SMS_F2013_04

The website is up and sort of running, and one of the handouts back there when you came in was the various list of courses. Um, you're gonna have to take each one of these — should be about 12 units. You should not take this one down here, because the last time I lectured this was 2000... what we're doing right now is 2009. What Dr. Belmar is doing he has not ever done before, so you could do for your third choice, or if you're doing a second and third choice, if you're only taking one of the live 12 units, uh, 12 hours of lectures, you can pick one or two of these. Or, one student is interested in potentially taking the course twice, which you could do, you might have to take it as special problems, but you'd have to watch three sets of these extras on video. There's only about seven total, some of these are redundant. For example, I taught this first time in September 2000, summer 2012, and then I taught it again that fall because I wanted to get it right the second time, hopefully. They're both on there, you don't have to take them both, so it's not really two choices. You can look at the date and see which one's the more recent. That doesn't mean it's better more recently, it just means it was given more recently, okay.

I actually should have these going back for 25 years, but I don't know that they've all been kept. I would keep them, just like I expect my mother to keep each one of my little pictures I drew as a kindergartner. Actually I never went to kindergarten, but anyway. So one thing I wanted to, um, I meant to do yesterday — I talked about the various price of materials, the pound of weight saved in different industries, and I actually was going to hand around — [Tom produces a piece of steel.] this is a piece of steel from General Dynamics. It's HY80, it's a high strength submarine hull steel, and it's a weld that they gave me when I was down there about 30, 35 years ago. It represents two dollar a pound type of material, okay. You can make steel out of nuclear submarine hulls — nuclear submarine hulls — this, so I don't know.

Okay, this is, um, well, we passed these around when Dr. Belmar was talking about growing single crystal turbine blades. [Tom holds up a sectioned turbine blade.] This turbine blade would go on either a 747 or 757 type engine. It's sort of interesting because it would have been a single crystal, but they took it and they caught filleting this, okay. Pratt Whitney gave me this. They take a wire EDM and they section it so you can see the inside, and the inside of this thing has got all kinds of turbulators because they're going to put cooling gas through here. I'll show you later what that does. But basically they pump 1000 degree Fahrenheit gas as the cooling gas. Remember the outside of this blade is going to see an environment of about 3000 degree Fahrenheit combustion gas, and it has to be cooled, because if it's not, the metal melts at 2400 degrees Fahrenheit, okay. So if you didn't have cooling gas your engine would melt — not a good thing.

But they basically grow it as a single crystal, and this is a seed crystal with a particular crystallographic orientation, and they cast the whole thing in an investment cast mold. If you take the casting thing you'll learn about that. And they grow it very slowly, takes about a day in the furnace, it's a million dollar furnace. And they can grow about — well if you're Pratt and Whitney or if you're General Electric, you tend to grow about 24 of these things at a time in the same furnace. If you're Rolls-Royce you grow four at a time. So if Rolls-Royce has a $300,000 furnace that grows only four blades at a time, the other people tend to do lots of blades in a more expensive furnace. So here, you reach that — good thing you've got long arms. [Tom passes the blade around.] So that represents aircraft type of material at $200 a pound, although that blade would sell for about $7,000 a piece. But the whole engine and the airframe and everything, the whole aircraft would be less expensive.

This I passed around before, I'll pass it around again. [Tom holds up a composite sample.] This is part of the X-33 space plane, it's a composite material that cost about $12,500 a pound. So when you're talking about material selection, you have to talk about what industry you're in, okay. If you're in the automotive industry or the railroad industry, they're not interested in twelve-thousand-dollar-pound composite structural materials, okay. If you're in the aerospace industry or the spacecraft industry, they're sort of cost insensitive, they're performance based, okay, and they will pay a pretty penny because they can save $25,000, $20,000 a pound — actually they don't really save the $20,000, so they can get an extra pound of payload up, okay, in space for the same rocket booster and everything. So that's just to give you some examples of that stuff. So I finished up on that.

Um, today is going to be talking about property limits and productivity. So far as productivity, this is still sort of economics. Paul Krugman — anybody know who Paul Krugman is? You're saying yes, you know who is he? But he used to be — well okay, that's actually well put, he was actually an economist at MIT, okay, where he did the work that got him the Nobel Prize, okay. He left MIT for Stanford, so he's one of these extinct volcanoes, okay, as Lester Thurow, dean of the Sloan School, used to call them. Uh, but Paul Krugman wrote a book 20, 25 years ago called The Age of Diminished Expectations, and the first sentence in the book was, "To live well a nation must produce well." And I gave you the key thought yesterday — what's the most productive country in the world? The good old USA. But it's the law of comparative advantage. We tend to have them make a lot of products in China or Taiwan or Malaysia or whatever, because we can make more money doing something else with our time, hopefully, okay. We can use financial tricks and steal everything from the whole world — oh no, sorry. The Boston Globe this morning pointed out that the disparity — the top one percent of the wage earners in the United States took home 19.3 percent of all the income last year, and that's the greatest disparity since 1928 or '29 or something. So I don't know if they're trying to tell us something about the next great depression or something.

Anyway, today I'm going to talk a little bit about — actually I'm going to talk quite a bit about that wonder material, the one no one ever wants to talk about, steel, okay. And you'll get tired by talking about steel, but I'm only going to do it for the next couple of lectures. I actually will get down to talk about some of the properties of steels. One of you asked the question of why are there so many different steels, and I'm going to try to answer that question, but probably not today. But when we're talking structural materials, we still make big objects, big structures, critical structures like nuclear reactors out of steel, and there's a reason for it. We also make ships. [Tom shows a slide of an ocean liner.] This is kind of an old ship, it's Queen Elizabeth or whatever, or Queen Mary, I don't know, one of those queens. Says — it's the United States, it's neither one, okay. It was going backwards, no wonder I couldn't tell the difference. Now you can read United States on the side. Anyway, they don't build cruise liners like this anymore, but that's the picture I had.

Um, and I handed out, but we didn't go over yesterday, this overhead which comes out of Ashby's book. This was out of Ashby's first edition of his book where he tried to predict in 1980 — so remember this is 1980 uh when he wrote the book and so we're right in here — he was showing the use of different metals, polymers, composite, ceramics as structural materials over time. And he went all the way back on this very non-linear time scale to 10,000 BC, and the first metal used was gold. They didn't use very much of it. They used a lot of wood, skins, and fibers. The fibers we're talking about, flax, you know, organic fibers, plants. Composites — yeah they use that same type of fiber material with some of the ceramic material, and they would make straw brick or paper, um, at different times in ancient history. And they would use stone, flint, pottery, glass — he's got glass coming in about 2000 years ago. He's actually pretty accurate on a lot of these things.

When he talked about future metals, he was talking in 1980 — aluminum lithium alloys for aircraft, dual phase steels in automobiles, microalloy steels for pipelines, and new super alloys for aerospace and stuff. And he showed that, you know, kind of in after World War II and just after, metals dominated, and he was predicting, just like all the other pundits were predicting, that the metals would decrease to something less than dirt, okay, because — anyway they weren't, and there's a reason for that. I wasn't predicting that myself, which is why 10 years later I wrote this paper, "The Future of Metals." In fact I was going around trying to tell people that metals were still an important material, but that's another story, and I got hammered by a lot of people. But they don't hammer me anymore because they just don't want to remember that I was predicting that when they were predicting something else, anyway. Polymers and elastomers, and he's predicting, oh, we're going to have high temperature polymers. Well, the useful temperature of polymers has probably increased by 5 degrees, from 500 to 505 degrees Fahrenheit in the last 20 years, okay. And there's actually some reasons for that. But these high temperature polymers also tend to cost $100 or $200 a pound, they're not cheap, okay. The type of polymers we still use in high volume are these things like polyethylene and polypropylene, okay, some of the cheapest polymers in the world. Polyethylene by the way has the same chemical formula basically as candlewax, it's just got a longer chain molecule, okay. It's CnH2n+2, okay, and that's the same as paraffin, okay.

And composites — predicting this big growth in composites, we'll probably talk about that today. And ceramics and glasses — well in the early to mid '80s, oh, they had tough engineering ceramics. And maybe I might as well tell you about toughness right now. What is toughness? We start out historically, we measured the strength of a material in terms of its tensile strength. And the first person to do something like this — this is a picture from Galileo's notebook showing the bending of a beam under a load. And over here, I'm sure he'd — I don't know if he had A and B in there, but anyway C and D, but in any case, he described the strength of a beam under a load. And he actually understood that, gee, they tend to break back here, you know, where they attach to the tree trunk. Why is that? It's the maximum bending moment if you know anything about mechanics, right. So people knew about strength of materials in the 1880s and they would run a tensile test, okay. [Tom holds up a tensile test bar.] Here's the tensile test bar, I'll pass it around. Has what we call a cup and cone fracture on the top, which you can't see very well, but if I pass it around you probably can.

So that's kind of 1880s, after Henry Bessemer taught people how to make steel. Andrew Carnegie became the richest man in the world. In today's dollars Andrew Carnegie would be worth about 300 billion dollars. I mean, so he was the richest man in the world, he exceeded Bill Gates or Carlos Slim or any other rich guys today, okay, in terms of his wealth. But in any case, um, it wasn't really until after World War II we started to take an appreciation for it, but there's this property called toughness. People actually measured it back in the olden days. [Tom holds up Charpy bar samples.] This is some Charpy bars that I actually produced when I was an engineer, a 25 year old engineer at Bethlehem Steel. And there's half of one which is a brittle fracture, and the other one is the ductile fracture that stopped the impact hammer. The Charpy bar, you make these little one square centimeter by ten centimeter long bars, you put a little two millimeter notch very carefully, very precisely machined, and you whack it with a big calibrated hammer. It's just a big pendulum, and it could be 260 foot pounds of energy comes in, hits it, snaps it in two, or it doesn't snap it, okay. In one case every time it doesn't snap it you have to spend $400 to recalibrate the machine. They didn't like me, I was coming up with some pretty tough steels. Not that it was great rocket science to make tough steels.

But what's the difference between strength and toughness? That's the question right now.

Student: [Force / load.]

Okay, the force, right, how much load it will take in pounds, you were going to say. Yeah.

Student: [Energy answer.]

Right, but all those answers are correct. The way I like to say it, um — strength is a measure of the force of fracture, toughness is a measure of the energy of fracture, okay. Force is different from energy, right. But a tensile test, I'm just finding how many pounds it takes to rip that thing in two, that's the force of fracture. The pendulum swinging and hitting, in a shock load — usually called an impact load, okay, but it is a shock load — that's the energy of fracture. And it doesn't always have to be an impact or a shock load, it can be — as we've learned from fracture mechanics, which came out by the study of glasses in the 1920s — toughness can actually be slow loading.

And I will now give you my demonstration, which I've used many times. You'll find me doing this on, I can't remember, the History Channel or National Geographic, anyway, one of these when I talked about the Titanic. They wanted to ask me about Titanic. Anyway, if I take a piece of paper, which paper turns out to be a brittle material — and how do I know it's brittle? I'll show you in a little bit, okay. [Tom takes a piece of paper.] So if I pull on the edge of a piece of paper I can pull with pounds of force, okay. If I put a notch in it, put a defect in the surface, it takes ounces, not pounds. So that defect controls the strength of the material, and that's known as the science of fracture mechanics. And I know it's a brittle material because I can put it back together, and it essentially matches without any significant deformation. If it was a piece of taffy I couldn't put it back together and get the same shape I started with. This piece of glass — hey, I can put crazy glue on it and make it look like new, almost, except for the cracks, okay.

Anyway, um, so brittleness occurs below the yield strength of the material — this is actually a definition — occurs below the yield strength of the material, and ductility occurs above the yield strength of the material. What is the yield strength of the material? Well, it's a sort of fuzzy region in between, okay. If I look at a stress strain curve — [Tom draws on the board.] it looks something like that. This is, you can call it load in pounds versus length if you want, or strain, or however scientific you want to be. And somewhere in here there's a change in slope. When it's mostly linear we call it Young's modulus, or Hooke's law — it goes back 400 years. When it actually is a ductile material like a piece of copper or a piece of rubber, it will bend over eventually, and somewhere in this bend-over region is what we wanted to define as the yield point of the material. And we do that most commonly by taking the point two percent offset strain, or sometimes in the old days they used to take point five. And the reason is, their machines weren't that precise back 80 or 100 years ago to be able to measure 0.2 — that's two parts in a thousand, right, so they were lucky to do five parts in a thousand. But somewhere there is this funny region in between, but this is brittle and this is ductile. I've actually seen a British dictionary, it says anything with half a percent strain or better is ductile, and anything below is brittle. It's not a bad definition, okay.

But what happens to a brittle material? The brittle material strength is controlled by the flaws, just like that piece of paper. A ductile material, the strength is controlled by the ductility or the yield strength of the material. It doesn't fail brittlely, it actually stretches before it breaks. And I do that — uh, I do that all the time. Probably five times a year someone comes to me and says, "oh this thing broke in a brittle manner," and I look at it and say, the steel deformed, or the aluminum deformed before it broke, and it didn't fail in a brittle manner, it stretched. That is something that people often — it's the obvious and they don't look for it.

Now I have a demo of brittle versus ductile, both plastics. [Tom holds up two plastic samples.] Polyethylene or polypropylene, I'm not sure which one it is, but I can bend it all I want. This one's been bent into a nice U before, comes back mostly, okay. I can bend it back the other way. If I keep doing this forever, longer than you and I want to be here, it will break in fatigue. This is a piece of polymethyl methacrylate, better known as plexiglass. And they didn't take the paper backing that keeps it from looking scratched off. And if I break that — [snap] I never got three pieces before. But if you look carefully, you will see a little what we call a shear lip on the compression side — a positive shear lip on the compression side, and a brittle fracture in between. I'll pass the other one around, except it's just a bar of white plastic.

Student: [Question about spaghetti breaking into three pieces.]

Is that right? Gee, I've never done that. I'd assume this is before cooking. Yes. Um, you know, that might be true. I'll have to think about that. I'm not sure that's true, because the actual fracture of a brittle fracture is somewhere between a third and approaching the speed of sound, and the speed of sound in the solid material is like 3,000 meters per second. So we're talking, in a piece of spaghetti, you know, 10 to 100 microseconds. So if it's — you're going to unload the other one much quicker than — you know, I'll have to think about that. If that's true we can all go home and get out the spaghetti, and you can still eat it and cook it afterwards, so there's no waste here, okay. We can all do the experiment. We'll come back after a round-robin test and find out how many pieces we get our spaghetti to break into on average, okay. I don't know, it's not something I've done studies on, but in any case, good point though. Good point for discussion. It makes me — I will never look at a piece of spaghetti the same way again, okay.

Uh, I won't — in fact, when I was a student actually, Professor Wuensch was my sophomore advisor, and he used to teach crystallography, and crystallography is the study of symmetry of crystals and whatnot. And the students used to say, you'll never look at bathroom tile the same way again. I mean he would give us some mosaic tiles from some Islamic mosque or somewhere, you know, some famous thing on the quiz, and we would have to figure out the symmetry features of that tile.

So which brings up another good point, that they don't do hacking like they used to around here, but the Media Lab building as you cross the street from the chemical engineering building — has anyone noticed the artwork on the outside? They built the building and the students started calling it the bathroom tile building because just these square pieces of gray anodized aluminum or whatever. So MIT likes to be famous, and they are sort of famous in the Boston Globe for having outdoor artwork. You know, Henry Moore sculptures and things like that. If you walk around campus, most of you just ignore these things, but we have a lot of expensive artwork on campus. It's too heavy to take away. But the Great Sail, which actually has a function — to prevent the wind tunnel going under the Green Building. Anyway, so they commissioned an artist to come up with some artwork for the Media Lab, and she did. If you read the MIT hack books, this is in there. Anybody know this story? Okay. So she came up with three tiles — red, blue, and yellow. She took primary colors and she made three tiles, and they're there on the building. The students saw this, and so they decided to add a fourth — lime green, okay. So this is pretty innocuous hack. It took several weeks before anyone who had any knowledge of what her art was noticed it. And when they did, she hit the ceiling. I mean, the only — the funniest thing about the whole thing was her reaction to the whole thing, okay. It wasn't that great a hack, I mean it was pretty simple, but her reaction made the whole thing so much more worthwhile.

Which — also, does anyone know the hack of No Knife? Okay, so over here in the lobby — just off the lobby between the elevators in Building 10 — there's a display place, and they have artworks displayed in there, kind of traveling shows. And so they had a bunch of sculptures going on, this is about 20, 25 years ago. And the students found a little corner in there that wasn't as occupied with sculptures as everything else. They took a trash can, you know, the big deep square gray ones, turned it upside down, went over to the student center, got a tray, you know, a cafeteria tray, and they got a glass, a plate, a fork, and a spoon, and they put it on there like it was a place setting, and they had a nice little sign above there that they entitled it "No Knife" because there was no knife. And it had a description of the existentialism of not having something sharp, or whatever, you know, if you've ever been to some of these artwork things. It was very humorous, I thought. But actually I don't think — the author actually may have been different artists, who, so no one could get offended, I don't know, but I always thought No Knife was pretty clever thing. Anyway, MIT humor is a little different.

Anyway, okay, so fracture toughness versus strength. There are limits to properties. We can't just get any property we want when we want to select a material. [Tom shows an Ashby plot.] So this is fracture toughness versus strength on an Ashby plot, and it turns out — what would you like? You'd like to have lots of both. You'd like to be up in this corner if you could, as far up there as much strength and as much toughness as possible. But you kind of poop out here at a strength of — well, what's he got, it's in megapascals, I don't even know what megapasc— oh this is toughness, okay. You end up with a toughness of about two or three hundred megapascals per square root of meter, or megapascal root meter. We don't have this graph — um, I think it might be in the one that had behind the one... anyway you don't have to have this graph, it's just another — I'm going to show you ratio analysis diagrams. It might be among these. But I could — this is the handout from yesterday that had the Ashby's plot, and I've told Jerry to put all this stuff on Stellar, and you're right, it's not in there. I don't know if it's another one, but I can get a copy if everybody wants, but it doesn't really matter from my point of view. I could use modulus here and just talk about limits to properties.

The modulus, the highest modulus is basically ceramics and tungsten at about 60 million psi, okay, whatever that works out to in pascals — well you can read it here, uh, five or six hundred gigapascals, um. And strength and toughness, there are limits — I mean that's all, that's the only point I wanted to make here, there are limits to the properties of materials. Metals are only so strong, ceramics are only so strong. Ceramic — they're only so tough, that's this whole thing of Ashby kind of drawing these circles on a log plot of the properties for different materials, okay. You'd like to be way out here but you just can't get any further.

So let's take an actual design situation where you'd like to have a lot of modulus and some strength and some toughness. And the example I want to give you is, back in the old days when I injured my knee and tore the cartilage, they'd have to lay your whole knee open in surgery, literally. You have a scar on your leg that's six or seven inches long, and you'd be in a cast for like two or three months and then you'd be on crutches for six months. It was major surgery to go in there and get out that broken cartilage. As a result I now have broken cartilage still after 40 years — 40 some years in my left knee, okay. I've never had it repaired. Kept me out of Vietnam, okay. But anyway, um, they flunked me in the physical because of the torn cartilage. I said, really? Then I found out they could bring me in as an enlisted man. I said, really? Anyway, so any case, but I still got it. And then I tore the cartilage on my right knee, so now it's symmetric, I can't walk either way, um, in any case.

They've gone to microsurgery, and in the old days of the first microsurgery, got the thing down to like a one or two inch scar, and they have this thing called a Ranger, which is nothing more than a stainless steel nibbler. And the surgeon squeezes the trigger on this thing, and this little tube goes past the blade, and he can go in there and he can look with fiber optics as he's doing this, without opening up your whole leg, and he can nibble away your cartilage and just take pieces of it out a little bite at a time, okay. Like a mouse nibbling on cheese — I guess it's the same — maybe it's a rat — no, anyway, uh, whatever it is.

Um, now they've gotten it smaller, and so about 20, 25 years ago a company that made these instruments came to me and said, well the surgeons can actually get these things smaller and you can go in a half inch incision with my— called microsurgery, sort of a big thing 20, 25 years ago, for microsurgery, they said. But the problem is the things are too flexible, as you get thinner and thinner in your beam, the stiffness of the beam goes as the cube of the thickness — just basic moment of inertia from mechanics of materials, okay. And they said, what could we use? Well, they were using steel, which was right up here, and steel is about 30 million. I said, well you could use molybdenum, which is about 50 million, I don't know if you want to use tungsten because it's sort of brittle at room temperature, but you could use molybdenum and get 50 million. But I thought about it for a while. I said, what you really ought to use — and I don't know if it's on here, it's on some other plot that has toughness or stuff, maybe it's on — oh here it is, it's on this one with modulus — I said what you could use is aluminum oxide. Use sapphire.

Well, I forgot to bring my chunk of sapphire in. Maybe I'll remember tomorrow. Okay, I have a chunk of sapphire about that big, it's worth pennies nowadays, I think. Grow it in great big boules, okay. But I said, make sapphire, because they can grow tubes of sapphire, they can grow sheets of sapphire, sapphire rods. And I said, not only that, you can dope it with a little chrome and you can call it ruby and tell the MDs that you're selling them ruby instruments, okay. You can color code them — this would be red ruby, this one could be emerald — actually emerald's not exactly the same, but anyway, you could — they're very hard, wear resistant, have a higher modulus than steel. And just think of the marketing potential — sapphire instruments, okay. They didn't like it. But we actually had the machining techniques to be able to make these things, and I could have designed it. We — oh, they didn't like the idea. So hey, they paid my bill anyway, um, so I guess all was well.

Anyway, so, it turns out — what happened — we learned about toughness, this property of toughness, around the turn of the 20th century, the first turn — you know, to the 20th century around 1900. That Charpy bar, it was just celebrated about five years ago, the 100th anniversary of Charpy testing, okay, it's still used. Uh, but what happened was — actually before I show you that, what happened was in World War II we had some problems, okay, with the Liberty ships. Anybody know the Liberty ship story? Okay. This is one of my cherished possessions, one of my — [Tom produces a bound report.] yeah, I'm going to show it to you. This is the MIT copy of the 15 July 1946 — oops, what happened? What did I do? Did I turn something off? Oh, obviously I turned something off.

Okay, good. So this is the 15 July 1946 report of the US Navy, Report of Investigation on the Methods of Construction of Welded Steel Merchant Vessels. And in fact, some of these tabs — anyway, one of my graduate students was walking over to the student center once, and MIT Libraries was selling all their old worthless books. He picked this up for two bucks and gave it to me, okay. Here's the famous picture of the Schenectady at dry dock. It never really had been out to sea and it just sort of broke in two, okay. The one I like, which you don't usually see in the textbooks, is the Esso Manhattan, this one. Oh, what'd I do, something on these buttons — oh, it's showing up there, okay. This is the Esso Manhattan, this one's at sea. Now it's a lot better to do it at dry dock if they're going to do this, then do it at sea.

In any case, they lost — of the 4,694 welded steel merchant vessels built by the Maritime Commission in World War II, 970 suffered casualties involving fractures. 24 vessels sustained a complete fracture of the strength deck — that's not — this is both strengths and shear strakes. One vessel sustained a complete fracture of the bottom. Eight vessels were lost, of these four broken in two, four were abandoned after fracture occurred, four additional vessels broken in two but were not lost, et cetera, et cetera. So the whole world wanted to know, and three places started doing research on brittle fracture of steels and welded construction. In Britain, they formed the British Welding Research Institute, which is now the Welding Institute, in Great Britain, just outside Cambridge. In the United States, they had two places. One was the Naval Research Laboratory, they obviously were interested, and the other was a place called MIT, okay. Building 4 and 8 — anyway, actually Building 8 mostly.

So anyway, this is called a ratio analysis diagram. It's developed by Pellini in the 1950s or '60s at the Naval Research Laboratory, and it's a complicated slide. I haven't given you this one — this particular one. I've given you another one. My paper, "The Future of Metals," has kind of a composite. But this one is the fracture toughness versus strength of steels. I'm going to show it for titanium, I'm going to show it for aluminum, and then I'm going to show you composites and ceramics and plastics. Something that, I don't know, anyone else ever does. But your fracture energy for steels of low strength — I say low strength, these are your kind of carbon steels down here, actually this is yield strength, so your bridge steels and stuff would be even lower than this, maybe way back here at the end of the slide — but 10,000 foot pounds, that's a lot of, this dynamic tear energy, well that's a lot of energy. And this is the plastic region. As you get up to higher strengths like 180,000 pounds per square inch, you're now getting approaching the strength of what we use for steels for landing gear on aircraft. You find that the toughness drops off, the energy of fracture drops off as you increase the strength, and it keeps on dropping off until you get up to things like piano wire and things like that, and the stuff really doesn't have much toughness.

You lose — you're not sacrificing toughness for strength if you go to the highest strengths. But it's interesting, they put some lines on here which I'm not going to talk too much about, but these basically have the critical section thickness when you get a flaw big enough to cause the brittle fracture to run, okay. And if it's — well I'll show it to you later — there's this value of 2.5 and down here value of 0.6. And they try to design — you could design here but it gets expensive and heavy because you can get higher strength, for a fracture mechanics point of view you want to be in here, you don't want to be in these regions down here, okay, so far as that goes. But kind of remember some of those numbers of 10,000 in terms of toughness.

Now I want to show you, I'm going to prove why steel is so unique, okay. Here's aluminum and titanium. This is all out of the Metals Handbook if you want to go get it. But aluminum, we're now talking about 2,000 rather than 10,000 as the maximum, strength five times lower, toughness. And then you've got the 2.5 and 0.6, but your strength levels — this is where the steel started, the aluminum's a low strength material. A guy who used to be a professor at Lehigh University and then went, left there and became director of research at US Steel 40 years ago, he used to talk about aluminum as the "near metal," okay, meaning it almost had toughness. But it actually does have toughness compared to ceramics, but I'll show you that.

Here's titanium, and it's got twice the toughness of potentially of aluminum, and it's got pretty good strength, not as high as steel that can go up here. And the drop-off is around 180 for titanium, it's around here at 120, 130 where the drop-off is. But that puts titanium, aluminum and steel in perspective. Why is the Navy interested in steel, titanium and aluminum? Anybody know? They build submarines, and you want the lightest weight material possible for a submarine. Why? Because if you lose power you'd like to pop to the surface rather than sink to the bottom, okay.

What happened to the Thresher in '62 was, it came out of Portsmouth Naval Shipyard on sea trials. They had a tender right above it, was doing sea trials, and they had a major break in one of their main water cooling pipes going to the ocean. They were doing a controlled deep dive. This pipe just happened to be into the reactor compartment, and they flooded the reactor compartment and they lost all power. And when you lose power, you're supposed to be able to take the compressed air in your ballast tanks and blow out the water in your ballast tanks, or take the compressed air in some of your tanks and blow out the tanks. They had a problem, they weren't able to completely blow the tanks, and they started rising up to the surface. As they got close to the surface they just started going down. And the guys on the ship on board were listening to this on the, you know, the screams of the men as they were just slowly, you know, going down to their death. This created a major problem in the US Navy. Admiral Rickover was not happy. Congress was not happy. Most of this stuff is sort of — well they haven't completely declassified all the information, but it was well known in the papers. I used to live in Virginia Beach, Virginia, and so it's all over investigations all over the papers, because that's a Navy town.

But anyway, the nuclear submarine program, the whole nuclear navy shut down for about two or three years, and they ended up creating the US Navy SUBSAFE — manufacturing and production quality control, well ahead, 30 years ahead of American industry, world industry, in terms of quality control. And this was for shipbuilding, because of this major disaster. There's actually a book — actually it's this one right here. [Tom holds up Petroski's book.] Henry Petroski. If I know — does anybody know who Henry Petroski is? Oops. He's a professor down at Duke University. He wrote this book, To Engineer is Human: The Role of Failure in Successful Design. He was elected to the National Academy of Engineering same year I was, for having written this book, with the idea that we only learn from our mistakes, okay. The Hyatt Regency collapse is in here, and if you watch some of the other videos I'll talk about that and use his book. But the theory is we keep on building things bigger and bigger until we hit the limit. And then we have a big failure, a bunch of people die, and then all of a sudden we kind of say, what's going on? Like the space shuttle Challenger, someone brought that up the other day.

Anyway, so those are ratio analysis diagrams. Here's my ratio analysis diagram, which you have in "The Future of Metals," where I put together — and we have this stress intensity factor, or toughness, K1c divided by the yield strength, to 2.5 per inches square root of inch, or actually times square root of inch. And over here is general plastic yielding, the thing will just deform like rubber, okay, if you have this type of toughness and strength ratio. We don't usually design that. The elastic plastic mixed mode of failure, which is where we usually do our design of structures, between K over sigma y 2.5 and K over sigma y 0.6. Elastic plane strain fracture is brittle fracture, we usually don't like to design in brittle fracture, okay. So we like to design in here.

Well, what's the best material of all? Steel. You need to learn this answer, okay. Steel, okay. Titanium is pretty good but it's a little pricey. Aluminum is way down here, and it's actually about the same as composites, which is why there is sort of a trade-off in aircraft design, aircraft structure design, between aluminum and composites. However, aluminum — when they first started building the 777, the Boeing 777 which was like 20 years ago, 25 years ago, they announced this — there's going to be more than half composites. When it was finally built it was like 10 or 15 percent composites. Does anyone know what happened? They priced it out, just like the X-33 space plane. Those composites are expensive, okay. We're going to talk about that. But they have equal fracture toughness, strength, as aluminum, but they're nowhere near titanium or steel.

And here we have plastics. Now there's really nothing wrong with plastics, they just don't have a lot of strength unless you draw them into long fibers like Kevlar, and they have strength in one direction, and you can't make everything in the world out of a string, okay. And ceramics are sort of interesting. They actually get strong — as they get stronger they actually get tougher. That's because ceramics are full of critical size flaws. Their toughness is so low, that any small imperfection — and by a small imperfection I mean in high strength ceramics an imperfection less than the size of a human hair, like a tenth of the size of a human hair, can degrade the structure completely in terms of fracture toughness and strength — or not, in turn the fracture toughness is so lousy the strength is degraded.

Which brings me back to another Robert Sprague quote, which I didn't bring the overhead for, but Sprague's law — yeah, what sort of living condition is that? Anything with anything tensile, in compression — the biggest use of any composite in the world is Portland cement, mortar and rock. That's a composite material, but you design it for compression, and you put steel rod in when it has to be in tension. So I'm not knocking composites completely. I'm just saying when people talk about high performance composites, they're often not worrying about the cost. And that's where you get Jim Williams' corollary, where whenever you first hear about the properties of a new material — whenever you first hear about the cost of a new material, write it down, because that's the lowest cost you'll ever have.

Sprague once said, material scientists think that structure controls properties, materials engineers know that defects control properties. So that piece of paper that I tore might be plenty strong with no defects, but all materials have defects. And the question is what size is the defect, okay. And that's a simple little equation in fracture mechanics which we can go through, but, um, we won't go through right now. Um, so as usual I'm going a little bit slower than I thought, uh, but it is almost time. Anybody have any other questions?

So composites — well let me back up here. All these materials except ceramics are viable structural materials because they all fall between this little pie-shaped region of elastic plastic mixed mode. You can get polymers that are plenty ductile, okay. You can get them that are also somewhat brittle, that — you know, smoky plexiglass is down over here somewhere, and you have to be careful how you design for it, but let's face it, polycarbonate is way over here. We used to use it as bulletproof glass, okay. So plastics, across the whole field. Aluminum crosses the whole field. The toughest aluminum in the world is an aluminum called 2025. Many of you have heard of 2024 aluminum, the aluminum copper alloy. 2025 has been around since 1925. It was named right after 2024. It's 15 times tougher than any other aluminum alloy, very low strength. I only know of one application: propeller blades. And you can think about it — wouldn't I like to have toughness in a propeller? Wouldn't I rather have a propeller blade that bends before it breaks and snaps? Yes, it's sort of a critical structure.

Composites go across a huge range, but in most cases they're not the best for fracture or impact and things like that. Titanium, as long as you keep strength down, it's pretty good. And steel's pretty good. All these materials are viable structural materials from a toughness strength ratio analysis diagram. So I'm not knocking them. But tomorrow — actually probably next week I'll talk about — I'm going to actually get into steels and how we pick steels and what are the advantages of steels, what are the disadvantages. You can think about — I wrote down this morning in my outline, what's the Achilles heel of steel? So that's a question for you for the future, for next Wednesday we'll talk about that. But tomorrow I'll talk about the history of manufacturing of some materials and productivity gains over the centuries of thousands-fold that changed the whole industry of a number of different industries, okay.

That's it for today. I try to start right at 8:30 and knock off by 9:20 because some of you have to get to the next class.