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Fatigue
Part 2
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6-8 Fatigue Strength : Basics
Low-cycle fatigue considers the range fromN=1 to about 1000 cycles.
In this region, the fatigue strength is only
slightly smaller than the tensile strength .
High-cycle fatigue domain extends from 103
to the endurance limit life (106 to 107 cycles).
Experience has shown that high-cycle fatigue
data are rectified by a logarithmic transform
to both stress and cycles-to-failure.
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Fatigue Strength at Different
N Define the fatigue strength at a specified number of cycles as
By combining the elastic strain relations, we can get
Define fas the fraction of tensile strength. The value offat 103 cycles isthen
To find b, substitute the endurance strength and the corresponding cyclesand solving for b as
For example, for steels when
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Fatigue Strength : General
For actual mechanical applications, the fatigue strength
calculated above is extended to a more general form as
: cycle to failure
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Endurance Limit Modifying
Factors The endurance limit of the rotating-beam specimen might differ from
the actual application due to the following differences fromlaboratory tests.
Material : composition, basis of failure, variability
Manufacturing : method, heat treatment, fretting corrosion, surface
condition, stress concentration
Environment : corrosion, temperature, stress state, relaxation times.
Design : size, shape, life, stress state, stress concentration, speed,fretting, galling
Modifying factors ofsurface condition, size, loading, temperature,and miscellaneous items are proposed by Marin to quantify thesedifferences.
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Marin Modification Factors on
Endurance Limit
where
= surface condition modification factor = size modification factor
= load modification factor
= temperature modification factor
= reliability factor
= miscellaneous-effects modification factor
= rotary-beam test specimen endurance limit
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Surface and Loading Factors
Surface Factor : the surface modification factor depends on thequality of the finish of the actual part surface and on the tensilestrength of the part material. It can be calculated as
Loading Factor : the axial and torsional loadings results in differentendurance limit than that of a standard rotating-bending test. Theload factor applies to other loading conditions as
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Size Factor
Size Factor : the size factor has been evaluated using 133 set
of data points in the literature. For axial loading, . Forbending and torsion can be expressed as
Effective dimension is introduced for non-circular cross sectionby equating the volume of the material stressed at and above95 percent of the maximum stress to the same volume in therotating-beam specimen.
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Temperature Factor
At temperatures lower thanroom temperature, brittle
fracture of a component
needs to be considered first;
at operating temperatureshigher than room
temperature, yield should be
investigated.
If only tensile-strength data
are available, polynomial
fitting to the data could
provide the temperature
Fig.2-9 : yield stress drops with
temperature
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Reliability Factor
Most endurance strength data arereported as mean values.
To account for the scatter of measurement
data, the reliability modification factor iswritten as
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Miscellaneous-Effects Factor
The miscellaneous factor intends toaccount for the reduction in endurance
limit due to all other effects, such as
residual stresses, different material
treatments, directional characteristics of
operations, and corrosion.
One should also treat the miscellaneous-
effect factor as a reminder that these must
accounted for, because actual values of
are not always available.
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Fatigue Stress
Concentration Factor
The fatigue stress concentration factorfrom the existence of irregularities or
discontinuities in materials is defined a
Let be the static stressconcentration factor, the relations
between fatigue stress concentration
and the notch sensitivity is
for bending and axial loadings
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Characterizing Fluctuating
Stresses
Fluctuating stressesoften of sinusoidalpatters due to thenature of somerotating machinery.
The peaks of the waveare more importantthan its shape.
Fluctuating stressesare described using asteady componentand an alternating
component.
F ti F il C it i f
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Fatigue Failure Criteria for
Fluctuating Stresses
Gerber
modified Goodman
Soldergerg
ASME-elliptic
Langer
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Combination of Load Modes
Fatigue problems can be categorized into- completely reversing simple loads : can be handled using S-N curve; only one type of
loading is allowed with midrange stress being zero.
- fluctuating simple loads : can be resolved using a criterion to relate midrange and
alternating stresses; again, only one type of loading is allowed.
- combinations of loading modes : a combinations of different types of loading.
apply appropriate stress concentration factors to each type ofstress
calculate equivalent von Mises stress
select a fatigue failure criteriondiscard the load factor for torsional stress, consider axial stress
only.
C bi ti f B di
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Combination of Bending,
Torsion, and Axial Stressesapply appropriate stress concentration factors to each type of stress
calculate equivalent von Mises stress
select a fatigue failure criterion
discard the load factor for torsional stress, consider axial stressonly.
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Varying, Fluctuating Stresses
Instead of a single fully reversed stresshistory block composed of n cycles,
suppose a machine part, at a critical
location is subjected to.
A fully reversed stress for cycles, for cycles, ..., or
A wiggly time line of stress exhibiting many and different peaks and
valleys.
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Cumulative Fatigue Damage
The Palmgren-Miner cycle-ratiosummation rule uses linear damage
accumulation concept as
: the number of cycles at stress level : the number of cycles to failure at stress level
: the parameter determined by experiment, in the range
with an average value near unity