1. Linköping University Sören Sjöström IEI, Solid Mechanics

2. 2 High-cycle fatigue (HCF) Railway accidents and the Wöhler test Entgleisung 19.Oktober 1875, Bahnhof Timelkam (zwischen Linz und Salzburg) Catastrophe ferroviaire de Meudon (entre Versailles et Paris), 8 mai 1945 Mystery: Wheels and axles completely correctlydesignedstatically designed

3. 3 Fatigue: Wöhler test German railway engineer August Wöhler 1819-1914 t aa  a Roller bearing  (t) at a fixed point on the surface

4. 4 t aa  a log N f  a or log  a Fatigue limit 76543 Fatigue: Wöhler diagram LCF region HCF region

5. 5 t aa  a log N f  a or log  a Fatigue limit 76543 Fatigue: Wöhler diagram, continued t aa  a mm Increasing  m Other name: S-N diagram

6. 6 Haigh diagram  FLP  FLP ) =(  up  up ) mm aa  FL =  u  UTS =  B YY YY Allowed region t aa  a t aa mm

7. 7 HCF (High-cycle Fatigue) The Haigh diagram has been set up by standardised testing using a standardised test specimen, for instance: Polished In most data tables, a specimen diameter of 10 mm has been used

8. 8 I. Surface roughness Rough surfaces are more dangerous in fatigue than smooth surfaces Reduction! If fatigue data have been measured on ideally smooth (polished) specimens, how can we use them for a not so ideally smooth specimen?  FLP  FLP ) =(  up  up ) mm aa  FL =  u  UTS =  B ·u·u  up,  ·  up )

9. 9 In this example, (a) polished surface (b) ground surface (c) machined surface (d) ’notch’ (e) hot-rolled surface (f) corrosion in tap water (g) corrosion in salt water (all are for steel materials) Surface roughness, cont. Note that: Fatigue properties are dramatically worsened under corrosive conditions [(f) and (g)] The higher tensile strength the steel has, the more sensitive it is to surface conditions A bad surface can be very destructive

10. 10 II. Loaded volume  FLP  FLP ) =(  up  up ) mm aa  FL =  u  UTS =  B ·u·u  up,  ·  up ) The risk of failure for a given load increases with the amount of material loaded (Weibull statistics – the larger volume of material is loaded, the more likely is it that a fatally bad material point exists) Again, if the actual case loads a different volume than the standardised test specimen, we must therefore reduce the Haigh diagram.

11. 11 Loaded volume, cont. (a)  UTS = 1500 Mpa (b)  UTS = 1000 MPa (c)  UTS = 600 MPa (d)  UTS = 400 MPa Steel with (e) aluminium alloy Note: this effect is usually less than that of surface condition

12. 12 III. Stress concentrations If there exists a local region of raised stress,this region is of course dangerous from the point of view of fatigue. The maximum stress in such a region can be computed by using stress concentration factor K t diagrams. One example is shown in the figure

13. 13 The same reasoning as before about volumes and statistical risks can be applied. Since the volume having high stress is small, we need not take the full stress concentration factor K t into account; instead we define a fatigue strength reduction factor Stress concentrations, cont. q = notch sensitivity factor; depends on the notch radius and the tensile strength of the material

14. 14 Stress concentrations, continued In the diagram to the left, all curves are for steel. (a)  UTS = 1600 Mpa (b)  UTS = 1300 Mpa (c)  UTS = 1000 Mpa (d)  UTS = 700 Mpa (e)  UTS = 400 Mpa Note again that higher  UTS ⇒ higher q ⇒ higher sensitivity to high stresses in notches

15. 15 K t and K f are now used for increasing the nominal stress state: Nominal: ⇒ Increased:  FLP  FLP ) = (  up  up ) mm aa  FL =  u  UTS =  B (m,a)(m,a) (K t  m,K f  a ) Stress concentrations, cont. To be carried into the reduced Haigh diagram

16. 16 Further, one usually does not allow loads above the yield strength. (  up  up ) mm aa uu  UTS =  B (m,a)(m,a) (K t  m,K f  a ) is also entered in the Haigh diagram: Y Y Finally allowed stress states I.e., the line corresponding to

17. 17 Safety against fatigue Study the load point P (K t  m, K f  a ). Draw a straight line OC’ from the origin through the load point to the Intersection with the limit of the allowed region. mm (  up  up ) aa uu BB O C’ Define ’allowed length’/’used length’ as safety factor : P

18. 18 Safety against fatigue Study the load point P (K t  m, K f  a ). Alternatively: Draw a straight line DB’ from the  a axis through the load point to the intersection with the limit of the allowed region. mm (  up  up ) aa uu  UTS =  B P O B’ Define ’allowed length’/’used length’ as safety factor : D

19. 19 Safety against fatigue Study the load point P (K t  m, K f  a ). Another alternative: Draw a vertical line AA’ from the origin through the load point to the intersection with the limit of the allowed region. mm (  up  up ) aa uu  UTS =  B P O A’ Define ’allowed length’/’used length’ as safety factor : A

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24. 24 Further, one usually does not allow loads above the yield strength. (  up  up ) mm aa uu  UTS =  B (m,a)(m,a) (K t  m,K f  a ) is also entered in the Haigh diagram: Y Y Finally allowed stress states I.e., the line corresponding to

25. 25 III. Stress concentrations If there exists a local region of raised stress,this region is of course dangerous from the point of view of fatigue. The maximum stress in such a region can be computed by using stress concentration factor K t diagrams. One example is shown in the figure

26. 26 Haigh diagram  FLP  FLP ) =(  up  up ) mm aa  FL =  u  UTS =  B YY YY Allowed region

27. 27 The same reasoning as before about volumes and statistical risks can be applied. Thus, we need not take the full stress concentration factor K t into account; instead we define a fatigue strength reduction factor where the notch sensitivity factor q depends on the notch radius and the tensile strength of the material

28. 28 Or, shown in another way: Large deformation Fracture (static or fatigue) Instability

29. 29 Different failure types Large deformation Too large stress Instability Plastic flow Creep Fracture Static fractureFatigue fracture

30. 30 History of a fatigue failure - - Initiation of a small crack - - Growth of the crack - - Final fracture

31. 31 t aa  a log N f  a or log  a Fatigue limit 76543 Fatigue: Wöhler diagram, continued t aa  a mm Increasing  m Other name: S-N diagram

32. 32 t aa  a log N f  a or log  a Fatigue limit 76543 Fatigue: Wöhler diagram

33. 33 Fatigue: Wöhler diagram

34. 34 History of a fatigue failure: Aloha Airlines’ flight No. 243, 28th April, 1988 13:25 13:48 X X X 13:5513:47

35. 35 Result: the one and only Boeing 737 convertible!

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38. 38 Examples of fatigue failure Aloha Airlines Boeing 737 ’convertible’ (28th April, 1988)

39. 39 Examples of designs in which fatigue analysis is essential

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