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

4

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

76543

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

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 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

27

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

32

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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