Overview of High Temperature and Thermo-mechanical Fatigue (TMF) Mechanical Science and Engineering, University of Illinois, Urbana, Il. 61801 Tel : 217 333 4112 Fax: 217 244 6534 e-mail: huseyin@illinois.edu 1
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 2
Examples of Components Experiencing High Temperatures Railroad Wheels undergoing Friction Braking Brake Rotors Pistons, Valves and Cylinder Heads of Sparkignition and Diesel Engines Turbine Blades and Turbine Disks Pressure Vessel and Piping 3
Railroad Wheels under Friction Braking 65 min, 462 C........... 110 100 min, min, 162 200 C C 95 min, 223 C 90 min, 249 C 80 min, 85 314 min, C 279 C 75 min, 354 C 70 min, 401 C 120 min, 133 C 200 122.5 min, 78 C 125 min, 24 C 100-3x10-3 -3-3 -2x10-3 -10 10 2x10-3 M echanical Strain -100 Stress (MPa) 55 min, 603. C......... 45 min, 572 C 35 min, 527 C 60 min, 615 C 50 min, 589 C 40 min, 552 C 5 min, 210 C 30 min, 497 C 25 min, 459 C 10 min, 295 C 20 min, 438 C 15 min, 362 C -200-300 4
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 Temperature Stress (MPa), Temperature ( C) 200 0-200 -400 Stress Laboratory Simulation of Stress at B1 Location in Railroad Wheel 0 100 200 300 400 500 600 Time (minutes) 5
Brake Rotor Cracking 200 100 cycle 1 cycle 20 cycle 36 cold stress (MPa) 0-100 -200 hot Cast Iron OP TMF Minimum Temperature = 150 C Maximum Temperature = 500 C Cycle Time = 4 mintues ε m = 0.6% N f = 37 cycles -0.3-0.2-0.1 0.0 0.1 0.2 0.3 mechanical strain (%) 6
Cylinder Heads (FEM and Fatigue Life Contours) Spark Plug Inlet Valve Exhaust Valve 7
Turbine Blades TF 8
University of Illinois at Urbana-Champaign Turbine Blades( Thermo-mechanical fatigue failure) 9
Turbine Blades (straintemperature variation) 10
Basic Terminology at High Temperatures What is a high temperature problem? Deformation under Constant or Variable Stress at homologous temperatures above 0.35 ( T/T m >0.35 where T m is melting temperature). Stress Relaxation: Decrease in Stress at Constant Strain Creep: Increase in Strain at Constant Stress 11
Isothermal vs. Thermo-mechanical fatigue High temperature fatigue testing or modeling Isothermal fatigue Non-isothermal fatigue HCF ε in 0 LCF ε in > 0 TF internal stresses TMF external stresses 12
Disk Specimen under TF loading (Simovich) 13
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. 14
Experimental Techniques at High Temperatures Test Frame High Temper atur e Ex tensometer LOAD CELL RF Induction Coil Induction H eater C/L A CTUA TOR TH ERMOCOU PLE C/L Control Tow er Strain, load,position control GPIB LA BWIEV Temper atur e Controller MACINTOSH IICi Loading History 15
Total Constraint T E σ ο ε net = 0 C Stress T O M echanical Strain T o t D B A σ ο α (T-To) 16
Total Constraint (ctd.) The compatibility equation ε net = ε th +ε mech = α (T-T o ) + ε mech When the net strain is zero and all of the thermal strain is converted to mechanical strain. Then, ε mech = - α (T-T o ) 17
Two-Bar Model(ctd.) T A, l 1 1 A, l 2 2 Department of Mechanical P Science and Engineering 18
Simple Relations Equilibrium : A 1 σ 1 + A 2 σ 2 = P Compatability : l 1 ε 1 = l 2 ε 2 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 19
The Concepts of Total, Partial, Over and Notch Constraint T A, l 1 1 A, l 2 2 - σ 1 E ε 1 = 2 C, C = A 2.l 1 A 1.l 2 C ; Total Constraint C finite ; Partial Constraint P 20
The Stress-strain Response under Total and Partial Constraint 21
The Stress-strain Response under Total and Partial Constraint (ctd.) 22
Stress-strain Behavior under Out-of-Phase versus In-Phase Stress T min Stress T max Mechanical Strain Mechanical Strain T max T min Out-of-Phase TMF Response In-Phase TMF Response 23
Some Definitions Stress T min σ max C Inelastic Strain range: σ T max B A Mechanical Strain ε in ε m - σ B E B + σ C E C σ min ε m 24
Comparison of TMF IP and TMF OP Tests on 1010 Steel (Jaske s Data) 25
TMF experiments of Coffin 26
Thermal Block Histories on Steels under Total Constraint 27
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Constitutive Modeling- Experimentally Determined Flow Rule 10 15 Al319- Solutionized Small SDAS 10 10 Plasticity n 2 =7.96 ε in /A 10 5 10 0 Power Law Creep n 1 =3.12 10-5 0.01 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 0.1 1 10 σ/κ ο 33
TMF OP 100-300 C 1.0% 200 100 C 100 Stress (MPa) 0 200 C -100-200 300 C STRESS1-2fea Stress1-2 STRESS300fea Stress300-6x10-3 -4-2 0 2 4 6 Strain 34
Hysteresis loops for the tests performed at 5x10-3 s -1 Stress (MPa) 240 180 120 60 0-60 20 o C 130 o C 250 o C 300 o C -120-180 experimental TNET -240-6x10-3 -4-3 -2-1 0 1 2 3 4 5 6 Strain 35
Drag stress recovery Hyteresis loops at 20 C for the material pre-exposed at 300 C 300 200 100 0 h 1 h 10 h 100 h Stress (MPa) -100 0-200 -300-0.6-0.4-0.2 0.0 0.2 0.4 0.6 Department Strain of (%) Mechanical Science and Engineering 36
Coarsening of the Precipitates 37
TMF OP Stress-Strain Prediction 300 TMF OP T=100-300 C, ε=0.6%, 5x10-5 s -1 Al 319-T7B Small SDAS 200 Cycle 1 Stress (MPa) 100 0 Cycle 350-100 -200 Experiment Simulation -0.4-0.2 0.0 0.2 0.4 Mechanical strain, (%) 38
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 39
Constitutive Modeling: Mechanistic Studies 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. 40
Life Prediction Modeling 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. 41
Coffin s Approach 42
Coffin s Approach (Frequency Modified Life) 43
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 44
Strain Range Partitioning Method(SRP) ε pp ε pc ε cp ε cp ε pc ε cc 45
SRP Data on Two Class of Steels (Manson et al.) 46
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. 47
Development of a Mechanism Based Failure Model (Sehitoglu et al.) Damage per cycle is sum of the dominant mechanisms D fat, D ox, D creep. The terms in the damage equations should be physically based, specifically, they should be linked to specific experiments, stress-strain behavior and microstructural observations. 48
Fatigue - Oxidation Models (ctd.) Neu, Sehitoglu, Boismier, Kadioglu, 1987-1 N f ox = h cr δ o BΦ ox K peff - β 1 ox 2 ε mech ε (1-a' /β) 2 β +1 This equation accounts for the strain range at the oxide tip hence the oxide-metal properties the shape of the oxide are included. Φ ox K peff depends on the temperature strain history and the temperature- time variation in the cycle. 49
Combined Damage Model Predictions 10-1 WAP319-T7B Small SDAS All Fatigue Results Mechanical Strain Range 10-2 10-3 300 C Dox=0 300 C Dox RT 40Hz 250 C 0.5Hz -5 s -1 250 C 5 x10-5 s -1 300 C 5 x10 TMF OP 100-300 C TMF IP 100-300 C 10-4 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Nf 50
Combined Damage Model Predictions (1070 Steel) 51
Combined Damage Model Predictions (1070 Steel) 52
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. 53
Fatigue Damage Equation Modified Strain-Life Relation ε mech 2 2 b = C ' 2b a 0 (2N fat f ) 1 b ' +ε f (2N f fat ) c ε' f a 0 C ' b c - initial pore size fatigue strength coefficient fatigue strength exponent fatigue ductility coefficient fatigue ductility exponent 54
Creep Damage Equation D cr = C c (m c 1)a 0 m c 1 tc 0 σ H σ H σ n+1 exp H RT dt m c C c,m c R H σ H σ a 0 - empirical constants - activation energy - universal gas constant - hydrostatic stress - effective stress - initial pore size 55
TMF IP versus TMF OP Comparison- Al 319 5 4 3 a 0 = 70 µm TMF-IP TMF-OP WAP EAP Prediction 2 300 µm 0.01 9 8 7 6 5 4 3 2 10 1 10 2 10 3 10 4 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 N f 56
Initial Voids and after TMF IP 57
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. 58
Future Directions (ctd.) 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. 59