Load Determination. Fatigue Life Predictions Infinite Life, Stress Life, Strain Life
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1 Durability Agenda Durability Basics Fatigue, Stress, Strain Load Determination Measurements, Multi-Body Simulation Loads and Damage S-N Curve, Cycle Counting Load Characterization Establishing Durability Targets: Superposition, Extrapolation Fatigue Life Predictions Infinite Life, Stress Life, Strain Life Accelerated Testing & Analysis RP-Filter, Mission Synthesis Page 102
2 SN Curve S-N curve 100 Stress log(cycles to failure) Cycles to Failure from a Constant Amplitude Load test Page 103
3 SN Curve Coupon Testing Machine Metal Coupon Loads Forc e 10 Cyclic Stress Time History Area 5 Metal Coupon stress (σ) Force/Area 0 1 cycle -5 time Forc e -10 Page 104
4 What is an S-N curve? The Jumbo Paper Clips experiment Angle / Load Cycles to failure Page 105
5 SN-Curve Fatigue Strength (Stress) MPa log ,000 1,000,000 10,000, ,000,000 N Number of Cycles to Failure log Page 106
6 SN Curve Fatigue Strength (Stress) MPa log ,000 1,000,000 10,000, ,000,000 N Number of Cycles to Failure log Page 107
7 SN Curve Low Cycle Fatigue High Cycle Fatigue Infinite High Cycle Fatigue Fatigue Strength (Stress) MPa log Elastic Region Elastic Region ,000 1,000,000 10,000, ,000,000 N Number of Cycles to Failure log Residual Stresses, Notch Severity, Manufacturing Page 108
8 SN Curve Low Cycle Fatigue High Cycle Fatigue Infinite High Cycle Fatigue Fatigue Strength (Stress) MPa log Elastic Region ,000 1,000,000 10,000, ,000,000 N Number of Cycles to Failure log Elastic Region Failure (red) Page 109
9 SN Curve Low Cycle Fatigue High Cycle Fatigue Infinite Low Cycle Fatigue Fatigue Strength (Stress) MPa log Plastic Region Plastic Region ,000 1,000,000 10,000, ,000,000 N Number of Cycles log Notch severity, material plasticity Page 110
10 SN Curve Low Cycle Fatigue High Cycle Fatigue Infinite Low Cycle Fatigue Fatigue Strength (Stress) MPa log Plastic Region ,000 1,000,000 10,000, ,000,000 N Number of Cycles log Plastic Region Failure (red) Page 111
11 SN Curve Low Cycle Fatigue High Cycle Fatigue Infinite Infinite Life Fatigue Strength (Stress) MPa log Infinite Life ,000 1,000,000 10,000, ,000,000 N Number of Cycles log Page 112
12 SN Curve Static Stress vs Strain Curve Ultimate Strength SN-Curve Cycle Stress vs Number of Cycles Stress Yield Elas Strength tic regi on 0. 2% Plastic region Failure Fatigue Strength (Stress) MPa Ultimate Strength Plastic Region Yield Strength Elastic Region Infinite Life Strain N Number of Cycles to Failure Page 113
13 SN Curve Static Stress vs Strain Curve Ultimate Strength SN-Curve Cycle Stress vs Number of Cycles Plastic Region Elastic Region Infinite Stress Yield Elas Strength tic regi on 0. 2% Plastic region Failure Fatigue Strength (Stress) MPa Ultimate Strength Yield Strength Enduranc e Limit Strain N Number of Cycles to Failure Page 114
14 SN Curve Fatigue Strength (Stress) MPa log Page 115 N Number of Cycles log Minimum 5 loads x 5 samples
15 What is an S-N curve? Wöhler tests Fatigue failure August Wöhler * Page 116
16 SN Curve SN-Curve Linear vs Log σ linear σ log Number of Cycles linear Number of Cycles log Page 117
17 Regions of the SN Curve Stress Level Low Cycle Fatigue k High Cycle Fatigue b 1 1 Fatigue Limit Endurance Limit Basquin s Law Nσ b = C Number Cycles to failure Fatigue limit, endurance limit: Expressions used to describe a property of materials: the amplitude (or range) of cyclic stress that can be applied to the material without causing fatigue failure. Ferrous alloys and titanium alloys have a distinct limit, an amplitude below which there appears to be no number of cycles that will cause Page 118 failure
18 Uniform Material Law (EN) / Universal Slope Law (SN) For steel, aluminum and titanium alloys, extensive statistical studies have been conducted that show a correlation between the ultimate tensile strength and the fatigue properties The UML estimation of these properties requires input of the elastic modulus (E) and tensile strength (Smax ) of the Page 119
19 Endurance (Fatigue) limit Material Steel (typical * UTS) Iron alloys (0.4 * UTS) Aluminium alloys (0.4 * UTS) Copper (0.4 * UTS) Endurance or Fatigue Limit (maximum) 690 MPa 165 MPa 131 MPa 97 MPa Note : Fatigue ratio = ratio between endurance limit and tensile strength Page 120
20 Load Cycle Terminology 10 5 What is one cycle? stress (σ) 0 time Page 121
21 Load Cycle Terminology 10 5 What is one cycle? stress (σ) 0 time cycle Page 122
22 Load Cycle Terminology 10 5 What is one cycle? stress (σ) 0 time cycle Page 123
23 Load Cycle Terminology cycle What is one cycle? stress (σ) 0 time Page 124
24 Load Cycle Terminology 10 5 σ upper What is amplitude of cycle? stress (σ) 0-5 time σ lower σ a = (σu σ l )/2 Sometimes called alternating stress σ -10 a = (5 - (-5))/2 σ a = (10)/2 σ a = 5 Page 125
25 Load Cycle Terminology 10 5 σ u What is range of cycle? stress (σ) 0 time 10 σ r = σ u - σ l -5 σ l σ r = σ r = Page 126
26 Load Cycle Terminology 10 5 σ u What is average/mean of cycle? stress (σ) 0 time 0-5 σ l σ a = (σ u + σ l )/2-10 σ a = (5-5)/2 σ a = 0 Page 127
27 Load Cycle Terminology 10 σ u 5 Has amplitude of cycle changed? stress (σ) 0 time σ l NO -5 σ a = (σ u σ l )/2 σ a = (10 0)/2 σ a = 5-10 Page 128
28 Load Cycle Terminology 10 5 Has average/mean of cycle changed? stress (σ) 0 time YES -5 Mean = 5-10 σ a = (σ u + σ l )/2 σ a = (10 + 0)/2 σ a = 5 Page 129
29 Load Cycle Terminology 10 5 Has average/mean of cycle changed? stress (σ) 0 time YES -5 Mean = 5 Tension -10 Page 130
30 Load Cycle Terminology 10 5 Has average/mean of cycle changed? stress (σ) 0 time YES -5 Mean = -5 Compression -10 Page 131
31 Famous People In Fatigue Sir Robert Hooke British ( ) Hooke s Law of Elasticity in 1660 Goodman English ( ) Goodman s Rule in 1899 MA Miner English ( ) Miner s Rule in 1945 August Wohler French ( ) Wohler curves in 1867 Richard Von Mise Austrian ( ) Theory of Plasticity 1913 Tatsuo Endo Japan ( ) Rainflow Counting in 1968 Restricted Siemens AG 2013 All rights reserved. Smarter decisions, better products.
32 SN Curve Miner s Rule Time Signal SN-Curve Damage Tally Cycle Count Cycles to Damage stress (σ) time N (# cycles to failure) Key: D tot = Total Damage (when D=1, failure occurs) N = # of Cycles to failure from SN Curve n = # of Cycles in load signal Page 133
33 SN Curve Miner s Rule Time Signal SN-Curve Damage Tally D 1 =n 1 /N 1 =2/6 =.33 stress (σ) time 0 5 N 1 =6 N (# cycles to failure) 10 n 1 = 2 Key: D tot = Total Damage (when D=1, failure occurs) N = # of Cycles to failure from SN Curve n = # of Cycles in load signal Page 134
34 SN Curve Miner s Rule Time Signal SN-Curve Damage Tally D 1 =n 1 /N 1 =2/6 =.33 stress (σ) D time tot = D 1 + D 2 N 2 =4 N 1 =6 D tot = =.83 N (# cycles to failure) D 2 =n 2 /N 2 =2/4 =.5 n 1 = 2 n 2 = 2 Key: D tot = Total Damage (when D=1, failure occurs) N = # of Cycles to failure from SN Curve n = # of Cycles in load signal Page 135
35 SN Curve Miner s Rule Time Signal SN-Curve Damage Tally D 1 =n 1 /N 1 =2/6 =.33 stress (σ) time 0 5 N 2 =4 N 1 =6 N (# cycles to failure) 10 D 2 =n 2 /N 2 =3/4 =.75 D tot = D 1 + D 2 D tot = = 1.08 n 1 = 2 n 2 = 3 Key: D tot = Total Damage (when D=1, failure occurs) N = # of Cycles to failure from SN Curve n = # of Cycles in load signal Page 136
36 How to understand fatigue content of loads? Palmgren (1924)-Miner (1945). Damage accumulation rule Assume that, during the service life, we have 500 loadings of type 1 (defined by mid-value and magnitude), 1000 loadings of type 2 and loadings of type 3, the Palmgren Miner rule states that failure occurs when where n i is the number of applied load cycles of type i, and N i is the pertinent fatigue life Page 137
37 SINE COUNTING DEMO Tec.Ware with sines.ldsf Page 138
38 Double number of cycles Page 139
39 Double number of cycles Page 140
40 Double damage Page 141
41 SINE CHANGE AMPLITUDE DEMO Tec.Ware with sines.ldsf Page 142
42 Double amplitude of cycles Page 143
43 Double Ampitude of cycles Page 144
44 95% difference in damage Page 145
45 Life very sensitive to changes in load Load Number of cycles to failure is a function of Load and k factor log Life=(load) -k k 1 load k=3 k=5 k=7 life life k Load 5 life log Number of Cycles to failure Reducing the cyclic load applied to an optimally shaped steel component with 13% doubles life Page 146
46 Logarithmic nature of fatigue load log log Wöhler-line life=(load) -k k 1 Life (#cycles) load k=3 life k=5 life k=7 life As k increases, small changes in load cause big change in life Page 147
47 SN Curve Adjustments Page 148
48 SN Curve Adjustments: Surface Finish Rougher surface more chance of crack Page 149
49 SN Curve Adjustments: Loading F F F Rotating Beam Fatigue Tester Axial Torsion Bending Page 150
50 SN Curve Adjustments: Loading Fatigue Testing and Analysis Lee, Pan, Hathaway F F F Axial Torsion Bending Page 151
51 SN Curve Adjustments: Size Bigger = BAD (For same stress!) Kuegel 1961 Page 152 Fatigue Testing and Analysis Lee, Pan, Hathaway
52 SN Curve Adjustments: Size Bigger = BAD (For same stress!) Page 153
53 Notch Factors Theoretical Stress Concentration Factor (Function of Geometry) Max Local Stress Nominal Stress Notch Sensitivity Factor q r = root radius ρ = material Property Fatigue Testing and Analysis Lee, Pan, Hathaway Endurance Limit is divided by the fatigue notch factor Fatigue Notch Factor (Function of Geometry and material) S = ' e S K e f Page 154
54 SN Curve Adjustments: Mean Stress load history constant amplitude life curves log σ σ Compression: Increase Life σ m t σ m : mean stress Tension: Decrease Life log N σ m <0 σ m =0 σ m >0 Page 155
55 Page 156
56 General Observations Aircraft engine blade performance critical One blade fails, engine is destroyed (blade failure test to make sure nacelle remains intact is required test) Blades are constantly being re-engineered as new alloys are developed for increasing temperature performance. Higher temperatures make aircraft engines run more efficiently Tests are typically non-contact, emphasis on SN curves, resonant frequency, damping and mode shapes Page 157
57 Aircraft Engine = Blades Blades of differing sizes are used throughout engine to compress air Page 158
58 Blade Engineering Blades must: Compress Air Survive and not fatigue Withstand high temperatures To survive and not break, the following types of tests are done: Sine dwell testing to develop SN curve for blades Resonant frequency tests Ensure blades have different resonant frequencies on given ring Damping of modes also critical Sine and resonance tests are done with controlled temperatures Page 159
59 Typical Lab Blade Lab Tests Performed by Applied Mechanics lab, usually broken into: Static tests Dynamic tests (vibration group) Page 160
60 Common Test Fixtures Test Article/Blade Microphone Hammer Production Impact Test All blades from production tested for resonant frequencies Non contact measurement One FRF produced Pratt+Whitney has 3 impact carts for this Page 161
61 Common Test Fixtures Translational Laser Test Article/Blade Translational Laser Translational Laser Modal Test Detailed analysis Done occasionally Multiple non-contact laser measurements Excitation via Speaker or Impact hammer FRFS, Mode Shapes, Resonant Frequencies and Damping desired output Speaker Page 162
62 Common Test Fixtures Sine Dwell Sine dwell on resonance Develop SN curves for whole, damaged and blended blades Sometimes thermal chamber used Page 163
63 SN Tests During normal usage, blades can be damaged by Foreign Objects which are ingested by engine (stones, etc). This is FOD (Foreign Object Damage). FOD reduces expected life of aircraft blade. Page 164
64 Blending Normal Blade Damaged Blade Maximum life Blended Blade Damage creates Stress concentration, significant degrade to life Page 165 Aircraft maintenance periodically inspects blades. They grind/smooth damage (ie, blend it) to reduce stress concentration.
65 Blending Blending allows aircraft engines to be used longer before complete dis-assembly occurs. Blending can be done with blades in place. Page 166
66 Page 167
67 General Observations Aircraft engine blade performance critical One blade fails, engine is destroyed (blade failure test to make sure nacelle remains intact is required test) Blades are constantly being re-engineered as new alloys are developed for increasing temperature performance. Higher temperatures make aircraft engines run more efficiently Tests are typically non-contact, emphasis on SN curves, resonant frequency, damping and mode shapes Page 168
68 Aircraft Engine = Blades Blades of differing sizes are used throughout engine to compress air Page 169
69 Blade Engineering Blades must: Compress Air Survive and not fatigue Withstand high temperatures To survive and not break, the following types of tests are done: Sine dwell testing to develop SN curve for blades Resonant frequency tests Ensure blades have different resonant frequencies on given ring Damping of modes also critical Sine and resonance tests are done with controlled temperatures Page 170
70 Typical Lab Blade Lab Tests Performed by Applied Mechanics lab, usually broken into: Static tests Dynamic tests (vibration group) Page 171
71 Common Test Fixtures Test Article/Blade Microphone Hammer Production Impact Test All blades from production tested for resonant frequencies Non contact measurement One FRF produced Pratt+Whitney has 3 impact carts for this Page 172
72 Common Test Fixtures Translational Laser Test Article/Blade Translational Laser Translational Laser Modal Test Detailed analysis Done occasionally Multiple non-contact laser measurements Excitation via Speaker or Impact hammer FRFS, Mode Shapes, Resonant Frequencies and Damping desired output Speaker Page 173
73 Common Test Fixtures Sine Dwell Sine dwell on resonance Develop SN curves for whole, damaged and blended blades Sometimes thermal chamber used Page 174
74 SN Tests During normal usage, blades can be damaged by Foreign Objects which are ingested by engine (stones, etc). This is FOD (Foreign Object Damage). FOD reduces expected life of aircraft blade. Page 175
75 Blending Normal Blade Damaged Blade Maximum life Blended Blade Damage creates Stress concentration, significant degrade to life Page 176 Aircraft maintenance periodically inspects blades. They grind/smooth damage (ie, blend it) to reduce stress concentration.
76 Blending Blending allows aircraft engines to be used longer before complete dis-assembly occurs. Blending can be done with blades in place. Page 177
77 Failure Modes Page 178
78 Page 179
79 Page 180
80 Page 181
81 Component SN Curve Page 182
82 NOT EVERYTHING IS A SINE WAVE! Page 183
83 SINE SUM DEMO Tec.Ware with sines.ldsf Page 184
84 Sum in Time Domain Page 185
85 Amplitude quite different due to phasing Page 186
86 Amplitude and number of cycles difference Page 187
87 Large difference in damage Page 188
88 Cycle Counting EASY HARD Page 189
89 How to understand fatigue content of loads? Rainflow counting Potential damage? Rainflow counting Potential damage Page 190
90 Durability load data processing Rainflow counting - methods Rainflow Count Rainflow counting Basic damage event : closed hysteresis loop Rainflow counting = counting of closed hysteresis loops in time signal Load history from load level to load level Damage calculation Closed hysteresis loop Classification into bins Rainflow Matrix: at any from-to cell: entry for the numbers of cycles Damage from to Lines of constant mean and constant amplitude in a rainflow matrix standing hystereses Page 191 hanging hystereses
91 Counting methods in fatigue analysis Rainflow variations Endo 1967 De Jonge 1968 Clormann/Seeger 1986 ASTM point counting Oscillation counting Memory counting First definition Range-pair-range Counting all hysteresis cycles in stress-strain path Standard Most effective and general online method Two-dimensional distribution (dimension independent) Mathematical aspect (hysteresis operator, independent of dimension) Page 192
92 Rainflow Counting Pre-Processing steps Steps Motivation, justification Hysteresis filtering reduces number of samples, endurance limit Peak/valley-filtering reduces number of samples, does not affect hysteresis cycles Discretization necessary for counting Page 193
93 Rainflow Counting Hysteresis filtering gate size Only cycles with range greater than gate size are kept Page 194
94 Rainflow Counting Peak-valley Filtering Keep only sample which are reversals Example of hysteresis and peak/valley filter t Page 195
95 Rainflow Counting Discretization of time signals Physical range is divided into a number of bins. Sampling points are mapped to the centers of their bin (enabling counting procedures) L t Page 196
96 4 Point Cycle Counting Technique 1. Chose four Consecutive stress points S1, S2, S3, S4 2. Define Inner Stress S2 -S3 3. Define Outer Stress S1 -S4 4. If inner stress range <= to outer stress range and the points comprising the inner stress range are bounded by the outer. Page 197
97 Famous People In Fatigue Sir Robert Hooke British ( ) Hooke s Law of Elasticity in 1660 Goodman English ( ) Goodman s Rule in 1899 MA Miner English ( ) Miner s Rule in 1945 August Wohler French ( ) Wohler curves in 1867 Richard Von Mise Austrian ( ) Theory of Plasticity 1913 Tatsuo Endo Japan ( ) Rainflow Counting in 1968 Restricted Siemens AG 2013 All rights reserved. Smarter decisions, better products.
98 Rainflow Counting Page 199
99 Rainflow Counting Page 200
100 Four Point Rainflow Counting rainflow matrix Page 201
101 Four Point Rainflow Counting from 5 6 rainflow matrix to Page 202
102 Four Point Rainflow Counting rainflow matrix Page 203
103 Four Point Rainflow Counting rainflow matrix Page 204
104 Four Point Rainflow Counting rainflow matrix Page 205
105 Four Point Rainflow Counting rainflow matrix Page 206
106 Four Point Rainflow Counting rainflow matrix Page 207
107 Four Point Rainflow Counting rainflow matrix Page 208
108 Four Point Rainflow Counting rainflow matrix Page 209
109 Four Point Rainflow Counting rainflow matrix residue Page 210
110 Example Residue Repeated Block Residue cycles for a repeated block: Count the sequence (RES,RES) with the 4-point algorithm Page 211 Additional residue cycles are displayed in the matrix ( * ) and are taken into account for the damage accumulation.
111 Residue Page 212
112 How to understand fatigue content of loads? Rainflow -> RangePair -> Damage distribution 0 Mean Compression Standing 0 Range Hanging Tension Page 213
113 How to understand fatigue content of loads? Rainflow -> RangePair -> Damage distribution Low Damage Large Damage Page 214
114 How to understand fatigue content of loads? Rainflow -> RangePair -> Damage distribution Demo? Folding: No distinction between standing/hanging cycles Axes rotating: X-axis = Mean Y-axis = Range Unsymmetric from/to RFM Symmetric from/to RFM Range/Mean RFM RangePair Cumulative Damage Take SN curve into account for pseudodamage distribution RangePair Cumulative Cycle Count Cumulative: Integration of cycle count curve. RangePair Cycle Count Only range of cycle is kept. Mean value is ignored Intersection with X-axis = total damage in signal Intersection with X-axis = total # cycles in signal Page 215
115 REAL DATA RAINFLOW Demo Page 216
116 Level Crossing versus Rainflow Counting with respect to level crossing = Problem: The amplitude values of the cycles are lost with the level crossing technique Page 217
117 What if the Part is Rotating Like Gear Teeth Traditional Method - Rotating Moment Histogram torque revolution tooth load Input => Load and Shaft RPM Page 218
118 Tooth Loading Model torque time [s] rotational speed tooth load tooth load time [s] In each completed revolution the reference tooth touches its counterpart once. Only then it experiences the applied torque. Page 219
119 What if the Part is Rotating Like Gear Teeth Traditional Method - Rotating Moment Histogram Gear Tooth is loaded once per revolution Each bin represents fixed load level Integrate Rotational Speed to get revolutions in bin (loading Cycles) Sum over all load bins Page 220
120 Rotating Moment Histogram - Output Number of revolutions at a given load level torque Page 221 revolutions
121 Rotating Rainflow Counting Page 222
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