Overview of High Temperature and Thermo-mechanical Fatigue (TMF)
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1 Overview of High Temperature and Thermo-mechanical Fatigue (TMF) Mechanical and Industrial Engineering, University of Illinois, Urbana, Il Tel : Fax: huseyin@uiuc.edu 1 Page 1
2 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 Page 2
3 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 Page 3
4 Railroad Wheels under Friction Braking 65 min, 462 C min, 162 C 100 min, 200 C 95 min, 223 C 90 min, min, 279 C 80 min, 314 C 75 min, 354 C 70 min, 401 C 120 min, 133 C min, 78 C 125 min, 24 C 100-3x x x10-3 Mechanical Strain -100 Stress (MPa) 55 min, 603 C 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 10 min, 295 C 25 min, 459 C 20 min, 438 C 15 min, 362 C Page 4
5 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) Stress Laboratory Simulation of Stress at B1 Location in Railroad Wheel Time (minutes) 5 Page 5
6 Brake Rotor Cracking cycle 1 cycle 20 cycle 36 cold stress (MPa) 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 mechanical strain (%) 6 Page 6
7 Design-Manufacturing-Life Prediction Methodology for Cylinder Heads and Blocks 7 Page 7
8 Percentage of Vehicles with Aluminum Engine Blocks and Heads(*) Heads Passenger cars 78% 85% 95% Light trucks 20% 40% 60% Blocks Passenger cars 13% 30% 50% Light trucks 5% 10% 20% (*) Delphi VIII Study, Page 8
9 Cylinder Heads (FEM and Fatigue Life Contours) Spark Plug Inlet Valve Exhaust Valve 9 Page 9
10 Turbine Blades TF 10 Page 10
11 Turbine Blades( Thermo-mechanical fatigue failure) 11 Page 11
12 Turbine Blades (straintemperature variation) 12 Page 12
13 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 13 Page 13
14 Isothermal vs. Thermo-mechanical fatigue High temperature fatigue testing or modeling Isothermal fatigue Non-isothermal fatigue HCF De in» 0 LCF De in > 0 TF internal stresses TMF external stresses 14 Page 14
15 Disk Specimen under TF loading (Simovich) 15 Page 15
16 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. 16 Page 16
17 Experimental Techniques at High Temperatures Test Frame High Temperature Extensometer LOAD CELL RF Induction Coil Induction Heater C/L ACTUATOR THERMOCOUPLE C/L Control Tower Strain, load,position control GPIB LABWIEV Temperature Controller MACINTOSH IICi Loading History 17 Page 17
18 Total Constraint T E σ ο ε net = 0 C Stress T O Mechanical Strain T o t D B A σ ο α (T-To) 18 Page 18
19 Total Constraint (ctd.) The compatibility equation e net = e th +e mech = a (T-T o ) + e mech When the net strain is zero and all of the thermal strain is converted to mechanical strain. Then, e mech = - a (T-T o ) 19 Page 19
20 Two-Bar Model(ctd.) DT A, l 1 1 A, l 2 2 Department of Mechanical P and Industrial Engineering 20 Page 20
21 Simple Relations Equilibrium : A 1 s 1 + A 2 s 2 = P Compatability : l 1 e 1 = l 2 e 2 Strain : e 1 = e 1 e + e 1 in + e 1 th e2 = e2 e e 1 th = a ( T- T 0 ) e 1 in = inelastic (plastic) strain e 1 e = elastic strain 21 Page 21
22 The Concepts of Total, Partial, Over and Notch Constraint DT A, l 1 1 A, l σ 1 ε1= E2 C, C = A 2.l1 A1.l2 C ; Total Constraint C finite ; Partial Constraint P 22 Page 22
23 The Stress-strain Response under Total and Partial Constraint 23 Page 23
24 The Stress-strain Response under Total and Partial Constraint (ctd.) 24 Page 24
25 Stress-strain Behavior under Out-of-Phase versus In-Phase Stress T min Stress Tmax Mechanical Strain Mechanical Strain T max T min Out-of-Phase TMF Response In-Phase TMF Response 25 Page 25
26 Some Definitions Stress T min σ max C Inelastic St rain range: σ T max B A Mechanical Strain ε in ε m - σ B E B + σ C E C σ min ε m 26 Page 26
27 Comparison of TMF IP and TMF OP Tests on 1010 Steel (Jaske s Data) 27 Page 27
28 TMF experiments of Coffin 28 Page 28
29 Thermal Block Histories on Steels under Total Constraint 29 Page 29
30 Classification of IF and TMF Studies Metallurgical Studies : (a) Damage Mechanisms (Crack nucleation from slip bands, precipitates, porosities, surface and internal oxidation, grain boundary cavitation) (b) Alloy Development Mechanistic Studies : (a) Constitutive Modeling ( phenomenological:non-unified and unified models for stress-strain prediction) (b) Life Prediction Modeling (Crack nucleation (stress, strain, time), Crack Growth (Mean stress, crack length) 30 Page 30
31 Classification of IF and TMF Studies (ctd.) Engineering Application : (a) Material Selection (b) Early Design (c) Residual Life Assesment 31 Page 31
32 Constitutive Modeling- Experimentally Determined Flow Rule Al319- Solutionized Small SDAS Plasticity n 2 =7.96 ε in /A Power Law Creep n 1 = σ/κ ο 32 Page 32
33 TMF OP C 1.0% C 100 Stress (MPa) C C STRESS1-2fea Stress1-2 STRESS300fea Stress300-6x Strain 33 Page 33
34 Hysteresis loops for the tests performed at 5x10-3 s -1 Stress (MPa) o C 130 o C 250 o C 300 o C experimental TNET x Strain 34 Page 34
35 Drag stress recovery Hyteresis loops at 20 C for the material pre-exposed at 300 C h 1 h 10 h 100 h Stress (MPa) Department Strain of (%) Mechanical and Industrial Engineering 35 Page 35
36 Coarsening of the Precipitates 36 Page 36
37 TMF OP Stress-Strain Prediction TMF OP DT= C, De=0.6%, 5x10-5 s -1 Al 319-T7B Small SDAS Cycle 1 Stress (MPa) Cycle Experiment Simulation Mechanical strain, (%) 37 Page 37
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 38 Page 38
39 Mechanistic Studies 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. 39 Page 39
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. 40 Page 40
41 Coffin s Approach 41 Page 41
42 Coffin s Approach (Frequency Modified Life) 42 Page 42
43 Coffin s Approach Advantages: (1) (1) Simple to to use; use; accounts for for frequency effects effects Disadvantages; (1) (1) Not Not sensitive to to location of of hold hold time time within within the the cycle cycle (tension or or compression). (2) (2) Does Does not not account for for creep creep damage effects effects (3) (3) TMF TMF life life prediction not not explicitly handled. (4) (4) No No stress-strain model model 43 Page 43
44 Strain Range Partitioning Method(SRP) ε pp ε pc ε cp ε cp ε pc ε cc 44 Page 44
45 SRP Data on Two Class of Steels (Manson et al.) 45 Page 45
46 SRP Approach Advantages: (1) (1) Accounts for for location of of hold hold time time within within a cycle cycle Disadvantages; (1) (1) Life Life curves curves are are often often too too close, close, expensive to to generate all all these these curves curves (2) (2) Does Does not not account for for oxidation/environment effects effects (3) (3) TMF TMF Life Life prediction not not explicitly handled. 46 Page 46
47 Development of of a Mechanism Based Failure Model (Sehitoglu et 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. 47 Page 47
48 Neu, Sehitoglu, Boismier, Kadioglu, N f ox = Fatigue - Oxidation Models (ctd.) h cr δ o BΦ ox K peff - 1 ox β 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. 48 Page 48
49 10-1 Combined Damage Model Predictions WAP319-T7B Small SDAS All Fatigue Results Mechanical Strain Range ?C Dox=0 300?C Dox RT 40Hz 250?C 0.5Hz 250?C 5 x10-5 s ?C 5 x10-5 s -1 TMF OP ?C TMF IP ?C Department of Nf Mechanical and Industrial Engineering 49 Page 49
50 Combined Damage Model Predictions (1070 Steel) 50 Page 50
51 Combined Damage Model Predictions (1070 Steel) 51 Page 51
52 Combined Damage Model Advantages: (1) (1) Accounts for for TMF TMF loading. (2) (2) Damage due due to to oxidation and and creep creep are are included. Disadvantages: (1) (1) Requires some some time time to to understand how how it it all all works. works. 52 Page 52
53 Fatigue Damage Equation Modified Strain-Life Relation ε mech 2 2 b 1 = C ' 2b a 0 (2N fat f ) 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 53 Page 53
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 H R σ H σ a 0 - empirical constants - activation energy - universal gas constant - hydrostatic stress - effective stress - initial pore size 54 Page 54
55 TMF IP versus TMF OP Comparison- Al a 0 = 70 µm TMF-IP TMF-OP WAP EAP Prediction µm N f 55 Page 55
56 Initial Voids and after TMF IP 56 Page 56
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. 57 Page 57
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. 58 Page 58
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