consider this mechanical parts even if
you design them
well satisfying mechanical strength
criteria it may fail due to a phenomenon
called fatigue historically many design
disasters have happened by neglecting
effect of fatigue factor
to understand what is fatigue let's
consider this metal wire you have to
break it so how will you break it will
you pull it from both ends or will you
do this
you bend the wire upward and downward
repetitively
your answer is obviously the second
option because this method requires less
effort compared to the first case this
is a well-known example of fatigue
failure so how does material fail due to
fatigue
answer for this question let us have a
close look at stress variation in wire
cross-section
when you bend it downwards bending
stress is induced in the wire it will be
tension at top area and compression at
bottom area
when wire is at equilibrium there will
not be any stress on wire cross-section
when wires bending upwards there will be
compression at top and tension at bottom
so if you trace stress-induced at a
point with respect to time it will vary
like this as a fluctuating stress with
time
initially the point will have positive
stress after that zero then negative
stress the same cycle repeats again and
again
such fluctuating stress is the root
cause of fatigue failure
when such fluctuating stress act on a
material it will initiate something
called micro crack this crack will begin
to grow with fluctuating load and over
time it will cause an abrupt failure
this is why failure due to fatigue is a
dangerous affair unlike failure due to
static load fatigue failure happens
without any warning it doesn't even make
a neck and the failure is completely
unpredictable
the same phenomenon can happen for axle
of this motor where it is undergoing
fluctuating stress due to gravity effect
of this mess
this rail wheel when it is contact with
with the track produces a high contact
stress but when the wheel rotates stress
gets relieved when it comes back to
original position contact stress arises
again
so this also is a case of fluctuating
stress it may fail due to fatigue if we
do not design it properly
same is the case with gear pair here
contact stress arises at mating point
now the most important part in fatigue
analysis relationship between stress
amplitude and number of cycles it can
execute before it fails
what will happen as stress amplitude
decreases
yes you are right as stress amplitude
decreases number of cycles required for
failure increases
anyway we will analyze this trend more
systematically we will draw number of
cycles in xyx stress amplitude and
y-axis both in logarithmic scale
let's start with the maximum stress a
material can withstand its ultimate
stress so this will happen as you
increase the stress even before
completing one cycle the material will
get broken so this will be the
corresponding point in SN graph
if you decrease the stress amplitude it
will execute more number of cycles
before it fails
decreasing stress even further it will
be able to execute even more number of
cycles
so this will follow a trend like this
forever you can see after particular
stress amplitude even with slight
decrease in stress number of cycles
required to make it fail increases
drastically
or in short if you have stress amplitude
below this limit number of cycles to
make it fail jumps to infinity or
material never fails after this limit
this limit is known as endurance limit
below endurance limit it is safe to
operate the material engineers always
try to design the components by keeping
stress amplitude below endurance limit
you can see that endurance limit is way
below ultimate stress value
it is a good approximation to consider
this two regions as linear
but here we had a case of complete
stress reversal where stress mean value
was 0 what will be the maximum stress
limit for this case where stress
reversal does not happen it has got a
mean value and amplitude for this
purpose we have to use something called
the Goodman diagram
in a goodman diagram mean value of
stress is drawn on x-axis amplitude of
stress is drawn on y-axis
when main value is zero we no safe
stress limit is same as endurance limit
when amplitude of stress is zero it is
same as a static loading condition so
safe limit for attention is ultimate
tensile stress at tension and safe limit
for compression as ultimate tensile
stress for compression
according to Goodman analysis safe
stress amplitude limits for all other
cases lie on straight lines connecting
this points
so for a particular stress mean value we
can find what's the maximum allowable
safe stress limit from this diagram it
will be here
similar analysis can be done considering
safe limit of amplitude zero condition
as yield strength of material this is
known as sober burg diagram generally
Goodman analysis is the most preferred
one
to learn more on fatigue failure check
the second video thank you