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FATIGUE
• Fatigue is the progressive and localized
structural damage that occurs when a material
is subjected to cyclic loading.
• The nominal maximum stress values are less
than the ultimate tensile stress limit, and may
be below the yield stress limit of the material.
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ANALYSIS OF FATIGUE
• Stress life approach
• Strain life approach
•
Fracture mechanics approach
In this presentation we shall see about Stress life
approach.
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STRESS LIFE APPROACH
• This nominal stress (S-N) method was the first
approach developed to try to understand this
failure process
• The nominal stress approach is best suited to
that area of the fatigue process known
as high-cycle fatigue
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Stress Cycles
Typical Fatigue Stress Cycles,
(a) Fully Reversed (b) Offset, (c) Random
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The S-N Curve
• In high-cycle fatigue situations, materials
performance is commonly characterized by
an S-N curve, also known as a Wohler curve
• Most determinations of fatigue properties
have been made in completely reversed
bending (i.e., R = –1), by means of the so-
called rotating bend test
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• The stress level at the surface of the specimen is
calculated using the elastic beam equation,
S= Mc/I
S- the nominal stress acting normal to the cross-
section
M- the bending moment
c - the distance of the surface from the neutral axis
I - the moment of inertia
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• S-N data are nearly always presented in the
form of a log-log plot of alternating stress
amplitude versus cycles to failure, with the
actual Wöhler line representing the mean of
the data
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Limits of the S-N Curve
• The S-N approach is applicable to situations
where cyclic loading is essentially elastic
• This means that the S-N curve should be
confined on the life axis to numbers greater
than about 10,000 cycles in order to ensure no
significant plasticity is occurring.
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The Influence of Mean Stress
• Most basic fatigue data are collected in thelaboratory by means of testing procedureswhich employ fully reversed loading
• Most realistic service situations involvenonzero mean stresses
• Fatigue data collected from a series of tests
designed to investigate different combinationsof stress amplitude and mean stress arecharacterized by Haigh diagram
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HAIGH’s diagram
• Notice that the influence of mean stress is
different for compressive and tensile meanstress values for a given number of cycles to
failure
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EMPERICAL RELATIONS
• Several empirical relationships which relate
alternating stress amplitude to mean stress
have been developed
• Of all the proposed relationships, two have
been most widely accepted
1. Goodman :
2. Gerber :
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Factors Influencing Fatigue Life
• Component size
• The type of loading
•
The effect of notches• The effect of surface finish
• The effect of surface treatment
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RAINFLOW CYCLE COUNTING
• The signal measured, in general, a random
stress S(t) is not only made up of a peak alone
between two passages by zero, but also
several peaks appear, which makes difficultthe determination of the number of cycles
absorbed by the structure
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• The counting of peaks makes it possible toconstitute a histogram of the peaks of therandom stress which can then be transformed
into a stress spectrum giving the number of events for lower than a given stress value.
• The stress spectrum is thus a representationof the statistical distribution of thecharacteristic amplitudes of the random stressas a function of time
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Rules of the flow
• The origin of the random stress is placed on
the axis at the abscissa of the largest peak of
the random stress
If the fall starts from a peak :
a) The drop will stop if it meets an opposing
peak larger than that of departure.
b) it will also stop if it meets the path traversed
by another drop previously determined
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c) The drop can fall on another roof and tocontinue to slip according to rules a and b
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If the fall begins from a valley:
d) the fall will stop if the drop meets a valley
deeper than that of departure
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e) the fall will stop if it crosses the path of a drop
coming from a preceding valley
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f) the drop can fall on another roof and continue
according to rules d and e.
• The horizontal length of each rainflow defines
a range which can be regarded as equivalent
to a half-cycle of a constant amplitude load
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• Lets explain it with an example.
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• First, the stress S(t) is transformed to aprocess of peaks and valleys. Then the timeaxis is rotated so that it points downward.
• At both peaks and valleys, water sources areconsidered. Water flows downward accordingto the rules
•
Let X denotes range under consideration; Y,previous range adjacent to X; and S startingpoint in the history
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Details of the cycle counting are as follows:
• S=A; Y=|A-B| ; X=|B-C|; X>Y. Y contains S, that
is, point A. Count |A-B| as one-half cycle and
discard point A; S=B
• Y=|B-C|; X=|C-D|; X>Y. Y contains S, that is,
point B. Count |B-C| as one half-cycle and
discard point B; S=C
• Y=|C-D|; X=|D-E|; X<Y
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• Y=|D-E|; X=|E-F|; X<Y
• Y=|E-F|; X=|F-G|; X>Y. Count |E-F| as one
cycle and discard points E and F.• Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is,
point C. Count |C-D| as one-half cycle and
discard point C. S=D.
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• Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is,
point C. Count |C-D| as one-half cycle and
discard point C. S=D.• Y=|D-G|; X=|G-H|; X<Y.
• Y=|G-H|; X=|H-I|; X<Y
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• Count |D-G| as one-half cycle, |G-H| as one-
half cycle, and |H-I| as one-half cycle
• End of counting.
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