DP_S2012_03

Thing that was important. Or the other things we talked about, tolerances. So I handed this out and I'm going to say a little bit more about tolerances here. But the other things I want you to know, that Poisson's ratio is 0.5 and Delta V is zero as long as you have a solid material. If it's a porous [?] material, Delta V doesn't have to be zero because you can forge out the pores. But generally for deformation processing, Delta V of solid materials — solids and liquids are not very compressible, okay. And so therefore Delta V is essentially zero at the types of strains we're talking about. Strains that can be 100% or 200% elongation of a material. If we're rolling something or extruding it, we can have huge elongations, and so any change in volume is in fractions of a tenth or a hundredth of a percent. So for all intents and purposes Delta V is zero, okay. There may be some voids in the material from the casting or whatever and I might close those up, but compared to the types of strains I'm doing in stretching the material, the volume's constant, okay. I'm not worried about the fourth decimal place. That's for the physicist, let them worry about the fourth decimal place. It's not significant.

Okay, do other people have questions? I'd much rather answer questions than give my lecture. I've heard the lectures before, they're boring anyway. Actually they're not that boring the first time, hopefully. But I did want to talk about tolerances. And tolerances — I'd put up this thing on tolerances and now I've handed out a copy. You couldn't have read the one that I put up before, you can hardly read this, but you've got one in front of you now. Does anybody know what controls the tolerance down here, which is — if I was talking about a one-inch-long thing and I can get a tolerance of one one-thousandth of an inch, that's one part in 10 to the 4th, right? What controls that? Why can't I get one part in 10 to the 5th as a tolerance in manufacturing? I can get it, I can get one part in 10 to the 4th, it says here, okay. Here's 10 to the minus 3, this is 10 to the minus 4, and polishing, lapping, and honing is getting me down to something like two parts in ten thousand. No one knows what the fundamental limitation is. Yeah?

Student: [suggests grain size]

Just a guess, grain size. Well, it could be grain size, it's a good guess. And later on we'll talk about orange peel and how large grains don't deform uniformly at the surface and you will get a surface roughness that can be a lot more than that. It's called orange peel because it has the texture of an orange and it's actually about the same depth, okay. Very clever the way the people talk about these things.

Anybody know what these are? [Tom produces a set of gauge blocks.] If you took my welding class I actually do a thing — these are Johansson blocks or Weber blocks. These are gauge blocks that a machinist uses, okay. And they use them because they're very precise in their dimensions. In fact it comes with a certificate of standards. This is traceable to the National Bureau of Standards, and this one is 3 inches, made out of chromium carbide. You can buy them out of steel, hardened steel, but they tend to rust, and if they rust they no longer have their precision. But typically these are precise to about 50 millionths of an inch in dimension. And if you're a machinist and you don't use a micrometer — if you're trying to get down to a tenth of a thousandth, you can get down to a thousandth or maybe a fraction, maybe a half a thousandth with micrometers. You know what micrometers are, right? I didn't bring some with me. But you actually ring these together. They have polished surfaces, and if you ring them together — this is the experiment for the adhesion class — but you can actually get them to support weight, just by the little bit of oil on your — actually shouldn't be your finger oil, but a little bit of oil on the surface, and the oil becomes an adhesive and they will hold together. And if you take my welding course you get to calculate the force of adhesion, depending on the thickness of that joint.

But they come with their certificate that tells you that they're accurate to — some of them are accurate to plus the worst, a gauge plus or minus three microns. What's three microns? A human hair is — how many microns? Three microns — a human hair is 75 microns, so this is one twenty-fifth of a human hair. That's the coarsest one. You can get them plus or minus 1 micron, plus or minus 0.8 microns. That's the laboratory master standard. But when you read it, it says 1.0 inch equals exactly 25.4 millimeters. That's actually a definition of how we define the inch based on the metric standard. Calibrated at 68 degrees Fahrenheit, 20 degrees centigrade, and 45% relative humidity. So what's important there? Temperature. It also tells me on the back side of this sheet the coefficient of thermal expansion. For steel — actually for chromium carbide — is 4.7 micro-inch per inch per degree Fahrenheit. It's 8.5 micro-inch per inch per degree C. So for most of the materials — steel, stainless steel, tungsten carbide, chromium carbide, or zirconium oxide that you might make gauge blocks out of — the coefficient of thermal expansion is about 10 to the minus 5 per degree C. In fact steel is 10.3 times 10 to the minus 6, so it's 1.03 times 10 to the minus 5 per degree C. So steel is about 10 to the minus 5. Well, 10 to the minus 5, if I had a 10 degree temperature change, it's no longer that size anymore, that precision. So temperature sort of limits you here. You have to start defining length in terms of at what temperature, right, when you're getting down to making something precise.

These gauge blocks were polished and lapped to be very flat and very smooth, even more so than you see in that graph. But to be down at 50 millionths of an inch you actually have to start talking about temperature. And in fact if you go in the ball bearing industry, they will actually measure the balls to 50 millionths of an inch, and you have to go into a room that's air-conditioned, temperature and humidity controlled. And they have the super-duper micrometer. You've seen micrometers, little hand micrometers — the micrometers to measure the balls for very precision ball bearings are the size of a small lathe, okay. And they are in a room that is temperature controlled and humidity controlled, 'cause a 2 degree Fahrenheit change in temperature will screw up your measurement, okay. So when we talk about precision in these tolerances — when you get to these types of precision, you're getting down to where other things have an effect, okay. And I've seen people make measurements, not very often, where they say "oh we measure this" and they're getting all this precision in what they're doing, and I say "and at what temperature?" and they say "what do you mean?" Because unless they define the temperature of the measurement, when you get to some types of precision some people claim — so there's a difference between precision and accuracy, but that's another lecture, okay.

I also mentioned beer cans and Coke cans, and I found this in some of my junk this morning. [Tom produces an aluminum can.] The aluminum can by Alcoa. So I'll pass this around, and inside here I just happen to have Will Pet Do to Aluminum Cans What Aluminum Did to Steel, presented by Ferro Catrakis [?]. Dr. Ferro Catrakis — he doesn't put it on his card, but he was Joel Clark's first doctoral student about 1976 or '77, and he works for Charles River Associates, an economics consulting firm. And he's a vice president over there, at least I think he still does. He might be retired now. Anyway this is one Back[ofen] [Backofen] — Coors cans — that, it's actually fairly thick, it's kind of banged up over the years. Typical soda can or beer can. Anybody know how thick the wall is? It's probably around five thousandths of an inch, about one and a half human hairs, okay. And they've been using supercomputers to design these, 'cause they have to hold a certain amount of pressure, okay. And in fact Coke cans are a little more tricky than beer cans because the pressure in the carbonation in a soda is higher than the carbonation in beer, okay. So the pressure can be higher.

Anyway, here's a little description of aluminum cans for the lay person. It actually points out there that in order to make the can — and we're going to talk about this later. Today's a little bit of a descriptive lecture to just help you understand where we're going with some of these things. If I wanted to make something in the shape of a beer can — this happens to be copper, and these are Backofen's as well, I haven't polished them in the last 30 years, they're actually probably brass, they look like other than copper — you actually have to go through a series of steps, because there's something called the limiting drawing ratio. You start out with a sheet and you punch out a cylinder, and then you draw the cylinder into a cup, it's called cupping, and then you redraw, second draw of that cup into this shape, and then you redraw again, and eventually with this they did four draws in order to get this. What would have happened if I took that great big sheet and tried to draw it in one draw to this? I would have just punched a hole in the bottom, I would have punched the bottom out, because I have to deform all that surrounding material without having so much force on the end that I don't shear the end right off. And when we get to sheet metal forming, which is sort of the end of my lectures, we'll talk about that.

But to cup it — it says in that little Alcoa thing when they're making the cans, it says for the body, they call it the body, okay, rather than the top — I think they — the rather than the top, I think they call it — the top is very complex 'cause it's got the pull tab and stuff, but the body's a little simpler. But the body, it says they're doing 200 strokes a minute. So that's a little more than three times a second. And the stroke is probably about four or five feet, just so you know. And you can now start calculating — this is probably — the tooling is probably going at 60 or 70 miles an hour here, okay, to go up and down. And they do 200 strokes a minute, that's three strokes a second, and 14 cups per stroke in this press, 'cause they have a great big wide sheet of aluminum and they're not just punching out one can at a time, they're punching out 14 cups at a time. At three strokes a second, that's 42 — in a one can line that's 42 cans a second coming off there, which is almost two cases. Right? Three and a half, or one and three-quarters cases, or whatever. No — what is — no cases — no, it's cases, it's one and — yeah, it's one and three-quarters — no, it's, yeah, it's one and three-quarters cases a second.

And I think I mentioned to you, Beeran [?] — my first big consulting job anyway was at a brewery in New York, and they were filling bottles and cans at 20 a second, okay. So now, one of the problems with this industry is you got to build that can line, or the bottle line if you're making glass bottles, right next to the facility that's doing the canning, okay, that's putting the beer in or the Coca-Cola in. 'Cause you can't transport all that air, okay, very far. Typically you can transport it about a couple hundred yards, okay. You can't afford to transport it much further than that. So typically the can companies will build right next to the bottling companies, okay, just for your information. And you might spend $10 million on can line presses and stuff for the tooling and everything. It's pretty impressive to see it. I saw a full-size can line, not in an operational can line, but I was at Alcan Research once and they had a full-size thing, and it was kind of a two-story-high bay about half the size of a football field, okay. Now, not all of you probably could have fit it into one-fifth the size of a football field, they had other stuff around it, but it's a big piece of equipment, okay. And it's making things very fast. And another thing is interesting is the paint line to put the label on. You have to also be painting these things at a couple of cases a second, and that's another trick, okay, but we won't get into that, okay.

So those are some of — that's more of a review than I should have done. But I prefer to tell stories than most of these other things. If nobody has any questions — oh actually I can pass around, this is a little — I can pass that around if you want. [Tom passes a set of progressive draw samples.] I'll pass this around. This is also one of Backofen's things, and it's a whole series of cups. There's the original cup, and this is the final product before they trim the end. It's sort of rectangular with big corners.

I don't think any of you are old enough to know what this is. Maybe Carl, have you ever seen one of these? Did you ever look? Huh? Like a case for a relay or something? It's actually a case for a tube in a tube TV. I mean the old, before we had lots of transistors, back when I was a child, okay. You look in the back of a TV and you had a bunch of little glowing vacuum tubes from the days of vacuum tubes. You actually would put them in a little aluminum case, you'd surround them, to protect them from breakage and stuff. And so here is a set of draws. They don't make this anymore — or actually they probably do, but it's not a big industry like it used to be. Kind of buggy whips, but nonetheless.

Another thing I'll pass around, since we're going to talk about extrusion today — this was one of my first things. You know, I've been collecting these things. I stole Backofen — when he left them — actually I appropriated them, okay, no one else wanted them, and I took them. And I think actually some people have sort of learned that it's worth collecting these things over the years. It may not be something that you can use right away, but if you collect for 30 — it's sort of like writing a diary every day or something, you know. Each anal — each daily incremental, each day may not be significant, but when you put the whole thing together after 35 years you actually have something of significance.

This was one of the first things that I ever collected. I went to Pittsburgh to a firm, I can't even remember the name of it because it was over 30 years ago, and they were doing what's called cold heading. In this course we'd call it extrusion. And cold heading was developed after World War 2 when they discovered that if you took a piece of steel and phosphated the surface — and I actually cover this when I do adhesive bonding, because phosphated surfaces are how you prepare surfaces for adhesive bonding — you can take a steel rod and you can shear it. This is the sheared piece of a three-eighths inch steel rod. It used to feel soapy. Not much soap, most of us have fingered this a lot for the last 30 years. Not that we do it every day, but once a year. This is the first sizing operation where they take that and they just squeeze it and to size it precisely, put a little indent on one end. This is the next operation, where they actually start an internal, a backward extrusion, and they start make a deeper indentation. This is the next one where they actually go deeper and the thing is now getting taller. This is the next operation where they put a flange on it, okay, a head on it. Then they have another operation — and don't, this is the one I don't want you to lose, I've lost it a couple times over the years, I'm about to lose it again — this is the only piece of waste from this process. This is the hole they punch out of the middle of that flange. So this is what you end up with. These two go together, got a hole in it 'cause they punched out that little ring. Then they knurl the outside, just a — then they thread the inside, and then they plate it. And what is it? It's a machine screw with a knurl. And so if I'm a woodworker and I want to put my thing together with machine screws, I can use this insert and drill a hole in the wood, slam this in, the flange keeps it from pulling through, and now I put my machine screw and I can really have a good strong joint in a piece of wood furniture, okay.

But to make this simple little part, which you might buy for 20 cents at a hardware store, you have to go through quite a few forming operations. And before World War II — where we, right after World War II — when they developed the phosphating technology to hold the stearate lubricant. Anybody know the other name for stearate? Soap, okay. That's why it feels soapy. If we — if I do a lecture here on lubrication, we'll go through that. But if you just try to do oil all those extrusion operations, you have so much sliding against the workpiece, the oil would be gone, okay. You have to have some peanut butter that has sticking power through long stretching of that. They're popping those things out at about 10 a second, maybe 20 a second. You walk through this plant with big ear — they don't give you earplugs, they give you, you know, the things that cover your ears, because the decibel level in that plant is probably above the threshold the pain level, with the machinery pounding away at that speed and stuff.

And they don't just make little parts like that. I've been through a plant in Detroit where they make most of the steering components for the car. If you look down where the wheel is and you see the steering knuckles and these things that weigh — they can weigh 10 pounds on a truck, but on a car they might weigh a pound or two — they're made by cold forming. The ones on a truck at 10 pounds are might be done by warm forming, by all this deformation and forging at, you know, 5 or 600 degrees Fahrenheit, not 1,000 degrees. Usually they can do it at 500 degrees. But it's called cold heading, okay, because it's the same process that people use for centuries to put heads on nails, okay. But we can now make more complex things than heads on nails, okay, and we can make them very fast. The tooling is kind of pricey and stuff, but it's very efficient, okay. And you can get very precise tolerances off something like that, okay. But you better know how to make your dies, okay. And you're going to use the steel initially in a soft condition, but by the time it's finished it's gone way out on that stress strain curve. You might have annealed it so it's soft, by the time you finished hopefully you haven't gone out here to get fracture. But you've done multiple operations to get more and more stretch. And one operation might bring you to here, the next operation you're on a new stress strain curve that takes you out to here, the next one you're on a new stress strain curve that takes you out to here, and you do this five or six times, and your total strain is a couple hundred percent rather than the limitation of 30 or 40% that you have in a simple uniaxial test, okay. So that's the principle of multiple forming operations, and it applies to sheet metal too.

Unfortunately these are getting a little rusty. But this is something else that I probably consulted on 25 years ago in Detroit. I think the guy was an MIT alum. But the parts they were making were radiators, okay. And in order to make the tubes, they made everything from sheet metal, and they would stamp out — what we see here is a progressive die, okay. A piece of sheet that goes through a progressive die. Now most of the stuff I've seen in progressive dies — if you go down here to Attleboro, where they — the jewelry capital of the world — I used to consult for a company that went through seven tons of gold a year, okay. And they had continuous cast — they have three or four continuous casting machines for gold, and they make the gold sheet stock, which I think is 22 karat, that they sell to the — they make it, actually they don't sell it, they receive gold from the US Mint. They don't own the gold, the US Mint owns the gold. They receive it, they alloy it from 24 karat down to 22 karat, they roll it out into sheets, and send it back to the Mint, and the Mint stamps it out into little circles and then coins it. And that's where you get these collectors — I don't know, I don't even know — $20 gold pieces, which actually got about $800 worth of gold in them. They're 22 karat gold. But the Mint is trying to make money. We can't have gold coinage anymore since what, 1933 or something. Right after the Depression we went off the gold standard. Ron Paul will tell you about that, okay, and why we shouldn't have done that. I don't know what Ron thinks about the gold standard, but a lot of people with Ron's type of monetary policy — which, not, by the way, I'm not knocking that policy. I think we overspend, okay. I think it's going to come back to kill our grandchildren or maybe even us.

But anyway, to make these, they would make big sheets — actually I have several of these I can pass them around. [Tom passes radiator-die progressive samples.] But it's the same type of drawing operation as this. And they would start out with sheet and then you actually slit it. And you have to slit it because if you look carefully at these things, you're actually making a number of these that are later going to be maybe split into rows of two or three rather than even longer rows. And you'll see that, when you start making these little domes it sucks in, okay. If you didn't do this you would have — you would have fractured the material. And they have to first make a little dome, and deeper dome, and you can see eventually they punch out the hole and then they stack the holes together. This one actually has turbulators in it, and they braze the whole thing and make very inexpensive heat exchangers, okay. So out of carbon steel.

So that's that. I think another thing that I said I was going to pass around for you, we talked about surface roughness. [Tom produces a surface roughness gauge.] Here's a surface roughness gauge, so you can feel internal surface relative. This is actually what a machinist does. He goes and he kind of feels the piece's turning on the lathe and the milling machine. He kind of compares it, looks at it, okay. You can also do it a little more scientifically, but frankly this is something he can carry in his back pocket. Doesn't cost $10,000 to make the measurement. They have lasers that will measure this too, but you don't add a $10,000 laser to every milling machine in the shop. So he can measure surface roughness that way. So those are some of the other little things I wanted to talk about today.

So we talked about the general deformation zone geometry and the Delta versus yield strength plot, and that's the most important plot in Backofen. But the next chapter in Backofen is about friction, okay. Because friction — I told you the last time, Mond — or today's Wednesday, yeah, Monday — that in a hardness test you didn't have to worry about friction. But in fact this plot that I just handed you, which is chapter seven from Backofen, and friction dominates — this plot is for frictionless processing. We don't have frictionless processing. In fact what would happen if I had a rolling mill with frictionless processing? The same thing as if you had frictional [frictionless] shoes, okay. You couldn't walk down the hall if you had frictional [frictionless] shoes. You need friction, some friction. In order to roll, you have to have some friction to pull the material into the roll, okay. If it's frictionless, those wheels will be spinning all day long and the sheet would go — or the plate would go nowhere, right, if it's frictionless. So you have to have some friction.

And what we want to talk about — and it's a little bit descriptive today — is the effect of friction. And actually I'll spend a little bit of time here. You can get into some of the science of this — this is figure 8.1 of Backofen. Some of the science of this is, I've got some compressive pressure P that might be the yield strength, the local yield strength, I have some contact area K. And so from this I might be able to estimate some deformation zone geometry. Frankly the plastic deformation, this is a Delta is equal to 10 type operation, okay. This is high Delta operation, this is like a hardness test. But you will have a lubricant film which might get pushed aside under these very high pressures. I'm talking about pressures that can be three times the yield strength of the material. So the lubricant films don't always stay in place. That's where they had to learn about phosphating of those, you know, cold heading pieces. And so you got to start analyzing this. You may have a shear stress on this at the same time, it's causing sliding. It gets to be a little bit messy.

For whatever reason, Hosford — I think this is out of Hosford, it's out of your textbook that I gave you — figure 6.1. And by the way, I'm not giving you reading assignments out of the textbook. I don't care if you read those things. I want you to kind of learn some of the principles, and then one night you can curl up with Hosford and you can flip through it in an hour and a half and you can say "yeah, that's what he talked about." And then someday when you need to know it, you can hire a consultant, okay. So if I take an extrusion — and this could be — they've shown this as axisymmetric right here, but it could be — Backofen often likes to talk about plain strain strip, where you don't have any strain in the deep dimension going into the board. But this one he's drawn it with this little thing, so we're trying to extrude a rod. And initially I've got some little volume element of the rod that's going to be extruded, so it's just like a toothpaste tube, and I'm going to change it from this width and height, or this Delta L initial, to a Delta L1, which is the final. And as I've done this, okay, everything stays nice and rectangular, because this assumes a frictionless extrusion.

And in fact the next figure on Hosford is he says, well, it's not always homogeneous deformation. If I start out with a bunch of rectangles like this, I can make them flat rectangles and they're still perfect rectangles. But in fact I can get what we call redundant deformation. And redundant deformation is what I was trying to explain takes you up to the higher pressures on that deformation zone geometry. Remember, everything's nice and flat, Delta's less than one, frictionless, everything's uniform deformation, rectangles go to other flatter rectangles. But in the real world when I'm at a higher Delta operation like two or three or four, like extrusion, instead of a Delta of one, I'm going to get nonhomogeneous deformation. Why? Because there's friction at the interface. And the stuff at the surface where there's friction is not going to flow as fast as the stuff that's coming down the middle, duh, okay. Well, it turns out that causes redundant deformation. And that redundant deformation increases the extrusion pressure from the two times the yield stress — or the shear stress, which is equal to the yield stress — to 1.6 times, or whatever that deformation zone geometry curve tells me, depending on the Delta value, okay. And in the worst case, in a hardness test, it goes up to 2.57 times or something like that.

So today's key point is inhomogeneous deformation. Most of the materials processing deformation processing operations do not deform the material homogeneously. I'm going to show you that. And as a result, my grain structure, my properties, my surface finish, everything else is going to end up being controlled — my extrusion pressures or my forging pressures, everything's going to be controlled by the amount of inhomogeneous deformation, okay. I'm going to end up with residual stresses, and I'll show you that, okay.

Now you can — well, actually I might as well show you this. This is out of Making, Shaping and Treating of Steel. Making, Shaping and Treating of Steel, which US Steel used to publish. It's in its 11th edition now. But first 10 editions US Steel published it, then they ran out of money, and American Iron and Steel Institute has published the first volume of the 11th edition. Anyway, if I'm trying to make one of these — oops, sorry, okay I didn't mean to target you — over there, if I'm trying to make one of these little draws on a cup, out here in the outer flanges I'll get wrinkling. And if you actually look at some of those little aluminum cans that are going around, you'll see some wrinkling, I think, on one of those, maybe not. You also can get necking, because everything here is in tension, everything around here is in compression, circular compression, everything in here is in tension. Just gives you an idea of some of the types of defects that you might get.

But what I really copied this page for is, US Steel 30 years ago actually had someone do a computer calculation that if I had lubricant with some friction, I could design a die that's not just a bevel, a cone, okay, with straight sides. I could design a die — whether I can make it 'cause a lot of my dies for wire drawing are out of diamond, and it's hard to shape diamond to nice circular contours here — but I could design a contour that would take a square and turn it into a perfect rectangle even if I had friction, okay. You could do it. But the tooling is not that easy to produce. And if your friction coefficient changes, you get a different shape that the die needs to be, okay. So we don't try to control friction, we just try to deal with it. Well, actually we do try to control it, we try to live with it, I guess I should say.

Now, this comes out of Backofen, and this is his attempt to illustrate the differences in inhomogeneity. And IF is the inhomogeneity factor, okay, which he's got defined by an equation in his book. But this is lubricated strip, so this is strip drawing on the very bottom — which I haven't shown you yet, you'll see a wire draw. But they basically — I don't know if they took copper strip or brass strip or a steel, he doesn't tell me, but it was probably — I don't even know, it was one of his students, but anyway he doesn't reference it. They take something and they draw it partway through. They don't draw the whole thing, but they stop partway through. The thing started out and KNH, and it had a knoop hardness of 85. And of course you got work hardening on your stress strain curve, so as you deform it some and get some permanent plastic strain, the hardness increases. And so some poor graduate student sat there on the microhardness tester for days mapping the entire plot of the iso-hardness lines. And here they are for that type of very shallow angle. It's a 16% reduction. So this height should be 84% of this height. And if you look across here, very uniform hardness across there. A square over here becomes a nice square — a nice square-cornered rectangle over here. No inhomogeneous deformation, inhomogeneity factor is zero, okay.

If I increase the angle, I'll go from 85 not to 105 but to 120 up here, and I will have very inhomogeneous deformation, an inhomogeneity factor of 19%, if I do — that was lubricated. Everything else being the same, but now it's not lubricated, I will have a bigger — even bigger, but only about a 10 or 15% increase in homogeneity with no lubrication versus some lubrication. If I go to half the reduction, from 16 to 008 [0.08], I actually can get more inhomogeneous deformation. This is a higher Delta operation. Why? Compare this one versus this one. Why is this lower one higher Delta? More inhomogeneity. It's over a shorter distance. It's over a shorter distance. The height is the same, but look at the width of the deformation zone. It's just that little angle here, compared to that angle there, exactly. So you've learned — of course you don't have to come next time. So higher inhomogeneity because I've changed my the amount of deformation.

Here I've gone to wire, and the wire is axisymmetric deformation. In the strip I didn't have any strain into the board, so that's called plain strain. The strain into the board was zero. Plain strain means one of my strain tensor values is zero, okay. If I have axisymmetric deformation, I'm pulling in one direction, actually I'm compressing in two — none of my strains are zero. And so in wire drawing with axisymmetric deformation there is no plain strain. I actually have a situation that's similar to this one, as you look at it, but the deformation is twice as great. Why? It goes from — I mean look at this, it's got the exact same die angle, and it goes from this diameter to that diameter. These two diameters are the same, but the wire compared to the strip has got twice the deformation. One's compressing in two directions, the other one's only compressing in one direction. The area goes as the square of a circle and of a rectangle. If I'm only changing one dimension, it goes linearly to the first power, not the second power. So if I get 8% reduction here, I got to get twice as much reduction here, because it's axisymmetric. And that — but that means in this case the inhomogeneity factor goes down, okay.

Well why is that? Well, because I'm forcing the material to squeeze. The stuff in the center is hardly deforming at all, okay. I mean here there's a big plug of material that doesn't work — doesn't get hard, work very much. Here that plug of material that's not deforming — doesn't have a much — redundant deformation is not as big. So I can go through these types of things, and I can start analyzing. You don't have to analyze those things, some doctoral student had to once, you know, lucky him. But it creates defects.

So Backofen has a picture of this type of defect. And this is cracks formed in molybdenum bar rolled under high Delta conditions. Now he's passed away and I can't ask him, but he probably went up to Maine to do this or to get this. He was probably hired by a little firm up in Maine which was called Elmet — E-L-M-E-T — Corporation. It was later bought by Philips. The big Philips makes the DVD players and stuff in the Netherlands. And it was called Philips Elmet when I went there. And I went there because one of my former students, an undergraduate student, was from Maine. Charlie wanted to go back to Maine. He's still a Mainiac, okay. Speaks Maine, okay. If you know what Maine speak is, sort of almost Canadian. But anyway, Philips Elmet makes tungsten and molybdenum alloys. When I went there, IBM was buying most of their molybdenum sheet to make the computer chips. This was in the 1980s, not the computer chips but the interconnects for the fancy computer chips. Weren't the biggest computers, which were probably, you know, 16K rather than 64K type stuff. And you were down in, you know, 20 megabytes of storage in your computer or something. All sounds ridiculous to you now, but that's what it was back in the '80s.

Anyway, if you actually try to roll this — and Backofen in his book on the next page has a picture of the molybdenum bar that they're rolling — and it alligators. They're rolling this between two rolls that have semicircular cross-section, and the thing's got tremendous residual stresses. Look at it, just alligators out, and it's even got teeth like a crocodile. This is one of Backofen's samples that until about a year ago was in one piece. He got a piece of molybdenum from some rolling mill. I now have to hold it together with a thesis binder clip. [Tom holds up the bisected molybdenum sample.] But so they were rolling this thing, and it just split right down the middle, okay. [Applause sound on tape.] Okay. But it's the same type of alligatoring. There are residual stresses in this material, otherwise it wouldn't split in two directions. That's a result of inhomogeneous deformation. That's a result of the wrong Delta for the forming operation.

In addition — anybody in some of these cracks you have this white stuff, anybody know what that white stuff is? Anybody have an idea? Anybody know what the melting temperature of molybdenum is? It's about 2500 degrees centigrade. I can look it up, but you can look it up too. So if you're — and I probably have something later in my notes that would tell you what the forging temperature of something like molybdenum is, but it typically is going to be like 1800 degrees centigrade. Over 3000 degrees Fahrenheit — above the melting temperature of steel — to form molybdenum. The interesting thing is, that's 1800 degrees centigrade — at about 1,000 degrees centigrade the oxygen in the air will react with the molybdenum to form molybdenum trioxide, okay.

So when Charlie takes me into the rolling mill to watch them roll the big molybdenum plates or ingots or whatever, that were probably four or five inches thick and they're going to roll it into sheet that's like a sixteenth of an inch thick — not all in this one hot mill — but we go up in this pulpit, and the pulpit's big glass windows, kind of like, you know, at an angle, looking out like a control tower at an airport. And you see the door open to the furnace, to this room, and you see this white-hot, almost 2,000 degrees centigrade chunk of molybdenum slab come pushed out. And as it gets pushed out into the air, you start seeing white smoke come off — it's molybdenum trioxide. Molybdenum trioxide is volatile. They're rolling this in the air. And within 15 or 30 seconds, all you could see was a glow of this white thing through this white smoke cloud. I don't know why he took me up to show me the rolling operation, you couldn't see the rolling operation, you were looking at white smoke with this big white light behind it, okay. Actually that's probably why he went to show me, it was really impressive, let me tell you, okay. I wish I had a video I could show you, or take you up to Maine to see this. And the whole — then I understood why the walls and everything in this room were all white, okay. They were covered with, you know, half an inch of aluminum [molybdenum] trioxide. And so what you're seeing there in that white, just for your information, is molybdenum [Mo] trioxide in the cracks.

Now, so here's a Backofen picture of a wire drawing operation, and someone formed some little cracks right down the center. Now this is a fairly high Delta operation, okay. Internal fracture in a round wire induced by high Delta drawing. 2011 free-machining aluminum alloy. So this is aluminum alloy, and you can see the deformation. There's your width of deformation zone, and a Delta of three or four would only take you down to here. That means you're getting lots of inhomogeneous deformation. And this central plug — hey, it's just a tensile test, okay. It's hardly deforming at all, but I got enough tension I actually split it, okay. So it turns out you have to be careful in picking the right Delta for your operation. You can induce defects.

I like to show this one. This actually was in Backofen too, but the reason I like to show this one — this is Centerline cracks in extruded steel rods from Don Bliclet [?] — who's Don Bliclet [?]? Well, he's a graduate of this department. But it was my first boss. He was vice president of research at Bethlehem Steel when I was a young engineer in the research department. So he was my big boss then. Later when I came back here as a member of the faculty he was on the department visiting committee and things like that. But anyway.

Here's another one out of Backofen. I didn't know if I wanted to show you this, but I looked at it some more and I've never noticed this before, this morning, okay. Taught out of this book for three years — or two years, taught — learned out of it for one year and taught out of it for two more. This is a mild steel wire undergoing axisymmetric deformation. This is from 1931 — no, 1958. Um, one of those other defects was from 1931. Anyway, this is the type of high-nitrogen steel I mentioned before. You just pull it through the die a little bit and you can see where it deforms. So this is actually a fairly low Delta operation. There's the width, there's the height of the deformation zone. So this — if I call this the axisymmetric line going down the center — this is a Delta operation of like 1.5 or something. Not very high Delta. But look at — and so I can see the deformed region where everything is sheared. Nothing sheared back here, nothing sheared here, but look at this little arrow point right there. That's in tension. It actually started to slip and shear. You see that little arrow point right there? That's in tension at that location. All this stuff is in heavy compression, but as I get towards the center I actually get to tension, okay. Because of the inhomogeneous deformation, the compressive forces don't reach all the way to the center, okay. So there's more evidence of inhomogeneous deformation.

Here's Backofen just kind of showing you a rolling operation, and they call this alligatoring, okay, to split down the center. And he kind of is pointing out you get very bad residual stresses in your sheet or other things. And I guess I could have brought — I tell the story in some of my other lectures, I've got a washer from a Navy helicopter. And this washer is aluminum washer that 15 years ago, 20 years ago, it cost $350 for this little washer. It's about this thick, it's about this big around. It's the washer that holds the tail rotor for the Blackhawk helicopter, okay. And it turns out it failed — or one of them failed — on an Army helicopter. Now if it's a Navy helicopter it's called a Seahawk, if it's the Army it's a Blackhawk, and if it's the Coast Guard it's the Jayhawk, and the Air Force, Carl, is the — call Blackhawk? You call them Blackhawks too, okay. That's why I couldn't think of a different name for the Air Force. But anyway. And Jeremy knows all about these things, he did his thesis down in that plant, or he is doing his thesis down in that plant — or he spent the last six months there, okay.

Now the problem here that they had was they used a particular aluminum alloy in that helicopter, and by the way that same Blackhawk design, there's also a separate line that is the presidential helicopters. And we couldn't walk over there, could we, I couldn't, okay. Couldn't even walk over there 'cause those helicopters have got technology in them that I'm not supposed to know about, or believe even, right. Anyway, so an Army helicopter in Arkansas was doing a night vision goggles training exercise, and it crashed and killed six Army soldiers and two pilots. And anyway, it was because this aluminum washer was supposed to have been stress-relieved and was not, okay. It had residual stresses in it, and it got stress corrosion cracking. And if you take the welding videos I'll talk about — you know, you can hear about it there. Maybe I'll bring the — and I always like to tell the Navy guys when I'm teaching them during the summer that it was the Navy that found the first cracks, 'cause the Navy is the corrosion leader in the service, okay. They're surrounded by salt and moisture. And so if anything's going to corrode, ask the Navy, they'll see it first, okay. And in fact the first cracks did show up on Navy Seahawks. But the first fatality was on an Army Blackhawk. And fortunately it wasn't the president — one of the presidential helicopters — but it could have been, okay. Anyway, it's actually really gets sort of interesting.

But anyway, so let's talk about a simple type of forging operation where I might take something like this, which has got a Delta operation of — actually this could be less than one the way they've drawn this. And if I have — if I — oops, we've ran out of time. I guess this is for Wednesday or Friday, okay. Sorry, I didn't watch the clock.