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Fatigue of materials
Lec.1 High-cycle fatigue. Design with respect to fatigue limit.Wöhler diagram. Haigh diagram and reduction of the fatigue limit.
Lec.2 Design with respect to fatigue life, damage accumulationPalmgren-Miner hypothesis.
Lec.3 Fatigue from a material point of view.Guest lecturer. Johan Moverare
Lec.4 Fatigue from a structural mechanics point of view.Guest lecturer. Hans Ansell (Saab)
Fatigue of materialsIntroduction: Teaspoon example
Bend a teaspoonrepeatidly back and forth.After a while the spoon breaks with a snap.
Materials subjected to a time varying loading may fractureeven if the loading level is so low that stresses in the material always are below the yield limit of the material
Fatigue failure
Fig. Meso scale
The progression of a fatigue failure may be divided into 3 stages
1) Crack initiation phase2) Crackgrowth (crack propagation due to cyclic loading)3) Fracture (final rupture when the crack is long enough)
When fatigue life is to be determined the number of loading cycles to the final rupture has to be counted.
(no separaration between the different stages above is needed)
When designing for material fatigue, a calculated stress or strain in the material has to be compared with an experimentally determined fatigue strength of the material.
There is a high degree of uncertances
• The exact loading of a structure is perhaps not known• Hard to determine stresses due to local stress-concentrations or other geometrical imperfections
• The fatigue life will differ between identical tests
Material fatigue is sorted into
• High-Cycle Fatigue HCF (low stresses compared to the yield limit, large number of loading cycles to failure)
• Low-Cycle Fatigue LCF (high stresses, low number of loading cycles to failure, usually strain based fatigue life prediction)
High-Cycle Fatigue (HCF)
Definitions:
cycles loading ofNumber 2πωt
τtN ==
ωt σσσ(t) am sin+=
aσmσ
t
σ
ammax σσσ +=
ammin σσσ −=
)σ(σ21σ minmaxm +=
Mean stress:
)σ(σ21σ minmaxa −=
Stress amplitude :
Fatigue data are often given for two types of loadings
aσt
σ
mσt
aσσ
1) Alternating: ( )0am σσ 0σ == ,
Notation: 0σ σ ±=
Notation: 00 σ σ σ ±=
2) Pulsating: )σσ(σ 0am ==
B A σa += Nlog•
• ⇔= σa KNm
) (1σ a NloglogKm
log −=
aσ
Nlog0 1 2 3 4 5 6 7 8 9
0σm =
Fatigue life calculations (Wöhler diagram)
Nσ
N = number of loading cycles to failure
SN-curve (Wöhler diagram) for steel
Fatigue life calculations (Wöhler diagram)
SN-curve (Wöhler diagram) for steel
limit fatigueσσ FLu ==
aσ
Nlog0 1 2 3 4 5 6 7 8 9
uσ
0σm =
• The fatigue limit σu
Fatigue life calculations (Wöhler diagram)
SN-curves (Wöhler diagram) for different values of the mean stress σm
aσ
Nlog0 1 2 3 4 5 6 7 8 9
0σm =
Nσ
0σm1 >
m1m2 σσ >
• Effect of mean stress σm on fatigue life and fatigue limit σu
uσlimit fatigueσσ FLu ==
Fatigue life calculations (Wöhler diagram)
limit fatigueσσ FLu ==
aσ
Nlog0 1 2 3 4 5 6 7 8 9
uσ
• Statistical scatter
SN-curves is usually plotted for 50 % failure probability
Material data for fatigue limits are usually given fortension/compression, bending and torsion for alternating and pulsating loading.
Fatigue limits (notations)
Load
Tension/compression
Bending
Torsion
Alternating Pulsating
uσ±
ubσ±
uvτ±
upup σσ ±
ubpubp σσ ±
uvpuvp ττ ±
The Haigh diagram
Alternating: uσ±
Pulsating: upup σσ ±uam σσ , 0σ ==⇔
upaupm σσ , σσ ==⇔
aσ
Yσ
Yσ
uσ + +upσ
upσ mσUσ
Area where no fatigue failure occurs
Shows the fatigue limit as a function of the mean stress plotted in the σa - σm plane.Used to estimate the safety against fatigue failure
1) Insert the data for fatigue limits in the diagram
Uσ = ultimate strength
Yσ = yield limit
2) Insert the ultimate strength and the yield limit
To construct the diagram:
The Haigh diagram - Reduction of the fatigue limit
Factor
κ
λ
δ
Reduction of the fatigue limit due to:
Surface roughness
Size of raw material
Size of loaded volume ) τ,(σ uvub
Reduced diagram
uσ δ λκ
upσ δ λκ +
aσ
Yσ
Yσ
uσ + +upσ
upσmσ
Uσ
+
Reduction of the fatigue limit due to surface roughness (κ )
Reduction of the fatigue limit due to size of raw material (λ)
Reduction of the fatigue limit due to size of loaded volume (δ)
Inserting the service stress )σ,(σ: amP
P+
Reduced Haigh diagram
uσ δ λκ
upσ δ λκ +
aσ
Yσ
Yσ
uσ + +upσ
upσmσ
Uσ
+
limits fatigue reducing factors δ λ, κ,limits fatigue σ σ
strength ultimate σlimit yield σstressmean σamplitude stress σ
upuU
Y
ma
==
===
=
,
• Stress concentration factor Kt
In order to account for stress concentrations due to geometrical imperfections such as holes, fillets and notches in a loaded volume the mean stress is multiplied with the corresponding stress concentration factor Kt.
nommm σσ tK=
The stress amplitude is multiplied with the fatigue notch factor Kf at stress concentrations.
nomaa σσ fK=
• Fatigue notch factor Kf
nommm σσ tK=Stress concentration factor Kt
Stress concentration factor Ktnommm σσ tK=
Fatigue notch factor Kfnomaa σσ fK=
Safety against fatigue failure, safety factors
aσ
P
Reduced Haigh diagramYσ
Yσ
uσ upσ
upσmσ
Uσ
+
+ ++
+
O A
A’
B’
C’
Safety factors
constantσ when ma ==APAA'SF
constantσ when am ==OAOB'SF
Inserting the service stress P : )σ ,σ()σ ,(σ noma
nommam ft KK=
constantσσ when
m
aam ==
OPOC'SF