Linear imperfections.
We know the mechanism for dislocation--
sorry, for plastic deformation.
We know that you get a dislocation
and it allows the stepwise breaking and reforming
of bonds.
And there's a really quick and dirty dislocation.
And so we're starting to look at how
we can present obstacles or barriers to the movement
of a dislocation.
And what we're going to look at here
is how the presence of dislocations
can actually impede the movement of other dislocations.
So the first thing to appreciate is
that we've got to really understand the stress
state here in this dislocation.
And so I think if you imagined you had a piece of cheese.
So what color is cheese?
Well, it can be many colors.
It's going to be yellow.
And the very best I can do here, I'm
going to draw a piece of cheese that you're doing something to.
What are you doing to it?
Let's see if you can figure it out.
That's a somewhat strange looking piece of cheese.
But there it is.
Delicious cheese.
Funny yellow colored cheese.
And what are you doing?
Well, you're trying to cut it.
You're cutting it with-- what are you cutting it with?
You're cutting it with a knife.
Your knife is some sort of a wedge.
That's going to go down in there and cut
the cheese, if you will.
And if this is a piece of hard cheese,
you may even know that the cheese actually
starts to tear apart before the sharp edge of the knife
gets to touching the cheese.
The analogy I'm trying to build here
is that while this extra-- sometimes we
call it half plane of atoms-- half plane.
Why?
Well, because it doesn't continue all the way from top
to bottom.
It only goes halfway.
It's a plane of atoms coming in and out of the page.
It's a plane of atoms.
So that extra half plane of atoms
is like a knife that's being inserted in.
And this sharp edge here of the knife
is like the dislocation line.
That's the dislocation line.
Dislocation.
That's the linear feature, the tunnel, if you will,
running in and out of the page.
So what we're looking at here is what
the stress state in the lattice is
like because of the presence of the dislocation.
Well, it's like the stress state in the cheese because
of the presence of the knife.
So as the knife goes in there-- and what I'll do
is I'll draw the knife in there.
So there's the knife.
It's now actually in the cheese.
So there's your knife.
That's a wedge.
The knife is in the cheese.
And what's it doing?
Well, the knife pushes against the cheese, doesn't it?
It pushes against the cheese.
And what does that do?
Well, that compresses the cheese.
That's why actually, you don't cut cheese
with a big thick knife.
The best bet is to use a thin wire.
You can get a cheese cutter that's a thin wire
and it slices nicely through, because it doesn't
have all that compression.
So similarly, this extra half plane of atom
creates compressive stresses in the lattice.
Compression.
And what happens below the knife blade over here?
Well, below the knife blade, we have tension.
We have the knife blade.
The presence of that knife blade is pulling the material apart
even before the blade touches it.
It's in tension.
Similarly, the lattice down here is in tension.
And the important takeaway from this
is that we've got this stress field,
or sometimes we call it a strain field,
surrounding the dislocation.
And that's actually stored strain energy.
It's elastic energy, if you like thinking of it that way.
It's elastic energy stored in the lattice
in the form of these disturbances
from equilibrium spacing.
These atoms, if we modeled them--
I drew them with these little green lines--
but if you imagine them with little springs,
well, these are being compressed and pulled in tension away
from their equilibrium spacing.
And that's energy stored as strain energy.
Strain energy.
So there's this strain feel that surrounds the dislocation.
And so then what happens is well,
what if you've got one dislocation?
That's fine.
But what if you've got many dislocations?
Many dislocations.
Well, then what happens is the strain fields interact
and they repel one another.
Or they get in each other's way.
There's some other ways.
But they bump into each other, essentially.
They repel one another.
And the analogy that's often used, which is not too bad,
is it's like people moving in a crowded train.
You're trying to get off of a train.
Maybe it's a subway or you're trying to get off
of a bus or something.
If there's many, many people around you,
it's difficult to move.
Difficult to move.
And what's the result if it's difficult for a dislocation
to move?
If it's difficult for a dislocation to move, well,
what do we know about dislocation movement?
Dislocation movement was this linear imperfection.
It's the mechanism for plastic deformation.
Difficult for dislocation to move.
That is the strengthening.
It's harder to deform plastically.
So that's strengthening.
Strengthening, if I could spell it without-- there you go.
Difficult for dislocation movement.
That means we've strengthened it.
So how do you get more people on a subway,
you put more people on.
How do you get more dislocations in a material?
Well, that's the interesting thing.
You'll have to just take my word for it on this point,
but plastic deformation-- you can look up
the mechanism if you like.
But plastic deformation creates more dislocations.
So when you plastically deform something--
and if you see the stress strain behavior
for a metal like this, an elastic,
and it starts to strengthen.
That strengthening is because you've
created more dislocations.
And then the dislocations run into each other
and they impede one another's movement.
And finally just to give you a sense of how really incredibly
important dislocations are.
If you imagine that you took a piece of metal and you
cut it up.
And you measure, you recorded.
Say you had 1 millimeter by 1 millimeter area.
You cut from a piece of metal.
And then what you do is you go through
and you look at that in a really high powered microscope
and you count the number of dislocations running
through that square millimeter.
And you count the number of dislocations,
number of dislocation lines per square millimeter.
How many do you think?
What kind of number?
I mean, you've got a mole of atoms, it's 10 to the 23.
So you should be thinking probably a fairly good size
number.
But these are imperfections in the crystal.
So what are we looking at?
Well, on the low end, you could have about 1,000.
10 to the 3 dislocations.
All the way up to-- for something
that's been heavily cold worked with a lot
of plastic deformation-- about 10 to the 10.
10 billion dislocations per square millimeter.
A square millimeter, that's a tiny little area.
So there's a huge, huge number of dislocations in every metal.
And most metals-- you look around you--
most metals can be deformed somehow to their final shape.