Fatigue Failure Analysis

8/19/2019 Fatigue Failure Analysis

1/27

FATIGUE FAILURE ANALYSIS

Aditya Kumar Maharana

Mechanical Engineering

M-Tech, 2nd Year


2/27

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


3/27

"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


4/27

+ac, hammer

component sho'sno yielding #eforefracture)

Crac, initiation site

Fracture $one

.ropagation $one striation


5/27

/01 .orsche timingpulley

Crac, started at the 2llet


6/27

3ear tooth failure

Cran, shaft


7/27

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)


8/27

Fatigue Failure – Type of Fluctuating Stresses

σa

=

σmax

σmin

2

5lternating stress

ean stress

σm

;

σmax σmin

0

<


9/27

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


10/27

Fatigue Failure, S-N Curve

Finitelife

Innitelife

N 103

S′e

; endurance limit of the specimenSe‘


11/27

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


12/27

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


13/27


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)


14/27


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


15/27


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


16/27


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


17/27


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


18/27


=elia#ility factor Crel

The relia#ility correction factor accounts for thescatter and uncertainty of material properties

endurance limit)


19/27

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


20/27

%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


21/27

%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


22/27

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


23/27

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


24/27

- Syc


'odified (ood!an %iagra!


25/27


'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


26/27

)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


27/27

Thank You

Documents

Fatigue Failure Analysis