Linköping University
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Transcript of Linköping University
Linköping University
Sören SjöströmIEI, Solid Mechanics
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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 correctly designedstatically designed
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Fatigue: Wöhler test
German railway engineer August Wöhler 1819-1914
t
sa
-sa
Roller bearing
s(t) at a fixed point on the surface
F
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t
sa
-sa
log Nf
sa
orlog sa
Fatigue limit
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Fatigue: Wöhler diagram
LCF region
HCF region
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t
sa
-sa
log Nf
sa
orlog sa
Fatigue limit
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Fatigue: Wöhler diagram, continued
t
sa
-sa
sm
Increasing sm
Other name: S-N diagram
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Haigh diagram
(sFLP,sFLP) =(sup,sup)
sm
sa
sFL=su
sUTS=sB
sY
sY
Allowed region
t
sa
-sa
t
sa
-sa
sm
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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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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?
(sFLP,sFLP) =(sup,sup)
sm
sa
sFL=su
sUTS=sB
k·su
(sup, k·sup)
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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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II. Loaded volume
(sFLP,sFLP) =(sup,sup)
sm
sa
sFL=su
sUTS=sB
d·su
(sup, d·sup)
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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Loaded volume, cont.
(a) sUTS = 1500 Mpa(b) sUTS = 1000 MPa(c) sUTS = 600 MPa(d) sUTS = 400 MPa
Steel with
(e) aluminium alloy
Note: this effect is usually less than that of surface condition
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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 Kt diagrams. One example is shown in the figure
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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 Kt into account; instead we define a fatigue strength reduction factor
)1(1 - tf KqK
Stress concentrations, cont.
q = notch sensitivity factor; depends on the notch radius and the tensile strength of the material
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Stress concentrations, continued
In the diagram to the left, all curves are for steel.(a) sUTS = 1600 Mpa(b) sUTS = 1300 Mpa(c) sUTS = 1000 Mpa(d) sUTS = 700 Mpa(e) sUTS = 400 Mpa
Note again that higher sUTS higher ⇒ q higher sensitivity to high ⇒stresses in notches
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Kt and Kf are now used for increasing the nominal stress state:
tKKt afmt sss sin)(
Nominal: tt am sss sin)(
⇒ Increased:
(sFLP,sFLP) = (sup,sup)
sm
sa
sFL=su
sUTS=sB
(sm,sa)
(Ktsm,Kfsa)
Stress concentrations, cont.
To be carried into the reduced Haigh diagram
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Further, one usually does not allow loads above the yield strength.
(sup,sup)
sm
sa
su
sUTS=sB
(sm,sa)
(Ktsm,Kfsa)
Yam ssis also entered in the Haigh diagram:
Y
Y
Finally allowed stress states
Yam ss
I.e., the line corresponding to
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Safety against fatigue
Study the load point P (Ktsm, Kfsa).
Draw a straight line OC’ from the origin through the load point to theIntersection with the limit of the allowed region.
OPOCSFam
'
sm
(sup,sup)
sa
su
sBO
C’
Define ’allowed length’/’used length’ as safety factor :
P
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Safety against fatigue
Study the load point P (Ktsm, Kfsa).
Alternatively: Draw a straight line DB’ from the sa axis through the loadpoint to the intersection with the limit of the allowed region.
DPDBSFm
'
sm
(sup,sup)
sa
su
sUTS=sB
P
O
B’
Define ’allowed length’/’used length’ as safety factor :
D
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Safety against fatigue
Study the load point P (Ktsm, Kfsa).
Another alternative: Draw a vertical line AA’ from the origin through the loadpoint to the intersection with the limit of the allowed region.
APAASFa
'
sm
(sup,sup)
sa
su
sUTS=sB
P
O
A’
Define ’allowed length’/’used length’ as safety factor :
A
www.liu.se
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Further, one usually does not allow loads above the yield strength.
(sup,sup)
sm
sa
su
sUTS=sB
(sm,sa)
(Ktsm,Kfsa)
Yam ssis also entered in the Haigh diagram:
Y
Y
Finally allowed stress states
Yam ss
I.e., the line corresponding to
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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 Kt diagrams. One example is shown in the figure
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Haigh diagram
(sFLP,sFLP) =(sup,sup)
sm
sa
sFL=su
sUTS=sB
sY
sY
Allowed region
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The same reasoning as before about volumes and statistical risks can be applied.Thus, we need not take the full stress concentration factor Kt 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
)1(1 - tf KqK
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Or, shown in another way:Large deformation
Fracture (static or fatigue)
Instability
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Different failure types
Large deformation
Too large stress
Instability
Plastic flow
Creep
Fracture
Static fracture Fatigue fracture
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History of a fatigue failure
- - Initiation of a small crack
- - Growth of the crack
- - Final fracture
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t
sa
-sa
log Nf
sa
orlog sa
Fatigue limit
76543
Fatigue: Wöhler diagram, continued
t
sa
-sa
sm
Increasing sm
Other name: S-N diagram
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t
sa
-sa
log Nf
sa
orlog sa
Fatigue limit
76543
Fatigue: Wöhler diagram
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Fatigue: Wöhler diagram
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History of a fatigue failure: Aloha Airlines’ flight No. 243, 28th April , 1988
13:25
13:48
XX
X
13:55 13:47
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Result: the one and only Boeing 737 convertible!
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Examples of fatigue failure
Aloha Airlines Boeing 737 ’convertible’ (28th April,1988)
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Examples of designs in which fatigue analysis is essential
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