SMS_F2014_08

Uh subject okay, like I said I don't want something on selection of materials in the automotive industry or something. That's a little broad, uh, and covers something that you couldn't cover in a few minutes. Um, someone could say well why do we use stainless steel for surgical instruments, we've been doing it for a hundred years, and are there better materials. I mean that's a question that could be dealt with, so far as that goes.

You could take a question like, what, why did it take so long to introduce composites to aircraft structures. I mean we've been making, we made aluminum airplanes from the 1940s all the way still today, but we really didn't make an all composite aircraft until the 1990s. We put composites in aircraft but we didn't make it all composite aircraft, and that was the V-22 Osprey. And the only reason we did that was because it would never fly — that design would never fly unless they had the lightweight of composites. But you don't have to, you know, keep the topic very narrow and focused and you'll do a better job.

And you also, as I said, you pick any topic you want. You could talk about, you know, what your high school flagpole was made out of at your high school, okay, I don't care. I mean there's competition among materials for flagpoles, okay: fiberglass, aluminum, steel, okay, whatever you want. Um, but keep it simple, it's only supposed to be ten minutes. Means ten overheads max. If you try to do more you can but I'm still going to cut you off at twelve minutes, because we have to have some time to discuss things. So anybody have any questions?

The schedule is such that Dr. Belmar will do tomorrow. I'll be doing Monday Wednesday and Thursday of next week. Uh Tuesday there's no class because both he and I are out of town. He'll do Friday of next week. We'll see how coherent I am on Wednesday because I'm coming back on the red eye from California, okay, plane gets in at 5:45 in the morning, ought to be able to be here by nine to lecture. And if we keep that up we hopefully can finish by October 10th of the twenty-four live lectures. That depends on his schedule. The next week I would only have to cover one that next week. That doesn't mean that I won't give some, if he's not able to do the other four that I wouldn't give some guest lectures, but then so we might spill into the week of October 14th.

After that, since we have so many students in the class and so many presentations, I'd like to start some of the presentations. So Jerry's out today, my assistant, but we'll be passing around the thing and ask, how many of you are ready to give presentations. It's going to take like three weeks to go through all the presentations if we just do three a day. Then comes the question, I'm happy to start at 8:30. No one else is in this classroom at 8:30. But I don't want to — and I know some students would come at 8:30, I've done this before so we get four in a day. But I don't want to do it if it's just one student and me at 8:30, I would hope that some other students would show up. You don't have to come to every presentation, I have to be at every presentation. I actually learn a lot from the presentations, I think they're interesting, because it's something the students are interested in when they do it.

So in any case, how many people, can I have a show of hands, would consider coming at 8:30 if we actually tried to get four in a day? Okay great, okay there's enough people that — I appreciate your support for that and it also cuts down the number of days, because believe me, once daylight savings time ends and it starts getting a little dark when you have to come in, you'd much rather stay in bed, okay. I mean I know, I've seen it here every year, so far as that goes. Okay, any questions?

Yeah, what's the contribution of high speed steel? It typically has molybdenum or tungsten, okay. Uh what is high speed steel, not everybody knows what high speed steel is. High speed steel was invented — actually, there were two things that made Bethlehem Steel the world's second largest steel company. Andrew Carnegie started a firm called U.S. Steel, and he had a guy working for him, Charles Schwab, who was sort of the operations [head] of U.S. Steel. Charles Schwab decided to go to Bethlehem Pennsylvania and found this little iron foundry in Bethlehem Pennsylvania and started it. And there were two — this is around 1900 — so he broke away from Andrew Carnegie, and they learned to do two things at Bethlehem Steel that allowed them to grow rapidly.

One is they invented high speed steel. They found if you put molybdenum in the steel you can get very good high temperature properties, okay. Like at the thousand degrees C — 1000 C, no, uh, about seven or eight hundred C — the steel would not just soften, it would actually get, in fact if you plot it, can actually get a little bit harder. You start getting some precipitation of molybdenum carbides that would actually precipitation harden the steel at high temperatures, and so you could make drill bits, hard drill bits, and you could run those drills faster and get more productivity. So they later learned that tungsten did the same thing. We do all kinds of things now, but molybdenum is still one of the key ingredients to most high speed steels.

So that was one thing. The other thing that Bethlehem Steel learned to do is they learned to roll I-beams, okay. Before that if you wanted an I-beam you took a piece of angle iron and a piece of flat stock and you riveted this stuff together. And if you go look at buildings or bridges, mostly railroad bridges that are still around, but they were built before 1900, you'll see that they don't have rolled I-beams, they have riveted I-beams, which is very expensive way to do it. Some people say that New York City never could have become a city of skyscrapers if Bethlehem Steel hadn't learned to make rolled I-beams. It wasn't economical to build high-rise buildings.

Of course there was one other thing that made high-rise buildings possible. Anybody want to venture a guess? I mean this is just a wild guess, I wouldn't expect you to know. Otis Elevator. Who wants to walk up fifty stories every day? You certainly don't go out for lunch, you bring your lunch, okay. But Otis Elevator — the ability of Otis Elevator uh to get people up and down buildings. But it turns out you can build brick and stone buildings more than ten stories tall, but you have a lot of wasted space because the walls have to get really thick at the base in order to support the load up above. Um, so it really was a strength — the ability of rolled steel beams that allowed the production of skyscrapers. And they were still riveted together, they didn't weld them until the 1940s. Uh you wouldn't weld a critical structure until the 1940s. In fact they started welding ships in the 1940s and look what happened, they all started cracking. And we'll go over a little bit today. So hopefully that answer the questions, okay.

Yes. When they cast — well, first of all, back in the old days they would cast in small ingots, okay. And so the segregation wasn't, I mean if you're casting a typical ingot in the 1970s, could be four feet by two and a half feet in cross section, same size as an aluminum ingot today, okay. But in steel it weighs two and a half times as much, it might be twenty tons, okay. So if you melt 200 tons of steel you make ten ingots. Today you continuous cast the whole thing and you might make something that's ten inches thick by five feet wide or something to bend, or it could be ten inches square, okay, if you're making bar stock.

But in any case, uh, what was the question again? Oh how you prevent the segregation. So they made smaller ingots, they might have been making ingots back a hundred years ago that were ten inches square ingots. Today we make bigger ones, and how do they get rid of it. Well they started doing re-melting, okay. In the 1950s the Soviets did a lot of re-melting technology during World War II at the Paton [Patton?] Institute in Kiev, and it got picked up after the war. And they would either do vacuum arc remelting or electroslag remelting. The Soviets were electroslag folks, the United States we started doing vacuum arc remelting. So you cast an ingot, it's got all the segregation in it from solidification, the elements go in different places, and then you would take that and you'd put it in a furnace with an electric arc and you re-melt it.

And if you do it in the vacuum arc remelting — right now all the turbine disks, not just in steel but nickel based alloys, triple vacuum arc remelted to get homogeneity, get rid of all the gaseous impurities, oxygen nitrogen hydrogen, triple arc re-melted because that disk you're going to make is going to be a hundred thousand dollar disk, you can afford it. But you also need the quality because we have such demanding applications in terms of fatigue resistance and other things. So basically what we do today, yeah, we make sixteen inch diameter ingots for these special applications like aircraft landing gear and jet engine parts, but we triple vacuum arc re-melt. Well all of a sudden the cost is now getting to four or five thousand dollars a ton, okay, as opposed to a thousand or fifteen hundred dollars a ton. Okay, other questions?

Oh that just — that's, hey, that's what I was going to do actually. The significance, I — actually the first time I've ever put a newspaper on this thing, it actually improves the color rendition, okay. That's not the reason. But so I was traveling yesterday. The only time I ever read USA Today is when I'm traveling because I have time to sit there and eat breakfast. I mean like if I'm here I'm working. Anyway, uh, so here's an article: "Danger under our streets." And it's about cast iron and steel gas pipes corroding for the last hundred years. I told you first before it was in USA Today, right, on Monday, fortunately, okay.

But so there's an article in here and it goes on. It's actually a full page article here, which is — for USA Today I mean they rarely do more than one column. And here they've got cast iron pipes in the 1870s, and bare steel pipes in the 1950s, and plastic pipes in the 1980s, and they talk about the government requiring coding [coating] of pipes. If you want to read about externalities there's all kinds of interesting externalities. They're basically — and down here in Alabama, "a judge allows news on pipelines to flow." Well, that's an editor trying to make a catchy uh headline. But basically Gannett newspapers, which owns USA Today, own some little paper in Birmingham or something, and they want to publish how bad things are in different parts of the country.

Uh there's 80,000 miles of cast iron pipe, or 40,000, I remember the numbers are in here. And they have a significant number of failures, and they say oh people are dying each year. Well it's true, but given the fact we're at 80,000 miles it's not that bad. We have steel pipelines, you know, big — the big steel transmission pipes that come up from Texas are now all over the country. They're going to come down — Keystone, it's going to catch an oil pipeline that's gonna come down from Alberta and the tar sands, and so you hear about these pipelines. We have more pipelines than most of the rest of the world combined, okay. Maybe not, we're not half the world's pipelines, but we're probably thirty or forty percent of the world's pipelines. And that's a tremendous asset for this country to be able to transport things.

But the National Transport — this article talks about the National Transportation Safety Board has been beating up on the utilities to replace these things. The estimated cost, I think just for Con Edison, was going to be ten billion dollars, okay, to replace all of them. So you got this balancing factor, and it's a risk benefit analysis. You can't just shut the pipelines down, because guess what, you're all going to be shivering in the winter, okay, you won't have any electricity. That's how we transport energy in this country and that's why we can get energy at — well it's still expensive but at a reasonable cost.

I may, um, it's got all kinds of externalities. You got these uh public interest groups who are trying to force the utilities to do it. You could force the utilities to replace all this stuff in the next ten years but all of a sudden you find your electricity bills and your heating bills will double or triple overnight. You don't think there'd be an outcry on that, who's going to pay for it? Yes we got hundred-year-old pipelines, okay. Some people drive thirty-year-old cars that are hunks of junk right, but they do it because they can't afford a new one.

And there's always the public utilities commissions. Whenever there's an explosion in Massachusetts, the Massachusetts Department of Public Utilities goes in there. They have the authority to confiscate all the physical evidence, send it out, they usually send it to Mass Materials Research, which is this materials test lab out in Worcester. And they see this as a blank check because they make the utility pay the bill, but Mass Materials is doing the work for the state officials. State doesn't have the money to do it, but the law says they can require a report from the uh from the utility, whether it's NSTAR or it used to be Boston Gas or whoever it is.

Same thing on a federal level when they have a big gas pipeline. I had an explosion in Mississippi a few years ago when they actually when they were building it. Anything happens like that happens, the utility has to give a report to the — it's now part of the Transportation or TSA. What's TSA? Transportation Security Administration. Anyway used to be part of the Department of Commerce or Energy but it's pipeline — PHMSA. Pi-pipeline Health Safety Administration, and I can't remember what it is. But there's an organization, federal organization in Atlanta, and they get a report, and these reports cost hundreds of thousands of dollars, because the government has an interest to make sure it doesn't happen again. Just like OSHA is there to make sure there's another industrial accident, someone gets hurt, they go in and they will find people. They don't really care about what caused it so much, they just want to find the company.

And it's sort of interesting to see, you get involved in these things to see that, you know, the state regulators are just itching to give the biggest fine they can to the utility when something goes wrong. But then on the other hand the utilities are going around monitoring things, I talked about monitoring in my neighborhood and you know they stick things in the ground. They report that Pensacola Florida cannot account for four and a half percent of all the gas they buy. It just leaks out into the ground. And that's a typical value not just for gas pipelines, for water pipelines. I think Boston, the city of Boston, ten percent of the water they pump in from the mains, you know in western Massachusetts, never gets distributed or billed to homes or businesses, because it just leaks out through all the leaks in the pipeline, okay. So if you could fix it, you get four and a half, five, ten percent more profit right? If you could fix it at a reasonable cost.

It's an interesting balancing act. We put in infrastructure that had a lifetime of thirty or forty years and we've been using it for the last hundred years. It's sort of beyond its original lifetime, and it can cost — in the city of Boston cost a million dollars a mile to replace that pipeline because there's lots of other things around, okay. So um, if you're a civil engineer, for thirty or forty years the civil engineers are saying we have a ten trillion dollar deficit in repairing the infrastructure: all the highway bridges, the pipelines, the electrical utilities, and everything. They're all getting old, okay.

Well there's all kinds of inspection techniques that they have, and it depends on the type of pipeline. You know if it's the little two-inch diameter pipe that comes down the center of my street, which is the distribution pipe, and there's three-quarter inch pipe that comes off that to every house. Well right now I've got a plastic sleeve in my three-quarter inch pipe that was laid in like 1930-something, okay, because it started leaking. And they come by every year, they have to come by, and they put these little probes in the ground to sniff for methane in the ground. It's not supposed to be methane in the ground but if there is, it's sort of a hint there might be a leak near there.

So when they did this fifteen years ago at my house and another house about four houses down, they found methane in the soil, you know a foot and a half deep. They said ah-ha. So they go and they sleeve it, so I don't have a three-quarter inch pipeline coming in. I have about a three-eighths, or probably more than 5/16, probably 7/16. You know it's basically — it's fairly inexpensive, well it's not cheap, they have to go in and get in there and then they just put a plastic sleeve in, okay. And the plastic sleeve will, as far as we know, probably last 500 years, okay, so far as that goes. So they monitor it and they are replacing these things, okay. And when they replace them they're replacing them with plastic pipe, so — and the plastic pipe will last longer.

The problem is people still going to come along with the backhoe and dig it up, and then all of a sudden you have a catastrophic flow which can be explosive. Most of the explosions are not due to slow leaks, they're due to some big break. And that's what this article says — oh the cast iron pipes are a problem. Why? Cast iron pipes are brittle, all of a sudden they get catastrophic breaks and you release huge amounts of gas. I had a — no it wasn't uh cast iron, but I had one in New Jersey in Edison New Jersey fifteen, twenty years ago. And it was due to a backhoe that had scratched this pipeline. About — well the question was, was it ten years before or twenty years before, okay. And the backhoe had damaged the pipe about a quarter of an inch deep, and just the pressure cycles had caused the fatigue crack. When it finally got to critical flaw size and it goes completely, they had a 600 foot flame in the air at eleven o'clock one night.

And the people in the apartment — when they put this pipeline in it was only cows next door, okay, but now they had a big apartment building, and just the radiant heat from the fire melted the roof of the apartment building. They had to evacuate the apartment and people weren't happy about seeing a 600-foot flame in their front yard, okay. But well actually Johnny had a question, but my favorite part of that story is — well, what did they do? Every week they had a plane, a little, you know, Cessna or something, fly the route of the pipeline to look to see if any construction was going on. And this is one of the things they do, every week they would have someone, plug, and make sure that if they hadn't called Dig Safe, they caught those people, said you're not supposed to be digging on top of our pipeline without letting us know. And they will come out — I mean you call the gas company and you tell them you're about to dig, they will have someone there in fifteen minutes to make sure you don't damage their pipeline, okay.

So there's a lot of things they do, they don't want an explosion. They get a lot of grief from the regulators and everybody else, and it's not good for selling gas when you're blowing up homes, okay. They don't blow up that many homes, okay. There's a risk benefit, okay. Risk is frequency times consequences, okay. Well if you got a gas pipe, you have a water leak the consequences aren't that bad usually. You have a gas leak the consequences could be worse, okay. But they probably have just as many leaks in water lines as they do in gas lines, because they corrode the same, okay.

But my favorite story on the gas pipeline, it was in an asphalt plant. And if you know anything about New Jersey or Connecticut and maybe Massachusetts too, some of these types of businesses are sort of run by the mafia, okay. And it turns out, everybody swore that no one had been doing any construction in that area since 1984. This is like 1995. And all the records, and the plane had flown over — well the plane may have flown over, but they had big heavy earth-moving equipment, and they had little settling ponds for the asphalt production and stuff, and those ponds would move from time to time. So someone could have been digging underneath these ponds, you know, six inches deep, foot deep. They could have been digging there on one day when the plane didn't come by, okay.

The asphalt company and all the people that owned it swore no one had done any construction there since 1984, except when they excavated part of the hole after the explosion they found a completely buried 1988 Ford Bronco. So how did that get there if no one had ever dug a hole there, okay. Well I guess, you know, someone had just parked their Ford Bronco there in 1980 — their '88 Ford Bronco there in 1983. Anyway. And everyone says, "was Jimmy Hoffa in it?" That's the question I usually get. But in any case, so people don't always tell the truth on these things. So okay Johnny, you had a question?

Uh, if it occurs when the guy is doing the backhoe yeah you get the spark. Then this was a fatigue crack. And when you got gas coming out at 900 psi on a 42 inch diameter pipe, it'll find its own gas source. Could be 50 yards away, could be 450 yards away as it spreads out. I got a nice video of a tank, it's actually a production facility, a storage facility out in Wyoming, and we can see the release. This was liquefied, you know, natural gas, and you can see the release on the surveillance video. And you can see this white cloud of cryogenic you know liquid and gas, it just spreads out and you can see it go off the screen. And it's about four or five seconds later you can see the flame rushing back, okay, because it went off for about uh half — you know, 500 yards away until it found its own ignition source, and the flame comes right back to the source. Surprise surprise, okay.

So there's usually a source around, so finding an ignition source is not a hard thing for a big release. Again, a catastrophic release of gas. Yeah, okay other questions? Okay, so enough on that.

Let's get back to, before a couple days ago, there's competition among materials. Last time I talked about there are limits, physical limits, to the material properties, all based on the chemical bond strength when we're talking about mechanical properties. And we talked about modulus versus relative cost of a material. I got to get these things outside, out of these plastic sleeves. But in fact some ceramics and diamond have some of the highest moduluses, and that's around 60 million for all practical purposes. Turns out diamond is the best but you can't usually go buy bars of diamond to make structural parts out of. In any case about 60 million. Steel is about half of that. Aluminum's about 1/6 of 60 million, it's about 10 million. Titanium is about one third.

There's only so much modulus you can get. And I mentioned, what were the two ways of getting more stiffness in a part? I mean here's my medical instrument scissors, long handles you know to reach in there uh through all the blood and guts to snip something off. They're long slender — can't make them too slender or the thing will just bend, right? Well if you want, and you need something lightweight, you can make it into a tube. You can get modulus by material choice, which is strength of the chemical bond, or you can get geometric modulus by just making tubes or rods, hollow rods and things like that. So you only have two ways to influence the modulus, that's the material and the geometry.

Now we have other things like strength that we have to worry about. And both strength and modulus are related to the strength of the chemical bond, okay. If we put up the Lennard-Jones type potential, and we have the curvature here is down here — second derivative, energy with respect to distance, is the modulus. The first derivative is the force, second derivative is the slope of the force, which is the modulus, Young's modulus. The strength of the bond, the depth of this, is going to be on the order for primary bonds on the order of two or three electron volts, and it just doesn't get any stronger than two or three electron volts. That's what nature has given us.

Now it turns out if you calculate what that should be for a strength, it turns out three electron volts should be about three million psi strength. But we don't have a lot of materials that exhibit 3 million psi strength.

Yes. [Student asks about an aluminum alloy, possibly the casing of a laptop.] I'm sure it's, 5.005? Well that's better than I would have known, okay. 5.005, 5000 aluminum magnesium alloy, not heat treated, okay. Probably about 25 ksi yield right? Now that order. Right, there's an aluminum, from Novellus Aluminum. But you can get higher strength but they run into corrosion problems. I'm sure they use 5005 because it's easy to machine, reasonable strength. They're not worried about stiffness there if that's what you're thinking of. Well, impact resistance and scratch resistance and things. It's also anodized, I'm sure right. They want to look pretty, yeah okay. So they got to have a good anodized finish, okay, as far as that goes, and you got to be able to laser engrave my name on the back right. Anyway if you order it from Apple it's free engraving, done in China. Other questions?

Okay so let's talk about strength. You're limited in strength to about 3 million psi, and you get that by — if you take the welding course when I talk about surface energies and things like that — you just have to essentially take the force-distance relationship from this, that you get by differentiating this, and just integrate it back, F dot dr, and figure out how much energy there is when you pull apart two surfaces. And if there is no movement of the atoms, if you have a brittle material, no dislocations and movement of those atoms by other mechanisms, then it will take three million psi. And we prove that, okay. You can do the calculation.

Uh the calculation was done back in the 1920s when he first came up with these potentials. People — counting physicists — calculate, they said oh material should be 3 million psi. People said you're wrong, we never measured any material 3 million psi. By the 1950s they've made iron whiskers with a screw dislocation right up the center, and pull that in tension. There's no force on the screw dislocation, and so it's like a single crystal even though it's got a screw — that is sort of, but in the wrong direction to the stress — and they got 2.8 million psi on those iron whiskers.

You take sapphire fibers, over 2 million psi. And so NASA in the 1980s was having people here at MIT and other places grow sapphire fibers, they were going to incorporate that into structure. Well, that's fine, sapphire fiber is worth working with. Okay. The glass fiber in fiberglass is about a half million psi strength, okay. Problem is — okay we're going to get to that.

But if we want to look at strength versus relative cost, here your ceramics up here are your engineering alloys, which can be your composites, it can be your steels. This is the Ashby type plot. And here are some guidelines with different slopes, where you look at this is strength versus relative cost. And it's strength over density, and there's some relative cost gives you some function. And whether it's strength to the first power, half power, or third power depends on whether you're dealing with a plate, a beam, or a particle, like — I think you'll have to go back to Ashby — but it comes out of mechanics of the materials. You get a slightly different slope. Well really he's got this band here which is sort of where most of your engineering alloys are, okay. This is kind of wide band here. We tend not to use these unless they're in fiber form or something — these fancy ceramics. But of your really high strength engineering alloys they're mostly down along this band. Porous ceramics and things like that, you can get relatively high strength with relatively low cost. We're talking brick, okay, and stone and things like that, okay.

Um, but, and from the 18-50s or 80s until the 1950s, that's what all the mechanical and civil engineers, design materials engineers, designed to: strength. And then came along World War II and the Liberty Ships. And I've already shown you some of the Liberty Ships and how they broke in two. But I don't know that I showed you the number that broke in two, okay, or not just broken in two, had major failures, okay.

So uh, 4,700 welded steel merchant vessels were built. 970 of these suffered casualties involving fractures. 24 vessels sustained a complete fracture of the strength deck. One vessel sustained the complete fracture of the bottom. Eight vessels were lost, four broken in two. Well the U-boats got more of our ships than the shipyards did, but some of the shipyards, you know, in the brittle fracture got the rest of them.

So after World War II there were three places that decided they needed to study brittle fracture of steel. One was — there was a guy uh Richard Weck, who later became Sir Richard Weck, and he was a student, a postdoc or something at University of Cambridge. And he was peddling his bicycle around Abingdon in the countryside, and he decided this is where he wanted the British government to build him a welding institute to study welding and fracture, okay. And they did. And today Welding Institute in Britain is one of the premier institutes for studying fracture mechanics and particularly welded structures, but anything else. They get most of the money out of oil companies, okay, who have you know billion dollar rigs, and they don't want them to break. Because if they do, look what happened to BP, okay, cost them 25% of their net assets right? Uh, it'll never — well I don't know if they'll never be, but they're not the company they once were, okay. Because of a major failure which they didn't want to occur.

And we're not going to get into all the reasons why it did occur because I don't know. I was hired on that but I was unfortunately hired by the people who had one third of the liability along with BP. And BP indemnified them, so we never had to do any work because BP just covered the cost. Anyway. So Richard Weck started the British Welding Institute, and a guy Alan Wells came up — was one of his underlings. Alan Wells became director general of the British Welding Institute after Richard Weck, and when I came up for tenure Alan Wells wrote a letter for my tenure, okay. But Allen Wells in the 50s came up with the crack tip opening displacement technique of measuring the toughness of steels. He was a real gentleman. Richard Weck was a jerk, okay, but Alan Wells was a British gentleman.

Then there was another place. A guy named Bill Pellini of the Naval Research Lab in Washington. And later when Pellini retired from the Navy — Naval Research Lab — he came to a place called MIT in the Ocean Engineering Department, now known as Mechanical Engineering, okay. And Pellini wrote books, and I'll show you some of the things that he developed for the Navy to figure out how to build nuclear submarines without having them fall apart like the merchant ships did during the war.

And then the other place was a place called MIT, and here in the materials department. And Morris Cohen and Ben Averbach — Ben Averbach was my first materials professor, that lasted for two weeks or two recitations where I got out of that class. Uh he was terrible. He didn't know — this was 3.091. He couldn't handle the first day of 3.091, but anyway. But they did a lot of — those are the three places where really after World War II they came to understand toughness of materials. Not that we didn't know about toughness — had been explained by a British scientist A.A. Griffith back in the 1920s. And he was studying the fracture of glass, and he came up with a criteria, which is that there is a property of the material called — which we now call toughness, or fracture toughness — and it's going to be proportional to the stress applied times the square root of pi times the crack length, okay.

And I didn't bring — there are whole books this thick now with all the mathematical formula for different geometries of cracks in tubes and cracks in plates and cracks on the edge, cracks in the center, you know. It's called the Fracture Analysis of Cracks Handbook. I'm sure you all want to get your own copy. I have one.

Yes. [Student asks about historical context, perhaps about cutting tools.] Well they knew the cutting tools broke but they just replace it with another one. One of the reasons cutting tools have improved over the last thirty or forty years, actually from the 1950s to the 1980s, a lot of it was improvement in fracture mechanics, okay. But fracture mechanics — NASA used fracture mechanics on some of the 1960s missiles. They had some major failures. Rocket motor cases, very high strength steel, very thin wall, and they loaded them up with things and they just broke to smithereens, like shattered glass. And so there's big studies about that NASA did.

When I didn't know it, but when I was growing up and I was seven or eight years old, my best friend who was from Norway — and it turns out his father was working for Lockheed Martin — was Martin Marietta at the time, wasn't Lockheed Martin — in Marietta Georgia. And his father had been brought over from Norway because he was one of the world's experts in probabilistic fracture mechanics. I didn't learn that until about fifteen years ago. It was sort of hush and super secret, not that me as an eight year old would know anything about it, but nonetheless. Fracture mechanics in the 1950s and 60s was still a laboratory thing. By the 70s and 80s people were starting to apply it to other things.

The civil engineers never learned about it until 1994 and we had an earthquake in southern California called the Northridge earthquake. Twenty billion dollars worth of damage. They had never put into their codes and standards a seismic — real seismic requirements in California. You didn't have good seismic requirements for the buildings vibrating. Well the buildings vibrated in the earthquake and a lot of the steel connections snapped. And that's one of the reasons it was a twenty billion dollar loss. So now the civil engineers have redone all those codes and standards in the last ten or fifteen years, and our design has gotten to be much more sophisticated, okay.

But it takes about thirty or forty years for a scientific knowledge to actually make it into practice, okay. People don't do it — and just add cost — until usually they're faced with some serious catastrophic failure, okay. And the Navy had it first with the Liberty ships. Then the civil engineers had it with the Northridge earthquake, okay. NASA had it in 1960 with some of the rocket motor cases, which were high strength steel. So different industries kind of saw it at different times.

The plastics industry has had it several times because plastics can be very brittle or they can be very tough. And they put in some plastics that were not so tough and they had some major failures. They had billion dollar class action lawsuits to replace some of these things. So every industry just waits for its own failure to start correcting things. That's sort of the way it is. Other questions?

So anyway if we look at fracture toughness versus strength — and I think I handed this out to you before, several, a couple of weeks ago. It turns out, if you take this formula you can recast it as K squared over sigma squared, or you can put it pi sigma squared is equal to a, the crack length. That's actually if you're talking about an edge crack like this in a specimen. That is a — if you're talking about a crack in the center of a specimen like this, that's 2a, the length is a plus a, 2a total across there, okay. I say there's a big thick black book with gold lettering called Fracture Analysis of Cracks Handbook, wonderful book. You want to get to sleep, that's a good thing, anyway.

So toughness has a number of values here. We see the K squared over sigma, K squared over sigma. These are different lines, different guidelines for safe design. Up here it says yield before fracture, down here it says fracture before yield. These are brittle materials, these are ductile materials. These are the ones that only give you about 300 ksi strength, these are the ones that might give you 3 million ksi strength. But these — the critical flaw size, if you go through and calculate this formula which Griffith gave us in 1925, you calculate and find out for typical toughnesses here of a hundred mega pascals meters to the one-half — interesting units but nonetheless it comes out of this, it's the only way you can cancel units on both sides of that equation. You find that steels might have a hundred root meter. Steels are near the top of this in terms of toughness, they're not the highest strength. Ceramics are the highest strength. Even glasses are stronger than steel. I told you fiberglass has got glass fibers of a half million psi. There's no — well there are some steels half million, but most steel's the highest strength is about 250 or 300.

So glasses and pottery and brick can be stronger than steel in terms of hardness value. So there are stronger materials, but they're down a factor of ten. And so the critical flaw size in the steel, a really tough steel, the critical flaw size can be a hundred millimeters, four inches. What do we mean by critical flaw size? I don't think I've done — I've torn a piece of yellow paper, oh I've done it for you in other classes. I did in this class? Oh, well okay. I like to do it, okay. You can pull on it with pounds, you put a notch in it, takes ounces. You can lose a factor of ten in strength because you got notches in the material, except in steel. I got to put that notch in a good tough steel — I may have to put that notch in four inches deep.

So, to show you a picture, this is a guy used to be head of fracture at U.S. Steel, John Barsom's book. These are fracture toughness specimens of different sizes. When you get a really tough steel, you got to use something that's about three or four feet high and weighs tons, and a very big test machine. Here's a little small one, if you've got a steel it's not so tough. You have different sizes because you have to have — there's a criteria for your fracture toughness testing, this has to be wider, significantly wider, than the critical flaw size. This is a fracture toughness specimen made out of granite. I got this the first week I was here as an assistant professor, from Wendell Wilkenning who was finishing his doctoral thesis. Because Al Bakaven — who was actually one of the brighter faculty members I ever knew here, but he was sort of quirky in other ways — but well, everybody. Anyway, um, but Al Bakaven was curious about how the Egyptians were able to build the obelisk.

If you went through the fracture mechanics equations in the 1960s about how could you make this big long obelisk in the horizontal position and then you have to raise it up into something like the Washington Monument, right? Well, fracture mechanics would have told you, with the flaw sizes you have in granite, the thing should have broken under its own weight as you were trying to lift it to a vertical position. So how do they do this? Well it turns out they did it just like everybody thought they did, except what he found out in about mid-1970s — that's a three-phase material, got three different types of rock in there, and you actually form little cracks at the tip of that notch that toughen the material. So if you measure the fracture toughness of granite, because it's a composite material, it has about two or three times the toughness that you would predict from the toughness of silica, or the toughness of feldspar, or what's the other one — I can't remember, look it up in Wikipedia or whatever. There's three rocks in granite, okay.

And boy, in the 1980s the ceramics went to town. They were gonna start putting intentional little flaws in there so they get these microscopic cracks. The problem with forming microscopic cracks for toughness is what happens the second time you load it. Now it's full of microscopic cracks, okay, and they can't crack again, okay. So well it's only good for a shot. That was okay for the military and the ballistics and stuff, because hopefully you only get shot once. Uh if you get shot once and it's effective, then you will only get shot once. But anyway. Uh but the point is on some of these things, on glasses and stuff, what's the critical flaw size? 10 to the minus 3, 10 to the minus 4 millimeter. We're talking microns of critical flaw size.

Has anyone ever seen someone cut glass? How do they do it? Yeah, you take a silicon carbide tool or a hard steel tool, or a diamond tool is even best, and you take that glass and you can make a kind of an S shape like that score mark, and you just tap that glass on the edge of the table or something it'll break right there in the S shape. Because you just introduced a critical flaw size — you didn't have to put a very deep scratch in that material. That's the problem of ceramics, that's the Achilles heel of structural ceramics. They're brittle.

But let me tell you, were in the mid-1980s the whole world was talking about, oh ceramics don't corrode. Well that's a lie. They do corrode, they just don't corrode the same way as metals, okay. They get attacked by things too. And we're going to start building engines, automotive engines, and be able to operate at very high temperatures because ceramics have very high temperature capability much better than metals. And we're going to have a revolution and we have cars running a hundred miles a gallon because of high temperature ceramics and blah.

And I used to say this is ridiculous, this is absurd. I used to give talks, I said — I gave a talk down at NIST once — I said, you know, we will not have structural ceramics in critical applications because they don't have sufficient fracture toughness. After all, the only high volume materials we make — this is kind of the beginning of my starting to talk about these types of things, was thirty years ago — are Portland cement and toilet bowls. And I'd throw in the kitchen sink except you have to line it with cast iron to give it fracture resistance. Well cast iron has got lousy fracture toughness. Cast iron is down here at about ten, okay. Cast iron's — no I did find it there — actually if you look in the cast iron handbook it'll tell you it's eighteen, but who cares. Gray cast iron is about ten or eighteen mega pascal's root meter, which is better than ceramics, okay. It's a lot better than the ceramics down here, okay, or most of them over here. The best ceramics can almost meet cast iron but most of them are less, worse than cast iron.

So you make a kitchen sink, you know, and you didn't line it with cast iron and you drop a pot in the sink, shatters it, and got water all over your kitchen floor, okay. So ceramics have sort of a problem with structural materials. Not to say — you know the exception that proves the rule — we use more tons of ceramic Portland cement than we do of steel. We just have to do it in compression, okay, or we reinforce it with steel. We use reinforcing steel to take the tension loads, okay. But this type of plot tells you the critical flaw sizes. There's another plot that was generated by Pellini, called the ratio analysis diagram, and I'll show you the original ratio analysis diagram of Pellini.

[Student asks about cracks vs. grain boundaries.] Between using a crack length and perhaps like a grain boundary — do you, can you think of them the same way? Sometimes grain boundaries are the crack length, okay. You don't always have to have a physical geometric crack, sometimes you have a microstructural crack. In some materials the grain boundaries can be weak. But in ductile metals, the grain boundaries really don't cause problems, okay. In ceramic materials the grain boundaries can become the crack, okay. It turns out in metals with dislocations and movement and deformation, it turns out the finer the grain size the higher the strength of the metal, and the reason is you get a pile up of dislocations. And if you have big grain size, that gives you effectively a big long pile up of dislocations and a larger fracture length. I mean I'm sort of oversimplifying this a little bit, there is a grain size relationship for metals and strength.

But the metals stretch before they break. If you remember this plot I just had up here, it said yield before fracture and this is fracture before yield. If you look at a stress strain curve, the difference — and this is the definition of brittle versus ductile — this is a load, so you can think of it, if you're a metallurgist you think of it as sigma and strain, epsilon. If you're a civil engineer you call it P, which is the load in pounds, and what do they call displacement, d, displacement, okay. But anyway the curve looks like this for most materials. That's an engineering — this is the yield point, this is the Young's modulus elastic limit. If it breaks down here it's a brittle material. If it breaks up here after some ductility and stretch, it's a ductile material.

If you design your structure properly you want it have some ductility, you want it to leak before it explodes. You don't want to shatter. And so one of the criteria for pressure vessels is, if I'm going to make a pressure vessel that's going to be more than um — well if I'm going to make a pressure vessel two inches thick, I better use a steel that's got a critical flaw size of more than two inches, so that it will leak and stop the crack and I won't get the brittle fracture running through to cause the whole thing to shatter.

That was NASA's problem with the rocket motor cases. They weren't applying fracture mechanics. They had critical flaw sizes that are on the order of one millimeter in the steels if you don't pick the right steel or you get to too high a strength level. Bad design, okay. You want to have leak before break so you don't shatter before you have a catastrophic failure.

And in fact I had one of those things once, I told you the story about the America's Cup hardware. They want it to fail periodically. If it doesn't fail you've made it too heavy, because you're trying to win a race, and this is for some billionaire who's investing 100 million dollars in this yacht and he wants to have drinking privileges at the bar with his counterpart who spent 100 million dollars, another billionaire. And how do you rub his nose in it at the bar unless you win, okay. Pride is a big thing driving this type of stuff.

So this guy is a graduate of mechanical engineering — and the guy's PhD in mechanical engineering — runs a company called Nautica [Navtec?] down in Connecticut, and they make high-end hardware for the marine business. And they run 7,500 psi pressures on the hydraulics, on the winches and raising the uh sails and stuff on these America's Cup yachts. And they made it out of high strength 7075 aluminum. It's only — I've got the piece in my office, so I did the consulting for free if he gave me the part, and he gave me the part. But maybe I'll remember to bring it in on Monday.

It's about two millimeters thick, and the critical flaw size was one and a half millimeters. It was 7075-T6, perfectly aged for optimum strength, because they were designing it to make it as light as possible. But the problem is it shattered. And if one of the crewmen had been there right next to 7,500 psi he could have gotten an injection injury where the oil goes right through your skin into your bloodstream and everything else, or cut your fingers off or whatever. Not a good deal. You don't want to have to stop the race because you got an injury, a major injury.

So we redesigned it to a 7075-T651, I think there's no T6 — no, T7, anyway, I have to go back and look. But I looked up the properties, we had to make it a little thicker, okay, because we had lost strength. But the critical flaw size, the toughness, went up by a factor of two even though we only lost ten percent in strength, but we got a doubling of toughness by the different heat treatment. And now we would have a leak before the thing shatters, okay. So you might get sprayed with oil but doesn't blow up in the space, okay. So that's leak before break as opposed to fracture before yield.

So brittle materials are down here below the yield point, ductile materials are up here. You don't have to have twenty percent elongation, two percent elongation is usually enough, as long as you never fall below that, okay. I'll see you on Monday, and we'll talk some more about strength and toughness. Toughness is a critical thing for structural design.