Fatigue Failure Resulting From Variable Loading 1-2

8/4/2019 Fatigue Failure Resulting From Variable Loading 1-2

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I/C: KALLURI VINAYAK


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Variable Loading Variable loading results when the applied load or

the induced stress on a component is not constantbut changes with time

In reality most mechanical components experiencevariable loading due to

-

Example: Extrusion process

-Change in direction of load application

Example: a connecting rod-Change in point of load application

Example: a rotating shaft


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Fatigue Fatigue is a phenomenon associated with variable

loading or more precisely to cyclic stressing or

straining of a material

A TM D fini i n f f i

The process of progressive localized permanent

structural changes occurring in a material subjected

to conditions that produce fluctuating stresses at

some point or points and that may result in cracks or

complete fracture after a sufficient number of

fluctuations.


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Fatigue Failure- Mechanism

Three stages are involved in fatigue failure

-Crack initiation

-Crack propagation-Fracture / Rupture


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Introduction to Fatigue in Metals

Final rupture occurs

over a limited area,

characterizing a very

small load required to

cause it

Crack initiation, propagation and rupture in a shaft subjected to repeated bending

Crack initiation at

the outer surface

Beach marksshowing the

nature of crack

propagation


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Crack initiation at

the root of keyway

at B

Crack

propagation

occurs over a

Final failure over

the small area at

C due to sudden

rupture


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Connecting rod failed by fatigue failure

The crack got initiated at the flash line of forging.

Flashline of

forging


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Fatigue failure of a steam engine connecting rod due to PURE TENSION load.

No surface crack.

Crack may initiate

anywhere that is

the weakest orunknown source

of weakness.Radial direction of

crack propagation

In this rod, the crack

initiated due to forging

flake slightly below

the centre line.The crack propagated radially outward until some

time after which the sudden rupture occurred.


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Approach to Fatigue Failure in Analysis and Design

Fatigue life methods

Fatigue strength and endurance limit

Endurance limit modifying factors

Stress concentration and notch sensitivity

Fluctuating stresses

Combination of loading modes

Variable, fluctuating stresses, cumulative fatiguedamage


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Fatigue Life Methods

predict the failure in number of cycles N to failure for a specific type ofloading

33 10:(HCF)fatiguecycleHigh;101:(LCF)fatiguecycleLow > NN

Stress life methods

Based on stress levels only Least accurate of the three, particularly for LCF

It is the most traditional because easiest to implement for a wide range of applications

Has ample supporting data

Re resents hi h c cle fati ue ade uatel

Strain life methods Involves more detailed analysis of plastic deformation at localized regions

Good for LCF

Some uncertainties may exist in results because several idealizations get compounded

Hence normally not used in regular practice but only for completeness and special

occasions Linear elastic fracture mechanics methods (LEFM)

Assumes that crack is already present and detected

The crack location is then employed to predict crack growth and sudden rupture withrespect to the stress nature and intensity

Most practical when applied to large structures in conjunction with computer codes andperiodic inspection


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Stress Life Method

R. R. Moore high-speed rotating beam machine.

ure en ng y means o we g s an no ransverse s ear.

The specimen shown is very carefully machined and polished with a final polishing

in the axial direction to void circumferential scratches.

Number of revolutions of the specimen required for failure are recorded.

The first test is made at a stress that is some what under the ultimate strength ofthe material.

Next, the test is repeated for a lower load, and so on.

The results are plotted in the S-N diagram, which is either semi-log or log-log.


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pure reversed bending without transverse shear

SFD

BMDMb


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The S-N Diagram for steel (UNS G41300), normalized, Sut=812 MPa.

Endurance Limit,

It is the stress atwhich the

component can

sustain infinite

number of cycles


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Endurance limit for non-ferrous

metals and alloys

The plot in the S-N diagram never

becomes horizontal for non-ferrous metalsand alloys

- ,at a specific number of cycles, normally at

5*108 cycles, must be used as fatigue

strength


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For different aluminium alloys (which is non-ferrous)

For non-ferrous metals and alloys, the S-N diagram never becomes horizontal

and hence they do not have endurance limit. Hence, a stress at a specific

number of cycles, normally at 5*108 cycles, must be used as fatigue strength


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Estimation of Endurance Limit

Instead of referring to experimental data-bank each time, it shouldbe possible to quickly estimate the value of endurance limit usingsome kind of formula

To enable that, data has been generated for different types of steels, for endurance limit with respect to the ultimate tensilestrength

This plot seemed to closely follow a combination of two straightnes, o w c e secon e ng a mos or zon a a

ut=

MPa

For steels, Endurance limit :

conditionsloadingactualin thelimitEndurance

bendingreverseinobtainedlimitEndurance

1460700

146050

'

'

=

=

>

=

e

e

ut

utut

e

S

S

MPaSforMPa

MPaSforS.S


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Stress concentration

The single most influential factor leading to high

possibility of crack initiation

Stress concentration can be due to

Function of geometry (sudden change in

.

and surface texture (surface finish, presence of

disintegrations etc.)


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Stress concentration (Kt

)-revised

Kt=Theoretical stress concentration factor

stressominal

stressMaximum=tK

dw

( )

FEMassuchsimulationnumerical

orsexperimentthroughDetermined

stressNominal

max

=

=

=

t

nomt

K

K

tdw

P


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Actual / Fatigue stress concentration factor, Kf

Also called as fatigue strength reduction factor

( ) ( )

factorionconcentratstresslTheoretica

21)-6&20-6Fig.(fromy valuesensitivitnotch

1111

=

=

+=+=tsshearfstf

K

q

KqKorKqK

tables)fromfactor,geometric(or


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Notch Sensitivity plot for Steels and UNS A92024-T wrought Al alloys

(Reverse bending or reverse axial loads)

Fig: 6-20 ; page : 295


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Notch Sensitivity plot for Steels and UNS A92024-T wrought Al alloys

(Reversed torsion condition)

Fig: 6-21 ; page : 296


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Estimation of Kf

Kf= 1+q(Kt -1).When q=0, the material has no sensitivity to notches, and

hence Kf=1.

When q=1, or when notch radius is large for which q is almost

equal to 1, the material has full notch sensitivity, and Kf= Kt.

, . .

Use the different graphs as given to obtain q for bending/axial

and torsional loading.

Whenever the graphs do not give values ofq for certaincombinations of data, use either Neuber equation or

Heywood equation.


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Use the Neuber equation when the notch iscircular/cylindrical.

( )

111

1

+=+

= KqKand

r

aqtf

Estimation of Kf

radiusnotch

strength.ultimateoffunctioni.e),(

cons anma er aasancons aneu er saw ere

=

= Sfa ut

For steel, with Sut

in kpsi, the Neuber constant can be approximated by a third-

orderpolynomial fit of data as

38253

38253

)10(67.2)10(35.1)10(51.219.0:

)10(67.2)10(51.1)10(08.3246.0:

ututut

ututut

SSSaTorsion

SSSaaxialorBending

+=

+=


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Use Heywood equation when the notch is NOTcircular/cylindrical but is a tranverse hole or

shoulder or groove.

( )121

+

=aK

KK

t

tf

Estimation of Kf

sizeesize/groovdersize/shoulhole

335page15;-6Tablein thegivenarevalues

=r

a

where

t

Fatigue Failure Resulting From Variable Loading 1-2

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