Abstract

Twin-wall structures can be cooled both externally and internally, raising great potential for use in high-temperature applications. However, their increased geometric complexity imposes a range of potential failure mechanisms for consideration in design. The primary aim of this study is to identify the nature of such mechanisms by constructing Bree type interaction diagrams for idealized double-wall systems under cyclic thermomechanical loading that shows the combination of loading conditions for which cyclic plasticity (leading to fatigue failure)-creep ratchetting occur. Through an extension of the classical Bree analysis, we determine analytical boundaries between different regimes of behavior. We also quantify the effects of wall thickness ratio, temperature field, and yield and creep material properties. Local cyclic plasticity is shown to dominate over structural/global ratchetting when the yield strength reduces with temperature and/or when the temperature gradient through the hot wall thickness dominates over the temperature difference between the walls. Thus, we conclude that global ratchetting is unlikely to occur in the practical loading range of Nickel-based twin-wall turbine blades, but instead these systems suffer from local fatigue at cooling holes and excessive creep deformation. This is verified by 3D cyclic finite element (FE) simulations, demonstrating that the analytical approach provides a powerful, cost-effective strategy for providing physical insight into possible deformation mechanisms in a range of thin-walled components; highlighting the key trade-offs to be considered in design; and directing the use of computer methods toward more detailed calculations.

References

1.
Murray
,
A. V.
,
Ireland
,
P. T.
, and
Rawlinson
,
A. J.
,
2017
, “
An Integrated Conjugate Computational Approach for Evaluating the Aerothermal and Thermomechanical Performance of Double-Wall Effusion Cooled Systems
,”
ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition
,
American Society of Mechanical Engineers Digital Collection
, Paper No. GT2017-64711, p. V05BT22A015; 1–12.
2.
Skamniotis
,
C. G.
, and
Cocks
,
A. C.
,
2021
, “
Creep-Plasticity-Fatigue Calculations in the Design of Porous Double Layers for New Transpiration Cooling Systems
,”
Int. J. Fatigue
,
151
, p.
106304
.
3.
Skamniotis
,
C.
,
Courtis
,
M.
, and
Cocks
,
A. C.
,
2021
, “
Multiscale Analysis of Thermomechanical Stresses in Double Wall Transpiration Cooling Systems for Gas Turbine Blades
,”
Int. J. Mech. Sci.
,
207
, p.
106657
.
4.
Reed
,
R. C.
,
2008
,
The Superalloys: Fundamentals and Applications
,
Cambridge University Press
,
Cambridge, UK
.
5.
Murray
,
A. V.
,
Ireland
,
P. T.
,
Wong
,
T. H.
,
Tang
,
S. W.
, and
Rawlinson
,
A. J.
,
2018
, “
High Resolution Experimental and Computational Methods for Modelling Multiple Row Effusion Cooling Performance
,”
Int. J. Turbomach. Propuls. Power
,
3
(
1
), p.
4
.
6.
Murray
,
A. V.
,
Ireland
,
P. T.
, and
Romero
,
E.
,
2019
, “
Development of a Steady-State Experimental Facility for the Analysis of Double-Wall Effusion Cooling Geometries
,”
ASME J. Turbomach.
,
141
(
4
), p.
041008
.
7.
Murray
,
A. V.
,
Ireland
,
P. T.
, and
Romero
,
E.
,
2020
, “
Experimental and Computational Methods for the Evaluation of Double-Wall, Effusion Cooling Systems
,”
ASME J. Turbomach.
,
142
(
11
), p.
111003
.
8.
Courtis
,
M.
,
Murray
,
A.
,
Coulton
,
B.
,
Ireland
,
P.
, and
Mayo
,
I.
,
2021
, “
Influence of Spanwise and Streamwise Film Hole Spacing on Adiabatic Film Effectiveness for Effusion-Cooled Gas Turbine Blades
,”
Int. J. Turbomach. Propuls. Power
,
6
(
3
), p.
37
.
9.
Ngetich
,
G. C.
,
Murray
,
A. V.
,
Ireland
,
P. T.
, and
Romero
,
E.
,
2019
, “
A Three-Dimensional Conjugate Approach for Analyzing a Double-Walled Effusion-Cooled Turbine Blade
,”
ASME J. Turbomach.
,
141
(
1
), p.
011002
.
10.
Elmukashfi
,
E.
,
Murray
,
A. V.
,
Ireland
,
P. T.
, and
Cocks
,
A C. F.
,
2020
, “
Analysis of the Thermomechanical Stresses in Double-Wall Effusion Cooled Systems
,”
ASME J. Turbomach.
,
142
(
5
), p.
051002
.
11.
Cerminara
,
A.
,
Deiterding
,
R.
, and
Sandham
,
N. D.
,
2019
, “Transpiration Cooling Using Porous Material for Hypersonic Applications,”
Convective Heat Transfer in Porous Media
,
Y.
Mahmoudi
,
K.
Hooman
, and
K.
Vafai
, eds.,
CRC Press
,
Boca Raton, FL
, pp.
263
286
.
12.
Skamniotis
,
C. G.
, and
Cocks
,
A. C.
,
2021
, “
2D and 3D Thermoelastic Phenomena in Double Wall Transpiration Cooling Systems for gas Turbine Blades and Hypersonic Flight
,”
Aerosp. Sci. Technol.
,
113
, p.
106610
.
13.
Skamniotis
,
C. G.
, and
Cocks
,
A. C.
,
2021
, “
Designing Against Severe Stresses at Compound Cooling Holes of Double Wall Transpiration Cooled Engine Components
,”
Aerosp. Sci. Technol.
,
116
, p.
106856
.
14.
Skamniotis
,
C.
, and
Cocks
,
A. C.
,
2020
, “
Minimising Stresses in Double Wall Transpiration Cooled Components for High Temperature Applications
,”
Int. J. Mech. Sci.
,
189
, p.
105983
.
15.
Skamniotis
,
C.
, and
Cocks
,
A. C.
,
2022
, “
Thermal and Centrifugal Stresses in Curved Double Wall Transpiration Cooled Components with Temperature Dependent Thermoelastic Properties
,”
Int. J. Solids Struct.
,
234–235
, p.
111273
.
16.
Skamniotis
,
C.
, and
Cocks
,
A. C.
,
2022
, “
Analytical Shakedown, Ratchetting and Creep Solutions for Idealized Twin-Wall Blade Components Subjected to Cyclic Thermal and Centrifugal Loading
,”
Eur. J. Mech. A. Solids
,
95
, p.
104652
.
17.
Bree
,
J.
,
1967
, “
Elastic-plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent High-Heat Fluxes with Application to Fast-Nuclear-Reactor Fuel Elements
,”
J. Strain Anal.
,
2
(
3
), pp.
226
238
.
18.
Ponter
,
A.
, and
Cocks
,
A.
,
2013
, “
Thermal Ratchetting of Polycrystalline Metals with Inhomogeneous Thermal Properties
,”
Philos. Mag.
,
93
(
22
), pp.
2947
2966
.
19.
Chaboche
,
J.-L.
,
1986
, “
Time-Independent Constitutive Theories for Cyclic Plasticity
,”
Int. J. Plast.
,
2
(
2
), pp.
149
188
.
20.
Wan
,
V. V. C.
,
Jiang
,
J.
,
MacLachlan
,
D. W.
, and
Dunne
,
F. P. E.
,
2016
, “
Microstructure-sensitive Fatigue Crack Nucleation in a Polycrystalline Ni Superalloy
,”
Int. J. Fatigue
,
90
, pp.
181
190
.
21.
Jiang
,
J.
,
Yang
,
J.
,
Zhang
,
T.
,
Dunne
,
F. P. E.
, and
Britton
,
T. B.
,
2015
, “
On the Mechanistic Basis of Fatigue Crack Nucleation in Ni Superalloy Containing Inclusions Using High Resolution Electron Backscatter Diffraction
,”
Acta Mater.
,
97
, pp.
367
379
.
22.
Zhang
,
B.
,
Wang
,
R.
,
Hu
,
D.
,
Jiang
,
K.
,
Hao
,
X.
,
Mao
,
J.
, and
Jing
,
F.
,
2020
, “
Constitutive Modelling of Ratcheting Behaviour for Nickel-Based Single Crystal Superalloy Under Thermomechanical Fatigue Loading Considering Microstructure Evolution
,”
Int. J. Fatigue
,
139
, p.
105786
.
23.
Zhang
,
B.
,
Wang
,
R.
,
Hu
,
D.
,
Jiang
,
K.
,
Mao
,
J.
,
Jing
,
F.
, and
Hao
,
X.
,
2021
, “
Stress-controlled LCF Experiments and Ratcheting Behaviour Simulation of a Nickel-Based Single Crystal Superalloy with [001] Orientation
,”
Chin. J. Aeronaut.
,
34
(
8
), pp.
112
121
.
24.
Ma
,
Z.
,
Wang
,
X.
,
Chen
,
H.
,
Xuan
,
F.-Z.
, and
Liu
,
Y.
,
2021
, “
A Unified Direct Method for Ratchet and Fatigue Analysis of Structures Subjected to Arbitrary Cyclic Thermal-Mechanical Load Histories
,”
Int. J. Mech. Sci.
,
194
, p.
106190
.
25.
Lytwyn
,
M.
,
Chen
,
H.
, and
Ponter
,
A.
,
2015
, “
A Generalised Method for Ratchet Analysis of Structures Undergoing Arbitrary Thermo-Mechanical Load Histories
,”
Int. J. Numer. Methods Eng.
,
104
(
2
), pp.
104
124
.
26.
Dye
,
D.
,
Conlon
,
K. T.
,
Lee
,
P. D.
,
Rogge
,
R. B.
, and
Reed
,
R. C.
,
2004
, “
Welding of Single Crystal Superalloy CMSX-4: Experiments and Modeling
,”
Superalloys 2004 (Tenth International Symposium).
27.
Koiter
,
W. T.
,
1960
, “General Theorems for Elastic Plastic Solids,”
Progress of Solid Mechanics
,
North Holland Press
,
Amsterdam
, pp.
167
221
.
28.
Ponter
,
A.
, and
Karadeniz
,
S.
,
1985
, “
An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 1: Theory
,”
ASME J. Appl. Mech.
,
52
(
4
), pp.
877
882
.
29.
Ponter
,
A.
, and
Karadeniz
,
S.
,
1985
, “
An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 2: Applications
,”
ASME J. Appl. Mech.
,
52
(
4
), pp.
883
889
.
30.
Bradford
,
R. A. W.
,
2012
, “
The Bree Problem with Primary Load Cycling in-Phase with the Secondary Load
,”
Int. J. Press. Vessels Pip.
,
99–100
, pp.
44
50
.
31.
Bradford
,
R. A. W.
,
2017
, “
The Bree Problem With the Primary Load Cycling Out-of-Phase With the Secondary Load
,”
International Journal of Pressure Vessels and Piping
,
154
, pp.
83
94
.
32.
Chen
,
H.
, and
Ponter
,
A. R.
,
2006
, “
Linear Matching Method on the Evaluation of Plastic and Creep Behaviours for Bodies Subjected to Cyclic Thermal and Mechanical Loading
,”
Int. J. Numer. Methods Eng.
,
68
(
1
), pp.
13
32
.
33.
Zheng
,
X. T.
, and
Xuan
,
F. Z.
,
2012
, “
Shakedown of Thick Cylinders With Radial Openings Under Thermomechanical Loadings
,”
ASME J. Pressure Vessel Technol.
,
134
(
1
), p.
011205
.
34.
Reed
,
R. C.
,
Tao
,
T.
, and
Warnken
,
N.
,
2009
, “
Alloys-by-Design: Application to Nickel-Based Single Crystal Superalloys
,”
Acta Mater.
,
57
(
19
), pp.
5898
5913
.
35.
Hou
,
N. X.
,
Gou
,
W. X.
,
Wen
,
Z. X.
, and
Yue
,
Z. F.
,
2008
, “
The Influence of Crystal Orientations on Fatigue Life of Single Crystal Cooled Turbine Blade
,”
Mater. Sci. Eng. A
,
492
(
1–2
), pp.
413
418
.
36.
Gao
,
H.-F.
,
Zio
,
E.
,
Wang
,
A.
,
Bai
,
G.-C.
, and
Fei
,
C.-W.
,
2020
, “
Probabilistic-Based Combined High and Low Cycle Fatigue Assessment for Turbine Blades Using a Substructure-Based Kriging Surrogate Model
,”
Aerosp. Sci. Technol.
,
104
, p.
105957
.
37.
Chen
,
H.
, and
Ponter
,
A. R.
,
2004
, “
A Simplified Creep-Reverse Plasticity Solution Method for Bodies Subjected to Cyclic Loading
,”
Eur. J. Mech. A. Solids
,
23
(
4
), pp.
561
577
.
38.
Spiliopoulos
,
K.
, and
Panagiotou
,
K.
,
2014
, “
A Residual Stress Decomposition Based Method for the Shakedown Analysis of Structures
,”
Comput. Methods Appl. Mech. Eng.
,
276
, pp.
410
430
.
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