Professor Stephen Downing
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1 Professor Stephen Downing Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign Darrell Socie, All Rights Reserved
2 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50
3 local applied 1 2 a Inglis Solution a Applied stress Local stress Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 50
4 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 50 Neuber Glinka Seeger n 1 2 t K E Se K n 1 2 t K n 1 1 E d Se K S K K S * K S K K E e S K p t y t Limit p n 1 * * 2 p
5 S, e, Define: nominal stress, S nominal strain, e notch stress, notch strain, Stress concentration Strain concentration K K S e Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 4 of 50
6 K t S K K S e K t e Strain Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 5 of 50
7 K t First yielding Nominal Stress Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 6 of 50
8 K t S Actual stress K t S K t e Stress calculated with elastic assumptions K t e Strain Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 7 of 50
9 Stress and strain amplitudes Elastic nominal stress Substitute and rearrange K t S K t e 2 2 K t e 2 S 2 S 2E E The product of stress times strain controls fatigue life Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 8 of 50
10 steels 17 aluminums Fatigue Life, Reversals Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 9 of 50
11 steels 17 aluminums Fatigue Life, Reversals Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 10 of 50
12 10 5 E Fatigue Life, Reversals Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 11 of 50
13 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 12 of 50
14 Stress analysis and stress concentration factors are independent of size and are related only to the ratio of the geometric dimensions to the loads Fatigue is a size dependant phenomena How do you put the two together? Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 13 of 50
15 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 14 of 50
16 From Dowling, Mechanical Behavior of Materials, 1999 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 15 of 50
17 K t K f K t K f Large Notch Small Notch Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 16 of 50
18 K t K f K t Kf Low Strength High Strength Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 17 of 50
19 K t K t K f K f Low K t High K t Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 18 of 50
20 t f 10 8 K f = K t K f 6 4 Experiments K t Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 19 of 50
21 K f MPa u K f 1.8 K t mm No effect when << Full effect when >> Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 20 of 50
22 Ultimate Strength, MPa Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 21 of 50
23 hole K t = 2.5 slot K t = 5 diamond K t = 20 edge K t = 20 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 22 of 50
24 edge diamond slot hole displacement, mm Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 23 of 50
25 10000 Smooth specimen data 1000 Notched specimen K f Cycles Stress concentrations are not very important at short lives Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 24 of 50
26 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 25 of 50
27 S K t S S D a a D + a a << D K K t S a K a >> D S Da Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 26 of 50
28 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 27 of 50
29 Once a crack reaches 10% of the hole radius, it behaves as if the hole was part of the crack Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 28 of 50
30 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 29 of 50
31 da dn K c CK m Nonpropagating cracks K TH a K TH Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 30 of 50
32 Rotating bending Notched bar Notched plate nucleation fracture nonpropagating cracks K t Frost, A Relation Between the Critical Alternating Propagation Stress and Crack Length for Mild Steel Proceedings of the Institute for Mechanical Engineers, Vol. 173, No. 35, 1959, Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 31 of 50
33 For K t > 4, the notch acts like a crack with a depth D S fl K th D K t does not play a role for sharp notches! Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 32 of 50
34 K t = 10.7 K t = Ultimate Strength 780 MPa Yield Strength 660 MPa Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 33 of 50
35 1000 Strength Limited K t = 10.7 K t = Crack Growth Dominated Fatigue Strength Dominated Threshold Stress Intensity Dominated Total Fatigue Life, Cycles Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 34 of 50
36 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 35 of 50
37 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 36 of 50
38 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 37 of 50
39 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 38 of 50
40 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 39 of 50
41 notch plastic zone notch stress field D a crack tip plastic zone Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 40 of 50
42 Short cracks Notch plasticity controls Long cracks Crack tip plasticity controls K or a Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 41 of 50
43 a b b c d a c 1 st subcycle d 500 th subcycle 1026 steel /2 = /2 = Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 42 of 50
44 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 43 of 50
45 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors for Notches 4. Frost Data and K f 5. Small Crack Growth 6. Small Notches Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 44 of 50
46 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 45 of 50
47 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 46 of 50
48 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 47 of 50
49 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 48 of 50
50 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 49 of 50
51 Fatigue Seminar Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 50 of 50
52 Notches in Fatigue
Professor Darrell F. Socie University of Illinois at Urbana-Champaign 2002 Darrell Socie, All Rights Reserved
Notches in Fatigue Professor Darrell F. Socie University of Illinois at Urbana-Champaign 2002 Darrell Socie, All Rights Reserved Outline 1. Notch Rules 2. Fatigue Notch Factor 3. Stress Intensity Factors
Professor Stephen D. Downing
Professor Stephen D. Downing Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign 2011-2013 Stephen Downing, All Rights Reserved 1. Comparison to Wrought Metals 2.
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