You have to use a stress concentration factor in a brittle material every time,

and it's very important.

So in a brittle material, you use the static stress concentration factor Kt.

Okay, so continuing on, let's take a look at an example.

So if we have this shaft or rod, and it has a change in diameter, so

it starts out with a diameter of 24 millimeters, and then there's a fillet

radius of 4 millimeters, and it goes down to a diameter of 16 millimeters.

And they're saying it's aluminum, normally, it behaves in a ductile manner.

However, here it's operating below its transition temperature, so

it's going to behave in a brittle manner.

What's the max stress in the rod at a load of 40 newtons,

and we can see that the rod is loaded in tension?

And then here, we have the stress concentration factor chart.

There's a lot of these charts all over the Internet, in the back of textbooks, and

again, the most prominent resource is Peterson's Stress Concentration Factors.

And you can see,

the first thing is to make sure this is the correct chart to use.

So we see here, we have a rod, two different diameters and

an axial load with a fillet radius in between.

The second thing over here is it's going to tell you

what is it defining as your sigma nom.

And this is really important to understand what area are they calculating

your nominal stress from.

And here you see this little d,

that means they're calculating the nominal stress at the smaller diameter.

So that's exactly what we're going to do.

We're going to say stress, axial stress equals F/A.

And we need to use the smaller diameter to get my A,

so 4F divided by pi d squared is going to be, let's see.

40 newtons times 4 divided

by pi times 0.016 meters squared,

and I get about 0.2 megapascals.

Okay, so the next thing we need to do is we need to figure out

our stress concentration factor based off of this geometry.

And looking at the chart, we need two ratios to do that.

We need the R/D ratio, which is going to be 4 divided by 16, which is 0.25.

And then, we need a D/d ratio,

which is going to be 24 divided by 16, which is 1.5.

So here's my 0.25 place on the chart.

This line right here is 1.5, so I can see that I cross

it right about here, which is right about here.

So my Kt is going to be 1.52.

Okay, so now I figured out my sigma nom and my Kt, and I can plug in to

figure out the maximum stress or the stress that's actually occurring.

So my sigma max right here, which is going to be sigma nom times Kt,

so my 0.2 megapascals times 1.52, and

I get a stress of 0.3 megapascals in this example.

So you can see,

a stress concentration factor has a significant increase in the stress.

It's definitely 150% higher in this case, and therefore, it's

very important to consider if you need to use a stress concentration factor or not.