Failure Fatigue and Creep
Summary
TLDRThis script discusses mechanical failures due to fatigue and creep in engineering materials. Fatigue, responsible for 90% of mechanical part failures, is a sudden failure under fluctuating stress, often initiated from surface defects. Creep is the continuous deformation at elevated temperatures under constant stress, progressing through primary, secondary, and tertiary stages. The lecture includes examples of fatigue testing, the significance of stress amplitude and mean stress, and the use of Larson-Miller parameters for estimating rupture times at different temperatures. It emphasizes the importance of understanding these phenomena for predicting material performance and preventing failures.
Takeaways
- đ© Fatigue is a type of failure caused by fluctuating stress on structures, such as a bridge with cars driving over it, and can lead to sudden failure without warning.
- đ Fatigue can occur even when the maximum stress experienced by a part is less than its yield stress, and it's responsible for about 90% of mechanical engineering failures.
- đ A study by Sherry Labs showed that improperly installed bolts on a mining truck led to sudden wheel detachment, illustrating the real-world consequences of fatigue.
- đ ïž Fatigue testing machines simulate the dynamic stress on parts to predict their performance and lifespan under cyclic stress conditions.
- đ Fatigue behavior is often plotted on a graph with stress amplitude on the y-axis and the number of cycles to failure on the x-axis, showing different behaviors for steels and non-ferrous alloys.
- đ For many steels, there's a 'safe' stress level below which parts won't fail due to fatigue, while non-ferrous alloys often have no fatigue limit and require a specified fatigue strength.
- đŹ Fractography of failed parts can reveal brittle fracture surfaces and 'beachmarks', which are indicative of fatigue failure and provide insight into the failure process.
- đĄïž Surface treatments like shot peening and material modifications can enhance a part's resistance to fatigue by reducing stress concentrators and improving surface strength.
- đ Creep is the deformation of materials under constant load and elevated temperature, occurring in three stages: primary, secondary, and tertiary creep, with secondary being the most critical for long-term performance.
- â±ïž The Larson-Miller parameter is a useful tool for estimating rupture times at different temperatures and stresses, allowing for faster testing and extrapolation to service conditions.
Q & A
What is fatigue in the context of mechanical engineering?
-Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stress. It can lead to part failure even if the maximum stress is much less than the yield stress measured in tensile testing.
Why is fatigue failure particularly dangerous?
-Fatigue failure is dangerous because it can occur suddenly and without warning, similar to a brittle fracture. The fracture surface, when examined, often appears brittle, which can be deceiving about the nature of the failure.
What role does the installation of parts play in fatigue failure?
-The installation of parts plays a significant role in fatigue failure. Incorrect installation, as seen in the case of the mining truck wheel studs, can lead to premature failure even when the parts themselves are suitable for the service they are put to.
How can fatigue be simulated to test a part's performance?
-Fatigue can be simulated using specialized testing apparatuses that flex the part back and forth, rotating it through multiple directions and subjecting it to sinusoidal stress cycles. The stress parameters such as mean stress, stress amplitude, and frequency can be adjusted to simulate real-world conditions.
What are the two common types of fatigue behavior seen in materials?
-The two common types of fatigue behavior are one seen in many steels, where there is a safe stress level below which the part will not fail, and the other seen in non-ferrous alloys, where there is no fatigue limit and the material will eventually fail given enough cycles.
How is fatigue life defined in materials science?
-Fatigue life is defined as the number of cycles it takes to cause failure at a specified stress level. It helps predict how long a part will last before needing replacement under cyclic stress.
What are the three stages of fatigue failure?
-The three stages of fatigue failure are: 1) crack initiation, where a crack forms at a surface defect, 2) crack propagation, where the crack advances incrementally with each stress cycle, and 3) final failure, which occurs suddenly when the crack reaches a critical size.
What is creep, and how does it differ from fatigue?
-Creep is the deformation of a material under constant stress and temperature over time, often occurring in load-bearing parts at elevated temperatures. It differs from fatigue in that it involves continuous deformation rather than cyclic stress leading to sudden failure.
What are the three stages of creep?
-The three stages of creep are: 1) primary creep, with an initial instantaneous deformation followed by decreasing strain rate, 2) secondary creep, where the strain rate reaches a steady state, and 3) tertiary creep, where the strain rate increases leading to rupture.
How can the Larson-Miller parameter be used to estimate rupture times?
-The Larson-Miller parameter is used to estimate rupture times by plotting it against stress on a graph. By determining the parameter at a high temperature and then extrapolating to the service temperature, one can estimate the time to rupture at that temperature.
Outlines
đ§ Introduction to Fatigue and Creep
The script begins by defining fatigue as a type of failure in structures under fluctuating stress, such as a bridge with cars driving over it. Fatigue can lead to sudden failure even if the stress is below the material's yield stress. It's responsible for about 90% of mechanical engineering failures and often results in brittle fractures. An example is provided of a failure study by Sherry Labs on mining truck wheel bolts that failed due to incorrect installation. The importance of fatigue testing is emphasized, with machines simulating sinusoidal stress to predict part performance under cyclic stress. The script also introduces the concept of fatigue life and the two types of fatigue behavior observed in materials: one with a fatigue limit and one without.
đ Fatigue Behavior and Testing
This section discusses the fatigue behavior of steels and non-ferrous alloys, highlighting that steels have a fatigue limit below which they won't fail, while non-ferrous alloys do not. The concept of fatigue strength is introduced as the stress level for failure at a specified number of cycles. The script also explains the importance of considering probability curves for fatigue life predictions. Fatigue life is described as the number of cycles to cause failure at a specified stress level. The three stages of fatigue failure are outlined: crack initiation, crack propagation, and final failure. The use of fractography to analyze failed parts is discussed, including the identification of beachmarks and striations as indicators of fatigue.
đĄïž Creep and Its Impact on Materials
The script shifts focus to creep, which affects parts under constant load and elevated temperatures. Creep occurs in three stages: primary, secondary, and tertiary, with the secondary stage being the most critical as it represents the majority of a part's service life. The secondary creep rate is emphasized as a key parameter, and the temperature dependence of creep is discussed, noting that creep becomes significant at temperatures above 40% of a material's melting point. Methods to strengthen materials against creep, such as shot peening and modifying surface conditions, are suggested.
â±ïž Analyzing Creep Data and Estimations
This part of the script delves into analyzing creep data, with an example problem involving a steel alloy subjected to a tensile stress at a specific temperature. The concept of steady-state creep rate is introduced, and a method to calculate elongation after a given time is demonstrated. The script also covers how to determine the stress exponent 'n' from log-log plots of creep rate versus stress. An example calculation of the activation energy for creep using stress data at different temperatures is provided, illustrating how to use this information to estimate creep rates under different conditions.
đŹ Advanced Creep Analysis and Extrapolation
The script discusses advanced creep analysis, including the use of Larson Miller parameters and plots to estimate rupture times at different temperatures and stresses. The process of extrapolating creep data from high-temperature tests to predict performance at service temperatures is explained. The importance of understanding material flaws and their impact on failure is reiterated, with a summary of how temperature, stress, and material properties affect failure modes such as fracture, fatigue, and creep.
đ Summary of Engineering Materials and Failure Theories
The final part of the script summarizes the key points about engineering materials and failure theories. It emphasizes that materials often fail at stresses lower than predicted due to inherent flaws, which act as stress concentrators. The script outlines how failure types are influenced by temperature, stress, and loading rates, with a brief overview of the factors affecting fracture, fatigue, and creep failures. The summary concludes with a reminder of the importance of understanding these concepts for designing reliable and safe engineering components.
Mindmap
Keywords
đĄFatigue
đĄCreep
đĄStress
đĄYield Stress
đĄFatigue Life
đĄFractography
đĄShot Peening
đĄStress Concentrators
đĄStrain Hardening
đĄLarson-Miller Parameter
Highlights
Fatigue is defined as failure due to dynamic and fluctuating stress.
Fatigue can cause failure even if the stress is below the material's yield stress.
Fatigue is responsible for about 90% of mechanical engineering failures.
Fatigue fractures are sudden and can resemble brittle fractures.
A case study from Sherry Labs is mentioned, detailing a failure in mining truck wheel bolts.
Incorrect installation can lead to fatigue failure, as seen in the mining truck wheel case.
Fatigue testing machines simulate dynamic stress to predict part performance.
Fatigue tests can adjust mean stress, stress amplitude, and frequency.
Fatigue life is the number of cycles to failure at a specified stress level.
Fatigue behavior in steels shows a safe stress level below which failure doesn't occur.
Non-ferrous alloys may not have a fatigue limit, requiring a specified fatigue strength instead.
Fatigue life can be plotted on a logarithmic scale with cycles to failure on the x-axis.
Fatigue failure occurs in three stages: initiation, propagation, and final fracture.
Beachmarks or striations on fracture surfaces are indicative of fatigue failure.
Surface treatments like shot peening can improve resistance to fatigue.
Creep is the deformation that occurs under constant load and elevated temperature.
Creep occurs in three stages: primary, secondary, and tertiary, with secondary being the most critical.
The steady-state creep rate is crucial as parts spend most of their life in secondary creep.
Creep rate is influenced by temperature, stress, and material constants.
Larson Miller parameters can be used to estimate rupture times at different temperatures and stresses.
Engineering materials can fail at stresses lower than theoretical predictions due to inherent flaws.
Stress concentrators, such as sharp corners, can lead to premature failure and should be avoided in design.
Transcripts
hi so we're going to talk about fatigue
and creep and failure due to these
mechanisms today so first to Define
fatigue fatigue is defined as a form of
failure that occurs in structures that
are sub subjected to a dynamic and
fluctuating stress so you might imagine
um a bridge with cars driving repeatedly
over it so the number of cars on the
bridge at any given time might vary it
might be bouncy a little bit if it's a
flexible Bridge so you can imagine
something like that the thing about
fatigue is that Parts can fail even
though the maximum stress that the part
might be subjected to is much less than
the yield stress that you might measure
in a tensil testing machine um it's
actually responsible for about 90% of uh
life failures mechanical engineering
failures of parts and the bad part is
that it can occur suddenly and with and
without warning just like a a brittle
fracture um in fact the fracture is
brittle in nature if you examine it
using fractography you can see that the
surface looks like a brittle fracture
surface for for part of the surface at
least um so here in this picture there
was an interesting failure study done by
Sherry Labs the link is given below if
you'd like to read the full study but
the gist of it is these studs are bolts
were used to hold on the Wheel to a big
mining truck and of course the wheel
just fell straight off
um one day after the parts had been in
service for a long time they wanted to
know what went on it turns out that the
the bolts that they were using were okay
for the service that they were being put
to but they were in installed
incorrectly and that's why they failed
um but they failed after a certain
amount of use um and just all of a
sudden without warning so they were
interested in doing the failure study
you can see here if you look at the
bolts and remember what it looked like
when we did those tensile tests um these
do look a lot like brittle fracture so
you see these abrupt kind of um Parts
where you you have little to no necking
and when we zoom in and look at the
parts later we'll see what the fracture
surface actually looks like um but a lot
of it will look like a brittle brittle
surface now you can simulate fatigue of
course if you know that your part is
going to be subjected to fatigue you
would like to test the part and see how
it's going to perform in service and so
they've designed many machines um uh
fatigue testing apparatuses that um Can
can do this for you so a schematic of it
is shown here basically you have
something that flexes the part back and
forth and rotates the part through so
that it gets flexed in multiple
directions um and then it can do that
for as many cycles as you like um
basically what they do is they subject
it to this sort of beautiful sinusoidal
stress now in reality in service the
stress might not be that beautiful in
sinos soidal it might be much more
erratic um but machines do the best they
can to simulate that stress and what
they do is they set this stress
parameter here you can change the mean
or average stress and you can change the
stress amplitude you can change the
frequency of the um oscillations of the
stress and then you just run it to
failure you wait until the part breaks
and you do that for multiple scenarios
on the same type of material so that you
can get a feel for how that part will
perform under a cyclic applied
stress of course you want to replicate
the actual conditions of service as
closely as possible here's some images
of Some Testing apparatus that I found
online um basically the tester will
subject a specimen to a stress amplitude
that's on the order of 2third of the
tensile strength and then what you do is
plot the number of Cycles to failure
versus the stress so here's a a couple
images of those plots so here um what's
plotted in this case is the stress
amplitude you could change it you could
change it to the mean stress you could
plot whatever parameter you're
interested in regarding the stress on
the y axis and then on the x- axis you
plot n which is the number of Cycles to
failure
okay and so this is a logarithmic plot
with Cycles to failure here um there's
basically two types of fatigue behavior
that are seen commonly one type of
fatigue behavior is seen for many
different Steels that's the one up here
at top with this curve and then on the
bottom curve you see that for a lot of
non feris Alloys um and we'll talk about
those two scenarios so for these two
different scenarios here well for both
of them actually higher stress is
actually going to give a lower number of
Cycles to failure that's why the curve
goes up as it approaches and equals uh
low numbers okay it goes up there it
with your stress amplitude Okay so the
part will fail at a lower number of
Cycles if you subject it to a higher
stress not really surprising there okay
so um next what you see with some Steels
with many Steels is that for for these
Steels as long as you keep the stress
below what's termed a safe level the
part won't fail on you okay um so you
have to keep it at a low stress and then
what you are is you're in this safe
region here if because the Curve will
flatten out um as it approaches high
high numbers of Cycles so as long as you
keep it below that stress amplitude then
the part will perform um well okay
that's a Steel type Behavior but for
some materials um there is no fatigue
limit when you approach that limit that
flat out uh that flattening part of the
curve there that's called the fatigue
limit but for some materials non- feris
Alloys there is no fatigue um limit in
those cases they often specify a fatigue
strength instead and the fatigue stress
uh strength is the stress level for
failure at a specified number of Cycles
so you say well I would like my part to
perform for X number of years before I
recommend replacement so what's my
fatigue strength at that and then you
design your part um so that it will have
the specified fatigue strength that you
want for the number of Cycles to failure
that you want
okay okay now you have to be really
careful because those curves that I
showed were actually average curves and
statistically what that means is that
half of them are going to fail below
that level if you if that's your mean
curve then half of them are going to
fail below that a more appropriate
treatment might be a series of
probability curves um and so if you go
on and you become a materials engineer
material scientist I would hope that you
would do this sort of thing okay and
plot plot uh a a parameter and then stay
in the safe limit even for the low
probabilities of failure
now um another important parameter that
sometimes gets cited is the fatigue life
and the fatigue life is the number of
Cycles to cause failure at a specified
stress level so you specify the stress
level and then you see how long it is
till the person has to change that part
out basically um fatigue when it starts
it happens in three stages it usually
starts off with a crack or a scratch or
something like that so you have a a
defect in your surface it could be the
threading on your bolt it could be dent
in your surface a scratch a rusted spot
whatever and then at that point at that
defect a crack will form okay and this
usually happens at the surface and then
in the second stage that crack that's
formed will advance incrementally with
each stress cycle so every stress cycle
the crack will move a little further and
a little further and a little further
when it's reached a certain point some
critical size then the final failure
will happen like that and that's why we
say that you know fatigue failure
happens without warning because if you
don't know the crack is there all of a
sudden the part will just fail one day
and you've got yourself what looks like
a brittle fracture
failure now there's people that do these
analyses like the um example that we
showed earlier and then you can look at
the fracture surface and see what's
going on there's certain characteristic
things that they see um in these fatigue
parts so first of all this is an image
of one of those bolts that failed on
that we showed on that very first slide
and it's exhibiting something called a
beachmark it's also sometimes called
growth rings or uh clam shells um but
anyway it shows this kind of
characteristic layering look kind of
like a tree ring or a go growth ring um
and what happens there is the crack is
advancing but then um and it's being
subjected to stress but then the part is
taken out of service for some time maybe
everybody goes home for the night or
maybe maybe the part is on a bridge and
um there's not too many cars in the
bridge that late at night or whatever
okay so it's allowed to relax a little
bit and then it's subjected to the
stress again allowed to relax a little
bit subjective relax and this forms a uh
very distinct looking pattern that
people have learned to recognize as
being a sign of fatigue
failure um they're bigger they're
visible to the naked eye or with just a
simple little handheld lens now there's
also if you look at the part under an
electron microscope or a high power M
microscope you can see what are known as
striations inside these Beach marks and
the striations are microscopic and it
shows you the advance of the crack front
during just one stress cycle and looks
like little ripples all right now down
here in the lower right hand corner is a
um a part from a totally different
website that I've cited here and what
that looks like it'll show you the crack
formed it initiated down here at the
bottom and then you have your kind of
beachmark looking pattern down here
until the crack Advanced far enough the
flaw Advanced far enough that boom
you've got your brittle fracture failure
and this is what that surface looks like
okay so um so you can figure out a lot
from that
fractography now since most of these um
defects the cracks start at the surface
anything that you can do to strengthen
the surface is a good thing okay so you
can do what's called shot peening which
introduces um uh defects at the surface
um hardening strain hardening um you can
caror it you can alloy it in other words
alloing will strengthen apart and you
can also remove those stress
concentrators um if you have very small
radi of curvature very sharp corners or
anything like that on your part then
your fatigue will want to set in there
so anything that you can do to make the
radius of curvature larger would be good
um so that's also a good thing to think
about okay so that's fatigue and fatigue
life now let's talk about creep there's
some parts that aren't necessarily
subjected to cyclic loads with a stress
that varies in time but there may be a
loadbearing type thing they're supposed
to hold a long tense ESS for a long time
and it's not cyclic in nature just
really heavy all the time for example
those parts are subjected to creep okay
oftentimes these parts um say for
example if it's in a jet engine or
something like that this also happens at
elevated temperatures the part gets
really hot in service so if you have
kind of a constant load over time at an
elevated temperature your part is
subjected to creep okay so there's
there's three stages of creep first of
all when you first place the part in
service
um the very first day or whatever first
few days this is called primary creep
and in that you have first of all an
instantaneous deformation the part will
deform the instant that you put it in
service by some amount it'll get all
stretched out and then um the slope here
this instantaneous deformation the slope
will decrease with time until it reaches
the steady state which is the secondary
part they believe that this DEC decrease
in the slope with time of the strain on
the part which is called The Creep
strain that decrease in the slope is due
to strain hardening so the part the
metal is actually getting tougher in
service then it reaches a plateau where
the strained hardening is actually
battling with the recovery phase for the
part because remember the part is being
subjected to heat and then you have what
looks pretty much like a flat straight
slope there okay um and then that stage
is called secondary creep the um the
slope of that here we're plotting creep
strain versus time of service okay so
the slope of the secondary curve is
really important because the part spends
most of its life in that secondary um
time frame it spends most of that time
in the secondary stage the primary stage
doesn't take very long and neither does
the tertiary maybe just a few days for
each of them the secondary strain um
rate curve can can last for years so
that slope right there is very important
and we'll talk more about that and then
finally it exits the secondary creep and
enters the tertiary creep phase and then
the slope actually increases with time
until the part finally ruptures um so
you want to stay away from
that creep as you can imagine has a
temperature dependence the hotter your
part the more um the more your creep
strain rate will be um the faster the
creep will occur for Metals it becomes
important mostly at G than 40% of the
melting temperature then it really takes
off okay so that's something to bear in
mind okay so let's talk more about that
secondary creep regime okay your steady
state creep rate is actually constant at
a given temperature and stress you're at
that point where the strain hardening is
balanced by recovery and you've got that
constant looking slope okay so given a
temperature okay your your exponential
dependenc of your temperature is here so
you have the activation energy for the
creep and as long as that temperature is
held constant this exponential term here
is constant it's e to the minus Q over
RT um and that's the activation energy
for the creep there that q and then
there's your temperature okay now um
your strain rate is the strain which
remember is the change in length over
the length so that's the definition of
strain and a strain rate is how much
strain happens per per unit time okay so
that's your strain rate Epsilon dot then
you have a material constant in here of
course it's going to be bit different
depending on what your material is and
then you have your applied stress um
times raised to the power of n your
stress exponent
okay now if you do a log plot of these
things then they look like straight
lines okay um so your strain rate
increases with increasing temperature
and increasing stress don't worry too
much about the units on K they're really
strange okay um but it's basically just
a fit parameter that you would you would
get from the fit for a particular
material that you would
have okay so let me do an example
problem for you so that you can see what
some of these creep problems look like I
actually have about three examples here
to go through so this is um a steel
alloy okay s590 alloy and it 750 mm long
initially and it's exposed to a tensile
stress of 80 megapascals at 815 de
Celsius and so using this these plots
what we're going to do is determine the
elongation after 5,000 hours um assuming
that the instantaneous and primary creep
um elongation is 1.5 millimeters so
these curves here show the secondary
creep um Behavior and the instantaneous
and primary creep El a are given to you
basically as 1.5 mm so you just need to
figure out the secondary part and add it
onto the
primary all right so what we can do is
we know that the part was subjected to
80 megapascals at 815 C so I can look at
um my plot here and read off for 80
megapascals um from the 815 C curve
which is that red curve here and see
what the um the the creep rate is at
that value So reading that off the plot
I get 4 * 10- 6 inverse hours again the
units are a little strange on these
things um just Just Go With It okay so
here's my steady stra um steady state
creep rate that's my Epsilon Dot and
then what I can do is it asks me for
5,000 hours so I can multiply my creep
rate by my time so I have 5,000 times 4
* 10- 6 and I get
0.02 okay so that's my creep rate uh so
that'll give me my creep If I multiply
my creep rate by my time I get my creep
and that's equal to remember the uh
strain which is the change in length
over the length which is the change in
length over the initial length of 750
millimeters okay so that means I can
solve for my elongation and it's 15
millimeters and that's for my secondary
stage if I add that to the primary creep
I get 16.5 millimeters of elongation of
that part hopefully that helps
okay here's another question all right
these are all taken from your book if
the log of the creep rate is plotted
versus the log of the stress um as it
was previously a straight line should
result with a slope of n okay so using
the figure determine n for the s59 Alloy
at 925 Dees C that's shown here in the
orange curve okay so we're assuming that
the temperature is held constant so that
exponential term eus Q RT that's a
constant value okay so for this this
curve it's just shown here and it's some
value and so we're assuming here that
Epsilon dot is equal to K Sigma to the N
okay so um what I'm going to do is I'm
just going to choose two data points off
this line and figure out my slope of
that line and from that I can figure out
what my value of n is so the two data
points that I chose are the ones that
kind of crossed over one of these grid
Lanes two cross grid l lines here um and
so the two data points that I chose were
10 Theus 4 and 60 megap pascals it
looked like it intersected there and one
inverse hour or one hour and 200
megapascals so I chose those two data
points now if you look at what the log
log plot would be if I take the log of
both sides of this equation I get log of
my creep rate equals log of K plus n log
Sigma and then what's plotted here
though is the stress on the y a axis
okay so my slope then would not be n it
would be one over N I rearranged my
equation here to show that so I have 1
over n log of my creep rate equals minus
one over n log of K this just becomes my
intercept so it's unimportant to me for
my slope calculation and then that's
equal to the log of Sigma okay so if I
want to solve for just my slope that'll
give me my value of one over n here so I
plug in for my two data points my change
and my y y would be log of 200 minus log
of 60 and then the change in the X would
be the log of 1 minus the log of 10us 4
well if it's a log base 10 then the log
of one is just one right and then I have
minus minus 4 okay because the log of
10us 4 is minus 4 and then when I do
that I get
0146 and that's equal to one over N I
solve for n i get 9.6 so it's basically
10 right
okay so here um next question estimate
the activation energy for creep for the
s590 alloy using the stress data at 300
megap pascals and temperatures of 650c
and 730c assume n is independent of
temperature okay so in my example here
I've got my equation for my creep rate
Epsilon dot is equal to K Sig VN e minus
Q over RT so that's my assumption
there and yet again what I'm going to do
is I'm going to use my two data points
um and here my two data points are for
the 300 megapascal data okay so I have
two data points 300 megap pascals and if
I look at that um my creep rates um for
those 200 Mega 300 megap pascals if I
look at that that intersection of the
data then I get creep rates of 10us 4
inverse hours and - 2 inverse hours for
650 and 730 C which were the temperature
cited now K andn are those constant
those material constants that don't
change because this is for the same
material all these curves are for the
same material the s590 alloy so those
can be assumed to be the same and sigma
is given as 300 megap pascals for both
so from this I've got basically two
equations and two unknowns right um I
know my um my values my creep rate I
know my values of my temperature I don't
know my K Sigma to the n Bits but since
I have two equations I can just subtract
those two equations and then that
constant drops out so I end up with the
log a natural log of 10- 4us the natural
log of 10- 2 = q r * 1 over 13 - 1 923
okay and I solve this equation and I get
my Q there um plugging in for the known
value of my gas constant are 8. 314 Jew
per mole Kelvin now it's really
important that you realize that this
here in order to get rid of this
exponent I took a natural log okay so
that's not a log base 10 so my natural
log of 10us 4 isn't going to give me
minus four anymore you have to actually
plug it into the calculator okay make
sure that you check me out on that make
sure I did my math
right okay now sometimes you want creep
data but it would take a really super
long time to obtain because the life of
the part you expect it to be years for
example but you know that creep happens
at faster at higher temperatures so if
you want to do a test and you want it to
take a reasonable amount of time maybe
you heat the part up to a temperature
far above its service um temperature
that you know far above the temperature
you would expect it to have in service
and then you can extrapolate back for
the temperatures that it would actually
encounter in service and figure it out
that way okay so you just do the test
higher temperature and then figure out
what it would happen at a normal
temperature okay so we can use what are
called Larsson Miller parameters and
lson Miller plots to figure this out now
your lson Miller parameter just comes
from the same old equation that we've
been using this creep rate is equal to K
the n eus q over RT and you just apply a
bit of algebra to it so here's that bit
of algebra if you remember that your
creep rate is just your creep strain or
strain over a Time T then you can
rewrite your equation to look like this
okay so that your time is equal to your
strain over K Over Sigma to the * e q
over RT so basically I just flip the
equation and multiply um divide it
through by my um
string multipli through by my string now
I'm taking all this stuff out front
because I don't really care too much
about it I'm just going to call it a for
some constant right um and then I take
the natural log of both sides and I get
log of um natural log of T equals
natural log of a plus Q RT move things
over to the other side subtract it off
multiply through by my temperature and
then I get this relationship my
temperature times the log natural log of
my time minus that natural log of my
constant now this is equal to Q overr
okay now we can switch this over to a
log base 10 plot so that it more closely
matches your book and all that would do
is just introduce a proportionality
constant that we don't care too much
about anyway and maybe change what this
constant is here inside
okay that's all that would do and then
that is our lson Miller parameter l so
our lson Miller parameter L is the
temperature times the log of the time to
rupture plus some constant C and your
book says it tells you that this
constant C varies a bit but it's about
20 um I'm sure if you went through and
did the math you could figure out why
it's about
20 the repture lifetime is usually cited
in hours and it varies with the stress
so Larson Miller plots look like this
okay here you have your lson Miller plot
Larson Miller parameter times 10 the 3
so this is 12 * 10 3 16 * 10 3 so on and
so forth okay this is yet again for that
s590 iron that we've been citing a lot
and then that's plotted versus the
stress on the Y AIS so if you're an
American material scientist engineer you
have to get used to English units this
is PSI okay not MEAP pascals but PSI so
there it is um on that part of the plot
you can see the uh the SI units in your
book if you choose to do so okay and so
what this does is it shows you the
average of a set of Curves for these
Larson Miller parameters um and uh what
you can do you can use this to estimate
rupture times so you gather the data at
this high temperature yourself and then
you use your um your Larson Miller
parameter here which should be equal to
a constant right that constant Q over R
it should be equal to that constant and
then you can figure out
what the um the value is at the
temperature that you're interested in so
for example here let's estimate the
rupture time for a component made of
s590 iron at 173 Kelvin and a stress of
20,000 PSI okay so if you go to the
stress you're looking at which is 20,000
PSI and you go over to your curve then
you can read off what's your lar sillar
parameter is there and it's 24 * 10 3
okay so then you plug in 24 * 10 3 for
your Larson Miller parameter you plug in
your temperature there on the left hand
side and then you solve for that log of
the time to rupture um and the time to
rupture once you get rid of that log is
233 hours so you can um check that out
but that would be how you would maybe
extrapolate data when you don't want to
run the data at uh for for super long
time you just run it at a higher
temperature for or a shorter amount of
time okay that finishes off um what I
wanted to say about chapter eight in
summary engineering materials are not as
strong as predicted by the theory that
you might get from a ttile stress okay
they can uh fail at stress is much lower
than their yield stress um or their
tensile stress and the reason for that
is first of all because materials are
flawed they have a lot of flaws in them
um and those flaws the scratch as the
dings the dents um or even just voids
inside the part that might not be
visible to the naked eye they act to
stress concentrators and those stress
concentrators can cause failure as
stress is much lower than theoretical
values if you have a sharp corner in
your plot in your part you definitely
want to get rid of that you don't want
that included in your design because
that's a large stress concentration
right there that can help out with
premature failure which is totally
undesirable your failure type is going
to depend upon your temperature and your
stress okay um if you have a simple
fracture like it's
non-cyclic your stress is non- cyclic
and your temperatures are relatively low
then your failure stress is going to
decrease with increased maximum flaw
size decreased temperature and increased
rate of loading if you have a fatigue
situation with a cyclic stress then the
Cycles to fail is going to decrease as
your amplitude of stress
increases and the creep for creep the
time to rupture is going to decrease as
your stress or your temperature
increases so that's kind of a summary
all right um see you in class
Voir Plus de Vidéos Connexes
Understanding Fatigue Failure and S-N Curves
Reaching Breaking Point: Materials, Stresses, & Toughness: Crash Course Engineering #18
Basic Geomechanics for Hydraulic Fracturing
Topic 6: Fracture Mechanisms Lecture 4
An Introduction to Stress and Strain
Tensile Stress & Strain, Compressive Stress & Shear Stress - Basic Introduction
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