What we would like to do, is to calculate the stress necessary

to initiate slip if we recognize that the critical resolved

shear stress in this particular material is 30 MPa.

Now, what I would like to draw your attention to before we get further along

in this calculation, is the fact that the magnitude of the critical resolve

sheer stress in the BCC structure is much higher than it was in the case of the FCC.

So in BCC,

the characteristic is we're going to have a higher critical resolve sheer stress.

The question then becomes, why is that?

Well, in part we can ascribe some of that to the packing density

associated with the BCC structure as compared to the FCC structure.

Okay, so now let's continue on with our calculation.

So, we'll go back and we'll look at the equation for

the critical resolve sheer stress.

Now we're going to determine what the relationship between

the slip direction and the associated stress axis are.

And we find that that cosine of theta is equal to 1 over the square root of 3.

Now when we calculate with the value of the cosine of phi is,

again, we look at the dot products of the slip plane, and

we look at which is converted into a slip direction.

Remember the plane was the (110) and the normal to the plane is the (110).

So, consequently we can determine what the orientation relationship is

between the slip plane normal and the applied stress.

And we find that by taking the dot product of those two vectors and

dividing by their magnitudes.

And that turns out to be a value of 1 over the square root of 2.

So we put this in our equation,

and now what we see is that we get a value for the applied

stress that's necessary in order to initiate slip in this particular material.

Namely a value of 73.5 MPa.

So, when we do the calculation here, you should go back and review what the results

were, associated with the applied stressed necessary to initiate slip in the FCC.

And you're going to see that it is much larger value.

Now one of the things that particularly interesting about the body-centered

cubic crystals is that you can have, because of the fact that

the slip plane is not as close packed and it's not the closest pack.

It is the closest pack plane in the BCC, but

it is not as closely packed as it is in the FCC.

It turns out that there are a total of three different types of

planes where you can have slip in body-centered cubic.

So for example, we'eve been describing slip in the (110)

plane on the (110) plane in the <111> direction.

And we can also have slip on the (1 2-bar 1) plane in that same direction and

on the (2 3-bar 1) plane in the same direction.

So, we had the opportunity of having more slip systems operative.

Now, it turns out the fact that we have additional slip systems that are possible,

leads to a very important behavior with respect to body-centered cubic materials.

This is true of all body-centered cubic materials.

That there exists in BCC materials,

a phenomenon referred to as the ductile-to-brittle transition temperature.

That means the behavior above a certain temperature,

the material winds up being ductile and the material deforms easily.

At lower temperatures, that turns out that that's not the case.

Now the question then becomes, why and

how can we relate this to these different slip systems that we have in BCC.

Well first of all, what we know about the BCC system is that

the packing density is much lower in the BCC than in the FCC.

Which means that we can get some thermal assistance associated with

the deformation process as we go to higher and higher temperatures.

So, more slip systems become operative, and consequently,

the material can behave in a much more ductile way.

So, what we'll find is, at high temperatures, with regard to all

body-centered cubic materials, we're going to see a ductile behavior.

And at some lower temperature, we're going to see a brittle behavior.

And that's ultimately going to lead to some issues when we start using

materials such as steels when the temperature can become very low.

For example, in the Arctic where the steel is used in

construction, the engineer needs to be aware of what

the actual temperature may be in the environment.

And what the ductile to brittle transition temperature is,

in the particular steel that's being used.

Thank you.