Fatigue failure.ppt

8/19/2019 Fatigue failure.ppt

1/37

Ken Youssefi MAE dept., SJSU 1

It has been recognized that a meta sub!ectedto a repetiti"e or fuctuating stress #i fai at a

stress much o#er than that re$uired to cause

faiure on a singe appication of oad. %aiures

occurring under conditions of d&namic oadingare caed fatigue failures.

Fatigue Failure

%atigue faiure is characterized b& three stages

Crack Initiation

Crack Propagation

Final Fracture


2/37

Ken Youssefi MAE dept., SJSU '

Jac( hammer component,

sho#s no &ieding before

fracture.

)rac( initiation site

%racture zone

*ropagation zone, striation


3/37

Ken Youssefi MAE dept., SJSU +

- cran( shaft fatigue faiure due to c&cic bending and torsiona stresses

%racture area)rac( initiation site

*ropagation

zone, striations


4/37

Ken Youssefi MAE dept., SJSU /

0' *orsche timing pue&

)rac( started at the fiet


5/37


1.34in. diameter stee pins from

agricutura e$uipment.

Materia5 AISI6SAE /1/3 o#

ao# carbon stee

%racture surface of a faied bot. 7he

fracture surface e8hibited beach mar(s,

#hich is characteristic of a fatigue faiure.


6/37


7his ong term fatigue crac( in a high $uait& component too( a

considerabe time to nuceate from a machining mar( bet#een the spider

arms on this high& stressed surface. :o#e"er once initiated propagation

#as rapid and acceerating as sho#n in the increased spacing of the ;beach

mar(s; on the surface caused b& the ad"ancing fatigue crac(.

bic&ce cran( spider arm


7/37 Ken Youssefi MAE dept., SJSU <

=ear tooth faiure

)ran( shaft


8/37 Ken Youssefi MAE dept., SJSU

Hawaii, Aloha Flight 243, a Boeing 737, an upper part of the plane's cabin

area rips off in mid-flight !etal fatigue was the cause of the failure


9/37 Ken Youssefi MAE dept., SJSU 0

)up and )one

>impes>u Surface

Incusion at the bottom of the dimpe

>uctie

Fracture Surface Characteristics

Shin&

=rain ?oundar& crac(ing

?ritte Intergranuar

Shin&

)ea"age fractures

%at

?ritte 7ransgranuar

?eachmar(s

Striations @SEM

Initiation sites

*ropagation zone

%ina fracture zone

%atigue

Mode of fracture Typical surface characteristics



Fatigue Failure – Type of Fluctuating Stresses

σa =

σmax

σmin

2

Aternating stress

Mean stress

σm =

σmax

σmin

2

B



Fatigue Failure, S-N Curve

7est specimen geometr& for C.C. Moore

rotating beam machine. 7he surface is

poished in the a8ia direction. A constant

bending oad is appied.

Motor

Doad

Cotating beam machine appies fu& re"erse bending stress

7&pica testing apparatus, pure bending


12/37 Ken Youssefi MAE dept., SJSU 1'

Fatigue Failure, S-N Curve

Finite life Infinite life

F 13+ G 13+

S′e

H endurance imit of the specimenSe′


13/37 Ken Youssefi MAE dept., SJSU 1+

Relationship Between ndurance !i"it

and #lti"ate Strength

Stee

Se =′

3.2Sut

133 (si

200 ksi

Sut > 1400 MPa

Stee

3./Sut

Se =′

Sut


14/37 Ken Youssefi MAE dept., SJSU 1/

Relationship Between ndurance !i"it and

#lti"ate Strength

Auminum ao&s

Se =′

3./Sut

10 (si

1+3 M*a

Sut



Correction Factors for Speci"en$s ndurance !i"it

H endurance imit of the specimen @infinite ife G 139Se

′

%or materias e8hibiting a (nee in the S4 cur"e at 139 c&ces

H endurance imit of the actua component @infinite ife G 139Se

N

S Se

139

13+

H fatigue strength of the specimen @infinite ife G 2813Sf

′

H fatigue strength of the actua component @infinite ife G 2813Sf

%or materias that do not e8hibit a (nee in the S4 cur"e, the infinite

ife ta(en at 2813 c&ces

N

S Sf

281313+




Se = Cload C size C surf Ctemp Crel (Se′

Doad factor, Cload

*ure bending Cload = 1

*ure a8ia Cload = 0.7

)ombined oading Cload = 1

*ure torsion Cload = 1 if von Mises stess is use!" use

0.#77 if von Mises stess is N$% use!.


17/37 Ken Youssefi MAE dept., SJSU 1<


Size factor, C size

Darger parts fai at o#er stresses than smaer parts. 7his is

main& due to the higher probabiit& of fa#s being present in

arger components.

%or soid round cross section

d 3.+ in. @ mm C size = 1

3.+ in. F d 13 in. C size = .86&(d )'0.0&7

mm F d '23 mm C size = 1.18&(d )'0.0&7

If the component is arger than 13 in., use C size = .6




%or non rotating components, use the 02 area approach to cacuate

the e$ui"aent diameter. 7hen use this e$ui"aent diameter in thepre"ious e$uations to cacuate the size factor.

d e"ui# H @ A02

3.3




surface factor, C surf

7he rotating beam test specimen has a poished surface. Most

components do not ha"e a poished surface. Scratches andimperfections on the surface act i(e a stress raisers and reduce

the fatigue ife of a part. Use either the graph or the e$uation #ith

the tabe sho#n beo#.

C surf = A (Sut)b


20/37 Ken Youssefi MAE dept., SJSU '3


7emperature factor, Ctemp

:igh temperatures reduce the fatigue ife of a component. %or

accurate resuts, use an en"ironmenta chamber and obtain the

endurance imit e8perimenta& at the desired temperature.

%or operating temperature beo# /23 o) @/3 o% the

temperature factor shoud be ta(en as one.

Ctemp = 1 fo 7 /23o) @/3 o%


21/37

Ken Youssefi MAE dept., SJSU '1


Ceiabiit& factor, Crel

7he reiabiit& correction factor accounts for the scatter and

uncertaint& of materia properties @endurance imit.


22/37

Ken Youssefi MAE dept., SJSU ''

Fatigue Stress Concentration Factor, % f

E8perimenta data sho#s that the actua stress concentration factor is

not as high as indicated b& the theoretica "aue, $ t. 7he stress

concentration factor seems to be sensiti"e to the notch radius and theutimate strength of the materia.

$ f H 1 B @$ t 1"otch sensiti"it&

factor


23/37

Ken Youssefi MAE dept., SJSU '+

Fatigue Stress

Concentration Factor,

% f for Aluminum


24/37

Ken Youssefi MAE dept., SJSU '/

&esign process – Fully Reversed !oading for 'nfinite !ife >etermine the ma8imum aternating appied stress, σ

a , in terms of

the size and cross sectiona profie

Seect materia L S" Sut

Use the design e$uation to cacuate the size

Se K

fσ

a

=n

)hoose a safet& factor L n

>etermine a modif&ing factors and cacuate the endurance

imit of the component L Se

>etermine the fatigue stress concentration factor, K f

In"estigate different cross sections @profies, optimize for size or #eight

You ma& aso assume a profie and size, cacuate the aternating stress

and determine the safet& factor. Iterate unti &ou obtain the desired

safet& factor


25/37


&esign for Finite !ife

Sn = a (N)b equation of the fatigue line

N

S

Se

13913+

A

?

N

S

Sf

281313+

A

?

*oint ASn = .&Sut

H 13+*oint A

Sn = .&Sut

H 13+

*oint ?Sn = Sf

H 2813*oint ?

Sn = Se

H 13

9


26/37


&esign for Finite !ife

Sn = a (N)b

og Sn H og a B b og

App& conditions for point A and ? to find the t#o

constants aN and bN

o* .0Sut H o* a B b o* 13+

o* Se H o* a B b o* 139

a =(.&Sut

'

Se

b=

.&Sut

Se

1

+ o*

Sn K fσa = n

>esign e$uation

)acuate Sn an! e+a,e Se in the design e$uation

Sn H Se @

139O @

Se.0Sut

o*


27/37

Ken Youssefi MAE dept., SJSU '<

The ffect of Mean Stress on Fatigue !ife

Mean stress e8ist if the

oading is of a repeating orfuctuating t&pe.

Mean stress

Aternating

stress

σm

σa

Se

SSoderberg ineSut

=oodman ine

=erber cur"e

S Yied ine


28/37

Ken Youssefi MAE dept., SJSU '


Modified (ood"an &iagra"

Mean stress

Aternating

stress

σm

σa

Sut

=oodman ine

SYied ine

S

Se

Safe zone)

Th ff t f M St F ti !if


29/37


' S,



Bσm

σa

Sut

=oodman ine

S Yied ine

Safe zone

4 σm

)

S

Se

Safe zone


30/37

Ken Youssefi MAE dept., SJSU +3



Bσm

σa

Sut

Safe zone

4 σm

)

S

Safe zone

Se

' S,

%inite ife

Sn1=

Sut

σa σm

B

%atigue, σm > 0%atigue, σm ≤ 0

σa =

Se

nf

σa + σ

m =

S

n y

Yied

σa + σ

m =

S

n y

Yied

nf Se

1=

Sut

σa σm

BInfinite ife

) l i S C i f )l i


31/37


)pplying Stress Concentration factor to )lternating

and Mean Co"ponents of Stress

>etermine the fatigue stress concentration factor, $ f , app& direct& to

the aternating stress L $ f σa

If $ fσmax < S t-en t-ee is no ie!in* at t-e not,-" use $ fm = $ f

and mutip& the mean stress b& $ fm L $ fm σm

If $ fσmax > S t-en t-ee is o,a ie!in* at t-e not,-" ateia at t-e

not,- is stain'-a!ene!. %-e effe,t of stess ,on,entation is e!u,e!.

)acuate the stress concentration factor for the mean stress using

the foo#ing e$uation,

$ fm =

S $ f σa

σm

nf Se

1=

Sut

$ f σa $ fmσmB Infinite ife

%atigue design e$uation


32/37

Ken Youssefi MAE dept., SJSU +'

Co"*ined !oading

A four components of stress e8ist,

σ xa

atenatin* ,o+onent of noa stessσ

xm mean component of norma stress

τ8&a aternating component of shear stress

τ8&m mean component of shear stress

)acuate the aternating and mean principa stresses,

σ1a, σ2a = @σ/a 62 @σ/a 622

B @τ/a2

σ1m, σ2m = @σ/m 62 @σ/m 622 B @τ/m

2


33/37

Ken Youssefi MAE dept., SJSU ++

Co"*ined !oading

)acuate the aternating and mean "on Mises stresses,

σa′ = (σ1a B σ2a 4 σ1aσ2a16'

' '

σm′ = (σ1m B σ2m 4 σ1mσ2m16'

' '

%atigue design e$uation

nf Se

1

=Sut

σ′a σ′m

B Infinite ife


34/37

Ken Youssefi MAE dept., SJSU +/

&esign +a"ple

C1 C'

13,333 b.

9P 9P 1'P

D H 1.2d d

r @fiet radius H .1d

A rotating shaft is carr&ing 13,333 b force

as sho#n. 7he shaft is made of stee #ith

Sut = 120 ksi an! S y = &0 ksi. %-e s-aft

is otatin* at 11#0 + an! -as a

a,-ine finis- sufa,e. eteine t-e

!iaete" !" fo 7# inutes ife. se

safet fa,to of 1.6 an! #0 eiaiit.

)acuate the support forces, C1 H '233, C' H


35/37


&esign +a"ple Assume d H 1.3 in

sin* r = .1 an! S ut = 120 ksi ,

q @notch sensiti"it& H .2$ f H 1 B @$ t 1q = 1 B .2@1.< 1 H 1.9

)acuate the endurance imit

Cload = 1 (+ue en!in*)

Crel = 1 (#0 e.)

Ctemp= 1 (oo te+)

C surf = A (Sut)b

= 2.7(120)'.26#

= .7#&

3.+ in. F d 13 in. C size = .86&(d )'0.0&7 = .86&(1)

'0.0&7 = .86&

Se = Cload C size C surf Ctemp Crel (Se = (.7#&)(.86&)(.#/120) = 3&.#7 ksi′


36/37


&esign +a"ple

>esign ife, H 1123 8


37/37

&esign +a"ple

σa =

30##77

(2.#)3= 1&.## ksi

n H Sn

K f σa=

#3.3#

1.63/1&.##= 1.67 1.6

d H '.2 in.

)hec( &ieding

n = S y

K f σmax =

&0

1.63/1&.##= 2.8 9 1.6 oka

Se = 36.2 ksi Sn = #3.3# ksiL

Fatigue failure.ppt

Documents

Transcript of Fatigue failure.ppt