Finite Element Analysis of Fretting Fatigue

72 Pages·2017·7.87 MB·English

by  Gaute Sundstrøm Slettestøl

Finite Element Analysis of Fretting
Fatigue
Gaute Sundstrøm Slettestøl
Mechanical Engineering
Submission date: June 2018
Supervisor: Bjørn Haugen, MTP
Norwegian University of Science and Technology
Department of Mechanical and Industrial Engineering

Preface
This master‘s thesis was written at NTNU at the Department of Mechanical and
IndustrialEngineering. Thethesiswaswritteninthespringof2018,withawork-
loadof30credits.
I want to thank my supervisor Bjørn Haugen and co-supervisor Steffen Loen
Sundeforsupportandguidancethroughoutthethesis.
Trondheim11.06.2018
GauteSundstrømSlettestøl
i
ii
Abstract
Inthisthesisitisconductedaliteraturestudywhichlooksintothesubcategoryof
fatigue, fretting fatigue. Based on the literature study, different analyses are per-
formedwithdifferentgeometries,differentcontactformulations,planestrainand
plain stress conditions, and finally post-processing the results by analysing them
andtrytousepfatasaanalysistool.
The first analysis was performed on a Dog-bone geometry, where the goal was to
look for convergence in the results depending on the element size in the mesh.
For this a Python script was made, in order to automate the analyses. After this
was done, new analyses of the same geometry were performed in order to obtain
thestick/slipbehaviourwithitsbelongingstressdistribution.
Afterwordsanewgeometrywereanalysed,thiswasthemainstudyofthethesis.
The Dovetail is a frequently used fixing for turbine blades in the aerospace indus-
try,andhassomechallengesregardingwhatisbelievedtobefrettingfatigue. This
geometry is different from the previous one studied, but the goal was to use the
first study to compare with the results for the Dovetail. It was important to iden-
tifythestick/slipbehaviourhereaswell,andthepreviousworkwasimportantin
order to understand the Dovetail. The results obtained gave more understanding
of the stick/slip behaviour, about where the slip amplitude has peak values and
theinfluenceofthecoefficientoffrictionregardingtheslipamplitude.
iii
Sammendrag
I denne masteroppgaven ble det utført et litteraturstudie som ser på underkat-
egorien av utmatting, fretting utmatting. Basert på litteraturstudiet, ble forskjel-
ligeanalyserutførtmedflereforskjelligegeometrier,kontaktformuleringer,plane
strain og plane stress. Til slutt ble resultatene analysert og det ble gjort forsøk på
åbrukepfatsomanalyseprogram.
Den første analysen ble utført på en Dog-bone geometri, hvor målet var å se etter
konvergens i resultatene, basert på element størrelsen i meshet. Til dette ble et
Python script laget, slik at analysene gikk automatisk. Etter at dette var utført,
ble nye analyser med den samme geometrien utført, dette for å forstå stick/slip
oppførselenmeddetstilhørendespenningsdistribusjon.
Videre ble en ny geometri analysert, Dovetail, dette var hoveddelen av oppgaven.
Dovetailgeometrienerenhyppigbruktinnfestingforturbinbladeriflyfartsindus-
trien,ogharutfordringermeddetsomsannsynligviserfrettingutmatting. Denne
geometrienerforskjelligfradensomtidligereharblittstudert,måletvarÃeˇ bruke
resultatenefraforegåendestudie,medresultateneobservertiDovetailstudiet. Det
var også hær viktig å identifisere stick/slip oppførselen, og det foregående arbei-
det var viktig for å kunne forstå Dovetail geometrien. Resultatene som ble opp-
nådd, gav en bede forståelse av stick/slip oppførselen, om hvor slip amplituden
harhøyeverdieroghvafriksjonharåsiforslipamplituden.
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Table of Contents
Preface i
Abstract iii
Sammendrag iv
TableofContents vi
ListofFigures viii
1 Introduction 1
1.1 ProblemDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Methodology 3
2.1 Literaturestudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 FiniteElementAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Post-processinganddiscussion . . . . . . . . . . . . . . . . . . . . . 4
3 Theory 5
3.1 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.1 Notchfatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Frettingfatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 Mechanicsoffrettingfatigue . . . . . . . . . . . . . . . . . . 7
3.2.1.1 Stick/slipbehaviour . . . . . . . . . . . . . . . . . . 9
3.2.1.2 Friction . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 FiniteElementMethod . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3.1 Contactproblems . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.1.1 Tangentialbehaviour . . . . . . . . . . . . . . . . . 13
v
3.3.1.2 Normalbehaviour . . . . . . . . . . . . . . . . . . . 13
3.4 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Dog-bonestudy 19
4.1 Dog-bonewithfrettingpad . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.1 Materialproperties . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.2 Finiteelementmodel . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.2.1 Modelsetup . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.4.1 Pre-study . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.4.2 Mainstudy . . . . . . . . . . . . . . . . . . . . . . . 28
5 Dovetailstudy 35
5.1 Finiteelementmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1.1 Modelsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3.1 Lagrangemultiplier . . . . . . . . . . . . . . . . . . . . . . . 40
5.3.2 Coefficientoffriction0.3 . . . . . . . . . . . . . . . . . . . . . 42
5.3.3 Coefficientoffriction0.6 . . . . . . . . . . . . . . . . . . . . . 44
5.3.4 Coefficientoffriction0.9 . . . . . . . . . . . . . . . . . . . . . 46
5.3.5 Geometrywithradius . . . . . . . . . . . . . . . . . . . . . . 48
5.3.6 Pfatanalyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 Discussion 51
6.1 Dog-bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Dovetail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.3 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.4 Pfat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7 Conclusion 57
8 Furtherwork 59
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List of Figures
3.1 Fatiguecrackgrowthbehaviour . . . . . . . . . . . . . . . . . . . . . 6
3.2 Illustrationofthestickzone . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Graphoffrettingfatiguelifewithslipamplitude . . . . . . . . . . . 10
3.4 Node-to-surfaceconnection . . . . . . . . . . . . . . . . . . . . . . . 12
3.5 Softcontactformulation . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 Hardcontactformulation . . . . . . . . . . . . . . . . . . . . . . . . 14
3.7 LinearvsNonlinearstiffness . . . . . . . . . . . . . . . . . . . . . . . 15
4.1 IllustrationofDog-bone . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 2Dmodeloftestassembly . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Boundaryconditionsdiagram . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Theoutercontactsurfaces . . . . . . . . . . . . . . . . . . . . . . . . 22
4.5 Contactsurface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.6 Crosssection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.7 MeshoftheDog-boneanddetailtotheright . . . . . . . . . . . . . 23
4.8 VonMisesstress0.1mmelementsize . . . . . . . . . . . . . . . . . . 25
4.9 VonMisesstress0.03mmelementsize . . . . . . . . . . . . . . . . . 26
4.10 VonMisesstress0.015mmelementsize . . . . . . . . . . . . . . . . 26
4.11 Contactslipfor0.1mmelementsize . . . . . . . . . . . . . . . . . . 27
4.12 Contactslipfor0.05mmelementsize . . . . . . . . . . . . . . . . . . 27
4.13 Contactslipfor0.03mmelementsize . . . . . . . . . . . . . . . . . . 28
4.14 Contactslipfor0.015mmelementsize . . . . . . . . . . . . . . . . . 28
4.15 Stick/slipbehaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.16 Stick/slipbehaviourplanestress . . . . . . . . . . . . . . . . . . . . 30
4.17 Stick/slipbehaviourLagrangeMultiplier . . . . . . . . . . . . . . . 30
4.18 Frictionalshearstress . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.19 Frictionalshearstress,planestress . . . . . . . . . . . . . . . . . . . 31
4.20 Frictionalshearstress,LagrangeMultiplier . . . . . . . . . . . . . . 32
4.21 Shearstressandslipalongpath . . . . . . . . . . . . . . . . . . . . . 32
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4.22 VonMisesstress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.23 Stressinthex-directionalongthecontactsurface . . . . . . . . . . . 34
4.24 Contactpressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.1 Illustrationofdovetailassembly . . . . . . . . . . . . . . . . . . . . 36
5.2 Dimensionsofdovetailassembly . . . . . . . . . . . . . . . . . . . . 36
5.3 Radiusofthedovetail . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.4 Boundaryconditionsdovetail . . . . . . . . . . . . . . . . . . . . . . 37
5.5 Illustrationof2Dsymmetrymodel . . . . . . . . . . . . . . . . . . . 37
5.6 Detailofsection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.7 Mesh on dovetail, detailed for mesh around contact surfaces to the
right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.8 IllustrationofthepathinDovetailstudy . . . . . . . . . . . . . . . . 40
5.9 SlipamplitudewithLagrangemultiplier . . . . . . . . . . . . . . . 41
5.10 ShearstresswithLagrangemultiplier . . . . . . . . . . . . . . . . . 41
5.11 Stick/slipbehaviourwith0.3friction . . . . . . . . . . . . . . . . . . 42
5.12 Frictionalshearstress0.3friction . . . . . . . . . . . . . . . . . . . . 43
5.13 Vonmisesstress0.3friction . . . . . . . . . . . . . . . . . . . . . . . 43
5.14 Stressinthex-directionalongthecontactsurface0.3friction . . . . 44
5.15 Stick/slipbehaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.16 Frictionalshearstress . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.17 VonMisesstress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.18 Stressinthex-directionalongthecontactsurface . . . . . . . . . . . 46
5.19 Stick/slip0.9coefficientoffriction . . . . . . . . . . . . . . . . . . . 46
5.20 Frictionalshearstress0.9coefficientoffriction . . . . . . . . . . . . 47
5.21 VonMisesstress0.9coefficientoffriction . . . . . . . . . . . . . . . 47
5.22 Stress in the x-direction along the contact surface, 0.9 coefficient of
friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.23 Shearstressandslipamplitude . . . . . . . . . . . . . . . . . . . . . 48
5.24 VonMisesstressandslipamplitude . . . . . . . . . . . . . . . . . . 49
5.25 Stressinx-directionandslipamplitude . . . . . . . . . . . . . . . . 49
7.1 Possiblecrackinitiation . . . . . . . . . . . . . . . . . . . . . . . . . 58
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