Abstract

The paper focuses on experimental and numerical fatigue assessment procedures to evaluate the influence of multi-axial stress state caused by high centrifugal forces superimposed with bending loads due to blade vibrations on the lifetime of end stage blades from steam turbines. The experimental investigations on original-sized end stage blades were carried out on a test rig specially developed for high forces and multicomponent force application. This was based on detailed numerical simulations by the MPA University of Stuttgart. During the fractographic postexaminations of the tested blades using magnetic particle inspection, light and scanning electron microscopes, two competing damage mechanisms were identified that occurred at different locations. Numerical investigations by means of elastic–plastic finite element analyses were carried out to estimate the local stress conditions acting in the blade root. The local stresses and strains were postprocessed using the critical plane approach and advanced multi-axial fatigue damage parameters. Due to the high stress gradients at the edge of contact, over-conservative predictions may result if their effects are not taken into account. Based on the critical plane method in conjunction with fatigue damage parameters, an approach taking the stress gradient into consideration was developed to predict the fatigue life of the end stage blades. The approach is verified by the component tests on original-sized blades.

References

1.
Klenk, A., Frank, L. A., Sheng, S., Becs, B. J., and Droste-Helling, C.,
2018
, “BMWi-PTJ-Verbundvorhaben COOREFLEX-turbo (Turbomaschinen - Schlüsseltechnologien für flexible Kraftwerke und eine erfolgreiche Ener-giewende, Teilvorhaben 4.1.2), Endstufenschaufeln für hochflexible Fahrweise und hohe Startzahlen,” Fachlicher Abschlussbericht, Laufzeit: July 1, 2013 bis Mar. 31, 2018, Materialprüfungsanstalt Universität Stuttgart, Stuttgart.
2.
EPRI
,
2008
,
Steam Turbine Blade Failure Root Cause Analysis Guide
,
EPRI
,
Palo Alto, CA
, p.
1014137
.
3.
Waterhouse
,
R. B.
,
1981
,
Fretting Fatigue
, 1st ed.,
Applied Science Publishers
,
Barking, London, UK
.
4.
Hoeppner
,
D.
,
1992
, “
Mechanisms of Fretting Fatigue and Their Impact on Test Methods Development
,” Standardization of Fretting Fatigue Test Methods and Equipments, ASTM STP 1159,
American Society for Testing and Materials
,
Philadelphia, PA
, pp.
23
32
.https://www.astm.org/stp25809s.html
5.
Nowell
,
D.
,
Dini
,
D.
, and
Hills
,
D. A.
,
2006
, “
Recent Developments in the Understanding of Fretting Fatigue
,”
Eng. Fract. Mech.
,
73
(
2
), pp.
207
222
.10.1016/j.engfracmech.2005.01.013
6.
Fellows
,
L. J.
,
Nowell
,
D.
, and
Hills
,
D. A.
,
1997
, “
On the Initiation of Fretting Fatigue Cracks
,”
Wear
,
205
(
1–2
), pp.
120
129
.10.1016/S0043-1648(96)07302-4
7.
Wackers
,
P.
,
Arrieta
,
V.
,
Alquezar-Getan
,
M.
,
Constantinescu
,
A.
, and
Maitournam
,
H.
,
2009
, “
A Modeling Approach to Predict Fretting Fatigue on Highly Loaded Blade Roots
,”
ASME
Paper No. GT2009.10.1115/GT2009
8.
Heredia
,
S.
,
Fouvry
,
S.
,
Berthel
,
B.
, and
Greco
,
E.
,
2014
, “
Introduction of a “Principal Stress–Weight Function” Approach to Predict the Crack Nucleation Risk Under Fretting Fatigue Using FEM Modelling
,”
Int. J. Fatigue
,
61
, pp.
191
201
.10.1016/j.ijfatigue.2013.11.009
9.
Fouvry
,
S.
, and
Berthel
,
B.
,
2015
, “
Prediction of Fretting-Fatigue Crack Nucleation Using a Surface Shear - Sliding Size Crack Analog Parameter
,”
Procedia Eng.
,
133
, pp.
179
191
.10.1016/j.proeng.2015.12.649
10.
Shi
,
L.
,
Wei
,
D.-S.
,
Wang
,
Y.-R.
,
Tian
,
A.-M.
, and
Li
,
D.
,
2016
, “
An Investigation of Fretting Fatigue in a Circular Arc Dovetail Assembly
,”
Int. J. Fatigue
,
82
(
Part 2
), pp.
226
237
.10.1016/j.ijfatigue.2015.07.025
11.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press, Cambridge, UK
.
12.
Sinclair
,
G. B.
, “
Edge-of-Contact Stresses in Blade Attachments: An Analytical Approach With Implications for Varying Operating Conditions
,”
ASME
Paper No. GT1997.10.1115/GT1997
13.
Sinclair
,
G. B.
,
2017
, “
Friction Effects on the Edge-of-Contact Stresses for Sliding Contact Between a Flat Punch With Rounded Corners and a Half Space
,”
ASME J. Appl. Mech.
,
84
(
12
), p. 121002.10.1115/1.4037968
14.
Hertz
,
H.
,
1882
, “
Ueber die Berührung fester elastischer Körper
,” Journal für die reine und angewandte Mathematik,
92
, pp.
156
171
.
15.
Sinclair
,
G. B.
,
Cormier
,
N. G.
,
Griffin
,
J. H.
, and
Meda
,
G.
,
2002
, “
Contact Stresses in Dovetail Attachments: Finite Element Modeling
,”
ASME J. Eng. Gas Turbines Power
,
124
(
1
), pp.
182
189
.10.1115/1.1391429
16.
Ruiz
,
C.
,
Boddington
,
P. H. B.
, and
Chen
,
K. C.
,
1984
, “
An Investigation of Fatigue and Fretting in a Dovetail Joint
,”
Exp. Mech.
,
24
(
3
), pp.
208
217
.10.1007/BF02323167
17.
Fatemi
,
A.
, and
Socie
,
D. F.
,
1988
, “
A Critical Plane Approach to Multiaxial Fatigue Damage Including Out‐of‐Phase Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
11
(
3
), pp.
149
165
.10.1111/j.1460-2695.1988.tb01169.x
18.
Smith
,
K. N.
,
Watson
,
P.
, and
Topper
,
T. H.
,
1970
, “
A Stress-Strain Function for the Fatigue of Metals
,”
J. Mater.
, 5, pp.
767
778
.https://www.researchgate.net/publication/309476268_A_stressstrain_function_for_the_fatigue_of_metals_stressstrain_function_for_metal_fatigue_including_mean_stress_effect
19.
Szolwinski
,
M. P.
, and
Farris
,
T. N.
,
1996
, “
Mechanics of Fretting Fatigue Crack Formation
,”
Wear
,
198
(
1–2
), pp.
93
107
.10.1016/0043-1648(96)06937-2
20.
Lykins
,
C. D.
,
Mall
,
S.
, and
Jain
,
V.
,
2000
, “
An Evaluation of Parameters for Predicting Fretting Fatigue Crack Initiation
,”
Int. J. Fatigue
,
22
(
8
), pp.
703
716
.10.1016/S0142-1123(00)00036-0
21.
Fesich
,
T. M.
,
2013
,
Festigkeitsnachweis und Lebensdauerberechnung bei komplex mehrachsiger Schwingbeanspruchung
,
VDI Fortschr.-Ber. Reihe
5, Nr. 748, VDI Verlag, Düsseldorf.
22.
Gupta
,
S.
,
Fesich
,
T. M.
,
Schuler
,
X.
,
Bhasin
,
V.
,
Vaze
,
K. K.
, and
Roos
,
E.
,
2011
, “
A Critical Plane Based Model for Fatigue Assessment Under Fixed and Rotating Principal Direction Loading
,”
Proceedings of the 21st International Conference on Structural Mechanics in Reactor Technology
, New Delhi, India, Nov. 6–11, Paper No. 624.10.13140/RG.2.1.3453.1362
23.
Fouvry
,
S.
,
Kapsa
,
P.
, and
Vincent
,
L.
,
2000
, “
A Multiaxial Fatigue Analysis of Fretting Contact Taking Into Account the Size Effect
,”
Fretting Fatigue: Current Technology and Practices
, ASTM STP 1367,
American Society for Testing
, pp.
167
182
.10.1520/STP14728S
24.
Araujo
,
J. A.
, and
Nowell
,
D.
,
2002
, “
The Effect of Rapidly Varying Contact Stress Fields on Fretting Fatigue
,”
Int. J. Fatigue
,
24
(
7
), pp.
763
775
.10.1016/S0142-1123(01)00191-8
25.
Stieler
,
M.
,
1954
,
Untersuchungen Über Die Dauerschwingfestigkeit Metallischer Bauteile Bei Raumtemperatur
,
Technische Hochschule, Stuttgart
,
Doktorarbeit
.
26.
Neuber
,
H.
,
1958
,
Theory of Notch Stresses
,
Springer
,
Berlin
.
27.
Flavenot
,
J. F.
, and
Skalli
,
N.
,
1989
, “
A Critical Depth Criterion for the Evaluation of Long-Life Fatigue Strength Under Multiaxial Loading and a Stress Gradient
,”
M. W.
,
Brown
and
K. J.
,
Miller
, eds., Biaxial and Multiaxial Fatigue, EGF 3,
Mechanical Engineering Publications
,
London
, UK, pp.
355
–3
65
.10.1016/B978-1-4832-8440-8.50186-1
28.
Naboulsi
,
S.
, and
Mall
,
S.
,
2003
, “
Fretting Fatigue Crack Initiation Behavior Using Process Volume Approach and Finite Element Analysis
,”
Tribol. Int.
,
36
(
2
), pp.
121
131
.10.1016/S0301-679X(02)00139-1
29.
Araújo
,
J. A.
,
Susmel
,
L.
,
Taylor
,
D.
,
Ferro
,
J. C. T.
,
Ferreira
,
J. L. A.
,
2008
, “
On the Prediction of High-Cycle Fretting Fatigue Strength: Theory of Critical Distances vs. hot-Spot Approach
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1763
1778
.10.1016/j.engfracmech.2007.03.026
30.
Taylor
,
D.
,
2008
, “
The Theory of Critical Distances
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1696
1705
.10.1016/j.engfracmech.2007.04.007
31.
Socie
,
D. F.
, and
Marquis
,
G. B.
,
2000
, “
Multiaxial Fatigue
,”
Society of Automotive Engineers
, 1st ed., Society of Automotive Engineer (SAE),
Warrendale, PA
.
32.
Socie
,
D.
,
1987
, “
Multiaxial Fatigue Damage Models
,”
J. Eng. Mater. Technol.
,
109
(
4
), pp.
293
298
.10.1115/1.3225980
33.
Langer
,
B. F.
,
1962
, “
Design of Pressure Vessels for Low-Cycle Fatigue
,”
J. Basic Eng.
,
84
(
3
), pp.
389
399
.10.1115/1.3657332
34.
Forschungskuratorium Maschinenbau
,
2012
, “
Rechnerischer Festigkeitsnachweis Für Maschinenbauteile
,” FKM-Richtlinie, 6, überarbeitete Ausgabe, VDMA-Verlag, Frankfurt.
You do not currently have access to this content.