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Linköping University Sören Sjöström IEI, Solid Mechanics

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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

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3 Fatigue: Wöhler test German railway engineer August Wöhler t aa a Roller bearing (t) at a fixed point on the surface

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4 t aa a log N f a or log a Fatigue limit Fatigue: Wöhler diagram LCF region HCF region

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5 t aa a log N f a or log a Fatigue limit Fatigue: Wöhler diagram, continued t aa a mm Increasing m Other name: S-N diagram

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6 Haigh diagram FLP FLP ) =( up up ) mm aa FL = u UTS = B YY YY Allowed region t aa a t aa mm

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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

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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 ) mm aa FL = u UTS = B ·u·u up, · up )

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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

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10 II. Loaded volume FLP FLP ) =( up up ) mm aa 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.

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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

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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

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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

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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

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15 K t and K f are now used for increasing the nominal stress state: Nominal: ⇒ Increased: FLP FLP ) = ( up up ) mm aa 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

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16 Further, one usually does not allow loads above the yield strength. ( up up ) mm aa uu 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

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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. mm ( up up ) aa uu BB O C’ Define ’allowed length’/’used length’ as safety factor : P

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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. mm ( up up ) aa uu UTS = B P O B’ Define ’allowed length’/’used length’ as safety factor : D

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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. mm ( up up ) aa uu UTS = B P O A’ Define ’allowed length’/’used length’ as safety factor : A

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24 Further, one usually does not allow loads above the yield strength. ( up up ) mm aa uu 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

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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

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26 Haigh diagram FLP FLP ) =( up up ) mm aa FL = u UTS = B YY YY Allowed region

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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

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

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

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

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31 t aa a log N f a or log a Fatigue limit Fatigue: Wöhler diagram, continued t aa a mm Increasing m Other name: S-N diagram

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32 t aa a log N f a or log a Fatigue limit Fatigue: Wöhler diagram

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33 Fatigue: Wöhler diagram

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

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35 Result: the one and only Boeing 737 convertible!

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

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39 Examples of designs in which fatigue analysis is essential

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40 MARKERINGSYTA FÖR BILDER När du gör egna slides, placera bilder och andra illustrationer inom dessa fält. Titta gärna i ”baspresentationen” för exempel på hur placeringen kan göras.

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