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Structural Integrity Procedia 00 (2017) 000–000
www.elsevier.com/locate/procedia
XXVII International Conference “Mathematical and Computer Simulations in Mechanics of
Solids and Structures”. Fundamentals of Static and Dynamic Fracture (MCM 2017)
COMPARATIVE ANALYSIS OF STRESS-STRAIN STATE OF
SPECIMENS FOR THERMAL FATIGUE TESTS
Grishchenko A.I.a,*, Savikovskiy A.V.a, Semenov A.S.a, Getsov L.B.b
a
Peter the Great Saint-Petersburg Polytechnic University, Polytechnicheskaya 29, St.Petersburg, 195251, Russia
Scientific and Development Association on Research and Design of Power Equipment, 3/6 Atamanskaya str., Saint-Petersburg, 191167, Russia
b
Abstract
The development of gas turbine engines (GTE) leads to the expanding use of high-temperature superalloys. One of the most
important and high-loaded parts of the gas turbine engine is the nozzle and working blades. This is due to the fact that they
operate at high variable temperatures and stresses, when the material undergoes significant alternating cyclic plastic and creep
deformations. This leads to the need for a thorough study of its thermo-fatigue properties. Estimation of the thermal fatigue
strength of single-crystal blades of gas turbines is an actual problem that has not been finally solved. The purpose of this paper is
to compare the effectiveness of different types of specimens for thermal fatigue tests.
© 2017 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the MCM 2017 organizers.
Keywords: thermal fatigue tests, plasticity, creep, strength, superalloy, finite element simulation
1. Introductions
The inhomogeneity of the inelastic strain distribution in samples for thermal fatigue tests leads to inaccuracies in
the determination of the material constants used in calculating the durability of structural elements. Detailed analysis
of the temperature, stress and strain field distribution in samples allows to evaluate adequately the local
characteristics of thermal fatigue, as well as to analyze peculiarities of different types of samples for thermal fatigue
tests.
In practice, two thermal fatigue test methods are widely used (see Coffin (1954), Getsov (1976), Dulnev (1980),
Rybnikov (2005), Semenov A.S. (2014) et al.). The first method, proposed and developed in Coffin (1954), Dulnev
(1980), consists in cyclic heating of a clamped cylindrical specimen with different degrees of thermal constraint (see
Fig. 1). Variability of thermal constraint is achieved by the addition of rigidity element (2 in Fig.1). The necessity of
2452-3216 © 2017 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the MCM 2017 organizers.
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Author name / Structural Integrity Procedia 00 (2017) 000–000
adding this element is dictated by the fact that in real constructive elements the temperature deformation does not
completely transfer mechanical, but also compensates for the elastic strain of the volume of the part due to the
limited stiffness of the coupled volumes of material. As a rule, three types of specimens are used for thermal fatigue
tests Coffin (1954), Dulnev (1980) (see Fig. 2).
An important parameter of the experiment is also the moment of fixation of the sample. Depending on the
specimen fixation temperature, different coefficients of asymmetry of the cycle R can be realized. So, when the
sample is fixed at the minimum value of the temperature, we have a zero-to-compression stress cycle with R = -∞,
when the sample is fixed at the maximum value of the temperature, we have the zero-to-tension stress cycle with R
= 0. In this work the third specimen was observed (Fig 2с).
Fig.1. Schematic diagram of specimens for thermal fatigue test fixing. 1 - experimental specimen; 2 – added rigidity element
Fig.2. Cylindrical specimens for thermal fatigue test.
The second method uses rigidly fixed corset specimens from one polished surface (Fig. 3). For the tests, the
device shown in the Fig. 4 is used. This method is described in detail in Getsov (1976), Rybnikov (2005), Getsov
(2008), Getsov (2010) and Semenov (2014).
Fig.3. (a) Сorset specimen for thermal fatigue test, (b) fixed specimen.
Author name / Structural Integrity Procedia 00 (2017) 000–000
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Fig.4. Device for fixing of the corset specimen: 1 - dies; 2 - fixed specimen; 3 - isolating mica separator; 4 - fluoroplastic sleeves; 5 –tightening
dies bolts; 6 – isolating washers; 7 - bolts for specimen fixing.
Specimens of polycrystalline superalloy ZHS6F were considered. The high cost and complexity of thermal
fatigue tests have led to the need for their numerical modeling. The plastic strain range and one-side accumulated
plastic strain define number of cycles for macrocrack initiation. Thermal fatigue criteria are considered in Coffin
(1954), Getsov (1971), Manson (1973), Ostergren (1976), Halford (1977), Volkov (2008), Getsov (2009) and
Semenov (2014). The finite element (FE) analysis of the stress-strain state of different types of specimens for
thermal testing must be carried out.
2. Finite-element formulation of thermal fatigue tests problem
For cylindrical specimens, a half of the sample was considered in the axisymmetric formulation. The flexible
element was modeled by the addition of a fictitious material of given rigidity. With the aim of leveling the axial
temperature deformations of the fictitious material (this is dictated by the condition of its constant rigidity), the
coefficient of temperature expansion is given anisotropic - equal to zero in the longitudinal direction and equal to the
thermal expansion coefficient of the base specimen material in the radial direction. FE model of the specimen is
shown in Fig. 5a. The temperature distribution along the cylindrical specimen is shown in Fig. 5b. The sample was
fixed at the temperature, defined by equation:
Tfix
Tmax Tmin 02 Tmax
2
02 Tmin
(1)
Fig.5. (a) FE model of cylindrical specimen (1 – specimen; 2 - fictitious material of given rigidity); (b) temperature distribution along the
cylindrical specimen.
For the corset specimens FE modeling of thermal fatigue tests with taking into account of contact between
specimen and its tooling was carried out. The solid model of one fourth of fixed corset specimen is shown in
Fig. 6а. The temperature distribution is shown in Fig. 6b.
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Fig.6. (a) Model of a fixed corset specimen (1 – specimen; 2 - bolts for specimen fixing; 3 – dies; 4 – rib of dies); (b) temperature distribution for
the corset specimen.
3. Result of modeling
For both types of specimen, first ten cycles of heating-cooling were modeled. For the cylindrical specimen fields
of intensity of stress, total and plastic strains, at the maximum temperature of the first cycle are shown in Fig. 7. It
can be seen that the maximum stresses in the working part of the specimen. The field of plastic strain has an
inhomogeneous character (Fig. 7c). This can be explained by the inaccuracy in the experimental determination of
the temperature distribution along the specimen. Thereby, the obtaining the temperature distribution along the
cylindrical specimens by means of of the FE modeling of the electric heating of the specimen and its cooling must
be performed, and this is the goal of further research.
Fig.7. Distributions of von Mises intensity fields in the cylindrical specimen: (a) stress; (b) strain; (c) plastic strain.
The diagrams of axial stress and strain, plastic strain variation over time for the cylindrical specimen are shown in
Fig. 8. It can be seen that after the tenth cycle, the plastic strains achieves to 1.5% (Fig 8c). Stress-strain curves are
shown in Fig. 9. Deformation process passes into the steady state after second cycle.
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Fig.8. Axial stress (a), strain (b) and plastic strain (c) evolution for the cylindrical specimen.
Fig.9. Deformation curves: (a) – axial stress vs. axial strain; (b) – axial stress vs. plastic axial strain for the cylindrical specimen.
The distribution of the von Mises plastic strain intensity along the working part of the cylindrical specimen is
shown in Fig. 10 at the maximum temperature of the tenth cycle. The zone of uniform plastic strain (deviation less
than 5%) is 2 mm, or 6.6% of the sample working part length. Besides, the zone of inhomogeneous plastic strain is
observed in the region of 7 mm. This can be explained by the inhomogeneous of temperature distribution along the
specimen.
Fig.10. Distribution of the von Mises plastic strain intensity along the working part of the cylindrical specimen.
Stress and strain intensity field distributions in the corset specimen at the maximum temperature of the first cycle
are shown in Fig. 11. Fields of von Mises intensity of stress, total and plastic strains in the corset specimen
separately are shown in Fig. 12. Maximum stresses are localized in the working part of the specimen. The field of
plastic strains in the corset specimen is more homogeneous that in cylindrical specimen (compare Fig. 7c and Fig.
12c).
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Fig.11. Stress (a) and strain (b) intensity fields of the corset specimen and their tool set at the maximum temperature of the first cycle.
Fig.12. Distributions of von Mises intensity fields in the corset specimen: (a) stress; (b) strain; (c) plastic strain.
The axial stress, total and plastic strain evolutions for the corset specimen are shown in Fig. 13. It can be seen that
after the tenth cycle, the plastic strain accumulates to 4% and practically ceased to change after fifth cycle (Fig 13c).
Deformation curves are shown in Fig. 14. Deformation process passes into the steady state after fourth cycle.
Fig.13. Axial stress (a), strain (b) and plastic strain (c) evolution over time for the corset specimen.
Fig.14. Deformation curves: (a) – axial stress vs. axial strain; (b) – axial stress vs. plastic axial strain for the corset specimen.
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The distribution of the von Mises plastic strain intensity along the working part of the corset specimen at the
maximum temperature of the tenth cycle is shown in Fig. 15. The zone of uniform plastic strain (deviation less than
5%) is 0.3 mm, or 7.5% of the sample working part length. Plastic strains in the corset specimen are more
homogeneous that in cylindrical specimen (compare Fig. 15 and Fig. 10).
Fig.15. Distribution of the von Mises plastic strain intensity along the working part of the corset specimen.
4. Conclusion
Comparison of the plastic strain inhomogeneity in cylindrical and corset specimens for thermal fatigue tests was
carried out. The results of simulations show that both samples have approximately the same small zone of uniform
plastic strains (6.6% and 7.5% of specimen working zone respectively). The fields of plastic strains for both
specimens have a principle inhomogeneous character. One possible reason is a significant influence of the
inhomogeneous temperature distribution along the specimen. Thefore the computation of local maximal plastic
strain requires exact evaluation of thermal and stress-strain state that leads to the necessary of finite-element
simulation.
Acknowledgements
Work was made with finance support of RFFI (project №15-08-08779 A). Studies of the first three authors are also
supported by the SIEMENS Scholarship Program
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