Huseyin Sehitoglu
Department of Mechanical Science and Engineering 1
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Overview of High Temperature and Thermo-mechanical
Fatigue (TMF) Huseyin Sehitoglu Mechanical Science and Engineering, University of Illinois, Urbana, Il. 61801 Tel : 217 333 4112 Fax: 217 244 6534 e-mail: [email protected]
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 2
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Talk Outline
• Examples of High Temperature Problems • Basic Terminology at High Temperatures • Introduction to Constraint : Plasticity and ratchetting,
Out of Phase and In phase TMF • Experimental Techniques at High Temperatures • Fatigue Lives of Selected Materials under IF and TMF • Mechanics- Stress-strain Models • Life Models-Fatigue-Oxidation and Fatigue-Creep
Modeling • Future Directions
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 3
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
• Railroad Wheels undergoing Friction Braking • Brake Rotors • Pistons, Valves and Cylinder Heads of Spark-
ignition and Diesel Engines • Turbine Blades and Turbine Disks • Pressure Vessel and Piping
Examples of Components Experiencing High
Temperatures
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 4
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Mechanical Strain
-2x10 -3 -3 -3-10 10
.
.
.
..
.
.
..
......
.
..
.. ....
.
2x10 -3-3x10 -3
-100
-200
-300St
ress (
MPa
)
100
200
60 min, 615 C°°
°°
°°°
50 min, 589 C
55 min, 603 C45 min, 572 C
40 min, 552 C35 min, 527 C
°° °
°°
°
°°°
°°
30 min, 497 C25 min, 459 C
20 min, 438 C 15 min, 362 C
10 min, 295 C5 min, 210 C
65 min, 462 C
70 min, 401 C75 min, 354 C80 min, 314 C
85 min, 279 C°°
°
°°
°
90 min, 249 C95 min, 223 C
100 min, 200 C110 min, 162 C
120 min, 133 C
122.5 min, 78 C125 min, 24 C
Railroad Wheels under Friction
Braking
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 5
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Schematic of a Railroad Wheel, Strain-Temperature-Stress Changes on the B1 location under brake shoe heating (laboratory simulation based
on strain temperature measurements on wheels)
-400
-200
0
200
400
Stre
ss (M
Pa),
Tem
pera
ture
(°C
)
6005004003002001000
Time (minutes)
Laboratory Simulation of Stress at B1 Location in Railroad Wheel
Stress
Temperature
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 6
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
cold
hot -200
-100
0
100
200
stre
ss (
MP
a)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3mechanical strain (%)
cycle 1 cycle 20 cycle 36
Cast IronOP TMFMinimum Temperature = 150 °CMaximum Temperature = 500 °CCycle Time = 4 mintues∆εm = 0.6%Nf = 37 cycles
Brake Rotor Cracking
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 7
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Cylinder Heads (FEM and Fatigue Life Contours)
Inlet Valve
Exhaust Valve
Spark Plug
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 8
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Turbine Blades
TF
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 9
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Turbine Blades( Thermo-mechanical fatigue failure)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 10
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Turbine Blades (strain-temperature variation)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 11
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Basic Terminology at High Temperatures
• What is a high temperature problem? Deformation under Constant or Variable Stress at homologous temperatures above 0.35 ( T/Tm >0.35 where Tmis melting temperature).
• Stress Relaxation: Decrease in Stress at Constant Strain
• Creep: Increase in Strain at Constant Stress
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 12
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
High temperature fatigue testing or modeling
TMF external stresses
TF internal stresses
HCF ∆ ε in ≈ 0
LCF ∆ ε in > 0
Isothermal fatigue Non-isothermal fatigue
Isothermal vs. Thermo-mechanical fatigue
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 13
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Disk Specimen under TF loading (Simovich)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 14
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Limitations in our Understanding of High
Temperature Material Behavior •Experiments on TMF are missing (difficult, expensive). •Microstructural damage mechanisms are not well understood. •Stress-strain (constitutive) models have not been established •Proposed failure models have severe drawbacks.
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 15
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
ControlTower
LABWIEV
MACINTOSH I ICi
LOAD CELL
Loading History
High TemperatureExtensometer Induction
Coil
TemperatureController
ACTUATOR
GPIB
InductionHeater
RF
C/L
THERMOCOUPLEC/L
Strain, load,position control
Test Frame
Experimental Techniques at High Temperatures
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 16
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Total Constraint
T
Tot BD A
O
C
E
α (T-To)
σο
σο−
Mechanical Strain
Stre
ss
T
ε net = 0
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 17
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
The compatibility equation
εnet = εth +εmech = α (T-To) + εmech
When the net strain is zero and all of the thermal strain is converted to
mechanical strain. Then,
εmech = - α (T-To)
Total Constraint (ctd.)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 18
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Two-Bar Model(ctd.)
A , l 1 1A , l
22
P
∆T
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 19
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Simple Relations
• Equilibrium : A1 σ1 + A2 σ2 = P
• Compatability : l1 ε1 = l2 ε2
• Strain : ε 1 = ε 1 e + ε 1 in + ε 1 th
ε 2 = ε 2 e
ε 1 th = α ( T- T 0 )
ε 1 in = inelastic (plastic) strain
ε 1 e = elastic strain
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 20
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
The Concepts of Total, Partial, Over and Notch Constraint
ε1=-σ1E2C , C = A2.l1
A1.l2C→∞ ; Total Constraint
C→ finite ; Partial Constraint
A , l 1 1A , l
22
P
∆T
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 21
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
The Stress-strain Response under Total and Partial Constraint
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 22
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
The Stress-strain Response under Total and Partial Constraint (ctd.)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 23
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Out-of-Phase TMF Response
Mechanical Strain
Tmax
Stre
ss
Tmin
In-Phase TMF Response
Mechanical Strain
Stre
ss
T
minT
max
Stress-strain Behavior under Out-of-Phase versus In-Phase
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 24
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Mechanical StrainTmax
Stre
ss
Tmin
∆σ
σmin
σmax
∆εm
AB
C
Some Definitions
Inelastic Strain range:
∆εin ≅ ∆εm - σBEB
+ σCEC
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 25
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Comparison of TMF IP and TMF OP Tests on 1010 Steel (Jaske’s Data)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 26
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
TMF experiments of Coffin
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 27
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Thermal Block Histories on Steels under Total Constraint
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 28
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 29
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 30
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 31
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 32
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 33
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
10 15
10 10
10 5
10 0
10 -5
εin/A
0.012 3 4 5 6 7
0.12 3 4 5 6 7
12 3 4 5 6 7
10σ/Κο
Al319- Solutionized Small SDAS
Power Law Creep
Plasticityn2=7.96
n1=3.12
Constitutive Modeling-
Experimentally Determined Flow Rule
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 34
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
TMF OP 100-300°C 1.0%
100°C
300°C
200°C
-200
-100
0
100
200
Stre
ss (M
Pa)
-6x10-3
-4 -2 0 2 4 6Strain
STRESS1-2fea Stress1-2 STRESS300fea Stress300
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 35
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Hysteresis loops for the tests performed at 5x10-3 s-1
-240
-180
-120
-60
0
60
120
180
240
Stre
ss (M
Pa)
-6x10-3
-4 -3 -2 -1 0 1 2 3 4 5 6Strain
experimental TNET
20oC
250oC
130oC
300oC
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 36
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Drag stress recovery Hyteresis loops at 20°C for the material pre-exposed at 300°C
-300
-200
-100
0
100
200
300
Stre
ss (M
Pa)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6Strain (%)
0 h
1 h10 h
100 h
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 37
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Coarsening of the Precipitates
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 38
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
300
200
100
0
-100
-200
Stre
ss (M
Pa)
-0.4 -0.2 0.0 0.2 0.4Mechanical strain, (%)
TMF OP ∆T=100-300°C, ∆ε=0.6%, 5x10-5s-1
Al 319-T7B Small SDAS
Experiment Simulation
Cycle 1
Cycle 350
TMF OP Stress-Strain Prediction
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 39
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Constitutive Modeling:
Mechanistic Studies
Requirements for a good model: • Incorporate strain rate, temperature and mean
stress effect on stress-strain response • Incorporate temperature-strain induced
changes on material’s stress-strain response
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 40
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Constitutive Modeling: • Non-unified Plasticity (stress-strain) Models:
Plastic strains (time-independent) and creep strains are added.
• Unified Creep-Plasticity Models: Plastic strain and creep srain is combined as inelastic strain.
Mechanistic Studies
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 41
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Requirements for a good model: • Incorporate stress,strain, thermal expansion,
mean stress, stress state effect on life • Predict the effect of temperature, strain rate, metallurgical changes on life.
Life Prediction Modeling
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 42
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Coffin’s Approach
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 43
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Coffin’s Approach (Frequency Modified Life)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 44
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Coffin’s Approach
Advantages: (1) Simple to use; accounts for frequency effects Disadvantages; (1) Not sensitive to location of hold time within the cycle (tension or compression). (2) Does not account for creep damage effects (3) TMF life prediction not explicitly handled. (4) No stress-strain model
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 45
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Strain Range Partitioning Method(SRP)
∆ε∆ε
∆ε
∆ε∆ε
∆ε
pp
cp
cppc
pc
cc
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 46
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
SRP Data on Two Class of Steels (Manson et al.)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 47
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
SRP Approach
Advantages: (1) Accounts for location of hold time within a cycle Disadvantages; (1) Life curves are often too close, expensive to generate all these curves (2) Does not account for oxidation/environment effects (3) TMF Life prediction not explicitly handled.
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 48
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
• Damage per cycle is sum of the dominant
mechanisms Dfat, Dox , Dcreep. • The terms in the damage equations should be
physically based, specifically, they should be linked to specific experiments, stress-strain behavior and microstructural observations.
Development of a Mechanism Based Failure Model (Sehitoglu et al.)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 49
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
• Neu, Sehitoglu, Boismier, Kadioglu, 1987-
1Nf
ox = hcr δoBΦox Kpeff
-1β 2 ∆εmech
ox 2β +1
ε (1-a'/β)
This equation accounts for the strain range at the oxide tip hence the oxide-metal properties the shape of the oxide are included. depends on the temperature strain history and the temperature- time variation in the cycle.
Fatigue - Oxidation Models (ctd.)
Φox Kpeff
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 50
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Combined Damage Model Predictions
10-4
10-3
10-2
10-1
Mec
hani
cal S
train
Ran
ge
101
102
103
104
105
106
107
108
Nf
WAP319-T7B Small SDAS All Fatigue Results
RT 40Hz 250 C 0.5Hz 250 C 5 x10
-5s-1
300 C 5 x10-5s-1
TMF OP 100-300 C TMF IP 100-300 C
300 C Dox=0
300 C Dox
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 51
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Combined Damage Model Predictions (1070 Steel)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 52
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Combined Damage Model Predictions (1070 Steel)
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 53
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Combined Damage Model
Advantages: (1) Accounts for TMF loading. (2) Damage due to oxidation and creep are included. Disadvantages: (1) Requires some time to understand how it all works.
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 54
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
• Modified Strain-Life Relation
- initial pore size – fatigue strength coefficient – fatigue strength exponent – fatigue ductility coefficient – fatigue ductility exponent
C'b
ε f'
c
Fatigue Damage Equation
a0
∆εmech
2= C'a0
2−b2b (2N f
fat)−1b +ε f
' (2N ffat)c
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 55
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
- empirical constants - activation energy - universal gas constant - hydrostatic stress - effective stress - initial pore size
Cc,mc
σ
σ H
H∆R
Creep Damage Equation
a0
Dcr = Cc(mc −1)a0mc −1 σ H
σ H
σ n+1 exp −∆HRT
dt
0
tc
∫m c
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 56
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
TMF IP versus TMF OP Comparison- Al 319
2
3
4
5
6
7
89
0.01
2
3
4
5
101
2 3 4 5 6 7 8 9
102
2 3 4 5 6 7 8 9
103
2 3 4 5 6 7 8 9
104
Nf
WAP EAP PredictionTMF-IPTMF-OP a0 = 70 µm
300 µm
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 57
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Initial Voids and after TMF IP
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 58
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
Future Directions
• A simple model is developed to predict life for a given mechanical strain range, maximum temperature, and material. • Given a strain and temperature field in a component, the model can predict the most critical location where crack nucleation will occur.
Huseyin Sehitoglu
Department of Mechanical Science and Engineering 59
University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign
• Given an elastic strain, temperature history from FEM, the model is able to predict the stresses and plastic strains assuming the mechanical strain is equal to the elastic strain from FEM. This is known as the ‘ strain invariance method’.
• To predict component behavior the model
accounts for the initial defect size.
Future Directions (ctd.)