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Vol. 9. Issue 1.
Pages 875-881 (January - February 2020)
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Vol. 9. Issue 1.
Pages 875-881 (January - February 2020)
Original Article
DOI: 10.1016/j.jmrt.2019.11.027
Open Access
Performance optimization for a hole in an oxide forming alloy foil under considering frequency effect of vibration
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Mei-Ling Zhanga, Feng-Xun Lib, Zhen-Zhe Lic,
Corresponding author
a13868659593@163.com

Corresponding author.
a School of Pharmacy, Wenzhou Medical University, Zhejiang, 325035, P.R. China
b Ulsan Ship and Ocean College, Ludong University, Shandong, 264025, P.R. China
c College of Mechanical and Electrical Engineering, Wenzhou University, Zhejiang, 325035, P.R. China
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Abstract
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Figures (5)
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Tables (5)
Table 1. Experimental data.
Table 2. Case study of thermal cycling.
Table 3. Case study of thermo-mechanical cycling with different loading.
Table 4. Results under the condition of vibration having 10000cycles/min.
Table 5. Results under the condition of vibration having 5000cycles/min.
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Abstract

Some of the gas turbine components are exposed to high temperature corrosion. Therefore, the life cycle of gas turbine is directly affected by the durability of the components. The blades of the gas turbine are protected by film cooling holes under the condition of combining with thermal barrier coating (TBC) system. The TBC systems improve durability of the high temperature components under the condition of increasing the operating temperature. In order to improve the durability of TBC system, simulation and optimization methods were studied in this paper. Firstly, discussed a theoretical model under the thermal and mechanical loading conditions. In the following step, the hole deformations with the various thermo-mechanical conditions induced by high temperature environment and centripetal force due to rotation of the blade were optimized by design of experiments (DOE) method, in order to improve the durability of TBC system. Next, the deformations subjected to thermo-mechanical cycling induced by high temperature environment and vibration due to real operating condition were discussed. The results show that the effect of vibration is not significant compared to the effect of the centripetal force.

Keywords:
Thermally grown oxide
Gas turbine blade
Vibration
Optimization
Nomenclature
D

diameter of the hole

eg

TGO growth ratio

E

young’s modulus

f

objective function

G

shear modulus

h

TGO thickness

p

pressure

R

radius of the hole

T

temperature

T0

peak temperature

U

combined objective function

v

poison’s ratio

Greek symbols
Δα

CTE mismatch between substrate and TGO layer

µg

increment of growth strain of TGO layer

εθθ

strain at the interface between the substrate and TGO

σrr_sub

stress in the substrate along the lateral direction

σYsub

yield strength of substrate

σYtgo

yield strength of TGO

Subscripts
sub

substrate

tgo

TGO

Full Text
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Acknowledgements

The results are based upon the works supported by the Planned Science and Technology Project of Wenzhou City in China under Grant No. G20180004.

Appendix A

The plane stress condition was applied to the theoretical model. Firstly, when the elastic deformations of the substrate and TGO layer occur simultaneously, the stress and strain of the substrate and TGO layer are given as functions of p.

σθθ_tgo=−pRh (1)

σθθ_sub=p (2)

σrr_sub=−p (3)

εθθ_sub=ur_subR=p2Gsub=p1+vsubEsub (4)

εθθ_tgo=ur_tgoR=pREtgoh (5)

where G, E and ν are the shear modulus, Young’s modulus and Poisson’s ratio, respectively.

The sum of the hoop strains in the substrate and TGO layer, εθθ_subθθ_tgo was equal to the strain difference, εT.

εT is Δα ΔT or εg during cooling/reheating or during hold at the peak temperature. Hence the p can be related to εT as follows;

p=εT1+vsubEsub+REtgoh−1 (6)

The yield conditions for the TGO layer and substrate are given by Eqs. (7) and (8), respectively.

σθθ_tgo=σYtgo; (7)

22σrr_sub−σθθ_sub2+σθθ_sub2+σrr_sub212=σYsub; (8)

Here σYtgo and σYsub are the yield strengths of the TGO and substrate, respectively. When the TGO layer is in yield state, it is assumed that p remains constant, and hence, the strains or stresses are kept constant. While the substrate is at yield, and while TGO deform elastically, the region near the hole undergoing plastic deformation, and the radius of the plastic zone RP increase with the pressure. Hence the p and εθθ_sub are governed by Eqs. (9) and (10);

p=131+2InRpRσYsub (9)

εθθ_sub=365−4vRpR2−(1−2v)3+6InRpRεYsub (10)

where εYsub=σYsubEsub. Because the TGO is still deform elastically, the stress and strain in the TGO layer are given by

σθθ_tgo=233Rh1+2InRpRσYsub (11)

εθθ_tgo=233EsubREtgoh12+InRpRεYsub (12)

and Rp can be related to εT as follows;

εTεYsub=364RpR2−312+InRpR+233EsubREtgoh12+InRpR (13)

When the pressure reachesp=−σYtgohR, the TGO layer yields, too, it is assumed that p remains constant. The strains or stresses remains constant.

Under the thermo-mechanical cycling loads, applied an additional tensile stress, during the hold at the peak temperature. With the remotely applied stress,σ∞, the radial and hoop stresses at point A is given by

σrr_sub_m=σ∞20.96−2+GtgoGsubR−hR2+1−GtgoGsub21+GtgoGsubR−hR2+1+2GtgoGsub (14)

σrr_sub_m=σ∞22.88+2+GtgoGsubR−hR2+1−GtgoGsub21−GtgoGsubR−hR2+1+2GtgoGsub (15)

where the subscript m represents the mechanical stress remotely applied. The mechanical stress superimposed to the thermal stress is sufficient to cause creep deformation near the point A. To calculate the creep strain, the sum of the stress by Eq. (15) and that by Eq. (4) or (10) is substituted into the creep material properties of the substrate. That is the creep strain rate was calculated by

ε•ssε•o=σθθ_sub+σθθ_sub_mσon (16)

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Copyright © 2019. The Authors
Journal of Materials Research and Technology

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