DESIGN AGAINST FATIGUE

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29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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DESIGN AGAINST FATIGUE

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DESIGNING AGAINST FATIGUE

Fracture surface which usually exhibits smooth areas
which correspond to the gradual crack growth stage,
and rough areas, which correspond to the
catastrophic fracture stage.

The smooth parts of the fracture surface usually
exhibit beach marks which occurs as a result of
changes in the magnitude of the fluctuating fatigue
load.

Fatigue behavior of materials is usually described by
means of the S
-
N diagram which gives the number
of cycles to failure, N as a function of the max
applied alternating stress.


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DESIGNING AGAINST FATIGUE

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4

Types of fatigue loading

Alternating stress and Fluctuating stress

1.
Alternating stress: Stress varies from a positive value
to the negative value

Alternating tension


compression

Stress ratio, R =

min

/

max
=
-
1



DESIGNING AGAINST FATIGUE

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Types of fatigue loading


2. Fluctuating stress: Stress varies from a positive value
to a negative value.

Positive R value

Greater tensile stress than compressive stress



max

=

m

+

v



max

=

m

-


v






DESIGNING AGAINST FATIGUE

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Fluctuating Stress Definitions

Mean Stress:

m

= ½(

max

+

min
)

Alternating Stress:

v

= ½(

max

-


min
)



The Mean Stress is analogous to a static
stress, while the Alternating Stress
represents the amplitude of the fluctuating
stress.

7

Figure (a)


S
-
N curves for carbon steel





(b)
-

S
-
N curves aluminum alloy





DESIGNING AGAINST FATIGUE

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DESIGNING AGAINST FATIGUE

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S
-
N curve is a graphical representation of the maximum
applied stress versus the number of stress cycles N before the
fatigue failure on a semi
-
log graph. For ferrous metals like
steel the curve becomes asymptotic at 10^6 cycles. The
completely reversed stress which a material can withstand
10^6 cycles without failure is called ENDURANCE LIMIT of
the material.

For non ferrous materials, the curve slopes gradually even
after 10^6 cycles. These materials do not have a limiting value
of endurance in true sense. In these cases endurance limit is
expressed as a function of number of cycles.

DESIGNING AGAINST FATIGUE

In the majority cases, the reported fatigue strength or
endurance limits of the materials are based on the test
of carefully prepared small samples under laboratory
condition.

Such values cannot be directly used for design
purposes because the behavior of a component or
structure under fatigue loading does depend not only
on the fatigue or endurance limit of the material used in
making it, but also an several other factors including :

Size and shape of the component or structure

Type of loading and state of stress

Stress concentration

Surface finish

Operating temperature

Service environment

Method of fabrication

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Endurance
-
limit modifying factors





e

= k
a
k
b
k
c
k
d
k
e
k
f
k
g
k
h

e


Where

e

= endurance limit of component



e
’ = endurance limit experimental


k
a

= surface finish factor (machined parts have different finish)


k
b

= size factor (larger parts greater probability of finding defects)


k
c

= reliability / statistical scatter factor (accounts for random
variation)


k
d

= operating T factor (accounts for diff. in working T & room T)


k
e

= loading factor (differences in loading types)


k
f

= stress concentration factor


k
g

= service environment factor (action of hostile environment)


k
h

= manufacturing processes factor (influence of fabrication
parameters)

DESIGNING AGAINST FATIGUE

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DESIGNING AGAINST FATIGUE

k
a

=
Surface finish factor

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DESIGNING AGAINST FATIGUE

k
b

=
Size factor

Large engineering parts have lower fatigue strength
than smaller test specimen

Greater is the probability of finding metallurgical
flaws that can cause crack initiation

Following values can be taken as rough guidelines :

k
b
= 1.0 for component diameters less than 10 mm

k
b

= 0.9 for diameters in the range 10 to 50 mm

k
b
= 1


[( D


0.03)/15], where D is diameter
expressed in inches, for sizes 50 to 225 mm.

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DESIGNING AGAINST FATIGUE

k
c

=
Reliability factor

Accounts for random variation in fatigue strength.

The following value can be taken as guidelines

k
c

= 0.900 for 90% reliability

k
c

= 0.814 for 99 % reliability

k
c

= 0.752 for 99.9 % reliability


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DESIGNING AGAINST FATIGUE

k
d

=
Operating temperature factor

Accounts for the difference between the test
temperature and operating temperature of the
component

For carbon and alloy steels, fatigue strength not
affected by operating temperature


45 to 450
0
C
k
d

= 1

At higher operating temperature



k
d
= 1


5800( T


450 ) for T between 450 and
550
o
C, or



k
d
= 1


3200( T


840 ) for T between 840 and
1020
o
F

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DESIGNING AGAINST FATIGUE

k
e

=
Loading factor

Accounts for the difference in loading between
lab. test and service.

Different type of loading, give different stress
distribution



k
e
= 1 for application involving bending



k
e
= 0.9 for axial loading



k
e
= 0.58 for torsional loading


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DESIGNING AGAINST FATIGUE

k
f

=
Fatigue stress concentration factor

Accounts for the stress concentration which may
arise when change in cross
-
section

k
f
= endurance limit of notch
-
free part


endurance limit of notched part

Low strength, ductile steels are less sensitive to
notched than high
-
strength steels

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DESIGNING AGAINST FATIGUE

k
g

=
Service environment factor


Accounts for the reduced fatigue strength due to
the action of a hostile environment.

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DESIGNING AGAINST FATIGUE

k
h

=
Manufacturing process factor

Accounts for the influence of fabrication parameter

Heat treatment, cold working, residual stresses and
protective coating on the fatigue material.

It is difficult to quantify, but important to included.

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DESIGNING AGAINST FATIGUE

Endurance limit/Fatigue strength

The endurance limit, or fatigue strength, of a given material
can usually be related to its tensile strength, as shown in
table (next slide)

The endurance ratio, defined as (endurance limit/ tensile
strength), can be used to predict fatigue behavior in the
absence of endurance limits results.

From the table shows, endurance ratio of most ferrous
alloys varies between 0.4 and 0.6

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Theories of Fatigue Failure

Gerber Criterion

Goodman Criterion

Soderberg Criterion


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The failure points from fatigue tests made with different steels and combinations of
mean and variable stresses are plotted as a functions of variable stress and mean
stress. It shows the three criteria for failure of the materials when subjected
combined stress.

The most significant observation is that the failure point is little related to the mean
stress when stress is compressive. It means that fatigue failures are rare when the
mean stress is compressive.

Theories of Fatigue Failure

Gerber Criterion




Goodman Criterion



Soderberg Criterion



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1
2










e
v
u
m
n
n




n
e
v
u
m
1






n
e
v
y
m
1






The theories are defined as given below:

limit
endurance
is
stress
yield
is
sterss
variable
is
stress
mean
is
where
e
y
v
m