MSE_F2017_03

Today this will be the last day where we have the MIT Video Resources doing the videotaping, and then it'll just be Brian and others after that. Simone will be lecturing on the next two days, Thursday and Friday, and then I think I'm in on Monday next week and Simone is on the rest of the week, because I'm gonna be gone for the rest of next week so far as that goes.

No questions? Gee, I find the PowerPoint presentations stifle questions. It's better when I ramble and tell stories, that creates questions. Anyway, how are we set to go?

Okay, we've been talking about cost and availability of materials, and yesterday I gave you a lot of different metrics and numbers about the value of a pound saved in different industries, whether it's shipbuilding, automotive, aerospace, or whatnot. And we talked about, those actually varied by two orders of magnitude in each one of those industries. And then I mentioned that it's only about ten to twenty percent of the actual cost of a fabricated part that's been inspected, past quality control, and ready to ship — is actually the material cost. And so the materials department, once you didn't think that, everything is all materials, but in fact it's only ten or twenty percent of the cost of a manufactured product. And the real costs are things like design, inspection, fabrication. The actual material costs that goes into the structure of a car, the basic metal frame of a car is only five hundred to a thousand dollars, okay. And so we could talk about having all aluminum vehicles and stuff, but the big cost in say an automobile, the biggest single cost is the, is life insurance for the workers — not life insurance but health insurance. It's about twenty percent of the cost of the car for the workers.

But in any case, you can talk about two orders of magnitude difference between the value of a pound saved in ships versus automobiles versus aerospace. But you can go down a little bit finer scale than just looking at two order magnitude differences in whole industries. One of the things you can look at is speed versus cost. Lightweight is important for structural materials, the faster an object moves. And it turns out, if you've got a completely stationary object, let's say it has a value of $200 a pound on the frame of an aircraft, a Boeing commercial jet. If you actually are talking about something that goes really fast, like a turbine blade, that $200 a pound could be worth ten times as much as part of a turbine disc, or $2,000 a pound. I'll show you that in a second.

But because of that, specifically per disc, people have been looking at — the Air Force in particular has been looking at, for years, something called a bladed disc, or a BLISK. And that basically is the — do you have a disc with these turbine blades essentially mechanically joined on the end, and you have, that makes a big fat joint, compared to if you could weld those together. And that heavier section out here on the rim means that the hub has to be stronger because the greater centrifugal force due the weight out top of the rim, okay. It's just great big flywheel in the sense. And so if you take the weight out up here, you can save weight here. So there are follow-ons.

And so when I tell you it's $200 a pound for the value of a pound saved on an aircraft — well I remember back in 1990, I don't know if I mentioned this before, but back in 1990 we had some students in the what's now the LGO program go out to Boeing, and they found it was a hundred and eighty-eight dollars a pound savings. It wasn't two hundred. Well you know, my two hundred is sort of rounded numbers, it's one significant figure, right. And it's even not that significant, but it could be up to a variation of that of a factor of ten depending on the speed.

But to give you an idea, it turns out, just looking at the innards of this — is actually is a commercial aircraft — but if you save twenty pounds on one of the discs that's spinning around in this engine, that means you can actually save two hundred pounds on the engine as a whole, due to the corollary weight savings, okay. And that means that on the airframe you can save two thousand pounds, and two thousand pounds on the airframe at two hundred dollars a pound is worth four hundred thousand dollars. And so just getting that weight off the disc, which goes very fast, is very important if you can do it, okay. And people spend a lot of time and a lot of modeling to try to do that for weight savings.

But the faster it goes, the more important it is. In automotive, it turns out that sprung weight is more important. That means the weight on the axle, where the wheels are spinning around. The wheels are not necessarily — well, they're spinning around and they have angular momentum and they have inertia that the car doesn't have. The car is going forward, okay, the same rate as the tread is going around. But in fact there's more energy in that spinning wheel. And so your brakes, whichever kind of brakes, are more important. So people have tried for years to replace the cast-iron brake calipers, or some of these cast-iron components, with things like aluminum, but it turns out they had some problems because brakes can get hot, and in fact they do get hot. And if aluminum gets that hot, it actually can distort and deform and your brakes don't work. And that's a real problem.

If we go to aerospace structures, an example of weight savings being critical to the whole structure is the X-33 spaceplane, which was supposed to replace the space shuttle. And they had a 1.3 billion dollar NASA project to design the X-33. Actually the X-33 was a half-size vehicle, and it was gonna fly all the way from Edwards Air Force Base to Dugway proving grounds in Utah. It was going to get up to above a hundred miles, which makes it space, but it wasn't going to go around the Earth. It was just a demonstration vehicle. But they wanted, this was going to be before SpaceX came along, this was going to be a reusable vehicle. And the Space Shuttle, as you remember, was not completely reusable. We had the main tanks that just were disposed of every time, and then they tried to recover the solid rocket boosters and stuff, but the actual thing that got up into space was a lot smaller. This whole thing would have gone into space.

But in order to meet the design requirements and all the energy it takes to get out of Earth's gravity, you had to actually make the tanks, the fuel tanks, part of the structure, okay, that carries the load. And so the fuel was going to be hydrogen and oxygen — H2O, one oxygen tank, two hydrogen tanks. So this was a very environmentally friendly vehicle. But it turns out these tanks themselves had to carry basically all the load. The payload was just a little box in here. It's not a small box. This liquid hydrogen tank, I saw one of them at Edwards Air Force Base, and it's about the size of a two-story house, okay. So you've got three two-story houses here so far as that goes. But they had these struts in between, and that was the structure, and basically on the outside was just a skin. The outside did not have any substantial structural strength. These three fuel tanks were basically the main structure, and these were Inconel and titanium forgings that were holding everything together, and they were big, okay. They were a good size, because you were talking about something that weighs hundreds of thousands of pounds.

This is actually a piece of the liquid hydrogen tank. It's a composite material. It's Nomex honeycomb for core — which you know probably by the other trade name of Kevlar — and is adhesively bonded together, and has got graphite fiber reinforced skin on the outside. And it was all adhesively bonded. It was all part of a project in the early 90s, as twenty-five years ago, to build the whole thing in 33 months. From design, a contract award, to flight was supposed to be 33 months. And that was something the Defense Department came up with because of the first Gulf War. They had to retool a lot of their equipment before they invaded Iraq. It took about six months to retool and build things, because they, the military wasn't designed to fight a desert war, and so they had to redo things. And so they learned they had to rapid prototype. That was a big — rapid prototyping was a big buzzword in the early 90s, and this was a 1.3 billion dollar rapid prototyping project. And there's lots of problems that go along with that, and in some of the other modules I probably discuss it in more detail.

But in any case, it didn't work because the composites — that composite cost about twelve thousand dollars a pound to fabricate. It was fifty million dollars for a 4,000 pound liquid hydrogen tank. So that tank only weighed four thousand pounds, twice the size of a house.

Another aerospace example: the very first all-composite major aircraft. Now there were small little two-seater, you know, personal planes that people had made all composite before, out of fiberglass as far as that goes, were in existence. But this was the V-22 Osprey, which is the Marine helicopter. The Air Force has some and the Navy has some, but it was really developed for the Marine Corps. And it's a tilt-rotor helicopter, so it can fly as a regular two-rotor plane if you tilt the rotors forward, which means it can go 300 miles an hour. Helicopters cannot go 300 miles an hour. Anybody know why? They top out at about 180. It's because the tip of the blade going around — there's a leading edge and a trailing edge of the blade — and the one that's leading, when you're going forward at 180 miles an hour and you've got the rotational velocity, you get to supersonic velocities and you get instabilities and your blade falls off, the helicopter comes crashing down. But in any case, the tilt rotor allows you to fly like an airplane and then hover like a helicopter. And this was critical in the raid when they got Obama — Osama — but they haven't gotten Obama yet, that's in the works, okay. When they got Osama bin Laden, okay, they could come in quietly, not like a noisy helicopter, and then they could tilt them and land in rocky terrain. This was all carbon-fiber composite. It started out, was supposed to be like a 15 million dollar helicopter. It ended up being 65 million apiece, okay. It's one of the more notable overruns in the Defense Department, okay.

Some things that are very big and heavy, but don't go very fast and don't take much energy — it doesn't take much to push something through the water. So you can make this out of steel. You don't need lightweight, you need low cost, because these things are really heavy. I mean, some of these new cruise ships are as big as an aircraft carrier or bigger, so far as that goes, and hold more people. There are other plenty of other things, like — oops — pressure vessels that are intended to be stationary. They can be made out of steel and they don't move at all. So steel is fine for things that don't move, but when you need to move very quickly, you need the lightweight, and that means aluminum or fancy composites, but that drives the cost up, okay. And so there's a lot of money spent on light-weighting of materials.

Now just in general, if you want to know, feel what lightweight means — someday I gotta get a piece of one-inch aluminum, but this is just aluminum ingot, but it's similar in size to a piece of zinc, which I had someone name zinc bar. And this is basically the same density as steel, okay. So this is the density of steel, which is about seven and a half specific gravity. This is density of aluminum, which is about 2.7, and this is magnesium, which is about 1.8 or 1.9. So you can feel them. [Tom passes samples around the class.] Pass them around. Hit your neighbor, bludgeon them. I wanted to get one of beryllium, but it turns out beryllium is only 1.6, which is almost the same as magnesium at 1.8. And a piece of beryllium that size would probably cost something on the order of a hundred thousand dollars, okay. I do have a little piece of beryllium I could bring in that I paid $100 for. It's a little mirror that goes into a camera for outer space. Anyway, so lightweight is important, but only if something moves, and the faster it moves the more important it is. One of the advantages we know of plastics is they're lightweight, and so we try to use them in a lot of our applications.

So let's change topics a little bit, and let's talk about the fact that there are inherent limits to the properties of materials. We can't get something that's stiffer than diamond, okay. Diamond's about 60 million modulus, steel's about 30 million, aluminum about 10 million, most plastics are around five million okay at the top end. So we could just talk about stiffness of a material, but the stiffness is related to the strength of the bonds between the atoms. And this is a plot of the bond energy between two atoms. So if you had an atom right here at the origin and you have another one out here, this is the energy well. As they come together, they're attracted by either different types of bonding, and they reach an equilibrium distance of separation at the bottom of this trough, and then they start to repel each other as the nuclei, you're trying to squeeze the nuclei together, okay. And that all relates to things like thermal expansion. The restoring force, which would be the spring constant, the curvature of the bottom of this well is basically equal to Young's modulus, so far as that goes.

And so we can look at these things, and diamond has the highest Young's modulus. And the polymers, which have low stiffness, have high thermal expansion. Z — nobody know what material has the highest coefficient of thermal expansion by far? I was surprised when I discovered this a couple years ago. Rubber, okay. Elastomers, rubber bands have a tremendous coefficient of thermal expansion. And I'm sure there's some good explanation in the entropy of rubbers that explains that. But the forces bonding atoms together can be described as primary bonds, which can be covalent, metallic, or ionic. And you can talk about a bond length, and the covalent, ionic — all three of these have similar energies, anywhere from — this is in kilojoules per mole, but in electron volts, which I like to use, they're all kind of one, two, three electron volts. Metallic bonds are not as strong as covalent. Covalent would be like diamond, strongest material we know, or ceramics, typically ionic, which are almost as strong. Metallic bonds are not as strong, but they interact over a larger distance. They interact over more than one atomic distance. These others really only see the atomic energy, or the bond energy, about one atomic distance away. Metallic bonds actually go for two or three atomic distances away, and that's because the electrons form an electron cloud. And so the electron that was originally a valence electron that was originally associated with one atom might actually have some bond attachment energy associated with an atom two or three atoms away. And that gives metals some of their interesting ductility properties and whatnot.

Other types of bonds — Van der Waals bonds and hydrogen bonds — are an order of magnitude or more weaker. And this is actually the Achilles' heel of plastics in terms of higher temperature materials. They're held together with Van der Waals bonds, and so their melting temperatures or dissociation temperatures are going to be, well, they don't get above about 300 degrees centigrade in general, okay. Whereas these things can go to 3,000 centigrade, being ten times stronger. And hydrogen bonds are kind of a special case and are stronger than Van der Waals. Anybody know — there's another type of bonding for all you chemists out there that I haven't listed. It's called dispersion bonding, and it has to do with the way things like liquid oxygen or liquid nitrogen form condensed phases, okay, or liquid helium. Well liquid helium's a little special case. But it's basically things start behaving in a unified way at lower temperatures, hundreds of degrees centigrade below room temperature.

Now you can also look at the fact that there are limits to properties in terms of bonding. This is the enthalpy of a transition of either boiling or melting. These are boiling temperatures. The highest boiling temperature of any materials around 6000 degrees, and the highest melting temperature, that should be tungsten, 3,300, that top point right there, okay. And you can see that the melting temperature and the energy of the bonds are fairly well correlated, and they're actually known for well over 200, about 200 years, as Richards' rule and Troutman's rule, okay.

So there are limits. I can remember once, I used to consult with a division of Johnson & Johnson that made surgical instruments. And back when I tore the cartilage of my knee 40 years ago, it turns out if you had to have an orthopedic surgeon do surgery on your knee, you would be in a cast for about two or three months, and you would be on crutches for about six months, because they had to lay your whole knee open, okay. Then they got, in the 1980s, they got to what they called minimally invasive surgery, where they basically just make a slit on your knee, rather than opening up the whole knee and exposing everything. They would just put a little slit in there and they go in with very fine tools, and then they, I used to work on some of these tools when they break. But they were going in, nibble away the cartilage. They had a little tool called Roger, and maybe just a surgeon would just kind of go in there like a mouse taking a bite of the cartilage, and you pull out a piece of cartilage, you go take another bite. But he didn't have to open up the whole leg. And you could be back, you wouldn't have to be in a cast for two months, and you could be on crutches for two months, and be walking around two months later. So I still have two torn cartilages, one in each knee, but because it was such an ordeal to repair it back in the old days. But they always wanted to get finer, and they do all kinds of minimally invasive surgery, because you don't have to stay at a hospital as long. It's worth a lot of money to be able to come up with instruments that can do this.

But the problem is you get too slender, okay, and things will start to bend, right. They're not stiff enough. And there's two ways to get stiffness in a material. You can either go to a stiffer material like diamond — diamond's the stiffest material, but it's only two times better than steel. So if the factor of two will do it for you, use diamond rather than steel. It doesn't make sense. But in any case, the other way to get stiffness is to change the cross-section. [Tom holds up a flat piece of plastic, then a tubular piece.] This is just a piece of flat plastic. This is a piece of similar plastic but it's in a tubular form. And although I can bend this one very easily, this is one that doesn't have a bend in it yet, and I can bend it, but because it's tubular it takes a lot more force to bend it. Because you've got a sectional modulus. You have Young's modulus, which is property of the material and the bonding, and you have the sectional modulus, which is a function of the geometry of what you have. And something that's tubular can be lightweight and stiff without being an expensive material. So the plastic could be stiffer than steel if you make it big enough with a big enough hole, okay. And this is a nice ductile plastic that doesn't easily fracture.

And I showed you before, I think, bending of a piece of brittle plastic that doesn't take much of a bend before — watch your eyes — who's got — [Tom snaps a brittle plastic sample.] As I missed you, okay. But anyway, that's a brittle material. That's, this is a ductile material. So there were different properties of materials.

And it turns out that type of strength as a measurement of force goes back to Galileo. He actually came up with a beam theory. He didn't have all the sectional modulus formulas, but we now know that the stiffness goes — the sectional modulus goes as the height times the width times the cube — I'm sorry, the cube of the height times the length times the width, okay. So it's b-h-cubed, the height cubed. And here's his little weight and very fancy tensile machine here. Currently we can actually do these things in a computer better than Galileo did it, and we can make more complex shapes in the computer. We can apply loads in a more complicated distribution, and we can calculate the stresses in this easier than we can measure them. So for most of my career, when I was your age, it was easier to go out and measure it in a machine. Today the computer codes for stress analysis are so sophisticated that you can actually do a much better job in the computer if all your assumptions are correct, okay. I love it when people do finite element analysis and try to cram it down my throat, because I can always cram harder back, okay.

But there's more than just force a fracture. But really it was about in the 1880s that people started designing bridges and buildings using concepts — well, they used some of the concepts of Galileo, but they didn't have the mathematics to go with it until the 1880s. That was when they started developing beam theory mathematically. And that kept us going very well until World War II, when we learned you also have to understand something about the energy of that fracture. So there's the force of fracture, which I just demonstrated, but there's also the energy of fracture. And the energy of fracture is how much energy is absorbed under the stress-strain curve.

And I can illustrate that with two different materials. First I take a piece of brittle material known as a paper. And what happened was, they came up with — well first of all, let me back up. They came up in 1901, a Frenchman came up with a Charpy [test], and he just took a 1 centimeter square bar, 10 centimeters long, with a 2 millimeter notch in it. And he put it in a machine with a big hammer. And these machines have about 240 foot-pounds of energy. If you got hit by this, you would know it. In fact it would probably break a number of bones in your body if you got hit by this pendulum as it swings down. But basically you just measure how much energy is absorbed. So the pendulum, if there was no sample in there, would swing all the way home, list, all the way back up — 98% of the way back up, because it's only a little bit of friction here in the bearings. But if you got a piece of steel that it has to break into, then it will absorb energy, and so you measure on a little dial up here. Pretty simple machine. It was 1901. And that measures the energy of fracture in foot-pounds of energy. Typical machine nowadays will have about 240 foot-pounds. So this little hammer might weigh 40 or 50 pounds and be lifted up a number of feet in the air, comes swinging down and hit something.

If it's a brittle material, the force of fracture can be fairly large. [Tom demonstrates with paper.] I don't know if I've done this for you already, but if I've done it for you already in one of the introductions — I can pull on this with several pounds of force. But the science of fracture mechanics, which came up starting in 1925, basically said if I put a flaw in the material, a little notch, it takes ounces. You can do this yourself and you can feel it. It takes almost no force with a little notch. And that's the science of fracture mechanics, and that has to do with the energy of fracture. And I take a material that's ductile like rubber, and I pull on that with a notch, and it doesn't just rip, it doesn't tear. It basically blunts the crack into a U, and the stress concentration is less. So rubber is a very forgiving material in terms of fracture mechanics. Paper is a brittle material. When I put this paper back together it matches okay, just like I break a coffee cup and I can put it back together with Krazy Glue, right? Because they're all the parts match. If I broke something that was ductile, it has to stretch.

And an example of a material that has both ductile and brittle material behavior is — where — we call this stuff silly putty. [Tom produces silly putty.] There you go. Sorry, been a while since I played with silly putty. But silly putty — whew, I had a flaw in my silly putty, got to weld it together. Anyway, silly putty is a very ductile material. It's almost Newtonian, okay. And you can stretch it out like glass, okay. Has anyone ever played with silly putty and pulled it very quickly? And what happens? It snaps. Now I gotta make it smaller so I'm strong enough to pull it quickly. But it's brittle fracture, okay. Silly putty is a material that can be either ductile or brittle depending on how fast you fracture it. So there are lots of complications, and this has given jobs to metallurgists for decades trying to understand this.

The Charpy bar — if it's ductile material, the fracture will be nice and deformed and everything else. This is brittle material, just snaps, just like my piece of clear plastic that I did.

Now what happened is in World War II we built a number of Liberty ships. And this Henry Kaiser — heard of Kaiser Aluminum, or Kaiser Permanente health care? Same Henry Kaiser. He decided that we could build ships just like we build automobiles on mass production line. And this is from one of his shipyards in Oregon, and they built thousands of Liberty ships for World War II. And T2 tankers, which were basically the same thing. They weren't very large ships, but they built them. And it — but they broke up in two. And I guess I should probably show you a picture of they're breaking up in two. There's a Navy report from 1946 after the war, and the classic picture is the USS Schenectady. I actually liked this one. And this was at dry dock over in the West Coast, and it just, no one got hurt or anything, just kind of broke into from brittle fracture. This was in the North Atlantic, in the middle of the ocean. Now this would be a little more traumatic, okay.

And if you go to the next page of this, they actually did a movie a couple of years ago on a Coast Guard rescue off Cape Cod. It's a true story from 1952. And the T2 tanker, that was of the same class as the Liberty ships of World War II — this was only seven years after World War II — and it split open, and then the Coast Guard had to go out and rescue them. If you've seen the movie, okay.

Let's go back to the report. This is report to the Secretary of the Navy 1946, "Design and Methods of Construction of Welded Steel Merchant Vessels." And it turns out this whole problem — they formed three research groups. One was at the Welding Institute in Great Britain, which was formed because of this problem of the ships breaking up, formed in 1946. And George Irwin, who was head of the mechanics division at the U.S. Naval Research Laboratory in Washington DC, actually is now called the father of fracture mechanics because of the studies that he did on the Liberty ships. And the third place was, of course, three here at MIT — Morris Cohen and a few other people were doing the science of brittle fracture, okay.

And this is from the report. There were 4700 welded steel merchant vessels. 900 suffered — almost a thousand suffered casualties involving fractures. These are all brittle fractures. 24 vessels contained a complete fracture of the strength deck. One vessel sustained a complete fracture at the bottom. Eight vessels were lost, 26 lives were lost. And it happens that in steel this type of fracture occurs at low temperatures and heavy seas. Well, heavy seas is just high stress, okay. So those are the conclusions.

People did lots of study through the 1950s, and it turns out what happened is George Irwin took a formula — not a very complex formula — that had been developed in 1925 by Alan Griffith in England. And Alan Griffith basically was studying brittle fracture of glass. Anybody ever seen glass cut? How do you cut it? You just score it with a little diamond or a carbide tool, and then you whack it, okay. And it breaks right where you have this notch. Same thing as the brittle piece of paper, except you need — glass is more brittle than paper, and you need an even smaller notch, in just a thousandths of an inch scratch in the glass, and you could cut through a piece of glass that's a half inch thick by just whacking it with the back end of your palm of your hand.

So Griffith worked out the mathematics, and it turns out here's the math. The fracture toughness of the material is equal to the stress applied times the square root of pi-a. And that comes out of the math of the formula, but this is called the fundamental equation of fracture mechanics. You might know the force of fracture, the stress is equal to the force divided by the area. Well that's a pretty simple formula for the force of fracture. The energy of fracture all boils down to this, and there are whole books written for different geometries.

And it turns out, Alan Wells — he's up here because he wrote a letter for my tenure case, but Alan, he also worked in the 1950s on — you ever heard of the Comet aircraft? He was the one to figure out why the Comet aircraft came down. Comet aircraft had square windows. They were the first — some of the first jets to fly across the Atlantic, and they were just falling out of the skies. And the problem was, they're in the bottom of the ocean and no one could figure out why. And Alan Wells came along and said, square corners not a good idea, stress concentrations, you got the cracks. And they had to prove it, but they did prove it. But he also did some of the more practical work in fracture mechanics.

So fracture toughness is now measured with a compact tension specimen, and I've shown you one of these in granite. And it turns out you have three modes of fracture. You can have the pure tensile mode, where you just pull on the compact tension specimen — it has a notch in it and you pull on it and it grows that way. You can have mode 2, which is a shear fracture, where you push one end in and pull the other one out. And you can have mode 3, which is another form of shear in the opposite direction, where you basically are tearing, okay, something. And it turns out the behavior of the material changes depending on the thickness of the material. And so this is plane stress, mixed mode, and plane strain. You get a different stress state. And this has kept mechanical engineers and metallurgical engineers busy for the last 50 years, and it's gotten to a fairly sophisticated state. Although in practice most metallurgists ignore it, okay, which — you ignore it at your peril, both in the design and an understanding of the failure. Most of the times you can understand the failure with fracture mechanics easier than you can with a great big fancy finite element programs, okay.

Fracture toughness versus strength. This is strength as the force of fracture, so we've got strength as a stress. This is fracture toughness as a K — we thought K-1-C, we don't have to get into the details of that. And it turns out this is an Ashby plot for all the different materials, and you find that way up here, you want to be at high strength and high toughness, if the thing's not going to fracture. And where do we have the best material? Well, happens to be steel. I told you, you're gonna get tired of my using the word steel, okay. Most people in MIT, you know how to spell steel with the A, not with two E's, okay. But in fact you have composites in here, and they can start approaching metals. But you've got copper alloys, nickel alloys, actually could be better than some of the steels. Titanium alloys are in here. So you got all the metals. Aluminum is not anywhere near as good. That's why one of the guys who was director of research at U.S. Steel, and been a professor at Lehigh before that when I was a young engineer, he used to call — he was working at a steel lab — he called aluminum "the near metal" because it wasn't as strong or energy absorbent as aluminum [steel]. But you can get around some of those problems, okay.

Here is some of your fancy ceramics, considerably lower in both toughness and strength, but primarily in toughness. Here, things that people used in ancient times like cement and pottery, and woods are — let's see — what — so here's woods. Woods are in here. Woods are actually pretty good. They have a fibrous nature, and so they have woods perpendicular and parallel to the grain. And polymers actually sort of bite the dust when it gets to real strength and toughness, and so far as that goes. But that doesn't mean that these things can be used in different applications, because of other advantages.

But that's one of the things about selection of materials. You gotta decide what industry. First thing I would do is what industry am I talking about, because I need to know whether it's going to be $2 a pound or $200 a pound or what, okay. That gives me, that throws out 90% of the materials in most cases. I need to know how fast something goes, okay, to see if I can pay a premium for whatever it is I'm designing. I then need to know what temperature capability I need. If room temperature is all I need, most cases — many cases plastics are fine. If I don't need exceptional strength at room temperature, they're easy to manufacture. I mean, I can form plastics much easier than I can form metals or ceramics. If I need really high temperatures, I may have to go to ceramics, but then I got some brittleness problems that I gotta get over. Anyway, there are certain regimes, and if you ask some of these questions that we've already been over, you'll be able to figure out what types of materials you should be looking at.

Now out of all this stuff that George Irwin looked at, George Irwin came up with something that we don't use very much anymore, but I still think it's a useful way to look at different classes of metals. Irwin was interested in — was being funded a lot by Rickover and the submarine programs, okay, in the 50s. And this is the ratio analysis diagram of steel, where he's looking at toughness versus strength, okay. Those are the two criteria — energy of fracture versus strength, force a fracture. And it turns out all the steels in the world kind of fall in this big band, okay. And you can have very tough steel but at low strength, you can have very strong steel but at lower toughness, and the question is, how tough is tough enough? And that's what these lines along here — these actually tell you, for a given stress level, what the size flaw you can tolerate in inches, okay. This is in thousands of pounds per square inch, this is in foot-pounds of energy absorption — kind of like a sharp, great big Charpy test. But here you can tolerate a two millimeter flaw in the steel at this strength level. This is two hundred twenty thousand pounds per square inch — that's about eight hundred thousand, or eight hundred mega Pascals — that's very strong. And if you're at the yield strength of the material, you could tolerate that two millimeter Charpy and still have a fair amount of ductility here. If you are only at half the yield strength, your critical flaw size is a centimeter, okay. And if you are at lower stresses — your typical design stresses may be a third — and you might have three quarters of an inch as a critical flaw size for a piece of steel even at 200 ksi.

Student: Yes — do you expect — well, they're gonna need some [statistics] like the stress to be and like, you know, airplane versus like a bridge, like what's the range on that?

Okay, no, not really. It turns out, let's go with a building. I'll go to the structural welding code, or I can go to the American Institute of Steel Construction, and the — based on yield stress rather than ultimate tensile stress, it's about, it's typically about two thirds of yield, okay. That's for the base material. The weld metal will be one third of yield. We have a twice as much safety factor for welds because we know they're gonna have defects in the welds, okay, if I go to the structural welding code. So it depends on whether it's just a straight steel plate or if it's a welded plate. This is all in both the Structural Welding Code of the American Welding Society and in the American Institute of Steel Construction for buildings. So basically the safety factor is 1.67 on force. And then the question is, do you need to have an energy of fracture criteria for a building? Well, we never really worried about that a whole lot after the 1950s when Irwin explained how important the energy of fracture was. We didn't change the building codes. So when the Northridge earthquake came to Southern California in the 1990s, the building snapped in the earthquake and caused billions of dollars worth of damage. So in the 1990s, forty years after Irwin, we started incorporating impact or energy of fracture requirements on the building, of the steel in the buildings, okay.

Now I asked you a question about a bridge. What's the safety factor for a bridge? It's not 1.67 on strength, it's 2.0 on strength. So let's talk safety factors here. I mean it's a good question. So if I want to talk about a building — and here's the safety factor based on strength, it's 1.67. If I'm talking about a bridge — and these are steel in general, it actually sort of applies to aluminum — it's 2.0. If I want to talk about impact, in bridges and buildings you're talking about — this was all about 1990 — we finally incorporated it 40 years later, after we had a billions of dollars of loss at Northridge, okay. If I want to talk about an aircraft, well, aircraft is mostly fatigue, it's aluminum, and because of that, just like bridges it's about 2.0, but going up to 10.0 on a safety factor.

Why? You can tolerate a crack in a bridge. The bridge won't come falling down because we have a redundant structure. It's built sort of as an egg crate type of construction. There's lots of different ways to design bridges. But I had a building in New York City — you had a nine-foot crack in a nine foot beam, okay, at the bottom of the building. It was a 20-story building over the George Washington Bridge approach into Manhattan, and there's a pretty rough area of town. When I went there, there's all these little empty plastic capsules on the sidewalk, okay. And they had — the manager's, the building manager's office was bolted in about ten different bolts, and big heavy bolts, like a prison door. And I just remember the story that I went in to look at this nine-foot crack in a nine foot beam, but they had another ten beams holding the building up, okay. So there's redundancy. And so they had to shut down one of the approaches into New York City, on one of the, well one or two of the lanes of traffic, which is a problem. But when the tenants heard about the crack in the basement, they wanted to go get some of the crack, okay. Which — anyway.

Aircraft — we've probably known about impact since the 1990s and had some criteria, mostly because people like Boeing and the Air Force and others are faster adopters than the civil engineers for bridges and buildings. Does that answer your question? I mean it's a long involved answer to something that depends on the industry. It depends on the type of building or bridge or whatever. It depends on the type of material, okay. And there are still industries that have not yet figured out what they learned from their Northridge earthquake, okay. Fine.

Anyway, so getting back to this, this is the ratio analysis diagram for steel. And the interesting thing, if I go here to more typical strength steels, like if I took the highest strength steel they put in a bridge on a highway, which is 100 ksi — okay, 100 ksi is over here. My critical flaw size is like two and a half inches. If the, you know, the design strength is gonna be, you know, three-fifths, okay, of the yield strength, or it's going to be half of the yield strength, my critical flaw size is two and a half inches. I'm not gonna have brittle fracture. And those things we've designed it out, in general.

Student: [Question about whether codes treat the flaw as a sharp crack.]

Yes. But in general the codes treat it as a sharp crack because they don't know, okay. So they take the most conservative approach. If you know your flaw is porosity, you can tolerate five times the size flaw with porosity, which is a blunt notch, as opposed to a crack. Most codes will say no cracks allowed, period. In fact, if you really know you have a statically loaded structure like a building, there are cracks in everything. In fact there's a story about — back in the 1980s the Air Force wanted to run a study, acoustic emission study, on airplanes that had cracks in them, to see if they could detect the cracks using acoustic emission. When the crack grows it sends out a little burst of noise and you could pick it up on a little sensor. And the general said, you're not going to fly one of my aircraft with a crack. So they had to go to Australia, because the Australian generals were smarter — they knew their planes were full of cracks, okay. And in fact, the planes that you ride on, and go to Logan Airport and get a plane, are full of cracks, folks. But the flaw size — we know how big a crack we can tolerate.

Brian is going to talk later this semester about how do we detect the flaws, and typically we can detect flaws of an eighth of an inch in size or larger, with very good, like ninety percent accuracy. And so we got critical flaw sizes of two and a half inches — what do I have to worry about a half-inch flaw? And I have this all the time where people come to me and they say, oh we found a sixteenth of an inch flaw. I said, forget it, okay. We don't even try to find those, because we cannot reliably find them, they're too small. And I'll say, I can do fracture mechanics, and I can prove to you that you would have to have a one-inch flaw before you should worry, okay. And we know how fast they grow in fatigue. It's called structural life assessment, and Dr. Belmar has got a module on structural life assessment. There are whole books written on it.

Student: [Question — partially captured — about clustering or cumulative defects, possibly "Frank, this Frank, or is it basically like the weakest link, the biggest one — do you think it can?"]

Yeah. If it's full of them, it's like a piece of perforated paper, okay. I can tear this paper off and I know exactly where it's gonna rip, mostly okay, because it's perforated at the top, right. And that's a cumulative set of defects. And sometimes when we process materials, like we bond them together, we have a weak line at the bond line, because it's got a bunch of porosity or inclusions or whatever, and we have to worry about that. Except, over time people have developed a certain amount of experience. And so let's say for porosity, I go to the structural welding code, and it will tell me I can tolerate, for a given strength steel, six pores no larger than an eighth of an inch in a 12-inch length of weld. So I can have six little BBs in 12 inches, for example. If you have clustered porosity, usually they say draw a big circle around it and treat it as one big pore, which is a little conservative, but it's the best you can do. It's only in the last five to ten years that fracture mechanics has been able to actually calculate the fracture behavior of clustered porosity. It's a very complex problem to get those stress fields overlapping and everything. So we usually just say, oh well, treat it as if it's all one big flaw. If you do that, you will reject a lot of things that will be fine.

But to give you a specific example, in 1992 the US Navy was building a two billion dollar submarine down here in Groton, Connecticut, called the Sea Wolf. It was the 21st century submarine. It had been designed by Admiral, or Captain, Millard Firebaugh, who was an MIT grad, got a PhD in — which now of course is course 13 — when it was Ocean Engineering. And he was in charge of designing the Sea Wolf in the 1980s when I first met him. They built it in 1992, and a guy was grinding the outside surface of the hull. The hull has to be about 30 feet in diameter, plus or minus a quarter of an inch, okay, smooth, okay. Because little ripples of a quarter of an inch, like the weld reinforcement, will create noise, sonar noise, and they'll find you, okay. So a guy was grinding this and he noticed, as he was grinding the stuff, there's — he saw the swarf — anybody know what swarf is? If you like Scrabble, that's not a bad Scrabble board. Swarf is the particles that come off in grinding, okay. He saw the swarf was lining up in little sixteenth-of-an-inch things. The welds were full of little sixteenth-inch cracks, and they hadn't found them. They had done their inspections but they hadn't found them, because their equipment is designed to find eighth of an inch and larger, because that's what the standard says, because that's what you can reliably find. He noticed it, and he said, hey, I've never seen that before. And he tells somebody, and they found the entire submarine — 18 percent of the hull was completed — the entire submarine was full of these little cracks.

And so Captain Firebaugh was now Admiral Firebaugh, and he was chief engineer of the Navy. And he asked for companies and two individuals — and I was one of the two individuals — to come down and advise the Navy on looking over General Dynamics' shoulder and saying, how are you gonna repair this, okay. If you take my welding metallurgy course, you'll hear the rest of the story, but they did repair it at a cost of two billion dollars. Congress was not necessarily happy, okay. But they had to repair it.

But I remember going to one of these meetings — I think it was the second meeting — and I was introduced to two captains in the Navy, and one of, they said, this captain owns the ships, the submarines out there, this captain maintains the ships. I mean, it's just the division of labor. And they wanted to know, because on some of the earlier submarines they hadn't built the whole entire hull out of this hundred ksi steel. They were using the old HY-80 in the past. But they had, just to get experience with a hundred ksi steel, they had built some sections — okay, little small circular sections of the hull were the HY-100. And they wanted to know if they were going to have to derate these submarines that are out there floating around in the ocean. And I said, no, no, you don't have to worry about it. Fracture mechanics says that the critical flaw size is probably three or four inches in your steel, okay. In fact they design it so it's thicker — the critical flaw size is thicker than the thickness of the steel. And I can't tell you the thickness of the hull of the steel because that's classified. And if you knew it, and you also knew the 30-foot diameter, which is not classified — anybody can take a picture of a ship and tell that — you could calculate how deep the ship can go, okay, just as a structural designer.

So I can't tell you how thick the wall is, but I can tell you in Rhode Island, where they build these things, and they turn them up on their side, like a coffee cup, when they're welding. They weld four vertical seams at a time rather than one horizontal seam, they can go faster. They actually built a hundred million dollar building to do it inside, because the Soviet satellites could take a picture of the end of that cylinder and measure the thickness from a hundred miles above within a quarter of an inch out of a number of inches, okay. So they — anyway.

I said no, you don't have to worry about, your critical flaw size is probably three to five inches. And what it means is, when these things come back for their maintenance every year or every two years, you should go in there and you should see by non-destructive test techniques if those little sixteenth-of-an-inch cracks have grown. And if they haven't grown any bigger than an eighth of an inch, you can send it out again. I said, you'll probably be able to go out for the entire life. You don't have to derate the submarine. They can go at maximum depth and maximum stress. You're all right, okay. Just do a little extra inspection when you come back from maintenance each year or each two years.

That's how we live with aircraft. The aircraft have fatigue cracks all over them. Well, what we learn is where those cracks grow. We know where to look. So it's not just a guessing game. We have a lot of experience, and that's how, that's what structural life assessment's all about.

So anyway, let me just show you, there is a ratio analysis diagram for aluminum which you can study, and there's one for titanium. And we'll conclude the video taping with that. And when I'm here on Monday we'll go back through some of these things. But we have now sort of completed the videotaping for MITx, and we now — we can go in and you can ask your questions to your heart's delight. And I much prefer when you ask a question, so I can digress, okay.