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So, last time we talked about how static loading is constant over time,

where fatigue loading varies with time in either magnitude,

point of application, or direction.

We talked about how fatigue failure is sudden and

catastrophic, that it occurs below the yield strength, and

there is complex high variations in both the theory and in the testing data.

So, the theory is not fully understood and, at this point,

I'd like to offer you some caution when running fatigue analysis.

That often your lab data will be different than your operating conditions,

so you're going to pull data to do analysis that's often run in a lab.

And if that lab is not perfectly replicating your operating conditions,

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there's going to be very big differences in your predictions.

So, these high variations in fatigue failure and when it occurs

means that we've developed some engineering practices to account for

these differences that I'm going to show you in estimating the endurance strength,

and estimating the SN diagram.

But, it's really critical to be conservative

in your analyses because of the high variation in fatigue failure and

components and the difference in operating conditions and laboratory data.

And it's also very important to validate your analysis with testing.

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So, in static failure,

you pretty much aren't going to worry about life or time of operation.

You either apply the load and it fails or you apply the load and it doesn't.

There's some more complex mechanisms that we're not going to get into, but

it's straight forward that way.

Fatigue, you're constantly applying and removing a load.

And so the question comes up is how many times can you do that, or

how much life does your part have at a certain load level?

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So how they test for fatigue is they take something called a rotating beam specimen.

Now this specimen's a shaft, they put it in four point bending.

So it's actually going to look, if you exaggerated

the distortion, it would be something like this.

And so, they're going to take the shaft,

they put it in the four point bending machine and then they start to rotate.

And what happens is the filament along the top of the shaft is first in compression.

And then it rotates down and

it goes through the neutral axis where it experiences no stress.

And then, it rotates down again, and

it goes into the bottom of the beam where it is going to experience tensile stress.

And then, it rotates back through the neutral axis and then,

back into compression and that's typically one cycle.

So you've removed and reapplied the load in one cycle.

This is called a fully reversible load and that means you're going

from 0 up to 20, down to negative 20, and then back to 0.

Or maybe you're going from 0 up to 100 down to negative 100 back to 0 and

so on and so forth.

So in fully reversible loading, your stresses are equal in magnitude.

And you go from tensile to compression to tensile to compression.

So, SN diagrams hold for this fully reversible loading condition,

the strength life diagrams that we're going to look at.

If I looked at the stresses, what would happen is if I started at the neutral axis

and I rotate down, I'm going to end up in tension, so my stress goes up to 20 ksi.

I'm going to go down to 0, as I go through the neutral axis.

I'm going to go down to -20 as the filament comes up into compression and

then I'm going to go back to 0 as the filament comes back to the neutral axis.

So it's seeing a fully reversible stress.

And what you can do is you can run tests, so

if they gather a whole bunch of these rotating beam specimens

made of the material that your part or component is going to be made out of,

they can run what we call an RR Moore rotating beam specimen test.

And it gives you something called an SN, or

strength life, diagram and this is what that diagram looks like.

So on the x-axis, we have Number of Stress cycles, N, to failure.

So how many cycles or how many rotations can you go through before that beam fails?

On the y-axis we have Fatigue Strength, which is capital S, subscript f and ksi.

So what is the strength that your component can see, for

how many cycles before it fails?

And typically this is done in a log, log graph.

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So let's put a stress on the beam that's just lower than the ultimate strength.

And then we're going to see how many times we can rotate it, and

it will eventually fail.

But maybe you could rotate it three times before the beam failed.

And then you go to a slightly lower stress and you place that on the beam.

And you see how many times you can rotate it before it fails.

And maybe you hit eight cycles and you keep repeating this.

And for steels, the trend looks something like this.

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So, in the region between 1 to 10 to the 3rd,

you get something called low cycles and your strength is not falling off a lot,

it's pretty close to the ultimate strength still.

When you get above 10 to the 3rd, you start to see a pretty quick drop off and

this is a relatively linear relationship in the log log realm.

And then, when you get above 10 to the 6th,

you see your strength is no longer dropping off at all.

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And then, we have finite life from

one cycle all the way up to a million or 10 to the 6th cycles.

This is the finite life range for most steels.

Above this, we hit something called the endurance limit.

So here our endurance limit is right below 50, it's about 49 ksi.

And as long as my stress is below 49 ksi, I can cycle infinitely.

So the part is never going to fail as long as you're below the endurance limit and

therefore, it has infinite life.

Now 10 to the 6th is something that most textbooks teach. In the automotive and

aerospace industries,

they tend to be more conservative and go into the 10 to the 8th,

10 to the 9th region.

And that's because they have data that shows that the metals

they use are dropping off a little more in strength.

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So, if we look at some actual data, this is from MIL HNDBK 5J.

This is 4130 sheet steel.

And you can see that right here is our S-N diagram, so they go

above 10 to the 3rd and you can see around 10 to the 6th, it starts to even off,

so the endurance limit is probably somewhere right around here.

You can also notice they're giving you all the test conditions, so

it's happening at room temperature in air.

This test was done with an axial, fully reversible load,

and the surface of the test specimen was highly polished,

electropolished, so that's really important to keep in mind.

Something to note, steels typically have endurance limits where aluminums don't.

And you can see that here in this data again from MIL HNDBK 5J,

this is an aluminum test specimen, 2014 aluminum T6.

And for a fully reversible stress,

you can see there's really no leveling off of the data.

So, over here we're in 10 to the 8th and

we're still seeing a pretty significant decrease in strength.

So aluminums are widely known not to have endurance limits.