Chapter 18: Extrusion Processes

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Hello everyone.

Today we are taking a massive block of material, heating it up, applying extreme pressure, and forcing it to flow.

Sounds pretty intense.

It is.

So if you're an engineering student, a material scientist, or just someone who's fascinated by how we reshape matter on an industrial scale, this deep dive is tailored specifically for you.

That's right.

Our subject today is Chapter 18 from Mechanical Metallurgy, and we are breaking down the entire process of extrusion.

And this isn't just about squeezing metal like toothpaste from a tube, is it?

No, not at all.

It's about conquering the difficulties associated with forming metals that are, well, otherwise really stubborn or even brittle.

Okay, so let's unpack this crucial process.

At its most fundamental level, extrusion is what exactly?

It's about forcing a block of metal, we call it a billet, to flow through a die opening.

Under immense high pressure, I assume.

Immense is the right word.

And the core mechanical goal here is a drastic reduction in its cross -section.

And from that, you can get all sorts of useful products.

Exactly.

You can get long products like cylindrical bars, hollow tubes, or even incredibly complex, irregular cross -sections.

Now, here's what I find interesting and where it gets really important for high -performance engineering.

Extrusion is often the only way to work with certain metals.

Yeah.

Or the really tough ones.

That's the key.

We're talking about stainless steels, complex high -temperature alloys, nickel -based superalloys.

The genius of the process lies in the mechanical environment it creates.

You mean the stresses it puts on the metal.

Right.

Extrusion relies on subjecting that billet to extremely high compressive stresses.

So those compressive forces are sort of our secret weapon.

They are.

That compressive environment is the key to preventing cracking or tensile failure that often plagues these metals.

Especially when you're trying to break them down for the first time.

Especially during that initial primary breakdown of the ingot.

With conventional rolling or forging, you introduce tensile stresses that can just tear these materials apart.

But by keeping the material in compression, we can safely impart a massive amount of strain.

You've got it.

That's why extrusion is often the preferred primary method for these tough high -strength materials.

So, our mission today is clear.

We're diving into the entire chapter, breaking down the classification, the equipment.

And crucially, the complex mathematics that govern all these massive forces.

We'll make sure every equation, every curve, and every diagram is crystal clear so you can transition seamlessly from the theory to actually applying this knowledge.

Let's do it.

Let's start with the basics then.

The classification.

How we actually initiate this metal flow.

Right.

So the chapter outlines two foundational ways to make a metal block squeeze through a hole.

We call them direct and indirect extrusion.

And the main difference is the direction of flow.

Absolutely.

It all comes down to the direction of the metal flow relative to the ram that's doing the pushing.

Okay.

So let's visualize the first one.

Let's talk about direct extrusion.

The chapter has figure 18 .1a for this.

Right.

This is sometimes called forward extrusion.

The setup is pretty intuitive.

You place the billet in a container.

And then a ram, using something called a dummy block,

just pushes the billet straight through the die opening at the other end.

Exactly.

The die is stationary, the ram pushes, and the extruded product moves forward in the very same direction as the ram.

It's conceptually simple, like squeezing a lemon, as you said.

But what's the immediate major engineering challenge that jumps out from that setup?

Friction.

That's the heavy penalty you pay for that simplicity.

Why so much friction?

Because the entire mass of the billet is sliding.

It's moving relative to the inner surface of the container wall.

Ah, I see.

So you generate these significant parasitic frictional forces all along that contact area.

And that means you need more force overall to get the job done.

Much higher total forces.

And critically, that force requirement changes dynamically throughout the process, which is something we'll see in the graphs later.

Okay, so that's direct.

Now let's contrast that with what you call the mechanical elegance of indirect extrusion.

Yes.

Also known as backward or inverse extrusion.

Figure 18 -1B shows this setup, and it's fundamentally different.

How so?

Well, here, the container remains completely stationary, and it's closed at one end by a plate.

The clever part is the ram.

The ram itself is different.

It is.

It's hollow, and it actually carries the die on its end.

So the ram pushes the die into the billet.

So the metal flows backwards.

Exactly.

The extruded product flows in the opposite direction of the ram's movement, passing right through the hollow center of the ram.

That seems like a complete inversion of the basic idea.

What is the massive engineering payoff for designing such a complex setup?

The massive advantage is the near complete elimination of relative motion between the billet and the container wall.

Ah, so the billet basically stays put.

It stays relatively fixed inside the container bore.

That means those friction forces we just talked about, they're essentially zero between the billet and the container liner.

And the total required power is much lower.

Substantially reduced compared to direct extrusion.

That sounds like the ideal solution, then.

You've limited the friction problem entirely, but surely using a hollow ram must introduce some pretty serious load limitations.

Precisely.

That is the practical constraint.

It's a trade -off.

You can't push as hard with a hollow tube as you can with a solid cylinder.

Exactly.

While the process is thermodynamically more efficient, you're forced to use that hollow ram for the metal to exit.

And that limits the cross -sectional area and the maximum mechanical load you can apply without.

Without breaking the ram.

Right.

Without compromising its structural integrity and rusting, buckling, or failure.

So the designer has to balance that efficiency against the capacity of the machine.

Now, extrusion isn't just for making solid bars.

We also use these principles to make things like tubes.

And for some really high -speed deformation processes.

Right.

So for tube production, you basically just attach a mandrel to the end of the ram.

And a mandrel is just a shaped rod, essentially.

Exactly.

And the thickness of the tube ball is determined by the precise clearance between that mandrel and the stationary die wall.

So you can start with a billet that's always hollow.

You can.

That's the easier way.

Figure 18 -8 shows the setup.

Or, you can actually pierce a solid billet first, using a separate hydraulic system that acts right along the same axis as the main ram.

And then there's the really high -speed version.

Impact extrusion.

It sounds like a mechanical punch.

It is.

Literally.

It's a very high -speed deformation process, often performed cold, specifically for producing short, hollow shapes.

What are some classic examples?

The classic ones are collapsible tubes for paint or toothpaste or maybe battery casings.

And why is this limited to softer metals?

Because of the extremely high strain rates, you get this rapid, intense deformation heating.

So the process is generally restricted to more ductile, lower melting point metals.

Things like lead, tin, aluminum, and copper.

Got it.

Okay, so to generate the kind of pressures we're talking about, especially for hot extrusion,

what kind of equipment are we looking at?

To get to the 800 to 1200 megapascals of pressure you need, we rely almost exclusively on massive hydraulic presses.

And they're categorized by their orientation, right?

Horizontal or vertical.

That's right.

And there are some really important trade -offs between those two types, especially when it comes to quality control.

Okay, so let's look at the vertical presses first.

These are generally smaller, maybe in the range of 15 to 50 meganotons in capacity.

But they offer some crucial operational advantages.

Such as?

Well, it's easier to align the ram and the tooling.

You can get a higher production rate, and they obviously save on floor space.

But the most important advantage, from a quality standpoint, is the physics of cooling.

How does gravity help the thermal profile?

I mean, it's just up and down instead of side to side.

In a vertical setup, the billet cools much more uniformly across its entire cross section inside the container.

And that's important because?

Because that uniform cooling is vital.

It prevents the development of sharp internal temperature gradients, which in turn gives you geometrically uniform deformation and a much more consistent final product quality.

And the horizontal presses,

I imagine these are the big workhorses of the industry.

They absolutely are.

They're the standard for most commercial extrusion of bars and complex shapes, with capacities that can go up to 140 meganotons.

Huge machines.

But they introduce a distinct quality challenge.

Because of that non -uniform cooling.

Exactly.

In a horizontal setup, the bottom of the billet is resting on the container floor, so it cools much more rapidly than the top surface.

And that temperature difference causes problems.

Big problems.

That gradient leads to non -uniform flow,

variations in internal heating, and it can result in warping or inconsistent wall thickness.

This is particularly challenging when you're trying to extrude thin -walled tubing.

So as an engineer, you're choosing between scale and tonnage on the one hand, with the horizontal press.

And maximum geometric uniformity on the other, with the vertical press.

We mentioned earlier the need for high ram speeds, especially for refractory metal, something like 0 .4 to 0 .6 meters per second.

That seems really fast for such a massive process.

It is fast.

And that speed is necessary to prevent the metal from cooling down too much, and to overcome its inherent resistance to deformation.

And you can't get that speed from a standard hydraulic system.

No.

Achieving that speed requires specialized hydraulic accumulator systems that can deliver a huge amount of power almost instantaneously.

But as we noted, for softer materials like aluminum and copper, speed actually has to be restricted.

That's a critical point.

If you push too fast with those materials, you generate too much internal heat from the deformation.

That can lead to a condition called hot shortness.

Where the material basically loses its ductility.

Its ductility just plummets, and it starts to crack or tear.

Plus going too fast degrades the uniform surface finish.

It's a very delicate balance.

That brings us to the tooling assembly itself.

Figure 1833 shows this stack of components that has to survive this, while this extraordinary environment of stress and thermal shock.

And constant oxidation.

Let's break down the stack that has to resist maybe 4 ,000 tons of force.

The die that's number 6 in the diagram is where all the shaping happens.

It's critical that it doesn't move.

So it's supported by a die holder in a massive bolster.

Right.

Numbers 5 and 7.

And this whole assembly is housed securely in the die head, which is number 2, and then sealed up against the container by a wedge.

And the key component that's in direct contact with the billet is the liner.

Number 4, the chapter mentions it's shrink fit into the container.

Why go to that trouble?

Ah, that shrink fitting technique is a really elegant piece of materials engineering.

How does it work?

Well, by shrink fitting it, the process produces a massive, beneficial, compressive press stress on the inner surface of that liner.

So you're squeezing it before you even start.

Exactly.

And that compressive layer is essential because the internal pressure during extrusion generates these massive tensile hoop stresses in the container walls, which want to tear it apart.

So the pre -stress cancels out the internal pressure stresses.

It effectively does.

It dramatically increases the container's working life and prevents catastrophic failure.

Clever.

Okay, now let's move to the actual shaping element, the dies themselves.

Figure 18 -4 shows two main types, dead -faced dies and conical dies.

Right.

With dead -faced dies, which you see in figure 18 -4a, you typically use them when friction is high or lubrication is poor.

What happens to the metal flow?

The metal that first enters the diegist refuses to flow into the sharp corners.

It creates a stationary chilled region of metal.

A dead zone.

A dead zone, or a stagnant wedge, exactly.

And this wedge of stationary metal then effectively acts as the die angle for the rest of the material that flows past it.

So the metal basically forms its own die angle.

That's fascinating.

It really is.

Now, contrast that with conical dies, shown in 18 -4b.

These are used when you have good lubrication, allowing the metal to flow smoothly.

And the key design variable here is the angle, right?

The semi -die angle, alpha.

Yes.

And generally, decreasing that angle, making it shallower, decreases the turbulence of the flow.

That improves deformation homogeneity and, theoretically, it lowers the required extrusion pressure.

But there's a catch.

You can't just make the angle arbitrarily shallow, can you?

No, you can't.

There's a point of diminishing returns.

If you decrease the angle too much, you greatly increase the surface area of contact between the flowing metal and the die face.

And more contact area means more friction.

Exponentially more friction.

Eventually, those friction forces start to dominate, and the required pressure actually starts increasing again.

So there's an optimum.

There is.

And this trade -off between friction and homogeneity is why the optimum semi -die angle, alpha, for most operations, settles somewhere between 45 and 60 degrees.

Okay, so we've covered the hardware.

Let's transition now from the hardware to the physics of the forces involved.

Right.

The force you need for extrusion is controlled by a tightly linked system of five principal variables.

And these are the levers that a practicing engineer really has to control?

These are the five levers, yes.

Number one, the type of extrusion, direct versus indirect, because that governs friction.

Number two.

The extrusion ratio, which we'll define in a moment,

it's basically the severity of the reduction.

Okay, what else?

The working temperature, which dictates the flow stress of the metal.

Fourth is the deformation speed, or RAM speed, which influences both the flow stress and the temperature.

And finally, number five, the frictional conditions at the die and container wall.

The relationship between how far the RAM travels and the pressure required is maybe the most fundamental diagram in this whole chapter.

That's figure 18T5.

Yes, this is a critical graph.

Let's spend some time walking through it.

So it's plotting extrusion pressure on the A axis versus RAM travel on the X axis.

It's showing the energy profile required to push the billet.

That's right.

So what's happening right at the start, at zero RAM travel?

Well, in the initial stage, for both processes, direct and indirect, the pressure shoots up rapidly.

Why that big spike?

That spike is the force needed to initially compress the billet to make sure it fills the container completely, and then to build up enough pressure to overcome the material's yield strength.

Until you hit the peak, the breakthrough pressure.

Exactly.

Once you hit that, flow through the die finally starts.

Okay.

Now let's look at the distinctive curve for direct extrusion after that breakthrough.

The pressure required progressively decreases as the RAM moves forward.

Why that steady linear drop?

That decrease is a direct visual consequence of the friction loss term disappearing as you go.

Can you break that down?

Sure.

The total pressure is the sum of the force you need for deformation plus the force you need to overcome the container wall friction.

As the RAM travels forward, the length L of the billet that's still inside the container gets shorter and shorter linearly.

And the friction is proportional to that length.

Precisely.

So since the area of friction is proportional to L, the friction force drops linearly, causing the overall required pressure to drop until you're just left with a small discard or butt.

That's really interesting.

It means that just by looking at the slope of that line, you can get a direct estimate of how big your friction losses are.

It's a powerful diagnostic tool.

Absolutely.

Now, conversely, look at the curve for indirect extrusion.

Almost perfectly flat.

After that initial breakthrough spike, the pressure remains approximately constant throughout the entire RAM travel.

That's the payoff we talked about earlier.

This perfectly flat curve is that geometric payoff.

Since there's no relative movement between the billet and the container wall, the frictional

Okay, let's formalize the severity of the deformation itself.

Let's talk about the extrusion ratio R.

The extrusion ratio R is our fundamental measure of reduction.

It's defined very simply as R equals A naught over AF.

So initial area over final area.

Exactly.

Where A naught is the initial cross -sectional area of the billet and AF is the final cross -sectional area after it's been pushed through the die.

And these ratios can be huge.

They can be vast.

For hot extrusion, you might see R values up to 40 to 1 for steel.

And for a soft material like aluminum, it can be as high as 400 to 1.

Now, the chapter emphasizes using R instead of the fractional reduction R.

Why is R a more powerful descriptor, especially for these massive operations?

That's a great question.

The fractional reduction is defined as R equals 1 minus 1 over R.

Okay.

The problem is, when you have these really large reductions,

R becomes kind of insensitive to the severity.

What do you mean by insensitive?

Well, for instance, moving from an R of 20 to an R of 50 is a massive increase in the difficulty and the energy required for the operation.

Right.

But the fractional reduction R only changes from 0 .95 to 0 .98.

It's a tiny change.

R scales far better with the actual strain you're imparting.

So it gives engineers a much clearer sense of the deformation severity.

That makes sense.

That severity brings us directly to the mathematical backbone in this chapter.

Let's look at the idealized extrusion pressure.

That's equation 18 to 1.

This is the equation that models the pressure you'd need under perfect conditions.

So no friction, no redundant work.

What's the formula?

It's P plus K times sigma bar naught times the natural log of A naught over A F.

Okay.

Let's break that down variable by variable.

P is the extrusion pressure we're trying to find.

Correct.

Sigma bar naught is the effective flow stress of the material at the working temperature and strain rate.

So how stiff the material is?

In a sense, yes.

And that term, the natural log of A naught over A F, is just the natural log of our extrusion ratio R that represents the effective strain you're putting into the material.

And what about that K factor, the extrusion constant?

What does that represent physically?

K is basically the factor that tries to correct this idealized equation for the realities of the process.

So it accounts for all the messy real world stuff.

Exactly.

It's an overall factor that accounts for flow stress, complexity, friction, and inhomogeneous deformation.

Since ideal conditions never exist, K is always empirical and it must be greater than one.

It's a penalty factor.

It's the penalty factor you pay for non -ideal mechanical flow.

That's a perfect way to put it.

So the implications are pretty straightforward, but profound.

The pressure you need is directly proportional to how hard the material is to deform the flow stress and linearly related to the natural log of the reduction ratio, which is the strain.

That's it.

To manage the forces, you either have to reduce the flow stress, which usually means increasing the working temperature, or you have to reduce R, the amount you're squeezing it.

Okay, so that leads us perfectly into the thermal and lubrication aspects of hot extrusion.

Right.

Because hot extrusion, which is so critical for reducing that flow stress, introduces this huge thermo -mechanical challenge.

You have to manage friction, temperature, and tool protection all at the same time.

And the general strategy is to use the minimum working temperature you can get away with, right?

Where the material is softest, but still solid.

Precisely.

We aim for the temperature just below the point of hot shortness, which occurs near the material's melting point.

And using good lubricants is what allows us to keep that temperature as low as possible.

Exactly.

Effective, stable lubricants let us minimize friction.

For high -strength materials like steel and nickel billets, we're talking about temperatures between 1 ,100 and 1 ,200 degrees Celsius.

And the pressures are just huge.

800 to 1 ,200 MPa.

Right.

Massive pressures.

We've established that ram speed increases the pressure.

Yeah.

But it also has this complex thermal interaction that we need to talk about.

It's a classic thermodynamic coupling problem.

What do you mean by that?

Well,

increasing the ram speed always increases the pressure required simply because the material's resistance to deformation goes up with strain rate.

Okay.

But that high strain rate also means that the mechanical work you're doing is rapidly dissipated as internal heat within the billet.

So if you increase the speed,

you also increase the internal temperature of the billet.

And that can push the material past its hot shortness limit, causing it to fail.

Exactly.

It requires a really delicate balancing act.

In fact, in direct extrusion, it gets even more complicated.

Oh, so?

Because the billet is constantly sliding forward and losing heat to the container wall, high speeds might actually be required just to compensate for that cooling.

So you have to speed up to keep it hot enough.

You have to speed up to generate enough internal heat to maintain a uniform temperature profile throughout the entire process length.

If you don't speed up, the back half of the billet can cool down too much, its flow stress spikes suddenly, and you can stall the press.

Wow.

Okay, so let's move on to discuss the complex way the metal actually flows inside the container.

Yeah.

Because that flow pattern dictates how much energy is wasted.

That's right.

And figure 18 -6 is the key diagram here, showing the different deformation patterns.

The required pressure is heavily determined by how much energy is spent on that redundant work, which is governed entirely by lubrication and the container interaction.

So let's start with the ideal scenario, which is figure 18 -6A.

This shows what we call homogeneous deformation.

If you look at the internal grid lines in the diagram, you'll see they stay relatively square and undistorted.

Until they get right up to the die entrance.

Right, until they reach that high strain zone.

This pattern is characteristic of systems with very low container friction.

Like with really good lubrication or hydrostatic extrusion.

Exactly.

When the flow is homogeneous like this, the energy you spend is almost entirely productive.

It's all going into reshaping the metal.

Now contrast that with figure 18 -6B, where the flow looks much more, well, turbulent.

This is sheer distortion, and it screams high container wall friction.

You can see the grid lines are completely warped near the wall.

They're subjected to extreme shear.

And this unnecessary shearing action, that constitutes the redundant work penalty we talked about.

So you're wasting energy.

They're spending excessive energy just tearing the metal apart near the walls instead of efficiently pushing it through the hole.

And figure 18 -6E shows the consequence when you have truly sticky friction.

This illustrates the formation of the dead metal zone.

Under conditions of very high friction, the billet's outer surface literally sticks to the container liner and chills.

So the flow separates.

It separates internally along a massive, severe shear zone, leaving this stagnant, chilled layer of the billet skin stuck to the container wall.

And that stationary wedge then acts as the effective die angle.

It does.

And while that can sometimes prevent rapid tool wear, the metal flowing past it is often which can lead to severe surface defects.

It's clear that the success of this whole operation, especially hot extrusion, really hinges on the choice of lubricant.

Absolutely.

The lubricant has to have a low shear strength to make sliding easy, but it also has to be chemically stable enough not to break down at temperatures over a thousand degrees Celsius.

And for the real tough guys of metallurgy, like steel and nickel -based alloys, the solution is glass.

It sounds strange, but yes, the most common and effective solution is glass.

This brings us to the famous Eugene Cigernet process.

I just find the elegance of using melted glass in a high -pressure mechanical process to be utterly fascinating.

It is remarkable.

The process is pretty straightforward.

You heat the billet up to, say, 1200 degrees Celsius, and then you coat it by rolling it over glass powder.

And the glass melts and sticks to it.

Right.

And that melted glass layer serves two absolutely critical functions.

First, it's the primary lubricant.

It maintains a low shear interface between that incredibly hot, stiff metal and the highly stressed tools.

And the second function.

Thermal insulation.

The glass coating acts as a crucial thermal shield, protecting the expensive dye and container tooling from the extreme heat of the billet.

Which extends the tool life.

Drastically.

Which is essential when you're dealing with these high -temperature alloys.

But the success of this entire process depends on one thing.

What's that?

Selecting a glass whose viscosity remains optimal at the specific operating temperature and ram speed.

So if it's too runny, it just drips off?

Exactly.

It runs off too fast.

And if its viscosity is too high, it creates unnecessary pressure resistance.

It's a very fine line.

So even with all this careful engineering, things can still go wrong.

Let's talk about the pitfalls.

The extrusion defects.

Right.

No matter how careful you are, defects that stem from friction, non -uniform flow, and temperature variations are a constant threat.

Let's start with the one caused directly by the friction we just analyzed.

Internal piping, or the extrusion defect.

Figure 18 .6 shows this.

It's also called the tailpipe defect.

This defect is almost exclusively rooted in direct extrusion.

And it's because of that friction -induced velocity gradient.

The center moving faster than the edges.

Right.

The center of the billet moves significantly faster than the periphery because of the drag at the container wall.

At the same time, the outer surface of the billet invariably picks up an oxidized contaminated skin.

And how does that contamination get from the outside to the inside of the final product?

Well, as the billet gets shorter toward the very end of the run, the frictional drag at the wall becomes so strong that the rear part of that oxidized outer skin is drawn inward along the shear zone.

It forms a funnel shape.

Oh, I can picture that.

And this funnel of contaminated oxidized material then flows right through the die along the central axis, creating a defect, a ring, or a pipe inside the extruded product.

And that makes the end of the product completely unusable.

So what's the standard engineering practice to mitigate this costly defect?

Well, the standard, albeit wasteful, method is simply to discard the last 20 % to 30 % of the billet.

The butt.

The butt, exactly.

Since the defect only appears toward the end of the travel, this discard guarantees the quality of the main product.

Is there a smarter way?

There is.

A smarter alternative is to use a follow -up block that's slightly smaller than the container bore.

This smaller block essentially leaves a thin layer of the oxidized outer skin behind, preventing it from ever entering the deformation zone in the first place.

Okay, moving from internal to surface issues, let's talk about cracking.

Surface cracking, or sometimes called fir tree cracking, shows up as these rough, transverse tears on the product surface.

Then what causes that?

It's overwhelmingly caused by excessive tensile stresses that result from high friction at the die face, or more often from excessive ram speeds during hot extrusion.

Back to that hot shortness problem.

Exactly.

If the material heats up too much from the rapid deformation, it enters that hot shortness

Its ductility plummets, and the residual tensile stresses literally cause it to tear itself apart.

So the solution is to slow down or cool it down a bit?

Usually, yes.

Slow the ram speed or lower the preheat temperature.

And what about the internal defects that don't involve surface contamination?

That would be center burst or chevron cracking.

This is an internal separation right along the central axis.

And what causes that?

It's caused by secondary tensile stresses that develop in that central zone, particularly as the material enters the die angle.

It tends to happen when the extrusion ratio R is low.

So you're not squeezing it enough?

Right.

You aren't reducing the area enough to drive massive compressive flow.

It also happens when frictional conditions are poor.

And finally, we also have to watch for coarse grain growth.

Which is when the microstructure gets messed up.

Exactly.

You get these regions of exaggerated grain growth either on the surface or towards the center because of localized temperature spikes and non -uniform deformation.

And that can severely impact the final mechanical properties like fatigue strength.

OK.

So that's what can go wrong.

Let's get back to the core of mechanical metallurgy quantifying the work required.

We start with the idealized uniform deformation energy approach.

Right.

We begin by defining the plastic work per unit volume, which we call use a bin.

This is the energy required only for the useful shape change, assuming no losses at all.

And that's equation 18 to 2.

That's right.

Up equals sigma bar times the natural log of R.

So the effective flow stress times the effective strain.

Precisely.

This tells us that the ideal work done per unit volume is proportional to the stiffness of the material and the magnitude of the strain we impose.

We then relate this work per volume to the total mechanical work that's delivered by the press ram.

Correct.

The total work, W, is just the plastic work per volume, Up, multiplied by the total volume of the billet.

And since work is also force times distance, or in this case, pressure, P times area A times length.

We can set those equal.

W equals Up times V, which also equals P times A times L.

That's equation 18 -3.

And if you solve that for P, you get the expression for the idealized extrusion pressure.

Right.

You just divide by A times L, and you get P equals sigma bar times the natural log of R.

That's equation 18 to 4.

This idealized pressure is the absolute thermodynamic minimum, representing 100 % efficiency.

But of course we know friction and redundant work exist, so the actual pressure, P sub E, will always be higher.

Correct.

And the difference between the ideal and the actual is quantified by the process efficiency, which is the Greek letter eta.

That's equation 18 -5.

Right.

The actual pressure, PE, is just the ideal pressure, P, divided by the efficiency, eta.

And since eta is the ratio of ideal energy to actual energy, the actual energy is always greater due to losses.

Eta has to be less than 1, which proves mathematically that the actual pressure, PE, is always greater than the theoretical minimum, P.

This leads us to what is probably the most powerful predictive equation in this section.

The formula for total pressure in direct extrusion, equation 18 -6, which explicitly separates out the different components.

Yes.

This is critical for practical engineering.

The total actual pressure, PE, is the sum of the die pressure, Pd, and the friction pressure, Pff.

And the formula for that friction pressure is?

PE equals Pd plus 4 times taff times L, all divided by d.

Okay, let's define the components of that friction term.

Tau f is?

Tau f is the uniform interface shoe stress between the billet and the container.

L is the length of the billet that's still remaining in the container, and d is the inside diameter of the container.

So just to be crystal clear, Pfd, the die pressure, incorporates the ideal deformation work plus the redundant work that's lost at the die phase.

That's right.

And Pff, the pressure component that's wasted purely by friction along the container wall.

That's it.

And this equation is the direct mathematical proof for the shape of that direct extrusion pressure curve we saw back in figure 18 -5.

Because the friction pressure is linearly dependent on the billet length, L.

Exactly.

As the ram moves forward and L gets smaller, Pff drops, causing the overall pressure, Pe, to decrease linearly.

The geometry controls the force.

Now to isolate that deformation energy, Pd, from the friction losses,

engineers often turn to empirical analysis methods, like those developed by Sachs.

Yes.

The empirical equation for die pressure, that's equation 18 -8, provides a way to estimate Pd based on geometry and the material's stiffness.

And that formula is?

Pd equals sigma bar naught times, in parenthesis, A plus B times the natural log of R.

Where A and B are just constants you find from experiments.

Exactly.

They're empirical constants, determined by experiment, and they're often related to the die angle.

For example, the chapter notes that A is about 0 .8 and B is about 1 .5 for a 90 -degree die.

And this allows us to calculate the force needed just for deformation, which is essential if we need to know how much heat is being generated.

That's the main application, yes.

We've stressed that speed is a critical factor.

Let's look at figure 18 -7, which visualizes the intensity of the deformation by mapping the strain rate distribution across the flowing metal.

Right.

So figure 18 -7 plots these contours of constant strain rate, which we call dot epsilon, typically in units of reciprocal seconds.

And what you see immediately is that the deformation is highly non -uniform.

Very non -uniform.

The strain rate is highest.

The metal is working the hardest right near the exit diameter, DE, and immediately on the face of the die.

And it drops off really fast as you move back into the container.

It does.

And this non -uniformity means that different parts of the billet are working at different flow stresses, which ultimately results in non -uniform final properties in your product.

So we need a way to connect the global process parameters, like ram velocity and geometry, to some kind of average material behavior.

And this is where the average mean strain rate, dot epsilon bar t, comes in.

Okay.

What's the basic definition?

It's equation 18 -12.

It relates the strain to the time, t, that's needed for the material to traverse the deformation zone.

It's dot epsilon bar t equals 6 times v times the natural log of r, all divided by t.

Physically, what is that telling us?

It's telling us that the rate of deformation is directly proportional to the ram velocity v and the severity of the deformation, which is the natural log of r.

And inversely proportional to the time the material spends undergoing that massive change in shape.

Exactly.

Faster flow, higher strain rate.

Now, when you incorporate the geometric complexity of the die angle, alpha, the full expression equation 18 -13, becomes quite intricate.

It does, but it's a synthesis of geometry and motion.

It's dot epsilon bar t equals 6 v times the natural log of r times the tangent of alpha, all divided by db cubed minus d e cubed.

And that tangent term shows that a steeper die angle increases the rate of deformation.

For a given velocity, yes, because it scales the speed of the shape change.

And that denominator, the volume term, accounts for how the strain rate is spread out across the total volume of material that's undergoing deformation.

Mastering this equation is vital for predicting flow stress and high -speed hot extrusion.

Okay, let's solidify all these mathematical concepts by walking through the worked example from the chapter.

This example, hot extrusion of an aluminum alloy, is brilliant because it proves just how dominating that friction term can be.

It really does.

So here's our scenario set up.

We're hot extruding an aluminum alloy.

The initial billet diameter, db, is 150 millimeters, and the final diameter, d e, is 50 millimeters.

And the flow stress is highly strain rate sensitive.

Very.

It's defined by the equation 200 times dot epsilon to the power of 0 .15 in megapascals.

We're also given a billet length of 380 millimeters, a ram velocity of 50 millimeters per second, and a semi -di angle of 60 degrees.

And we assume sticking friction.

Right, so the metal is shearing internally rather than sliding.

Okay, step one, calculate the extrusion ratio.

This is the easy part.

It's the ratio of the areas, which is just the square of the ratio of the diameter.

So 150 squared divided by 50 squared, that's 3 squared, which is 9, a reduction ratio of 9 to 1.

Perfect.

Step two, calculate the average mean strain rate, dot epsilon bar.

Using the simplified form that's derived in the chapter based on this specific geometry and velocity, we find that the strain rate is 4 .39 reciprocal seconds.

That is an extremely high rate of deformation, nearly five instantaneous changes in shape every second.

It's very fast.

Step three, calculate the flow stress, sigma bar, under these specific high -speed conditions.

We have to plug that calculated strain rate into the material's flow stress equation.

So we take 200 times 4 .39 to the power of 0 .15, and we get 250 megapascals.

Now wait right there.

This is a crucial finding.

It is.

If the strain rate had been one, the flow stress would just be 200 MPa.

But because the ram speed is so high, the flow stress jumps up by 50 MPa to 250.

That 25 % increase is purely due to strain rate hardening.

It really reinforces why speed control is so critical in hot extrusion.

Okay, step four, calculate the die pressure, pd.

This is the pressure required just to deform the metal through the die, including that redundant work factor.

Using the adapted Sachs analysis equation 18 to 7, with necessary empirical constants provided in the chapter, we get a die pressure of 797 MP.

797 MP, that's the deformation pressure.

That's right.

Step five, determine the container wall shear stress.

Tough.

Since the problem says we have sticking friction, the aluminum alloy is assumed to be chilling and shearing internally against the container wall.

So the shear stress is equal to the material's yield stress in shear.

Which, using the von Mises yield criterion, is approximately the flow stress divided by the square root of 3.

So 250 divided by root 3, which is about 144 MPa.

Correct.

Step six.

Now we use the fundamental direct extrusion formula, equation 18 to 6, to calculate the total extrusion pressure, pE, at the very start of the process, where L is at its maximum, 380 millimeters.

Right.

So we add the die deformation pressure, pD, and the friction pressure, pff.

That's pE equals 797 plus 4 times 144 times 380 over 150.

Which gives us 797 plus 1459, which equals 2256 MPa.

Wow.

Wait, nearly 2 .3 gigapascals of pressure?

Let's just look at those two components again.

The pressure needed just for deformation, pgeshD, was 797 MPa.

Right.

But the friction pressure, pff, is 1459 MPa.

And that is the pivotal takeaway of this entire example.

The friction component alone is nearly double the pressure that's required to actually reshape the metal.

So for every ton of force you need to actually do the work, you need two additional tons just to overcome the drag along the container wall.

It's incredible.

And it dramatically underscores why friction control isn't just desirable.

It is absolutely paramount for efficiency in direct extrusion.

And the final step, step 7, is calculating the total extrusion load p required from the press.

You just multiply the total pressure by the initial area of the billet.

So that's 2256 times pi times 0 .150 squared over 4.

And that gives us about 39 .9 MN.

Nearly 4 ,000 metric tons of force.

Just to start this one extrusion run, this example really demonstrates why you need those massive 140mm presses for large scale operations.

It certainly does.

OK.

Given these massive forces in complex thermal control, it's clear why engineers developed some specialized variants of extrusion.

Let's start with cold extrusion.

Cold extrusion really shifts the focus from massive primary breakdown to precision forming.

It's all about producing short symmetrical parts where dimensional control is absolutely critical.

Things like spark plug bodies or complex pins.

Exactly.

Or small hollow cylinders.

What are the engineering advantages of working cold, even though the flow stress is so much higher?

Well, primarily, cold working gives you excellent dimensional control and a superior, often mirror -like surface finish.

And you get strain hardening.

Exactly.

Since the process is done below the recrystallization temperature, the material strain hardens, so you get high final strength without having to rely on expensive alloying elements.

And this has some major historical applications.

The first major one was the mass production of steel cartridge cases during World War II.

Now, if friction is so dominant in hot extrusion, cold extrusion must demand a really Herculean effort in lubrication.

It absolutely does.

The sheer intensity of the sliding forces in cold forming means that conventional oils just fail instantly.

You need a really robust lubrication system.

And the classic method is?

The classic method involves applying a conversion coating, like zinc phosphate, to the billet which is then combined with a secondary layer of soap.

That system provides the low sheer interface you need to prevent cold welding or seizing the dye.

OK, so the other major variant, and maybe the most elegant answer to the whole friction problem, is hydrostatic extrusion.

Yes.

Hydrostatic extrusion is fundamentally brilliant because it completely changes the mechanical environment.

How does it work?

Instead of the billet touching the container wall, the billet is completely surrounded by a pressurized fluid, often castor oil or something similar, which exerts a uniform hydrostatic pressure, and that fluid environment forces the billet to flow through the dye.

So the fluid acts as a perfect medium.

This completely eliminates that decreasing pressure curve we saw in direct extrusion, doesn't it?

Absolutely.

Since the fluid fills the container bore, there is zero billet container friction.

The pressure versus ram travel curve is nearly flat, just like we saw for indirect extrusion in figure 18 -5.

Besides just eliminating friction, what are the geometric and quality benefits that this pressurized environment provides?

Well, first, the fluid acts as a perfect pressure transfer medium and a perfect lubricant, so you get an excellent surface finish and superior dimensional accuracy.

OK.

Second, because the lubrication is perfect, hydrostatic extrusion lets engineers use very low semi -dye angles, sometimes as shallow as 20 degrees.

And low dye angles mean less redundant deformation.

Which dramatically increases the process efficiency.

And third, it lets you extrude billets with very large length -to -diameter ratios.

You can literally coil extruded wire while it's being made.

Are there any mechanical limitations to this process?

Yes.

The main limitation is a practical one.

The maximum pressure you can achieve, which is usually around 1 .7 GPA, is constrained by the strength of the container vessel itself.

And you have to be careful to make sure the billet remains solid during flow.

And when the forces get too high, they augment the system.

That's augmented hydrostatic extrusion.

It's designed to solve problems like the frictional drag on the large amount of stored energy in the fluid.

You just apply an additional conventional axial force with a ram to assist the extrusion.

It gives you better control and higher throughput.

Alright, let's wrap up with the production of tubing, which is a major application of extrusion.

Yes.

Extrusion is fundamental to producing high -tolerance tubing in seamless pipe.

And that requires specialized tooling to manage the central cavity.

The first method is the standard mandrel and die approach.

Right.

Here, you use a solid or a pre -hollowed billet, and a mandrel is fastened to the end of the ram.

The clearance between that mandrel and the die wall defines the tube thickness.

And if you start with a solid billet.

As figure 18 -8 shows, a separate hydraulic system, acting coaxially,

first pierces the center cavity before the main ram begins the forward extrusion.

The second method, which is used mainly for softer alloys like aluminum, employs this incredibly clever piece of flow engineering.

The portal die.

The portal die, shown in figure 18 -9, is a master stroke in metal flow management.

A solid billet is forced into separate streams through these ports or holes that go around a central bridge and a short mandrel.

So the metal streams, separate,

flow around the mandrel's bridge, and then they have to rejoin before they exit the die.

That sounds like a recipe for a weak seam.

You'd think so, but that's the genius of the design.

They meet again in a special welding chamber that surrounds the mandrel.

And because it's all under immense pressure.

And because there's no chance for atmospheric oxygen or any other contamination to get in, the separate streams of metal are forced together and you get a perfectly sound pressure weld.

And this is good for complex shapes.

Highly efficient for producing complex, hollow, unsymmetrical shapes that would be impossible to make with a standard die.

Okay, finally, let's look at the major commercial process for seamless pipe and tubing, which is generally preferred over welded products.

The starting operation is often the Mannesman mill.

This is a truly spectacular mechanical operation known as rotary piercing.

It's illustrated in figure 18 -10A.

It's used extensively for steel and copper billets, and it employs two large barrel -shaped driven rolls that are set at a severe angle to the billet axis.

Tell us about the physics of that angle.

How does it pierce a solid metal block without a cutting tool?

It's amazing.

The angled rotating rolls simultaneously rotate the solid billet and pull it forward.

This combination of rotational force and compressive pressure from the rolls creates exceptionally high tensile stresses right in the very center of the billet along its axis.

And those internal tensile stresses are what tear it open.

They are sufficient to tear open the center cavity of the hot billet, forming a central hole.

Piercing is in fact regarded as the most severe hot working operation commercially applied to metals because of the magnitude of those induced internal stresses.

So the Mannesman mill creates the hole, but it can't provide sufficient wall reduction or concentricity on its own.

What are the subsequent finishing steps?

The process continues with subsequent tube elongation stages.

For instance, the Asel Elongator, which is figure 18 -10C, uses three conical driven rolls and an internal plug or mandrel to work the tube further.

And this makes the tube more uniform.

More concentric with smoother surfaces.

And then the very last step in production is often the reeling mill, figure 18 -10, which uses slightly oval shaped rolls to smooth and burnish both the outside and inside tube surfaces, ensuring you get the final dimensional tolerances and quality finish.

Alright, we have taken a truly comprehensive deep dive into mechanical extrusion.

We certainly have.

We started by classifying direct versus indirect flow, we analyzed the intricacies of tooling and lubrication, and we did a rigorous quantitative analysis of the forces and flow mechanics.

The overriding theme, especially in direct extrusion, seems to be this constant battle against friction.

Absolutely.

Let's quickly recap the fundamental mathematical relationships that have to remain crystal clear for any student.

First, the extrusion ratio, rA0Af, is your foundational measure of how severe the deformation is.

Next, the idealized pressure, P equals sigma bar LnR.

This defines the theoretical minimum energy required, and is dependent only on the material's flow stress and the effective strain.

Most importantly for engineering practice, the direct extrusion pressure, P e plus Wotoff FLD,

must be remembered.

This equation clearly shows that the total required pressure is the sum of the force needed to deform the metal and the force lost to friction, which drops linearly with the

And finally, the strain rate, dot epsilon bar equation, that's the one that connects the process speed V and geometric factors like the die angle alpha to the material behavior.

It lets you accurately predict how much the flow stress will increase during high -speed hot extrusion.

And visually, you should always hold onto figure 18 .5, that pressure versus ram probable curve.

The decreasing pressure in direct extrusion tells you friction is at work, while that constant pressure in indirect or hydrostatic extrusion confirms that you've effectively eliminated that massive friction component.

And as we saw in our worked example, the total load required for extrusion can be completely dominated by friction, often exceeding the load needed just for the deformation itself.

So that brings us to a final thought for you.

Go ahead.

Given the transition from high -temperature glass lubrication to the need for chemical coatings in cold forming, which process high -speed impact extrusion of a soft aluminum, or the

hydrostatic extrusion of a difficult high -strength alloy, do you think presents a greater challenge in lubricant selection?

The answer really lies in managing sheer stability versus viscosity.

Something to think about.

That's a great engineering trade -off to consider as you move from theory to application.

We've covered a lot of ground today, from dead metal zones to the powerful mathematics of maximum force.

Keep these critical relationships in mind as you continue your study into mechanical metrology.

Thank you so much for joining us for this deep dive into the world of force flow and mechanical forming.

It was my pleasure.

We'll see you next time.