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FATIGUE FAILURE ANALYSIS
Aditya Kumar Maharana
Mechanical Engineering
M-Tech, 2nd Year
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OUTLINE
• Fatigue Failure
• Why study Fatigue?
• Type of Fluctuating stresses
• S-N Curve
• Endurance Limit and Correction factors
• Fatigue Stress Concentration factor
• Eect of ean Stress and !esign for Finite life
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"t has #een recogni$ed that a metal su#%ected to arepetitive or &uctuating stress 'ill fail at a stress muchlo'er than that re(uired to cause failure on a singleapplication of load) Failures occurring under conditions ofdynamic loading are called fatigue failures)
Fatigue Failure
Fatigue failure is characteri$ed #y three stages *
Crack Initiation
Crack Propagation
Final Fracture
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+ac, hammer
component sho'sno yielding #eforefracture)
Crac, initiation site
Fracture $one
.ropagation $one striation
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/01 .orsche timingpulley
Crac, started at the 2llet
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3ear tooth failure
Cran, shaft
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4a'aii 5loha Flight 067 a 8oeing 979 an upper part of theplane:s ca#in area rips o in mid-&ight) etal fatigue 'as thecause of the failure)
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Fatigue Failure – Type of Fluctuating Stresses
σa
=
σmax
σmin
2
5lternating stress
ean stress
σm
;
σmax σmin
0
<
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Fatigue Failure, S-N Curve
Test specimen geometry for =)=)oore rotating #eam machine) Thesurface is polished in the a>ialdirection) 5 constant #ending load isapplied)
otor
Load
=otating #eam machine applies fully reverse #endingstress
Typical testing apparatus pure #ending
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Fatigue Failure, S-N Curve
Finitelife
Innitelife
N 103
S′e
; endurance limit of the specimenSe‘
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Relationship Between Endurance i!it and "lti!ate
Strength
Steel
Se ;@
A)BSut
AA ,si
9AA .a
Sut D 0AA ,si 6AA
.aSut > 0AA
,siSut > 6AA
.a
Steel
A)6Sut
Se ;@
Sut
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Correction Factors for Speci!en#s Endurance i!it
; endurance limit of the specimen in2nite life
I AG
Se@
For materials e>hi#iting a ,nee in the S-N curve at AG
cycles
; endurance limit of the actual component in2nite
life I AG
Se
N
S Se
AGA7
; fatigue strength of the specimen in2nite life I
B>A1
Sf @
; fatigue strength of the actual component in2nite life
I B>A1
Sf
For materials that do not e>hi#it a ,nee in the S-N curvethe in2nite life ta,en at B>A1 cycles
N
S Sf
B>A1A7
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Correction Factors for Speci!en#s Endurance i!it
Se ; Cload Csize Csurf Ctemp Crel Se@
Load factor Cload
.ure#ending Cload =
.ure a>ial Cload = A)9
Com#ined loading Cload =
.ure torsion Cload = if von ises stress is used use
A)B99 if von ises stress is NJTused)
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Correction Factors for Speci!en#s Endurance i!it
Si$e factor Csize
Larger parts fail at lo'er stresses than smaller parts) This is mainly due to the higher pro#a#ility of &a's#eing present in larger components)
For solid round cross section
d D A)7 in) 1mm
Csize =
A)7 in) K d D A
in)
Csize = )1G/d-A)A/9
1 mm K d D 0BAmm
Csize = )1/d-A)A/9
"f the component is larger than A in) useCsize = )G
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Correction Factors for Speci!en#s Endurance i!it
For non rotating components use the /B area approach to
calculate the e(uivalent diameter) Then use this e(uivalentdiameter in the previous e(uations to calculate the si$e factor)
dequiv ;
A/B
A)A9GGM0 dd 95
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Correction Factors for Speci!en#s Endurance i!it
Surface factor Csurf
The rotating #eam test specimen has a polished surface)ost components do not have a polished surface)Scratches and imperfections on the surface act li,e astress raisers and reduce the fatigue life of a part) seeither the graph or the e(uation 'ith the ta#le sho'n#elo')
Csurf = A Sutb
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Correction Factors for Speci!en#s Endurance i!it
Temperature factor Ctemp
4igh temperatures reduce the fatigue life of acomponent) For accurate results use an environmentalcham#er and o#tain the endurance limit e>perimentallyat the desired temperature)
For operating temperature #elo' 6BA oC 16A oF thetemperature factor should #e ta,en as one)
Ctemp = for T D 6BAo
C 16Ao
F
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Correction Factors for Speci!en#s Endurance i!it
=elia#ility factor Crel
The relia#ility correction factor accounts for thescatter and uncertainty of material properties
endurance limit)
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Fatigue Stress Concentration Factor, $ f E>perimental data sho's that the actual stress concentration factor
is not as high as indicated #y the theoretical value K t) The stressconcentration factor seems to #e sensitive to the notch radius andthe ultimate strength of the material)
K f ; < K t qNotchsensitivityfactor
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%esign process – Fully Reversed oading for &nfinite ife
!etermine the ma>imum alternating applied stress
σa , interms of the si$e and cross sectional pro2le
Select material O Sy Sut
se the design e(uation to calculate thesi$e Se
K f σa = n
Choose a safety factor O n
!etermine all modifying factors and calculate theendurance limit of the component O Se
!etermine the fatigue stress concentrationfactor K f
"nvestigate dierent cross sections pro2les optimi$e for si$eor 'eight
Pou may also assume a pro2le and si$e calculate thealternating stress and determine the safety factor) "terate until
you o#tain the desired safety factor
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%esign for Finite ife
Sn = a Nb
equation of the fatigue line
N
S
Se
AGA7
5
8
N
S
Sf
B>A1A7
5
8
.oint 5Sn = ./Sut
N ; A7.oint 5
Sn = ./Sut
N ; A7
.oint 8
Sn = Sf
N ;1
.oint 8
Sn = Se
N ; AG
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The Effect of 'ean Stress on Fatigue ife
ean stress e>ist ifthe loading is of arepeating or&uctuating type)
ean stress
5lternatin
g stress
σm
σa
Se
SySoder#erg lineSut
Goodman line
Gerber curve
Sy Yield line
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The Effect of 'ean Stress on Fatigue ife 'odified (ood!an
%iagra!
ean stress
5lternating stress
σm
σa
Sut
Goodman line
Sy Yield line
Sy
Se
Safe $oneC
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- Syc
The Effect of 'ean Stress on Fatigue ife
'odified (ood!an %iagra!
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The Effect of 'ean Stress on Fatigue ife
'odified (ood!an %iagra!
AFatigueσm D A
σa ;Senf
σa + σm ;Sy
n y
Pield
σa +
σm ;
Sy
n y
Pield
nf Se
1=
Sut
σa
σm
+nfinite life
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)pplying Stress Concentration factor to )lternating and
'ean Co!ponents of Stress
!etermine the fatigue stress concentration factor K f apply
directly to the alternating stress O K f σa
"f K f σmax < Sy then there is no yielding at the notch use
K fm ; K f and multiply the mean stress #y K fm O K fm σm
"f K f σmax > Sy then there is local yielding at the notch materialat the notch is strain-hardened) The eect of stressconcentration is reduced)Calculate the stress concentration factor for the meanstress using the follo'ing e(uation
K fm ;S
yK
f σ
a
σm
nf Se
;
Sut
K f σa K fmσm< "n2nite life
Fatigue design e(uation
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Thank You