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Fatigue
MIET Engineering College
Compiled by S Renold Elsen
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Introduction
Since many of the machine parts axles, shafts,
crankshafts, connecting rods, springs,
pinion teeth are subjected to variable or alter
nating loads (also known as fluctuating or fatig
ue loads).
Therefore we shall discuss, the variable or
alternating stresses in this course.
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Stresses developed in a rotating shaft
subjected to a bending load.
As the specimen rotates, the bending stress at
the upper fibres varies from maximum
compressive to maximum tensile while the
bending stress at the lower fibres varies from
maximum tensile to maximum compressive.
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Endurance Limit
It is defined as maximum value of the
completely reversed bending stress which a
polished standard specimen can withstand
without failure, for infinite number of cycles
(usually 107 cycles).
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Alternating stresses
The stresses which vary from a minimum
value to a maximum value of the opposite
nature.
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Fluctuating stresses
The stresses which vary from a minimum
value to a maximum value of the same nature,
(i.e. tensile or compressive).
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Repeated stresses
The stresses which vary from zero to a certain
maximum value.
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Mean Stress
Stress amplitude
Together,s
mands
acharacterize fluctuating stress
2'
minmax ss
s
m
2
minmax' ss
s
a
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Effect of Loading on Endurance Limit
(Load Factor)
Kb =Load correction factor for the reversed orrotating bending load.
Its value is usually taken as unity.
Ka =Load correction factor for thereversed axialload.
Its value may be taken as 0.8.
Ks =Load correction factor for the reversed
torsional or shear load.Its value may be taken as 0.55 for ductilematerials and 0.8 for brittle materials.
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Effect of Surface Finish on Endurance
Limit (Surface Finish Factor)
When the surface finish factor is known, then the
endurance limit for the material of the machine
member may be obtained by multiplying the
endurance limit and the surface finish factor.The value of surface finish factor is unity for a
mirror polished material.
The endurance limit for mirror polished materialis maximum and it goes on reducing due to
surface condition.
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Effect of Size on Endurance Limit
(Size Factor)
A little consideration will show that if the size of thestandard specimen is increased, then the endurancelimit of the material will decrease.
This is due to the fact that a longer specimen will
have more defects than a smaller one.Notes:
1. The value of size factor is taken as unity for the standardspecimen having nominal diameter of 7.657 mm.
2. When the nominal diameter of the specimen is more than7.657 mm but less than 50 mm, the value of size factormay be taken as 0.85.
3. When the nominal diameter of the specimen is more than50 mm, then the value of size factor may be taken as 0.75
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Effect of Miscellaneous Factors on
Endurance Limit
Other factors such as
reliability factor (Kr),
temperature factor (Kt),
impact factor (Ki) etc.
has effect on the endurance limit of a material.
In solving problems, if the value of any of the
above factors is not known, it may be taken as unity.
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Fatigue Stress Concentration Factor
When a machine member is subjected to
cyclic or fatigue loading, the value of fatigue
stress concentration factor shall be applied
instead of theoretical stress concentrationfactor.
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Factor of Safety for Fatigue Loading
When a component is subjected to fatigueloading, the endurance limit is the criterion forfaliure.
For steel, e=0.8 to 0.9 y
e=Endurance limit stress for completelyreversed stress cycle, and
y=Yield point stress.
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Notch Sensitivity
In cyclic loading, the effect of the notch or the fillet isusually less than predicted by the use of the theoreticalfactors.
The difference depends upon the stress gradient in the
region of the stress concentration and on the hardnessof the material.
It may be defined as the degree to which thetheoretical effect of stress concentration is actuallyreached.
The stress gradient depends mainly on the radius ofthe notch, hole or fillet and on the grain size of thematerial.
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Combined Steady and Variable Stress
The failure points from fatigue tests made withdifferent steels and combinations of mean and variablestresses are plotted in Fig. 6.15 as functions of variablestress (v) and mean stress (m). The most significant
observation is that, in general, the failure point is littlerelated to the mean stress when it is compressive but isvery much a function of the mean stress when it istensile. In practice, this means that fatigue failures arerare when the mean stress is compressive (or
negative). Therefore, the greater emphasis must be given to the
combination of a variable stress and a steady (or mean)tensile stress.
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Solving of combined stresses
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1. Gerber method,
2. Goodman method, and
3. Soderberg method.
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Gerber Method for
Combination of Stresses