Professor Darrell F. Socie University of Illinois at Urbana-Champaign 2002 Darrell Socie, All Rights Reserved

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2 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50

3 Stress Concentration Factor σ local = σ applied 1+ 2 a ρ Inglis Solution 1910 ρ 2a Applied stress Local stress Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 50

4 Notch Rules K 2 t K 2 t Se K K 2 p p = Se S = Neuber σ σε = E Glinka σ = σ dε = E Seeger * S e * Limit σ y = K t σε = S * + σ E + σ K 1 1+ n p 1 n σ K 1 n σ + K K t = S K 1 n Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 50

5 Define K σ and K ε after Yielding S, e σ, ε Define: nominal stress, S nominal strain, e notch stress, σ notch strain, ε Stress concentration Strain concentration K K σ ε σ = S ε = e Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 4 of 50

7 Stress and Strain Concentration Stress/Strain Concentration First yielding 2 K ε K t K t K 1 σ Nominal Stress Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 6 of 50

8 Neuber s Rule K t S Stress (MPa) σ ε K t S K t Actual stress e = σε Stress calculated with elastic assumptions K t e Strain Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 7 of 50

9 Neuber s Rule for Fatigue 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 σ 2 σ ε 2 2 ε 2 The product of stress times strain controls fatigue life Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 8 of 50

13 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 12 of 50

14 A Dilemma 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 13 of 50

21 K f Peterson s Equation 2070MPa α= σu K f 1.8 K t 1 = 1 + α 1+ ρ mm α ρ No effect when ρ << α Full effect when ρ >> α Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 20 of 50

25 Notched SN Curve Stress Amplitude, MPa 1000 Notched specimen Smooth specimen data K f Cycles Stress concentrations are not very important at short lives Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 24 of 50

26 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 25 of 50

29 Cracks at Holes Once a crack reaches 10% of the hole radius, it behaves as if the hole was part of the crack Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 28 of 50

30 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 29 of 50

31 Crack Growth Data 10-6 Crack Growth Rate, m/cycle da dn K c = C K m Nonpropagating cracks K TH 2 > σ1.12 πa π K,MPa m K TH Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 30 of 50

32 Frost Data Rotating bending Notched bar Notched plate nucleation fracture S nominal S fatigue limit nonpropagating cracks K t 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 31 of 50

33 Significance For K t > 4, the notch acts like a crack with a depth D S fl = K th πd K t does not play a role for sharp notches! Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 32 of 50

34 Specimens with Similar Geometry K t = 10.7 K t = Ultimate Strength 780 MPa Yield Strength 660 MPa Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 33 of 50

35 Test Results Nominal Stress Amplitude Strength Limited Crack Growth Dominated K t = 10.7 K t = 2.4 Fatigue Strength Dominated Threshold Stress Intensity Dominated Total Fatigue Life, Cycles Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 34 of 50

36 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 35 of 50

42 Crack Growth Crack growth rate Short cracks Notch plasticity controls Long cracks Crack tip plasticity controls K or a Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 41 of 50

43 Closure Observations a b σ b ε c d a c 1 st subcycle d 500 th subcycle 1026 steel ε 1 /2 = ε 2 /2 = Fatigue Seminar 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 42 of 50

45 Outline 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 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 44 of 50

52 Notches in Fatigue

Professor Stephen Downing

Professor Stephen Downing Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign 2002-2013 Darrell Socie, All Rights Reserved 1. Notch Rules 2. Fatigue Notch Factor