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
3
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
5
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
9
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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21
22
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
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