§1. HIP vessel aftermath and the Navy recuperator [00:02]
It's in the paper, but they sort of didn't tell everybody that the sixteen-ton piece landed a quarter mile away. If it had landed on somebody's house, the news people might have picked it up. But I can tell you that the safety officials, the fire department, the police department, the mayor's office — they were not happy to know that they had a plant that actually had something that could be sending sixteen-ton pieces a quarter mile away in a random direction.
The really interesting thing to me about this was that it was the world's only vessel that could do all the aircraft engines in the world. Fortunately, there was growth in the business and the company had another one coming on stream. They had ordered it about three years before; it was coming on stream in three months. So we didn't see a multi-billion-dollar problem.
This was ten years after that, and there have been some improvements in quality control in the mills, in understanding of the heat treatment and the water treatment, and in calculation of stresses. In some of the videos you're going to hear about the Navy's internally cooled recuperator on the surface ships, and how originally it was supposed to — this is just a big heat exchanger, take the stack gases from the oil-fired ships and preheat the incoming air so you get more efficiency. When you're just cruising along, a nice lazy stroll through the Pacific, you're operating at about ten percent efficiency because most of your heat's just going up the stack. You're not at full battle speed.
The problem is, you have to go back to the carrier to refuel — the destroyers and so on. Back in the days of the former Soviet Union, when people could hit you with something that has a very wide range, some of your other ships could be thirty miles away from the oiler or the carrier. So they were spending half their time off station going back to get fuel. They decided we can up our efficiency to thirty percent with this heat exchanger. They built it, and they found that it lasted not 100,000 hours but about two minutes, before it tore itself apart due to the transient thermal stresses. They fixed it, and I'm told now you actually do have ICRs in your ships. I remember I ended up being on what they call a Blue Ribbon panel, and we had to go out and look at it and say what was wrong.
For HIP, you can get dramatic improvements in properties such as fatigue properties. This is applied stress versus cycles to failure — just a fatigue curve. You actually go up by about twenty percent in stress, but twenty percent in stress in terms of fatigue life is like a factor of 400% in life, because of the slope of that curve. In high-cycle fatigue you get some very large increases in life. That's why you can afford to spend $1,000 an hour to put some of these things through there. And when you put them in the vessel, you're not just putting one disc or one cylinder in there, you're putting half a dozen discs at a time, so you spread it out. So HIP is one way to make a net-shaped part.
§2. Phase diagrams and zone melting [04:00]
Now let's finish up on solidification. How many of you have not seen a phase diagram before? Most of you have. A phase diagram is just temperature versus composition for an alloy. The pure material melts at some temperature. For many materials — you add carbon to iron, you add copper to aluminum — the melting temperature decreases. You add salt to ice and the temperature decreases and it melts. That's the principle of putting salt on the roads in the winter. It's also the principle of freezing ice cream. How does melting the ice freeze ice cream? Haven't you ever made homemade ice cream?
In order to melt the ice, you have to absorb the latent heat of fusion. If the ice turning to water is absorbing heat, it's got to get that heat from somewhere. It gets it from the cream, and it freezes the ice cream. It's sucking the heat out of the ice cream. You've got to think of your thermodynamics. That sounds like a homework problem — yes, it would be a good homework problem. Go make some ice cream.
In any case, you have a liquidus line and a solidus line, and the solidification folks like to describe that in terms of a partition coefficient K. K is just the composition of the liquid over the solid. So the first solid to form will be K·c₀. The average composition is whatever your average composition of your melt is, and the solid that forms will be K·c₀. If you first form a little bit of liquid, as you form more and more liquid, the liquid gets enriched in the B component, and it starts to increase in concentration of the alloy. They're assuming perfect diffusion in the liquid here, which is not really true — but in any case, you will actually sweep the concentration of the B component to the end of this thing if you solidify in one direction. And this is the principle of zone melting. Anyone ever heard of zone melting?
It was a big deal when I was a student because that was what happened in the 1950s when they first invented semiconductors, at Bell Labs. You needed very pure silicon or germanium. By very pure, we mean six or seven nines pure. What do we mean by 6-9s pure? 99.9999% — one part per million in purity. Seven nines is a tenth of a part per million, 100 parts per billion. That's what you need in silicon or germanium to make good semiconductors. How could you make that? The things will start to react with the wall of the crucible and give you that type of impurity level.
There was a technician at Bell Labs named Pfann. I think he had a high school diploma, but he certainly didn't have a college degree. He was the one who said, well, let's just keep melting it in one direction and sweep all the impurities to one end of the ingot. He put silicon in a little boat and pulled the boat through a furnace. As it solidified, he was sweeping all the impurities to one side. You do that about ten times and you've got something 6-9s pure. Cut off that end of the ingot, and you've got the crystal. That's still how we make really good quality silicon today. The whole semiconductor industry is based on a simple partition coefficient and solidifying things in one direction. You have to do it like ten times to keep sweeping all your trash to the other end, then cut off the end.
So all of a sudden in the 1960s — remember I was a student in the '60s — you could buy 6-9s pure tin or aluminum. It's no big deal today, but back in 1950 that would have been a big deal. Because if you want to go through the thermodynamics, entropy says that's a very expensive thing to do, to get the last few impurities out. As you get to 100% purity, entropy goes to infinity. It's dΔS/dx, if x is your concentration — hey, you're learning some math — where as X_B goes to zero, it goes to infinity. It takes infinite entropy to get the last impurity atom out of there. You can prove it through statistical mechanics.
So the point is, when you solidify something from one direction, you will get this segregation of your alloy elements. You'll get enrichment in the liquid, and that leads to microsegregation, which you don't always want.
§3. Constitutional supercooling, dendrites, and the Sea Wolf [10:43]
Back when I was a student they used to spend several lectures on what they called constitutional supercooling. I'm going to spend several minutes on it. This is that phase diagram turned on its side — flip it over ninety degrees, temperature versus composition. Here's the melting point, here's the solidus line, here's the liquidus line. If you map that onto this concentration, here's your c₀, your average concentration, and here's your K·c₀, the first solid to solidify. As you go along, you're pushing the solute ahead in the liquid, and you have a boundary layer here. Depending on how steep your temperature gradient is — because you're solidifying, this is colder than this, you're pulling this boat through the furnace — you can get to the point where this K value is such that the material here is actually supercooled. This enriched B material is what you call constitutional supercooling. By throwing the extra B atoms into the front, you enrich it, and that stuff wants to solidify if there's a nucleus.
That's exactly what causes these dendrites or these cells. Here's cellular growth. If you have a very steep gradient of temperature, you can suppress this instability. Here's a little instability, here's a big fully cellular growth. When it gets really unstable, you get the dendritic growth — you get instabilities along the side, and that creates the dendrites. Those dendrites create porosity in your casting, because the liquid can't get past all those little branches. It's kind of like a snowfall — underneath a fir tree, you don't have any snow on the ground because all the snow got caught up in the boughs. These dendrites can be a big problem because they represent microsegregation, inhomogeneities, increased porosity, regions within the casting that are rich in alloying element or deficient in alloying element, and that creates lots of problems.
Why can that be a problem? The whole Sea Wolf problem, two billion dollars it cost the Navy, was because the welding wire was too rich. It had too much of certain alloying elements, and it probably came from an enriched area of the casting. It was all drawn into wire, but they didn't draw the whole twenty-ton ingot into wire all at once. They cut it up in pieces, and so this part of the ingot was rich, this part was poor in alloying element. The lot they used turned out to be what they called high-side chemistry. If you had gone to that same ingot, you would find low-side chemistry elsewhere. The problem with the high-side chemistry: it had a yield strength of about 140 ksi, not 100 ksi, because it was enriched in alloy. At 140 ksi, your sensitivity to hydrogen is much worse. You can't tolerate anywhere near as much hydrogen. It was all within the Navy spec range, but it happened to be all the way at one end of the high-side chemistry. They always give you a range because there are these inhomogeneities in the casting. They got bit by segregation all the way back in the original ingot. Some of these things actually are important, and they do follow through the whole system and can sometimes create real problems for you.
We're not going to go through all the different ways that dendrites form. Here's where you've etched — this one shows up a little better. This is dendritic structure in a transparent organic. So this is an organic liquid that's solidifying, and you get these instabilities along the side. The distance from here to here is the primary dendrite arm spacing, and the secondary dendrite arm spacing is the little distance in between. It turns out that the size of the dendrite arms, or the spacing, is proportional to the cooling rate of the casting.
This is a plot from Flemings' book of local solidification time, which is one over the cooling rate. This is secondary dendrite arm spacing over eight orders of magnitude. We don't always plot a lot of real data over eight orders of magnitude, but there's a correlation. The secondary dendrite arm spacing, as I remember, goes to about the one-third power. If you cool really fast, you're down here, and your secondary dendrite arm spacing is less than ten microns. That's rapid solidification — very little inhomogeneity if you cool quickly. If you cool very slowly, like a great big ingot, a twenty-ton ingot or a twenty-inch thick piece of steel, you can have dendrite arms that are on the order of millimeters in size — huge dendrites. You can never diffuse away in the solid state that inhomogeneity; it would take millions of years at temperature. So we have to do lots of things to try to get fast solidification.
If you look at the primary dendrite arm spacing, this plots versus cooling rate, so it's got minus one-third slope rather than plus one-third — one case you're plotting cooling rate, the other one local solidification time. This is a bunch of aluminum alloys, and it shows 100 microns, ten microns. This type of stuff, months to diffuse away the segregation. This type of stuff, hours. So you actually could get a homogeneous melt if you do something like that.
Student: Would you ever use a HIP, for instance, to get rid of any defects that are in the material?
No, HIP will not do it, unless you start with something that's rapidly solidified powder, which has very small dendrites as a powder, and then you put the powder inside a jacket in the HIP. So you make a metal can — maybe you've got a nickel-base alloy and you put it inside a steel can, which is sort of like a big steel balloon at these temperatures, and you actually squeeze the powder together. HIP is used for a lot of powder processing. We get rid of the segregation by doing rapid solidification of powders, but then we have to weld the powders together. You weld them together in the HIP unit.
So you like to have rapid solidification to get rid of this microsegregation, which creates variations in properties throughout your bulk. If you just solidify it as a great big bulk casting, you're never going to get very uniform properties. The size of the imperfections is proportional to the size of the casting. If you make a micro casting of a little powder the size of a piece of cracked pepper, you can get rid of it in a HIP unit. Or you can sinter it together, and then forge it to help get rid of that porosity. But forging means you have to get a lot of strain into the material — kind of like kneading dough — which is actually where I want to go next.
§4. Gradient furnaces, single-crystal blades, and the generator rotor forging [19:56]
There's one other thing that Flemings actually invented a process for in the late '60s. In order to inhibit the dendrites from forming, you can grow in a gradient furnace. The steeper the gradient — hundreds of degrees C per centimeter — you can keep the dendrites from forming, and you sort of end up with zone melting. But if things aren't too bad, you're not sweeping everything ahead, if you design it properly. I didn't bring it with me again, but my little turbine blade that we passed around — those are grown in a gradient furnace.
I think I told you Rolls-Royce uses four blades on a little investment casting sprue. General Electric and Pratt, their casting shops use about sixteen or twenty-four on an investment casting sprue. They grow it as a single crystal in a gradient furnace. It takes about ten hours, because you have about a thousand-degree temperature differential over five or six inches in this furnace, and you slowly pull it through over about ten hours. You don't get dendrites because you suppress them with the steep gradient. You don't get constitutional supercooling that allows the instability for the cell to grow up into the liquid. You can get nice planar-front solidification — a very perfect structure. But it costs a lot of money. This gradient furnace is about three million bucks to grow sixteen blades a day or maybe thirty-two blades a day. You can start to see why these things start to cost $6,000 apiece. But if they allow you to use half the fuel over the life of the engine, it's worth it.
Flemings also showed that you could grow all kinds of structures off the equilibrium structure. This is a composite structure where you actually control the cellular growth. On a transverse section, you've got the grass — you're looking at the top of the grass — this is one phase over another. Longitudinal section, you get stringers like this. The paper is called "Growth of Composites from the Melt," and you're growing it in a gradient furnace just like these turbine blades. In the late '60s, everybody wanted to see if they could make better quality turbine blades by using this gradient growth technique. They do, in various ways, but they found they needed to go not just to this structure but to a complete single crystal structure. It was actually a very big deal when he did it, to show that you could get non-equilibrium structures by growing things in a very steep temperature gradient, and a lot of research was done on that.
Did I show you this picture before of one of the generator rotors? This is the generator rotor forging, and this is in one of the plants — I don't remember if this is U.S. Steel or Bethlehem Steel. Probably only one of them exists anymore in the United States. Bethlehem's steel plant is now in an amusement park in Bethlehem, Pennsylvania. These are the stairs going up — one floor, two, three, four, five, six stories tall. And here's your forging, may run 200 tons at this point, started out as about a 450-ton forging. By the time you forged it and lost all the oxidation — because you had to leave it in the furnace for a week before you got it up to forging temperature, and you grew an oxide scale that's an inch thick, and when you forge it, that all just comes off — you have a lot of waste. Then you machine it, and you're going to heat treat it. This was basically a system where they made battleship gun barrels in World War I. Not a lot of facilities like that in the world — a lot of crane capacity, a lot of big height. That's generator rotor forgings.
§5. Forging steps, cold heading, and the buy-to-fly ratio [24:36]
If I want to get rid of the inhomogeneities, I could start with rapidly solidified powders, or I can start with castings. If I give them ninety percent reduction, I can flatten out these dendrites — pancake them — so that they're so thin that I can stick them in a furnace and diffuse out things. Who cares if they're a millimeter thick? If I turn them into a tenth of a millimeter, I can put them in a furnace and anneal it out. I can do it multiple times, and that's basically what we do to get homogeneity in products by mechanical working.
So if I wanted to make a rotor disc for an engine — a jet engine, or a steam engine — these things could be more than six feet in diameter, they can be ten feet in diameter if you're talking about a big rotor. You start out with a billet of material, an ingot that you cast, and you do a pancake forge. People actually take plasticine, like Play-Doh, and do some of the modeling of this. Now you can do it on the computer, but before we had computers, we had Play-Doh. It's true. You can actually squeeze down on it. If you squeeze too much at once, the friction is going to cause cracking on the outside. You get a barrel-shaped ingot as you start to compress it into a pancake. So you actually have to lift it off, maybe reheat it, come in again with a new frictional boundary condition, and squeeze it some more to get a big reduction in your pancake.
The material will only take so much stretch before it breaks. [Tom produces a tensile specimen.] If you pull on something enough, it will break. It will neck down and break. Typically a metal will only give you like thirty percent stretch, maybe sixty percent if it's really hot, before it just breaks. That's because you can model the metal as if it's a non-Newtonian fluid. A Newtonian fluid is something that doesn't matter if it's different in cross-section — you can stretch it out and it will maintain the same general shape. If it had waves in it to begin with, you can stretch it out and it will keep the same general shape between the peaks and the valleys. Basically what we mean in a Newtonian fluid: stress is equal to the strain raised to some strain rate. This is dε/dt, m is the coefficient exponent. A Newtonian fluid is when m equals one. For a typical metal, m equals 0.2. So if you have any instability in a metal where it starts to thin down a little bit, that instability will grow. It will neck down and break at the thin spot. A Newtonian metal — you can have a little neck in there and you can pull it out a hundred miles, if it really is an m of one. The only Newtonian fluid that we might work with typically is glass — may have 0.9. Metals typically have 0.2.
So when we want to forge something, we have to do multiple steps. [Tom passes around a small forged insert.] To give you an example: this little simple part is basically a little metal insert that goes into a piece of wood so that you can put a steel screw in it without stripping the wood threads. You put together cheap particle board furniture from Walmart, and it has all these little inserts in it.
To make that little insert, you start out with a little piece of wire that you chop off into a little ingot. This little chunk of metal — you have to forge that. For the first one, they size it, and it's got a little bit of a cone here, about a millimeter deep. Then they start to punch a hole in the bottom — they extrude a little hole, but they can't make it all the way because it would crack if they went any further. So they do it again, they extrude it again. Then they put a head on it. Then there's one wasted piece of material — they punch the little hole out. Then they do a finishing sizing, then they knurl the grip on the outside, then they thread it on the inside, and then they plate it. Eleven steps of forging to make that part.
Student: What do you mean by knurl?
Knurling is just inscribing it — actually, they roll it on. They have a hard tool that has the same shape, and they put it in a lathe and put the hard tool up against it and spin it. That's called knurling. They make the same parts that weigh four or five pounds that might go in the steering component of a truck or a car. If you look at the knuckles and the steering components, they are cold forged or warm forged. This is called cold heading, because in the old days, the first cold heading was just putting a head on a nail. That's about all they could do before World War II.
Then someone learned — when you get to adhesive bonding, I usually end up talking about how they learned to phosphate the steel so it would hold onto the lubricant. A lot of the tearing was due to the frictional boundary conditions. As the steel of the part is rubbing against the tool that you're trying to forge it against, you can get welding between them. If you keep going, you're going to get surface cracking on your part, and you're also going to wear out your tooling very quickly. They learned to phosphate the steel after World War II, and the lubricant they use is basically soap. It's a stearate — soap is a stearate. Because they had this porous phosphate coating, it would hold lots of stearate, and it would smear that peanut butter lubricant all the way through. They could head that through eleven dies rather than twenty-five dies, so it becomes cheap enough to make those parts. You go through one of these shops with earmuffs — you don't just put little earplugs in your ears. The shop is probably 180 dB when it's going. The forging machine, on a little part like that, may be going seven times a second. I can't do anything seven times a second, but it's really pounding away.
So let's take a break, and we'll come back in about ten minutes.
You have to go through a lot of steps and a lot of different shapes before you get to the finished part. To give you an idea of what you might have to go through, the Air Force likes to call this the buy-to-fly ratio: how many pounds of metal do you have to purchase to make a forging that you can then sell as a part? Here's one where the finished part — part of one of these discs — weighs eleven pounds. If you do a cold die forging, it starts out at 210 pounds. That's a buy-to-fly ratio of almost twenty. Here's the hot die forging — if you do it hot, it's only seventy-two pounds, so that's obviously better. When you realize we're talking about alloys that may cost $100 a pound, and you've got a buy-to-fly ratio of twenty, you're now paying $2,000 a pound for the metal that you actually fly, without even the processing that's involved. So there's lots of money to be made in what's called near-net-shape processing.
§6. Superplasticity and Al Backofen [35:32]
Here is an example of a billet — just a big long bar. They rolled a bar from an ingot. This could be six inches in diameter, three inches in diameter, depending on what you're going to make out of it. This is a situation where they make a forging that has this kind of double-keyhole shape. They machine the chips out of it — 250 pounds becomes fifteen pounds. Here's another one where they do what's called isothermal forging — 126 pounds becomes fifteen pounds.
What's isothermal forging? Isothermal forging is something that was really developed by Pratt & Whitney, based on something that was developed in 1938 in Germany but was lost because of World War II. It was published in 1938, but because of World War II, no one ever paid any attention to it. It's called superplasticity.
Superplasticity was rediscovered in the early '60s by a faculty member in this department named Al Backofen. Don Avery was his graduate student. Avery and Backofen were trying to make finer and finer grain size metals. Backofen's specialty was what he called deformation processing. This is his book, 1972. I studied with him — he was the first guy I ever worked with as a sophomore.
After graduating high school, I got a job with the post office in Virginia Beach. I had to fill out a form and scored better than ninety-two percent, and so they hired me. One of the best jobs I ever had — $3.35 an hour. Typical wage for a student back then was a buck an hour. I was getting paid whatever a postman makes. I spent that whole summer driving around Virginia Beach in a station wagon delivering special deliveries. Actually, it was only the second half of the summer, when they found that I was trustworthy and I wouldn't just stop for a coffee and stay there for four hours. Back then a special delivery letter was an extra thirty-five cents in postage. They paid me $24 a day to deliver twelve letters in Virginia Beach that had $3.60 — if you want to know why the post office was losing money, I can explain it to you someday.
In any case, they liked me. I went off to MIT the next summer, I reapplied. But because of the Vietnam War, I scored 90-something again on the civil service exam, but I wasn't a veteran, which gave you a ten-point preference, and I couldn't beat the 108s. I would have had to score 108 to beat some of the veterans, which was fair. So I got a job at the Naval Air rework facility in Norfolk at $1.92 an hour, rebuilding jet engines mostly coming back from Vietnam. I needed to make that same amount of money to afford to come back to MIT, so I took another job at a buck an hour at the drugstore in Virginia Beach where I'd worked two years before. I was working 30 miles apart, two 40-hour-a-week jobs. That was not a great summer. The previous summer was great — cruising around Virginia Beach in a station wagon. Didn't have air conditioning but it was okay. For those of you who know Virginia Beach, it was at the time the fifth largest city in the world in area. My father used to say about Chesapeake, Virginia — third largest city in area — that it had more bears than people.
In any case, I decided when I came back for my sophomore year that I did not want to go through another summer like that. So I got a job with Al Backofen. He was my first instructor in materials. I started working in his lab. Backofen was one of the crustiest faculty members ever to be at MIT. He used to throw books at his graduate students, literally. There are a lot of great Al Backofen stories. But the man was also a genius in terms of deformation processing.
He was looking at titanium alloy and zircaloy, which is nuclear reactor material. He was looking at — if he made the grain sizes finer — and the reason he was looking at titanium and zircaloy is because he could cycle them between these phase transformations, so he could get extremely fine grain size, down to one or two microns in size. This would be called nanotechnology today. It's not nano, it's micro, but someone would call it nano today. He was measuring this m value — m is the strain rate sensitivity. Dion Lee, Korean, worked with Backofen early on. If he got to very fine grains, he could get elongations not of twenty or thirty percent — he could get a thousand percent elongation. Turns out m's a very strong function of grain size. If you get superfine grains, you can get extremely high abilities to stretch a material.
This actually is from 1934, the German paper — a tensile bar of superplastic material, bismuth-tin eutectic alloy. A lot of stretch. So now you've got something that acts like glass. You're not at one, but even glass is only about 0.9, and you can get seven as an m value in metals. It can go from 0.2 up to seven, if you get superfine grain size.
[Tom produces a superplastic candy-dish sample.] This belongs in the Smithsonian. It's been used as an ashtray before I got it. I told you about 8-137 — that was Backofen's graduate students' little short door, that was my first office. Backofen's last graduate student was graduating the week that I came as an assistant professor, and I recovered a lot of his old samples. Here's a forging sample, here's a rolling sample. These are Al Backofen's old samples that he left, because MIT was treating him like dirt — of course, he treated them like dirt, so I'm sort of fair in return.
He had a home up in Marblehead, and he decided that he would put it on the market for an outrageous price, $90,000. If anyone bought it, he and his wife — they had no children — were just moving to their farm in New Hampshire where he was growing Christmas trees. The first person came by, offered him asking price. He didn't quite figure out what the market really was. So he sold his house for $90,000 or $95,000 and moved to New Hampshire. Every three or four months he would come back down. He'd stop in and see me because I had been his undergraduate student, and he was always nice to undergraduates and master's students. It was the doctoral students he would throw books at and curse and throw out of his office. He got great results out of his doctoral students because he put them through so much pain. He never wanted to see a thesis that was more than thirty pages in length, a doctoral thesis. It would take them a year or two to condense their thoughts down to a nugget. His book is nothing but nuggets, okay. I read theses that are 400 pages long and they're telling me that Boeing makes airplanes. Thank you — I read for ten pages about Boeing makes airplanes. But Backofen's theses were so condensed, and his text is so condensed.
In any case, this is an aluminum-zinc alloy. What Backofen did is went down to Taunton, Massachusetts. He got some dies from the silversmiths — this was a candy dish die for making silver dishes. Ordinarily, to make a draw like that would take four or five drawing operations in the sheet metal. With a superplastic material that has 500% elongation, you can do it in a single draw. That is the reinvention of superplasticity after the German work in 1934. That's why it belongs in the Smithsonian. But this makes a nice ashtray. I don't smoke.
This is what you would do otherwise. If you had a piece of sheet metal, you'd take a blank — just a simple round blank. You would first draw it into something like this, then redraw it into something like this, then draw it again into something like this, and you finally end up with something like this. This is also Backofen. This is not all that different from the way you make beer cans or soda cans. Lots of different drawing operations. The die to make a beer can run for about two million dollars even today. Big machine, very complex, but a lot of work's been done on it.
So you have to go through lots of steps, because most metals have a lousy m value, and they'll rip with more than thirty percent strain. You have to go through operations that don't have more than thirty percent strain. You can repeat the operation, but if you want to get to something that has 200% strain to make it, you've got to do 0.2 to the sixth power or something to get all the strain.
Student: So is this happening with the metal at room temperature?
In some alloys, you can get it at room temperature. That aluminum-zinc alloy occurs at room temperature. In the nickel-based superalloys that they make turbine discs out of today, when you have isothermal forging — [Tom locates the forging sample.] — where you would ordinarily have to start with 250 pounds of a $100-a-pound alloy to make a fifteen-pound part, you would generate 235 pounds of chips in machining, which is pretty pricey. You start out with 160 pounds, 126 pounds, with a single set of dies. The dies are heated to the processing temperature, which might be 1,000° centigrade. Very expensive dies, but you only have to make one set. You don't slam it down like a hammer forging — you come in and squeeze it slowly. You probably do this in ten, fifteen minutes, but in a single set of dies, a single forging operation, near-net shape, a lot fewer chips. Look at how much money you're saving on machining.
§7. Deformation zone geometry [47:16]
Student: For these other stamping operations, what causes the system to relax so you can stamp it again?
It's actually the frictional boundary conditions. You've got lubrication on the surface, and as you stretch it out, you get non-uniform straining.
This is, in my opinion, the most important graph in Backofen's book. It's called deformation zone geometry. Frankly, a lot of the way I look at the world is based on Al Backofen's approach: how can you generalize everything into just a couple of simple principles? Here he has the pressure to do the forming divided by two times the shear stress. If you're going to change the shape of something, you're really shearing the metal. Two times the shear stress is really the tensile stress, the flow stress of the material. At 1:1, this is basically just a simple compression test. If P over 2τ_y is one, this is just a simple compression test. Doesn't matter whether you're talking about Play-Doh or lead at room temperature or nickel-based superalloy at 1,000° — this deformation zone geometry always applies for any homogeneous material.
What it says is, if you have a deformation zone geometry where Delta — the height of the deformation zone divided by the length of it — is less than one, you're just doing a simple compression test, and that's the load it takes to deform that. As you get to something like a hardness test, where you're running a punch into something that's very thick, if it's a non-work-hardening material, it's 1 plus π/2, or 2.57 times as much force. If any of you have ever done any hardness testing, you may know that there's a rule of thumb that the hardness of a material is three times the tensile strength. There it is — 2.57, add a little bit for work hardening, you get to three. So as a rule of thumb, a hardness test takes three times the pressure of a simple compression with a deformation zone geometry of one. You essentially are infinitely thick if you get up to nine or ten as a deformation zone geometry.
The deformation on thinner things is inhomogeneous. Here someone just took a punch with a 5 mm face and squeezed onto a plate that was 30 mm thick. They did it in a particular type of steel that has some nitrogen in it that, when you etch it properly — here they did a little bit of deformation, a little more, and a little more. You can actually see the deformation geometry, the localized plastic flow in the material. It's exactly what you get from this type of analysis. The one I just showed you with 5 and 30 is actually a deformation zone geometry of six, but this is one he's drawn at four, of Delta over h. This is inhomogeneous straining.
If you keep going on Backofen — here's a couple of Backofen inhomogeneous strains. This is good old plasticine clay models from 1931. Typical Backofen — nothing's new, it's just explaining the old stuff. Here we're extruding plasticine, and they put some grid lines on it. Originally it was a nice square grid. Here we have a nice tapered angle, here we have a sharp angle. If you're squeezing toothpaste out of a tube and you have a nice gentle angle, the strain lines are no longer straight across, but they're a lot less inhomogeneous than here. Look how that line changed. It's the same amount of reduction in area, the same diameter reduction, but you have a tremendous difference in the amount you're straining the material.
Student: The one on the far right — is that what's happening in all these pressing operations?
Yeah. You have some piece of metal in a forging press. It can be something like this, but it really depends on the angle. It's not all of these.
Student: So why can you then go in and do that again, as opposed to just doing all those?
Because you relax everything. You don't have the same friction. The reason I'm getting this inhomogeneous deformation is because the friction of the tool is pulling on this material here. Chapter 8 in Backofen's book is frictional boundary conditions. If you started out with a lubricant on the surface, if you don't have enough lubricant, you start cold welding the material to the surface. If you take it out and relubricate it, you can go further again. It has to do with the friction on the surface. If you start welding it together and it sticks, and you get more than thirty percent local strain, it breaks. But if you deform it, don't break it, take it out, put it in another tool that's lubricated again, then you can start deforming again. It's not the absolute strain, it's the local strain that causes the fracture.
That's why, on that little part I said they used iron phosphate to put a thick layer of lubricant on. If you get a thick layer of peanut butter in there, your lubricant takes you further and lasts longer. They don't relubricate between each one of those, but they have enough that when they put it in a new die, they get it relubricated properly. This is from one of his students' doctoral theses, where he looked at wire drawing. He just looked at the hardness of the material — Vickers hardness number, lubricated strip versus unlubricated strip, to emphasize how lubrication makes the difference. Here's the same angle, but the inhomogeneity factor — the ratio of the highest hardness to the lowest hardness — drops from about 1.28 to 1.23, depending on the lubrication. If you have a very shallow angle, you can get very homogeneous straining, depending on your angle and your lubrication. If you get too much strain at the surface, that's where the cracks start, at the surface. If you initiate a crack, you're done. You try to put it in another die, it's already got a crack there, then fracture mechanics tells you it's just not going to work.
There are other things that cause inhomogeneity. This is from the same student's master's thesis, 1965, where he was drawing with his inhomogeneity factor. You actually can set up tensile stresses in the center and cause these things to crack — that's a type of defect in wire drawing or extrusion. Backofen, of course, used his student's thesis. This comes from Don Bliquhouse. Bliquhouse was a student of Morris Cohen, and Don Bliquhouse was the vice president of research when I went to work for Bethlehem Steel. This is work that Don Bliquhouse did when he was at Bethlehem Steel, but he was a Morris Cohen student, so Backofen would never put a Morris Cohen student's pictures in his book. These are the internal politics of the MIT department. This is the extrusions of Bliquhouse, showing the type of defects you can get if you don't have the right lubricant, the right contact angle, the right percentage reduction. Something as simple as drawing wires through a die, which has been going on for 4,000 years — you've got to know what you're doing and get the right set of parameters, or you can just turn out junk. There's a whole science to this stuff.
§8. Rolling, the Z-mill, and the Alcoa air knife [58:07]
There's a science to rolling of metals, and we're not going to go through all of it. When you're rolling sheet metals or plates, you want to have nice big plates, nice wide plates, so that people don't have to make as many welds between plates if you're building something big, like a ship or a bridge. The problem is, you can't make the rolls too big. If you make the rolls too big, when the roll flattens — as you're compressing on the part, you're putting compressive stress on it, which causes the roll to actually slightly deform. There's a rule of thumb, which I've never seen anywhere except in Backofen's book, but I've experienced it a few times: at a ratio of sheet thickness to roll diameter of about 500, you can no longer get any deformation. You can roll through that thing and have the gap completely zero, the rolls in contact with each other, and when you put the elastic material in there and you get the elastic spring-back of the roll, at a ratio of diameter to sheet of 500-to-1, you can have zero gap and the thing will just go through there without deforming the sheet at all.
What that means is, you've got to have smaller diameter rolls to roll thinner material, which they do. But then if the roll gets too long, it just becomes a flexible beam. So they have backup rolls — they call this a four-high mill, because you've got the work rolls and you've got the backup rolls, which are larger diameter and stiffer. The work rolls have to be small diameter. Here they have something called a planetary mill — they put little rolls on here, and you get a surface that's all wrinkled, and you have to put it through a final roll.
The more interesting thing is a Z-mill. This is a Zener mill, where if you want to make foil material, it's a thousandth of an inch thick. They can roll material to a tenth of a thousandth, but they can only do it about a foot or a couple of feet wide, because the Z-mill work rolls can't be more than 500 times the diameter of the thin sheet. If I'm talking about 1-mil sheet, that can't be more than half an inch in diameter. If it's twelve inches long, that would just bow and break in fatigue. So a Z-mill — they call it Z, but it's Zener, this Hungarian metallurgist. He has a set of backup rolls, three backup rolls, then four backup rolls, and it goes through something like this to roll that foil down.
Foil can get to be very expensive — except, what's the most widely used foil in the world? Reynolds Wrap. Why is it called Reynolds Wrap? A guy named Reynolds. But he also had a bigger company. He started an aluminum company called Reynolds Aluminum because he needed aluminum foil to package his cigarettes. They're all in Richmond, Virginia, folks. Reynolds Aluminum was started by the guy who was making the cigarettes and wanted to have something that wouldn't lose or pick up moisture — he needed a sort of hermetic seal, not completely hermetic, but he wanted to keep the cigarettes at just the right moisture.
Aluminum foil is done by what they call pack rolling. They put a bunch of sheets of aluminum through and roll them. You may be rolling 100 sheets of aluminum in one pass in a special mill. I've been near an Alcoa foil roll, but they wouldn't let me get any closer. There's a little bit of technology here that they don't want everybody to know about, but it is called pack rolling. It's like taking a ream of paper and putting it through the rolls. The problem is, you now have to segregate it, because you have different amounts of deformation on the edges versus the center, because of the inhomogeneity, the frictional boundary conditions. So the thinnest aluminum foil comes from the top surface or the bottom surface, and the thicker aluminum foil comes from the middle.
Student: [Question about oxidation/lubrication on aluminum.]
Aluminum is nice because it has its own nice aluminum oxide. They probably do have some lubricant on there, but I haven't seen it, and you won't find a lot in the literature, because there's only so many companies that do it, and they don't like to tell everybody how they're doing it. It wouldn't be hard to duplicate. The world's largest rolling mill is located in Davenport, Iowa. It belongs to Alcoa, and they roll the plate for the wings of 747s.
It's not particularly high-tech. I've been there. I had a student do a thesis on it, on trying to control the gauge of the plate. The way they measure the gauge of the plate in the world's largest rolling mill — eight-foot-diameter rolls and about fifteen feet long — is, they have a guy with a little step ladder, two or three steps, wooden ladder, and they stop the mill, he pulls the step ladder up, pulls out a micrometer, goes up there and measures it. I saw that, I thought, as an old steel guy — you'd never do that in a steel mill. But the volume of aluminum is not as great, so they didn't do that.
What the student thesis was about — this is about twenty years ago — is they were finding that the plate was coming in off-gauge, and a significant fraction — I don't remember the numbers, but like twenty percent of the plate they would roll would not be the proper thickness. Well, they're only measuring at one location. In a steel mill they actually would have a radioactive source, measuring the intensity of the X-rays coming through, to determine the thickness. So they're measuring online along the whole length of the strip, but not in an aluminum mill. A thick plate is a little bit harder to do that with anyway — with the radiation you have to clear everybody out of the mill. So they only measured at one location. But if you looked along the length of one of these plates, they were getting things that looked like this. So the student went out, she had a thickness gauge after they finished rolling, and she actually mapped them. Some of them had it on both ends, some only had it on one end. If you measured here you got one thickness, if you measured there, on a 3/4-inch plate, you might be twenty thousandths thicker. That's why, depending on where they measured it, they were getting different values.
She came to my office — this is an LFM thesis. She came back, showed me the data. We were sitting in my office, and I'd visited the plant, and all I said — it's one of those "oh, I know what it is." It turns out, this is hot plate that the guy's rolling. Hot is only 700-800° F. To keep the rolls cool, they actually flood them with water. So this hot aluminum plate is going through a little waterfall of water. It's not a heavy waterfall, but it's raining on the plate.
They intentionally run the top roll just a little faster than the bottom roll, because if you're rolling and it's coming out in this direction, you don't want it to curve and go into the bed, which is a bunch of rollers that are holding the plate. If it does that, you get what they call a cobble. It jams into your roller bed and you just start tearing up everything, because you've got this massive — I don't remember how many thousands of horsepower you have on these rolls, but what's pushing on it is pretty strong, and you'll just destroy everything. So they want it to slightly curl up. They run the bottom roll a little faster than the upper one — slightly out of sync on speed, so you get a slight curve up.
You've got water coming down here, and I remembered when I was there, sometimes I would see water pooling on this little cusp. Sometimes it would come through nice and flat and the water would just roll off, but sometimes there was enough of a curl there that the water would collect right there on the end. What happens when it collects? 700° aluminum, boiling water right there. Thin film of boiling water cools this down, right on the end where it collects. Now this is cooler than the main body of the plate, and so when it rolls, it doesn't roll as much, and you get something that's a little thicker on one end or the other, depending on whether you pulled your water.
I had her go through and do some estimates. We could explain eighty percent of the variation they were seeing by our estimates of the cooling and how much increase in strength of the colder aluminum on the ends of the plates, depending on whether the water was on there. What's the solution? You blow the water off with compressed air. They've got plenty of compressed air in the plant. I figured it would cost about $10,000 to put an air knife on there — just blow the water off. Did they do it? No. They would have recovered the $10,000 on a single aircraft plate that they didn't have to scrap for being out of spec.
She turns in her thesis. I happened to know the guy Owen Richmond at the time, who was head of deformation at Alcoa labs. I said, hey Owen, we figured out what the problem is out there at Davenport. I explained it to him. I said, all you need is an air knife, won't cost more than about $10,000 to fix it. He says, "We'll get that done, Tom." I said, "No you won't." He looked at me. I said — you guys are a big bureaucracy, you won't be able to do that. There's no one there who would have the authority. I don't remember how snotty I was about it. I basically told them, no, they weren't going to fix it. This was Alcoa, 1990. Alcoa's whole philosophy was big-time "not invented here." If it wasn't invented at Alcoa, it was garbage. There was no value to it. So this wasn't Alcoa's idea, they weren't going to do anything.
He says, "Yes we will." I said, "Owen, I'll bet you $10,000 you won't." A year later we're sitting on the committee together again. I said, "Hey Owen, they ever put those air knives in Davenport?" He just turned around and walked away from me. I'll bet you they're still not there. So there's a little lesson there. I'll talk to you later.