the following equation:
S A A A Q q
p� �
�2 1 2 11 1( ) [ ( ) ], (10)
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Fatigue Strength and Life Prediction ...
Fig. 10. Curves for different defect ratios.
where Q is the percent of defect ratios, and values of coefficients A1, A2, q1, and p1 are
shown in Fig. 11. The fitting degree (adj. R-square) is 0.99659.
The fitting function model of the fatigue life cycle number N is expressed by the
following equation:
N A A A Q q
p� �
�4 3 4 21 2( ) [ ( ) ], (11)
where values of coefficients A3, A4, q2, and p2 are shown in Fig. 12. The fitting degree
(adj. R-square) is 0.99568.
Figures 11 and 12 show that the fitting degree of function models is very high.
Therefore, the predicted regularity of maximum stress and fatigue life cycle number can be
defined by Eqs. (10) and (11). And the maximum stress value S and the fatigue life cycle
124 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
H. Lin, H. P. Geng, Y. Y. Zhang, et al.
Fig. 11. Fitting function curve of maximum stress.
Fig. 12. Fitting function curve of fatigue life cycle number.
number N can be predicted by the defect ratio value Q (%). So the numerical prediction
method is given and provides an effective support to study on the blade maximum stress
and fatigue life under different defect ratios. It is significant for the fatigue strength
prediction of the gas turbine blade with a random defect ratio.
This first attempt covered the normal temperature state, while gas turbine blades
operate at high temperatures, where fatigue and creep interaction is observed, as well as
evolution of MC-type carbides into M23C6 ones. In view of high fatigue resistance of
MAR-M247 superalloy at temperatures of 650, 700, and 900�C reported in [17], the
proposed approach can be extended to the high-temperature range of the blade applications.
The respective follow-up studies are envisioned by the authors.
C o n c l u s i o n s
1. MAR-M247 nickel-base superalloy blade material was analyzed by the scanning
electron microscope, and the MC-type carbide defects, such as TaC, WC, TiC, and HfC,
were observed. Then the compositional analysis of carbide defects by the energy spectrum
analysis was performed, which depicted that TaC carbides amounted to 50% of the total
volume of revealed carbides.
2. Based on the above results, the finite element model for the simulation of the
turbine blade with randomly located carbide defects was constructed via the ANSYS
software, and stress-strain calculations were performed. Meanwhile, the blade operation
conditions were experimentally realized via a vibration-tensile combined experimental
setup with stress measurements using strain gauges applied to different parts of the blade.
3. The respective von Mises equivalent stresses obtained via simulation and test
measurements were found to be consistent and used to assess the blade fatigue life using
available fatigue curves and the Palmgren–Miner rule of damage accumulation.
4. Finally, based on the simulation and experimental results, the relationship between
the volumetric ratio of defects in the blade and its fatigue life was obtained. Further steps
on the model refinement and its extension to high temperatures are discussed, which are
assumed to have practical engineering significance.
Acknowledgments. This work was supported by National Program on Key Basic
Research Projects of China (No. 2013CB03570401), Program on Industry Science and
Technology Development Foundation of SAIC Motor (No. 20171039) and Core
Components of High-end Energy Power Equipment in Shaanxi Province and Project of
Running Diagnostic Public Platform (No. [2017] 377).
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Received 15. 03. 2018
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
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(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
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/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
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/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
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/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
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/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|