SMS_S2016_09

There's a particular time or date or something that you want to exclude. Okay we're going to have the room from 8:00 in the morning till 11:00 in the morning. Um, I'd be willing to start at 8 but I don't think most students are, but I think there's some students who might be willing to start at 8:30, like the three of you come early, right? Or the four of you, I include Papa. Um, not that we have to do that, but there are 46 presentations and if we're going to finish them, we've got about three weeks. Well, I want to try to finish them over the four-week period that includes spring break. So we got three weeks. If we have to, we can go later, but you know your other classes are going to start getting busy, and I know some of the undergraduates have said they want to avoid the week before spring break because that's when all the other classes will have their midterms and stuff. And that's fine, we got a third of the class of graduate students. And I've got to do some traveling in between here. Uh, for example, the ETH, I have to be in South Carolina. I think I'll find out later today.

Anyway, another question? Yeah. And then for the one-page summaries of each module, when are those due? Uh, before I have to turn in grades, which is kind of mid-March or mid-May, actually. You got to figure the last day of class, which is like May 10th or 11th or 12th or something. Yeah, that's fine. Yep. Oh yeah, I mean I don't have to turn in grades, the registrar doesn't know that I accelerate the class, okay. So, and there are some students who will always procrastinate till the end to finish their last module or to turn those things in. Um, as far as that goes, so I need them by the last day of class. Hopefully not everybody, I don't get 144 of them on the last day of class, you know, because obviously I wouldn't bother to read them all. And they don't have to be long, they don't have to be a one-page summary, it could be a half page, it could be bullet points of what are the key takeaways. You know, can you summarize in a few bullet points everything you learned in the class? For example, in this one, steel is unique in terms — I mean you know, that could be the thing you take away — in terms of toughness and strength and cost and repairability and a whole host of things we're going to talk about today.

But Dr. [Ballinger] decided that we should do something. He's been bugging me because I've never really worried about whether students actually watch the other modules. I mean, I've told you that I don't care, you know, sort of like my doctoral students would come to me and say, "When do I have to have my exam wr—" uh, not their exam but their thesis written. I'd say I don't care, I already got my doctoral degree, I don't need one, you know. They have to do it themselves. They said, "Give me a date." I've had several students like this. One of them took a year to write it. He just — he's the type of person that you have to — he has to have a deadline. And I said, "I'm not going to give you a deadline." He would beg me for a deadline. I'd refuse to give it to him. I said, "You know, you don't want to graduate, not my problem, okay." And I used to say, "You're supposed to be learning to be a professional. If you can't manage yourself, you know, set your own deadline, right? I don't have to set it for you. If I set the deadline, I tell him I need it the next day, right." But he couldn't do that.

So to me it's just as easy to get it done. In fact, the problem I have is if I don't get something off my desk within a week, the odds are that I will continue to say, "Oh that doesn't need to be done," and it'll never get done, you know, everything else would come in and come in ahead of it. So everybody has their own weakness in how they schedule, and we're all sort of overcommitted. I used to say half of what we do are things we don't really need to do. Problem is knowing which half of the things that we don't need to do, okay. Um, and I haven't ever figured out how to figure out which half are important, which half are not.

So, okay, since we got most of the people here, so I'll be lecturing today and Thursday. Dr. [Ballinger] will be in the other three days this week. He will finish up his module of eight lectures um this week, and I will finish up my module of 12 by next Tuesday. That's unless he decides he wants to do a 9th, or I decide I want to do a 13th or whatever. And so I haven't scheduled anything for the last three days of next week. And we could finish in something there, as far as that goes. But then, I'm sending around an email, my secretary is sending it around, typing it up now, putting it on Stellar, should come to all of you, um, that I'd like to start scheduling the presentations for the weeks of March 7th, 14th, and 28th, and April 4th — should have been a — I guess I didn't say that in there. I actually have April 4th on the schedule, okay. Although I hope we don't have to go that long, because the room is available from uh 8:00 in the morning to 11:00 in the morning each day. If we do two hours a day, and some people can't be here from 9:00 to 10:00 and they're taking all U modules online, um, but then hopefully they can come 10 to 11. And if they can't, I may run a couple of days at 8:30 uh to 9. Um, and they shouldn't have a conflict with that. Uh, I hope that people will come. We're going to videotape all of them, but we're not going to put them on YouTube for the world to see. And you need to check with — you have to check with uh Neil on how to do that. We can put them on YouTube, but you can put them on YouTube with limited access, okay. Neil should be able to tell you how to do that. Okay um, and if you want a copy of your presentation, you're welcome to a copy. Uh, I don't do anything with them, I haven't archived them for posterity. Uh, you might — your mother might want to, okay, or something like that. Okay, any questions?

Uh, I did have one little thing I just happened to see in a materials journal that they talked about — we've been, I mentioned rare earths, and they said the demand's going to reach $4.5 billion by 2019. And it actually gave a breakdown of where world's rare earth demand — and this whole thing talks about how in 2010, 2012, um China basically uh decided to cut their export quotas. That meant they refused to sell to Japan. That's euphemism for political warfare against Japan. Um, and so that's one of the externalities. 125,000 metric tons um in 2014 in lots of different areas. UPS — permanent magnets being the largest, a little over a quarter. Polishing of glass and ceramics — it turns out a lot of the rare earth oxides are very hard and make good polishing media. They're not really rare, okay, I think I mentioned that to you. We call them rare earths but they're not really rare in the Earth's crust necessarily. Um, metal processing turns out 12%. People use cerium in steel to tie up the sulfur, and there's a billion tons of steel, so it doesn't take very much cerium in steel to end up being a fairly large fraction of the total. Catalysts, phosphors um, a number of uses, battery alloys, I don't know — I even — I don't know what FCC's are.

Um, but in any case, but to give you an idea, okay, 125,000 metric tons compared to steel which is a billion metric tons. We're talking orders and orders of magnitude um larger. Um and we're talking about a world market of $4.5 billion. What's the market for steel roughly? It's three-quarters of a trillion dollars, okay. So 4 and a half billion is a drop in the bucket in terms of the size of the industry. If you were do the same thing with, let's say titanium — we all think of titanium as essential, and it is essential to our aerospace sector and our space sector, um, but titanium cannot even afford to have their own rolling mill. Essentially Timet, which is the world's largest titanium producer, they rent one day a month on a steel mill to roll titanium. So they can produce most of the world's titanium on one steel mill, one day a month. Um, you have to understand the difference in magnitude of these things.

Which — one of the reasons I kind of put it up — we talked about diamond being the highest modulus, in gigapascals it's a thousand gigapascals. Um, or uh, anyway, um, tungsten carbide is 450 to 650, depending on how it's put together. Um, tungsten and its alloys as an element, 380 to 411, so about 400. Molybdenum is almost as high um, so far as that goes. A mild steel is way down here at 200, one-fifth of diamond. Uh but it's still pretty high compared to all the other things. Titanium is only 116, and aluminum is 69, okay. It's only 7% of that of diamond. Copper is 124, it's about the same as titanium. Copper interestingly is very um crystallographic orientation dependent uh in terms of modulus. Um, so in any case, one of the things we had talked about before, was the last time, was material stiffness depends on both the modulus, which is a chemical bonding property of a material, the strength of the chemical bond, and the geometry.

And we talked about Timoshenko's book on the history of the strength of materials, and here's good old Timoshenko's text in 1950. And I showed you his picture of Galileo measuring the strength of a beam, okay. This is from one of Galileo's illustrated books, okay. And there's a beam and hang a weight on it, and Galileo started to figure out something about the strength of a material. Um, Young — there was Hooke's law in the 1860s [1660s], which basically said stress was proportional to strain, but then actually, this is Hooke right here. Uh, but Hooke had some drawings from some of his papers of trying to figure out the modulus of a material. And so one case he just took a wire and he hung a weight from it. In another case he took a um a balance, and he could weigh something and he could measure how much something was stretched. In another case here's geometry — he took the same type of wire and he made it into a coil, and you get a lot more deflection, okay. But if you go through the mathematics, it turns out — uh, actually, does anyone know what type of um stress is on a spring when you extend the spring? It's not a tensile stress. Turns out it's a shear stress, and it's equivalent — if that was, if you had straightened the whole thing out, it's equivalent to a twist, okay.

So anyway, so springs actually fail in torsion, even though they're operated in tension, but they're circular and so the stress axis changes and stuff. But anyway, so these are the types of things, and Hooke's sitting here trying to figure out the difference between these two things — the material property and the geometric property. It wasn't obvious in the 1650s that there were these two things that changed the stiffness of a material. But it was pretty important whether you're designing cathedrals and um big buildings like that or whatever. It turns out diamond is a structural material. We're going to talk a little bit more about it uh later. But what I'm going to pass around are two things from a company called Kinik. This is just a basically a toy, marketing tool. It's just a uh — I don't even remember what type of uh figure that is, but you can feel the diamond on here, you can see the diamond, you can see them in a nice regular array. We can essentially braze diamond in a very regular array. And this is a pad conditioner. Any semiconductor person here, you know what a pad conditioner is? Okay, if you look at this pad conditioner and you look at it carefully, you'll see the diamonds on here are in a very regular square array. We brazed them on it — well, I didn't braze them, but they — we can braze the diamonds in a very precise way.

And a pad conditioner basically — in making an Intel chip or something, you'll basically start with silicon, then you'll etch away — so that's subtractive manufacturing — then you'll deposit on some titanium, uh and then oxidize that or nitride that to titanium nitride, put on some uh copper, you keep on — you might do 200 steps of etching and adding and um chemical milling and things to make up this complex chip. Well every now and then the surface starts getting very bumpy, and so every now and then they have to go in and they basically polish that surface of that chip to bring it back to a nice planar geometry. So when they do their subtractive and additive manufacturing, they have a flat surface to work with. Well, it turns out they chemically polish — mechanically and chemically polish to bring it back to a flat geometry several times in the process. And they do that with these sponges that basically have diamond powder and stuff in them. Uh, I think it's diamond powder, but in any case those sponges that are the polishing compound — and they're actually applying electric current as they do this as well, so it's electrochemical polishing — they get clogged up just like any sponge could get clogged up with all the grinding swarf and stuff. And so they come in with pad conditioners — that's a pad conditioner, which is basically diamonds — and they basically eat the junk, okay, out of the holes in the pad conditioner. Um, and so it's a complex process, but um it's one of the many steps, and typically making a semiconductor chip will be about 200 steps, okay, one following another. And if you screw up one of them in one area of that wafer, the whole thing becomes junk. So uh, it's pretty amazing that we can do these things.

So I started to talk a little bit about the history of strength of materials, and it's going to get into fracture mechanics. Uh, we had Galileo about 1600, we had Hooke uh around 1660, um we had tensile tests around 1880, 1800s. We had Young, of Young's modulus, about uh about the same time, maybe a little bit after 1800. Um, we had railroad bridges — the big industry, just like the automotive industry is a huge industry today — the huge transportation industry, um, aside from whaling and ships uh in the 1800s, was railroads. And in fact, Andrew Carnegie became the richest man in the world, uh richer than Bill Gates is today on a constant dollar volume, by selling steel to the railroads. Just like um uh Bill Gates sells software to the computer makers — the computers are huge industry — um uh Andrew Carnegie sold steel to the railroads. But they had a number of railroad bridge failures, and they'd have railroad ties break, uh railroad rails break, uh derailments and things like that. In the 1880s they learned about stress concentrations.

Does anybody know what the first calculation of a stress concentration was? It's a hole in a plate. Simple little round hole. And someone calculated from first principles that the stress at the 3:00 and 9:00 position would be magnified by a factor of what? Come on, some of you know what the stress concentration around a hole is. Factor of three. So if the nominal stress is sigma right here, at 3:00 and 9:00 you have three sigma. And you can prove that mathematically, okay. Uh, the stress concentration as the stress dies off around the hole — and if you have a sharper notch, you can have higher stress concentrations. So people started learning about stress concentrations, and they started measuring tensile tests. Um, and they knew there was something different about uh metal that was ductile and metal that was brittle. They didn't know exactly what it was. They could see on the fracture surface that the brittle fractures looked sort of crystalline, and so they would say that the steel crystallized, okay, or the metal crystallized. They could see that even on cast irons and stuff. And so they — um, it wasn't until x-rays came along and they realized all metals were crystalline. Uh, and so it wasn't crystallization that was causing the brittleness. Um, but you'll still — I still see people, non-technical people now, talking about the metal crystallized when they say it got brittle. And that's well over 100 years since uh we learned that that's not the case. It's not the fact that it's crystalline, it's because it has mobile dislocations.

Does anyone know why metals have mobile dislocations whereas ceramics and polymers and other things don't have mobile dislocations in the crystal? Nope. Okay, um, well you know a dislocation is — right, it's a missing plane of atoms, uh or a twist if it's a screw dislocation. Um, and if you push on the dislocation, it turns out you can um you can essentially break one row of bonds at a time, rather than breaking all the bonds at a time. If I try to uh — I should have brought a telephone book. I used to rip telephone books in two to show students how to do this. Maybe on Thursday I'll remember to do it. But if you take a sheaf of papers, I can do it with this sheet of papers, it's not very thick um, and you just try to pull on it. I told you before, if you pull on the edge, it takes pounds of force, and if you have a thousand pages, it takes 1,000 pounds of force, if it took one pound for one page. Well if you were to take that page and you were to introduce a dislocation by making a little U in it like this, and then you break its back on a thick set of pages, you can break one page at a time, because you put one in tension at a time.

If you think about the shape of the U — and I've had people complain to me about whether this is a correct analogy — but you have pages like this. If you make a U shape in here, and as you bend it back, you'll put the top page in tension, and when that breaks, the next page goes in tension and it breaks, and you basically rip all the way through. So the trick to tearing a phone book in two — and I've done it with the Yellow Pages before in my youth, okay — is to grab it, make a U, a dislocation in it, and then just bend it, essentially breaking one page at a time, okay. The problem today is we now polymer-reinforce the paper, and I can't even do the MIT phone book anymore, okay, because the paper is actually too strong for me to do it. Maybe Arnold Schwarzenegger can do it, um, but in any case, you introduced a dislocation.

People knew that metals — well, with quantum mechanics in the 1920s, they knew the Lennard-Jones potential predicted the strength of crystals. Pure crystals without imperfections should be like 3 million PSI, 2 to 3 million PSI. They knew the actual strength was 10 times less or more, and they didn't understand why. Um, and then they postulated — two people, Polanyi and Orowan was in Hungary, and Polanyi somewhere else in Eastern Europe, I don't remember. Orowan ended up as a professor in mechanical engineering here. Um, but before he came here, he postulated dislocations by looking at the cleaning lady move the rug in his office.

So in Hungary he had this huge office apparently, and there was a nice big rug on the floor, and it had gotten out of kilter a little bit. And so um the cleaning woman came in, she was cleaning it, she says, "Oh, I need to move the rug." And he says, "Here, let me help you, because it's a great big rug." She says, "No, I don't need help." And she just put a little crease in the rug, okay. She took the rug and she basically put a little fold like this, and she kicked it across the room, okay. And the rug moved three or 4 inches by the width of that crease. And Orowan watched this and he thought, "That's it. That's how dislocations weaken a metal by a factor of 10." A mobile dislocation. And we have mobile dislocations in metals because metal bonds are uh not directional, they're not strong directional bonds like we have in covalent bonds. Um, and uh, the electrons are very non-localized, and so you can have um these things break one row at a time, just like that cleaning lady kicked the rug across the floor. So next time someone comes in to clean your office, pay attention to what they're doing. Uh, he would probably — I don't — he never did win the Nobel Prize. He was an engineer, they don't give Nobel Prizes to engineers, um, but in any case.

But people understood that some things were ductile and some things were brittle, and the problem with brittle materials is that you cannot predict the fracture behavior. And so there was this guy Griffith who was trying to understand the brittle fracture of glass, and he realized it was a flaw. And I've already showed you, I gave you the uh piece of paper that uh — you have a brittle material, paper being a brittle material — when you put paper back together after fracturing, it goes back together just like a coffee cup, you know, there's no deformation. Whereas you take a piece of metal or a piece of rubber, ductile rubber, and the crack tip blunts and it stretches, and when you try to put them back together, they don't fit back together at the end. Here's an old piece of rubber. I wish I could figure out what kind of rubber this is. For years I've been tearing it. Um, but this is the toughest rubber I've ever found. Um, I just don't know what type it is. I have to analyze it someday.

Any case, um, this is a plot of the stress-strain curve of a material, and I made this plot for a different reason, but in the yield, in the elastic region you have — it should be brittle elastic and ductile plastic. When the material's exhibiting ductility and then has a lot of strain, you absorb a lot of energy over here. You don't absorb energy here. And in the brittle elastic region, it depends on the size of the flaw, how much strength you have, okay. And that's fracture mechanics — explaining the size of the flaw. And Griffith came up with this theory in the 1920s, but we really didn't pay much attention to it until after World War II.

We had a number of problems, and this is the 1946 US Navy report on design and methods of construction of welded steel merchant vessels. It's an investigation that the US Navy ran right after World War II, because during the war they built Liberty ships, and these Liberty ships, they were building some of them from laying the keel to sailing away — they're building these ships in 2 weeks at the height of the war, okay. They really learned how to pump them out. They built uh 46 — 4,700 Liberty ships, of which a thousand suffered casualties involving fractures. 24 vessels sustained a complete fracture of the strength deck, okay — the top deck would give strength in bending. Um, one vessel sustained a complete fracture of the bottom, eight vessels were lost. Of these, four broken in two, 26 lives are lost, highest incidence of fracture occurs, blah. Anyway, um, the famous picture of the USS Schenectady sitting at dry dock, never had been out to sea — it just decided to break in two one day, okay, as it's sitting at dry dock. And if you go to a fracture book, this is the classic book they usually show. What they don't show is one of the plates from this book of the USS Esso Manhattan, where the same thing happened out in the middle of the ocean, which was a lot worse than doing this at dry dock, okay. So they lost a few ships.

And they came in, they did a study. There were three places where they did big studies of brittle materials after World War II, even though Griffith had explained the brittle fracture of glass. But no one understood why he was studying glass and fracture — everyone knew it was brittle. Uh, but Griffith had explained it was the flaw size, and he came up with the fundamental equation of fracture mechanics, which I wrote down the other day, that the toughness um of the material must be greater than the applied stress times the square root of pi times the crack length. Okay, if this is a specimen — typical fracture toughness specimen looks something like this, has some holes in it so we can grab it — and you essentially that's C is the crack length, okay. And you have a crack right here.

Um, I will show you — this is a fracture toughness specimen made out of granite, okay. This was done — this was part of Wendell Wilkening's doctoral thesis. He was finishing up his doctoral thesis here when I started, the week I was starting as an assistant professor. And Wink, we call him Wink, um, Wink was studying the fracture of granite because Professor Backofen, who had taught me mechanics when I was a sophomore, was curious about how they raised the Egyptian obelisks. You know, these things that look like the Washington Monument. And everyone had assumed they built it — they cut the stone in the horizontal position, it's all one stone, and they just lifted it up, okay. But if you did the fracture mechanics that people understood in 1970, it should have broken under its own weight. Such a brittle material — as you lifted it up, it should have fractured.

So um, he put uh Wendell on a doctoral thesis to try to understand the brittle fracture of stone. And he found out — well, they already knew — granite is a three-phase material. You can see white, black, and gray, three different crystal structures of three different minerals in granite. And what he found is at the tip of the crack you actually get little microcracks, and those microcracks absorb more energy than anyone ever thought they would have uh in terms of fracture behavior of things. And that's why the Egyptians were able to raise that obelisk up — it was more fracture toughness. You could postulate some flaw size, you can calculate the stress, you can estimate the fracture toughness, but the dynamic fracture toughness was greater than they had assumed. You only have three parameters here — applied stress, toughness of the material, and size of the flaw. And that's the science of fracture mechanics. Now there's lots of different mathematics that goes with it and whatnot, but fracture mechanics could explain these things.

After that, a number of ceramists started saying, "Oh, all we have to do to toughen ceramics, which are terribly brittle, is — all we have to do is we can introduce other phases that will cause these little cracks." And that's true for the first loading. What happens on the second loading? After you've already introduced those little cracks, you can't crack them again, okay. And that's some of — that led to, I told you, the ceramics fever of the 1980s, and people were going to make tough ceramics, and they were starting building jet engines out of ceramics and everything else. Well it didn't work. Um, ceramics are still brittle, metals are still ductile.

And started sort of with this Navy study, after the Navy study around 1950 or so, three places in the world did a major study of brittle fracture of welded uh vessels uh or ships and things. One was in Great Britain. There's a guy uh Richard Wek who was riding his bicycle outside of um Cambridge University, and he came along this little place called Abington uh in the countryside, and he said, "I want to build a welding institute here." And he got some money from the British government, and they built the British Welding Institute, which is now a large research organization mostly funded by big oil companies. Um, but the British Welding Institute did some very fundamental studies on the fracture behavior of welded steel structures. They are now a leading place for studying the fracture behavior of all kinds of materials for structural materials.

Another place was the Naval Research Laboratory. There's a guy Pellini at the Naval Research Laboratory in Washington DC, and he got money out of the Navy as a follow-on to this study, and he studied brittle fracture mostly of submarine steels. This was the days of Admiral Rickover and others. And anyway he uh he worked there. Another person was Professor Cohen in this department, who later became an Institute Professor. But Professor Cohen and a number of other people started studying brittle fracture, um, and those are the three key places. The most scientific study was done here at MIT. Uh, the British Welding Institute did a fairly scientific study, the Naval Research Laboratory did a more practical study. Uh, but that's where we really learned about brittle fracture.

And what they learned from the Navy report is, if a steel — if you basically took what they called a Charpy bar — and the Charpy bars have been invented in like 1905 in France, it's just a little one square centimeter bar. Should have brought one with me. Uh, it's 1 cm square, 10 cm long, has a 2 mm notch in it, and you whack it with a big calibrated hammer and you see how much energy it absorbs. So I told you toughness is measured in — it is a measure of the energy of fracture. If something's brittle, it doesn't take much energy. If something's ductile, it bends. You can do it with plastics, you can do it with steel.

This is polyethylene. I can bend polyethylene and it will not break. This is polymethyl methacrylate — it snaps. I knew there was no one over there, but anyway, you can look at the surface of these things. This is one — smoky. Uh, oh, actually this one broke. The whole metal middle section broke off. It's over — it's on the floor down here. We had a double fracture, which is unusual. Ordinarily you have a single fracture and it unloads everything else. If you look on the fracture surface here, you'll see a little shear lip — at least on one of the brittle fractures you should see a shear lip. Not very big for a shear lip Sunday. Um, now there's a little one on here, little 45° slant, which was the compression side of the fracture. Uh, there was enough stored energy in that — even though once one of them broke, the other one was close enough to breaking. We still run into brittle fracture today, okay, in all kinds of structures.

Um, see, I'll do this one. Um, well, I won't do this one yet. Uh, this was one I had a few years ago. Um, when they started making a lot of ethanol about 10 or 15 years ago to put into um — that one — to put into uh gasoline, you know, the 10% ethanol and gasoline, and using most of our corn crop to do that. Um, and you can talk about the politics of whether that made any sense. It turns out to make the um corn syrup, to make the ethanol, you have to separate — you have to crunch up all the corn stalks and corn and stuff, and then you end up having to separate the liquid from the solid. And to do that they do this in a big centrifuge. And the centrifuge is just a big spinning disc. It's about a three-ton disc of stainless steel, and it's got some holes in it. So as it spins, you put the uh silage inside this thing, and it's a wet silage, and you're trying to get the corn sugar liquid out of this thing so you can turn it into methanol [ethanol] to make a substitute for gasoline. And has holes in it, so you spin it around. And this thing is about uh — let's see, about 4 feet in diameter, weighs 3 tons, cross-section about like 10 by 15 inches or so. Spinning it, as I remember, was over a thousand RPM. And one of these things let go in China, okay. It had been made in Pennsylvania, had been cast in Pennsylvania out of a duplex stainless steel.

This is a piece of the fracture surface. If you look on the edge of this thing as I pass it around, you'll see a little bit of ductility — it started to stretch — but then you see the rest of this is just a terrible brittle fracture, because they didn't heat treat the steel properly. And they had one of them let go in France, almost killed somebody but didn't, and then they killed someone in China. Um, and anyway, so we had to figure out — well, I didn't have to figure out why it happened. Anybody knew why it happened once you look at how brittle the fracture surface was. Uh, and you had that much energy, and a spinning uh 3 tons at 1,000 RPM is a lot of momentum, angular momentum. Um, uh, but we had 700 of these around the world, and the question was, how do you inspect them? And turns out the critical flaw size for that was no more than 2 millimeters in size. If you measure the toughness of that improperly heat-treated steel, and you calculate what size flaw — just like a small flaw in glass will cause you to lose all your strength — in this case a 2 mm — less than 2 mm flaw in one of these drilled holes. And so you had fatigue cracks that would form at drilled holes because of a stress concentration from a hole. And you had to inspect this thing — it was about 10 inches deep. It's only a quarter-inch hole, but it was about 10 inches deep. How do you get in there to inspect it? Is that — do you just quit making ethanol and people quit driving their cars or whatever? Um, but we still have problems with brittle fracture.

Um, now it turns out Pellini, the guy at the Naval Research Laboratory, developed something called ratio analysis diagrams for steel, titanium, and aluminum. And I'll show you one of these. This comes out of the ASM handbook on fatigue and fracture, uh um, and — oops, yeah, here it is. By the way, before I show you — there's the ratio analysis diagram. Before I show you that ratio analysis diagram, let me show you some of the specimens.

If you go back to a book by a guy — a couple guys at US Steel back from the 1960s — when they started doing fracture toughness specimens, I passed around that little piece of granite, that's the uh fracture toughness specimen. These are fracture toughness specimens. They're called compact tension specimens, and there's the holes that you grab the thing in a great big machine. Here's a little one that's actually probably larger than my granite one. And you get bigger and bigger, until here's one sitting on a couple of 4x4s here in the lab. This one weighs tons, okay. Turns out you need to know how thick your steel is in order to measure the fracture toughness of the steel, and we'll go over some of that in a little bit here.

But Pellini basically — he was taking a very practical approach. He was working for the US Navy, and he wanted to know what kind of steels the properties of the steels were, because they were going to build nuclear submarines back in the 1950s. And he came up with something he called the dynamic tear energy, which is similar to a great big Charpy bar with a little notch in it that you hit with a hammer, versus the yield strength of the steel in KSI. And this is a ratio analysis diagram, RAD, for steels, okay, uh that he put together from lots of different things. Um, and this is the plastic region up here. Lots of toughness in low-strength steels. This 100 KSI tensile strength, you get up — and this is the plastic region where you're ductile. You get up here to very high strength, 300 KSI. Now this is the strength of aircraft landing gear, okay. You folks in Boeing — okay, this is where the landing gear are, 280, 300 KSI. It's what we call the plane strain region. And on this thing you can plot the size of the — if you take — reason you call it a ratio analysis, if you take this and bring it down underneath, K over sigma must be greater than square root of pi times C. So he's looking at the ratio of the toughness to the strength — energy of fracture to force of fracture — at the yield strength of the material. And from that he can calculate a critical flaw size. And this is the critical flaw size line right up here for 2 and 1/2 inches, okay. The critical flaw size is not a little 2 mm flaw, like that brittle piece of stainless steel I passed around. At this strength level, you need a 2 and 1/2 inch flaw to have the thing fail in a brittle manner at this strength level.

At a higher strength level, depending on whether your stress that you're applying is half of the yield stress or at the yield stress, a 10 mil flaw could cause the thing to fail in a brittle manner. So we're talking about aircraft landing gear, you got to inspect to 10 thou — 10 mils — for human hairs to make sure that thing is not going to fail in a brittle manner. And it's not a good day if it does fail in a brittle manner, okay.

So if you go through um, this is the what Pellini called the technological limit, okay, up here for steels. This is the toughest you could get steels. And they got them stronger and stronger, they lose their toughness at higher strength. This is the worst steel gets, okay, down here. All steels lie somewhere in between here. This is the plastic region, as Professor Parks who used to teach fracture in this department used to say, only the Navy can afford to design a submarine to be all plastic. Most of the structures we deal with are elastic-plastic, and we hopefully don't get too many structures that are plane strain toughness, because they're going to be like um the uh the glasses or the ceramics in terms of brittleness.

And here's a ratio analysis diagram that he did for aluminum alloys. And you have a similar type of technological limit. Your low-strength aluminums — but remember the steels went out to 300 KSI. The yield strength of the aluminums, a high-strength aluminum like an aircraft wing, is 70 to 80 KSI. Low-strength aluminum like beer can stock is up here in the plastic region — we have to form it. And so if you're talking about an aircraft wing, you could be talking about, depending on your stress level, you could be again be talking about flaws a millimeter in size that you have to find before the wing would just crack, okay.

And uh, off — and there's a similar plot, because the Navy at one time was interested in titanium submarines, which they're no longer interested in. Uh, the Soviets built one, or actually built several. Anyway, here's titanium alloys ratio analysis diagram. Doesn't go out to 300, it goes out to 170. Um, and it has the same general plot — plastic region, elastic-plastic, plane strain. And again in the plane strain region, you're talking about millimeter, half millimeter flaws that could cause the whole thing to fail. So you can go to very high-strength metals, but they're sort of starting to act a little bit more like ceramics, so far as that goes, okay. So you're giving up something in terms of the ratio analysis diagram.

It turns out — I've never seen anyone else do this — I plotted all these different materials on one graph once, okay. And um, some people probably think there's something wrong with doing this. Fracture toughness versus yield strength — the steels are up here, titanium here, aluminum's here, composites are here, um, plastics are down here. And ceramics — where are ceramics? Well, ceramics have tremendous strength, but lousy toughness. And so ceramics can go out to very high strength, but toughness is where flaws a thousandths of an inch in diameter can destroy a ceramic, okay. And the thing is, you can't inspect things down less than a millimeter in size in general. And so you have no way of knowing whether your structure is going to be catastrophically fail on you — you just have to hope that it won't, and a lot of people aren't willing to risk their life on hope, okay.

So any questions on why fracture toughness is important? So I'll now give you an example, a practical example. A guy who's a graduate of mechanical engineering here at MIT brought this to me. He works for uh Navtec. Now Navtec is a company that makes high-end marine hardware for like America's Cup yachts, okay. And it turns out, this was a cylinder of aluminum, high-strength aluminum, that they had designed for an America's Cup yacht, and had 7500 PSI hydraulic fluid in it. And it's got a wall thickness of about 2 and 1/2 mm or so, okay. And I don't know if we can still see it, this thing's getting a little old, but you have to be able to read a fracture surface. But the fracture didn't go all the way through. The initial fatigue crack — this thing did fail in fatigue, and if you can read a fracture surface, you'll see kind of lines radiating that way, some other lines running this way. The initial fatigue cracks there at the origin, and it ran about 2/3 of the way through before the thing blew up. And if you're standing right next to one of these things trying to raise the sails on your America's Cup yacht, and this thing blows up in your face, it's not a good day. At 7500 PSI hydraulic fluid, you can inject the oil right into your skin and your bloodstream, and it does all kinds of bad things when you start putting oil in your bloodstream. You end up with hands that die because they get no blood, okay, and stuff.

So he came in. It turns out on an America's Cup yacht, weight is so critical, weight is so critical, that they design things to fail periodically. If it doesn't fail periodically, you made it too strong, it's too heavy, okay. That's the design philosophy. Except you don't want it to fail unsafe, you want it to fail safe. Um, and so what they did — well, this was failing unsafe, I mean it was exploding. And so what they wanted was a leak before break, is what it's called in the literature. And a leak before break just means that if this is the wall of your fracture, you want the little fatigue crack to grow all the way through before it gets to critical size, so that you'll get a weeping leak, rather than an explosion and the whole thing shatter. It doesn't matter whether it's a little hydraulic thing like this or whether it's a great big pressure vessel — we want things to leak before break.

And so here's what he had. That piece of aluminum tubing was 7075 T6 heat treatment, so it's heat treated to the T6 condition. And turns out, if you look in the literature, the yield strength of that material is 73 KSI. Uh, the toughness, the fracture toughness, is 26 KSI square root of inch. And the wall was an eighth of an inch thick, 3 mm.

So this guy calls me up, and he was all concerned, it was a big rush. So I said, "Well, you can come by Saturday morning." So he came by my house Saturday morning, he brings me that, and he says, "We had one of these fail during training, and uh we can't have that. We need — we don't want to make things heavier." And he explained to me the philosophy in America's Cup hardware is, if you make it — if it doesn't fail periodically, you made it too heavy, okay. But you want it to fail safe. So I said, "Well what you need is leak before break. And the problem is you're going for maximum strength by giving it the T6 heat treatment. T6 heat treatment aluminum optimizes the strength. What you want is — you wanted the T73 heat treatment." And the T73 heat treatment basically overages, and you lose some of your strength, but you gain toughness. And so this drops to 63 KSI, and this is 30 KSI, and the critical flaw size for this is 4 mm. You drop strength, but you increase toughness. And now the T73 would be a leak before break, and it would fail safe by just a weak leak, as opposed to blowing up in someone's hand, okay. Fairly simple heat treatment change, well-known uh heat treatment improvement in toughness, loss of strength, but great improvement in safety.

And so he said, "Oh thanks, how can I help you, how can I pay you for this?" And I said, "Let me have the sample." And so that's what I got paid, by having the sample. Unfortunately, you could see the fracture when it was brand new, but that was probably 10 or 12 years ago, 15 years ago. And over time it's oxidized away and you don't see the contrast. But if you got it in a microscope, you would still be able to see it.

So design with structural materials is a balance between strength of fracture by force and strength of fracture by energy. And you need both. And it wasn't until the Liberty ships of World War II that we learned that you had to have toughness as well as strength. You couldn't just go for high strength. Uh, we use baseball bats now, okay, highest strength aluminum, up there around um 100 KSI strength, off the chart of the ratio analysis diagram that Pellini put together in the 1970s, okay. Today we got aluminum alloys, we can make them super strong, and we make them out of bats — make them into bats, which are very thin wall, and they typically will crack and they won't work very well as a bat before — and they don't shatter in someone's hands, but they uh — but they cost you another $300 to buy a new bat. And the bat companies think that's fantastic, okay. They last for — I mean, they could make these things that would last for one or two hits, okay. But people would really get upset if it failed after one or two hits. But doesn't matter, they still make them so it only takes 100, 150 hits before um you'll start developing cracks and have to buy a new bat, and they think that's fantastic, okay.

Um, but that's just difference in philosophy. Um, and it also proves what I said before — people in sports will pay anything to get the competition over their — other people in sports. Usually it's golfers, but in this case it's parents who want Johnny or Susie to hit a home run and beat the — so not so that Johnny or Susie can rub their friends' noses in it, but so the parents can rub the other parents' noses in it, right. I mean, it's just — it's sort of insane, okay, but that's what we do. Uh, we'll pay a lot of money for sports equipment, okay.

So that's it for today. I'll see you on Thursday, and we'll talk — um, I think we've covered most of the fracture mechanics stuff. I have lots of stories. I could teach a whole class on fracture mechanics, um, 12 lecture module. But uh, we'll start talking about steel and where it lies with regard to other things, at the outer limits of toughness and things like that, and that's why we use so much of it among the reasons. Okay, thanks.