[MUSIC].

Hi and welcome back.

In today's module, we're going to learn how to approximate the SN curve.

So, last module we were introduced to SN curves and

we learned how there's data from tests done on particular metals.

Sometimes you don't have this test data, and you need to approximate the S-N curve.

The approximation that we're going to learn is good for steels, and

it's good from 10 to the 3 to 10 to the 6 cycles.

Again, I'd like to remind you that fatigue failure is quite dangerous and

complex, and that these techniques are to approximate fatigue failure.

You should always be conservative in the assumptions you're making

when you do these analyses.

And you always need to validate the analyses with testing.

With that, here's our SN curve.

So, again we have the number of stress cycles on the bottom x-axis and

the fatigue strength on the y-axis.

And generally, and then we have the endurance limit right here, where for

steel if you are below this endurance limit you can cycle infinitely.

Now generally, this boils down to any combination of stress and

number of cycles in the green region, is safe.

And any combination of stress level and

number of cycles in the red region, your part will fail.

For example, you can't cycle at 100 KSI for 1 million cycles.

Your part's going to fail before you get to a million cycles.

Okay, so, let's break down the curve a little more.

The SN curve, so, if you have the data from testing, so

if you look at like Mil Handbook 5J or other handbooks or data that's in house.

You should always use that.

Sometimes, all you'll have is a tensile test for the material that you're using.

And in that case, you may need to approximate the SN curve.

So, from 10 to the 3 to roughly 10 to the 6 cycles, there's a logarithmic

relationship between the number of stress cycles and the fatigue strength.

And that can be approximated using this equation right here.

So, let's take a look at that.

So, this equation says that the fatigue strength is equal to a,

which is a variable that we'll calculate, times N to the bth power.

And N is the number of cycles or your life.

a and b are based off of the ultimate strength,

the fully adjusted endurance strength for your operating conditions and f.

And f is a fatigue strength fraction.

So, it's the fraction of fatigue strength remaining at 10 to the 3 cycles.

Now in this course, I'm going to give you f.

It will be given to you.

You can also reverse this equation if

you know the stress level that your part has to operate at.

And you're trying to figure out how long it can operate at that stress level.

You can reverse it and you can say,

the life is equal to sigma rev divided by a to the 1 over bth power.

If you're outside of this course, and you're trying to figure this out and

you need a resource to calculate f.

f can be calculated with these equations right here.

Where Ne is your endurance limit, and

Se prime is your endurance limit of a lab specimen.

So, this perfect, highly polished specimen.

There's also charts for f that you can utilize in Shigley's.

Alright, so I'm going to work through an example problem.

For in this case, we have a polished rotating beam specimen.

And it's in pure bending, and it's made of 4130 steel, which has an endurance limit

of 42 ksi, f value of 0.77, and an ultimate strength of 95 ksi.

And the first thing we'd like you to determine is the fatigue strength

of the part at n equals 10 to the 5 cycles to failure.

And so, this is fairly straightforward.

So, you'd simply say, Sf is equal to aN to the b.

In this case, your a is going to be f,

which is 0.77 times your ultimate strength of 95 ksi.

And that is squared divided by your endurance strength of 42 ksi.

And you get an a of 127.4 ksi.

For b, you're going to get a negative 1/3 log of 0.77 or

f times 95 ksi, which is your ultimate strength,

divided by your endurance strength of 42 and

you get negative 0.08.

And then you plug into this equation up here and you find that should be 1 there.

You'll find that your fatigue strength is right at 50.5 ksi.

So, the next thing they ask you to do is to determine the expected life

of this specimen under a completely reversed stress of 60 ksi.

And in that case, you can still use your a and

b values because they're not going to change.

Your ultimate strength and your endurance strength and your f value haven't changed.

It's just the load that's being applied has changed.

So, you can go ahead and calculate the life with this equation N Is equal to,

in this case, your, this should be a stress.

I'm sorry about that.

Okay, so your completely reversed stress of 60 ksi divided by a,

which is 127.4 ksi, to the 1 divided by negative 0.08.

And you get Nf equals 11790 cycles.

So, fairly straightforward calculations for all of you engineers.

So then, just to check your knowledge, a couple of questions here.

One, at a completely reversed stress of 50 ksi, the specimen has infinite life.

Is that true or is that false?

Two, at a completely reversed stress of 60 ksi

the specimen can survive 100,000 cycles.

Is that true or false?

And three, the specimen can withstand a completely reversed stress of 45 ksi for

at least 10 to the 5 cycles.

True or false?

So take a second, and figure these out.

And then we'll go through the answers.

Okay, so, the first one is false.

Your endurance limit is 42 ksi, right here.

And so in order to have infinite life you need to be operating

underneath the endurance limit and

a completely reversed stress of 50 ksi is above the endurance limit.

So, it's false.

At a completely reversed stress of 60 ksi,

it says that the specimen could survive 100,000 cycles.

Well, here we just figured out at 100,000 cycles, our stress was 50.5 ksi.

So, the specimen can't survive 100,000 cycles at 60 ksi.

It's going to fail before it hits it.

And then here it says, the specimen can withstand a completely reversed stress of

45 ksi for at least 10 to the 5 cycles.

This is true because this stress is below 50 ksi,

so you should be able to survive 10 to the 5 cycles.

What we've done is we've done the first step in solving more complex fatigue

problems.

And that's what we've determined is we determined

how to estimate the S-N diagram.

Now, in reality, if you don't have an S-N diagram,

you don't know your endurance strength, right.

You don't know your endurance limit.

So, what we're going to have to do is figure out how to estimate

the endurance limit and that's what we'll do in the next module.

See you next time.

[MUSIC]

Module 31: Approximating the SN Curve

Machine Design Part I

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