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You know them from other things, so you can make switches. Just let me know who this is, what the switches are, once the two of you negotiate. But I'm not going to become the marriage broker and try to figure out these switches. If you can't do that, you are welcome to videotape your own presentation and submit it to us, and I've basically said please do that by March 31st, which is more than a month away, so you ought to be able to do it. And Dr. Belmar and I can watch your presentation, and we'll be able to accommodate you that way. So if you have to be out of town — I mean, one person said I'm liable to be out of town for the whole two weeks. Well, I mean, you know, if you decided you wanted to be out of town for the whole two weeks before spring break, that probably is not just a problem in this course, okay. If you're taking any other course it's probably a problem, because there's a lot of students. Note that's when other classes are giving their midterms. I think I don't have any juniors in Course Three who were having a quiz on March ninth on that particular day.

Some of the people wanted to go at 8:30. I was surprised, okay, a little bit, how many people said they'd like to go early, which is fine because I get here at 6:30 or seven, so it's fine with me. So I don't think any of the people that got put in at the 8:30 slot were people who couldn't do it. In fact most people wanted to do it. And I was also surprised at how many people apparently didn't have problems in the 11:10 to 11 slot, which is not our regular class time. But in any case, hopefully it works out and we get 46 presentations. You're supposed to watch 20 of them, one of which can be your own. I guess you bring a mirror or a selfie or something. Even MI— we will not be putting this on YouTube. We'll be putting it on another system that only MIT students could access, and really only MIT students in this course would want to access it, unless you give it away to one of your friends — the information to one of your friends.

Yes, okay. Yeah, oh, there is a class list, I would think Pryon Stellar, or you could check with Jerry. You know my assistant Jerry Hill — she could email something out to people if there's a conflict. Yeah, did you tell me that, and I put you in the second week? Okay, that's my fault, and I might — TS, Jerry will help you with that. Well, I don't say I don't make mistakes, but I tried to avoid that, and maybe I just got confused. But no, I know that some people at Sloan are gone off on their Asia trip, and I thought I tried to avoid that. And then other people had other conflicts. Like I said, you know, technically this isn't advertised as an accelerated course that finishes up in the first half of the term, so any student who complained to the dean's office, I would have to accommodate them in some way. Well, I have accommodated — you can videotape your presentation and show it to me before April first, okay. So I have an accommodation so far as that goes. And I actually, I found the last couple of years, and I think this year, some of the students appreciate the idea that they could finish this up early. As I — apologize if I did put someone in the wrong slot just because I got confused. It's not the first time in my life, okay. Any other comments or questions? Yes.

There's three people per hour. Yeah, well, what I found is, we will lose on average two minutes as each of you fumbles around trying to get the audio visual to work with your computer. I will have a Mac here with the dongle. This is a VGA input to this thing. We've always gotten it to work, but sometimes we waste five minutes there, okay. I want you to do it in ten minutes, which means no more than 10 PowerPoint slides. I've seen students do it with 12 or 13, and they usually go over. I will tell you there's a very good correlation between one slide per minute, okay, and that doesn't matter whether it's a 10-minute presentation or a 30 or 40 minute presentation — one slide per minute. If you go faster than that, you're racing through it. Any case, so that's one idea. Most students keep to eight to twelve minutes, okay, and I will let a student go over by 12 minutes. I will time things, and it also depends on whether the person before you went under. I might, you know, I might be nice and let some — for some person, get a minute from them. But I will not let you go 15 minutes, because there will be some time for questions and answers, and the idea is that yes, it should be maybe seven or eight minutes for question answer, okay. I want there to be some question answer.

Some students have said they enjoyed the student presentations more than lectures, which is sort of offensive to me. But no, I mean, maybe true, but it just causes offensive — doesn't, anyway. No, I learn a lot from the student presentations too. So, and I'm not really offended by that. In fact, yours, I already told you, ought to publish, alright. He sent me a copy, and a couple people have sent me some emails, and I'm happy to comment on the topic, or whatever people really want to come by. You can come by and see me — well, we've only got eight days left before we start, okay. Any questions on the presentations? I want to be flexible, and I think you all know one of the goals of this course is to make it as stress-free as possible. That's not really completely possible in the MIT environment. The system is set up to try to create stress for students, and actually there's some good that comes out of that. There was probably more bad, but nonetheless.

So we've been talking about fracture toughness and strength of materials. And there's the force of fracture, which is tensile strength and yield strength, or in composites and polymers it may be just the ultimate tensile strength because they don't really have a yield point. But in any case, we have force of fracture, we also have energy of fracture. And energy of fracture, Griffith pointed it out in 1925. It didn't become important till World War Two and the Liberty ships kind of emphasized it. And even today we are still running into problems. The Northridge earthquake in the early '90s in California — all the codes and standards had designed to force of fracture, and they had no real criteria for energy of fracture. And you come along and have these static structures that get vibrated in an earthquake, and it caused five billion dollars worth of damage. Since then we've rewritten the codes and standards, and those structures now in California have to be able to absorb a little bit of energy, little vibration that comes around every now and then, okay. But there's still other industries that we still haven't really gotten around to helping people figure out what the energy of fracture should be.

There's also the fact that I haven't told you this part of the story. When the Navy did their study on the Liberty ships, that 1946 report found that basically, whether they use a Charpy [Sharpie] bar — and I think I mentioned this some other time, a [Charpy] bar is a little one centimeter square by 10 centimeter long piece of material. What happened to my [Charpy] bar? Oh, here it is. It isn't here. Okay, so here's a — [Tom locates a broken Charpy bar.] I'll pass this around. Here's a broken [Charpy] bar that was ductile and did not fracture all the way through, and so it forms sort of a V-shape, okay. So there's the V-shape. And here's another one that's shattered — not shattered exactly, it probably absorbed five or ten foot pounds. This one that bent like this probably stopped a hammer, big swinging hammer that had 264 foot-pounds, okay. You don't want to be kicked by a horse at 264 foot-pounds, okay. It will break a few bones. If it hit you in the head it will kill you, okay. But the other one probably fractured at 10 or 15 foot pounds.

The US Navy found the plates that had the problems, that had the fractures, started the fractures in the Liberty ships, were on the average of about five foot pounds. So one of the recommendations of that Navy inquiry was that the Navy require 10 foot pounds, so they doubled the amount of fracture energy that they found empirically had caused problems. Well, then people decided, well, we should put a safety factor on top of the 10 foot pound, so they made it 15 foot pounds. And by 1960, the Coast Guard had decided, well, we should put a bigger safety factor than just 15 foot pounds, we'll make it 20 foot pounds. So now we're four times what the Navy found was causing problems. And then I remember when I was working at a steel company, and the guy right next to the office next to me was in charge of what we call line pipe — the steel pipe for things like the Alaskan pipeline. And in fact they were building the Alaskan pipeline in the mid '70s, and they had plans to build other pipelines, and they wanted to have something that would really act like that really tough one, that tough steel, and they wanted 60 or 70 foot pounds. Wow, okay, it starts getting pricey to make steels that are that tough.

Now the US Navy does it for nuclear submarines, but nuclear submarines are sort of a different matter. I mean, it's a 22 billion dollar vessel, and you tend not to like to lose them. I try to keep track of them, find out where they last docked and things like that. It's not like losing your keys, but almost. Anyway, but people keep on wanting higher and higher toughnesses. Is that really necessary? Well, there are some reasons why it might be necessary. For example, when I worked for the steel company, they were building LNG tankers, you know, these great big tankers, steel ships that have great big aluminum spheres, and there'll be five of them. They're like five stories tall or five stories wide, these big aluminum spheres. And in order to hold that sphere you have to have a cylinder that you put the sphere on, and that was made out of steel, and that had to have toughness at minus 60 degrees Fahrenheit.

Steel has an Achilles heel that many steels, as they get colder, they go through what we call ductile-brittle transition and they become brittle at low temperatures. So I had to develop a steel that could be welded and maintained good toughness at minus 60 degrees. They were building these ships down here in Quincy shipyard, right down here in southern Massachusetts. At the time it had just been sold by Bethlehem Steel and it was owned by General Dynamics. It's now closed, and they're turning it into a parking lot for imported cars and stuff. But nonetheless, they were making these ships. And it turns out that at the time, Bethlehem Steel was selling a grade of steel — they had, the Coast Guard said, you have to meet 20 foot pounds. And it turns out the average toughness of the steel after they had heat treated it the first time was just like 20.2 foot pounds, okay. And every now and then they would have to do a second normalization heat treatment to get a finer grain size in the steel to give you toughness, and sometimes they would do a third. They would scrap the plate if they couldn't get a toughness up above 20 foot pounds after three tries of different heat treatments to get finer grain size.

By the way, fine grain size is the only thing we know of that gives you both toughness and strength, okay. Most things that give you higher strength give you lower toughness. We saw that in the Ratio Analysis Diagram. But fine grain size will give you both. And they would do this normalization heat treatment. Well, the average that they were shipping from Sparrows Point, Maryland, up to Quincy, Massachusetts, was like 20.5 foot pounds. It just barely passed. But every now and then they would find one that had 30 foot pounds of toughness. And so what they would do is — the Coast Guard required that you had to have a runoff plate to measure the toughness. And so if this was a plate, and you were welding the seam between these two tables, they would have a runoff plate like this, and they would weld that seam a little further into the runoff plate, cut off the runoff plate, send it to the lab and measure the toughness. So when they found this one plate that would come in once a month with 30 foot pounds of toughness, what do they do? They went and cut it up into runoff tabs. So what they were measuring was not the toughness of what was going to go in the ship. They were measuring the toughness of the best plate they could find. And that was one way to get around the spec. You know, of course, you know, if the ship had blown up because of that, someone probably go to jail, but nonetheless, that was what they were doing. And maybe that's why you need more and more toughness, because people are going to find more and more ways to slim things down and try to meet the spec, okay.

So I'm not necessarily opposed to people who are trying to increase properties beyond what we think are necessary, because other people are also very clever about beating the system, okay. So if we start looking at fracture toughness, an Ashby plot of fracture toughness and strength — here are the two parameters we've been talking about. And here's strength and here's toughness. If we look at this, we want to be as far up that way as possible. This is the Griffith criteria: K squared is equal to pi sigma squared — yeah, pi sigma squared times the crack length. So if you square this equation, K squared over sigma squared must be greater than pi C, and that is these lines right here. And these are the critical flaw sizes in millimeters. K squared over pi sigma squared C. 100 millimeters is a four-inch flaw size. That's a pretty big notch. In fact, many plates aren't even that thick. Like most plates are in that thing. So something that's crossing that line — there's not a whole lot of things that cross that line. Some steels and some fancy engineering alloys, copper alloys are very tough. But most things, critical flaw size of 10 millimeters, which is 1 centimeter, and that kind of goes through not the center but the 60 percentile line for most of the metals. Some of the woods are okay, and some plastics are fairly ductile.

I mean, I showed you polyethylene. Here's my polyethylene. [Tom flexes a polyethylene sample.] I can't break that, right, it doesn't snap. But if I took polystyrene, you saw what happened with polystyrene — it just shatters. And so why? Because polystyrene and things might be down around here, 10 to the minus two millimeters, that's half a thousandths, that's one-tenth of a human hair. Doesn't take a very big flaw to make polystyrene brittle, okay. So we know that all materials have some imperfections, and fracture mechanics has quantified that. You can look at the Ashby plot, and you can see why we use metals for structural materials, except for concrete which should be down here somewhere. Glasses, pottery, brick, cement and concrete right here, okay. Well, it's that still pretty small, but we usually only use cement and concrete in compression. And when it has to be in bending or tension, we use steel rebar, a reinforcement, to give it strength.

Ice is a structural material. In fact, in the mid '50s, Professor Kingery in Ceramics had a big project to look at the strength of ice as a structural material. Didn't really become an important structural material until they started building the oil fields in Prudhoe Bay in Alaska. And essentially they built man-made islands to go out there into the ocean, 100 feet deep. They built low islands. And in fact those islands were designed by a group of civil engineers who used to be here at MIT. And basically they would build the islands such that as the ice started to form, the islands have nice sloping walls of rock, and the ice would just kind of build up and be pushed up above the ocean, so far as that goes. But ice can be obviously a structural material. Anybody goes out ice fishing knows that it can be a structural material — except for the times when it's not thick enough.

One of my favorite stories, which has nothing to do with anything — so you never heard the story of the ice fishers? In, I don't know if it's Minnesota or Wisconsin or wherever — they're out on the lake, and they had at least, these guys will take their dogs with them and stuff, and they drove their pickup trucks out onto the lake. And they decided — rather, they wanted to drink beer more than ice fish. So they decided they were going to break some holes in the ice with some sticks of dynamite. So they had sticks of dynamite, and they threw the stick of dynamite out there to blow a hole in the ice. And the dog went and picked up the — went running after the stick of dynamite. He was used to playing catch with sticks, right? So he comes running back with the dynamite. These guys run, and the dog doesn't know what to do, so he gets underneath the pickup truck, and he and the pickup truck go blowing up. And so, better not drink too much beer. Just go ahead and drill your hole in the ice, don't try to blow it with dynamite. That's supposedly a true story, okay. Poor dog, he didn't know. But anyway.

So anyway, we have structural materials, all kinds of things like cement. Turns out wood, with the grain, is not very strong, but perpendicular to the grain it can be very strong. About two orders of magnitude greater critical flaw size. That's why we can split hardwoods with a wedge and a hammer and stuff, okay. Ceramics are way down here. I mean, the critical flaw size 10 to the minus 3 millimeter — I mean, that's nothing. That's why we can cut glass. And we talked about diamond and how strong it is. Diamond has one of the lowest fracture toughnesses. And if anyone knows the way they cut the crystals on the diamond — they basically, they don't even scribe it, because you can't scribe diamond. They just whack it with something, and if they whack it at the right angle — and people make a fortune who develop the skill, they can cut the diamond crystal right where they want it, because diamond is extremely brittle. Yes, very hard but brittle. Yes, do you — were you raising your hand, Brandon? Oh, no.

Student: So for the minimum flaw size, there obviously has to be some force or energy to split it, right? So what is that, like, what is that number, like, I'm guessing it's like, you know, hard to visualize for all the materials?

Well, it turns out it's in this stress intensity or toughness number. What Griffith did is, he said, okay, let's take something that's brittle and figure out, if I pull on it, I'm making it like a spring, I'm storing energy. One-half K X squared is the energy you store in a spring for a strain of X, right? There's a spring constant depending on the geometry, and the strain is X, and the energy stored is one-half K X squared. He said, if it fractures when I've got it under load — here's the load — if it fractures, I create two new surfaces, okay. I get the fracture surface, just like a piece of chalk, right? I fracture it, two new surfaces. There's a certain energy to form those surfaces. And if that energy exceeds — or if that energy exceeds the spring of energy, won't fracture catastrophically. If the spring energy is greater than the fracture energy, a brittle crack will just run, and it runs close to the speed of sound, typically one-third to one-half the speed of sound in the material. So it runs really fast. And so I think what you're asking is, where's the energy in here? The energy is basically the stored energy of the tension from the stress you've applied. That answer your question? And that's how he gets this formula, okay.

So he starts with a crack, an edge crack, that's C deep, you know, just like my little fracture toughness specimen — you got an edge crack of C deep, and you pull on it. And he calculated the stored energy in that as a function of strain. And in fact today, one of the ways the British would like to measure fracture toughness is a crack tip opening displacement. So if I have my fracture toughness specimen, some holes so I can pull on it here and here. And you're basically — you wonder what's happening right there at the crack tip. Turns out it's sort of lima bean shaped, okay. This is the plastic zone size right there. And you can measure, and you can do the bending beam formula of what the crack tip opening displacement is for some crack length C. And the higher the CTOD, the greater the toughness. And so the British will have standards where they specify, for a given geometry of test specimen of a piece of steel, you must have a CTOD greater than a quarter millimeter, okay. Crack tip opening displacement. So when you pull on it, how much are you stretching the opening — you've got some opening, put a little clip gauge on here just like a tensile strain gauge, the same apparatus as if you've ever done in tensile tests. You put a little clip gauge on to measure the strain. They put it right here and they measure how much it opens when you pull on it, okay.

It's basically, if you look at a CTOD curve, it's just like a stress-strain curve. Maybe doesn't have a yield point, but it's just, you know, the load increasing and then decreasing as you go up, and at some point it goes snap, okay. And that's when the energy of fracture becomes less than the stored energy of strain energy in the material. So it is an energy criterion for fracture, okay. And it's not a constant for all materials. Some materials can store a lot more energy than others. And in fact my example of a material that's sort of bilingual or something — [Tom locates Silly Putty.] I get some Silly Putty. And Silly Putty, if I want to study the force of fracture, I can just take the Silly Putty and I can pull it like that. And Silly Putty actually is something that is almost a Newtonian material, in that it just stretches hundreds of percent strain if you pull it slow. But the interesting thing about Silly Putty, and this is because as a polymer it has some very interesting mechanical properties — I can pull on Silly Putty slowly and it stretches. What happens if I pull it quickly? Nothing — if I pull it quickly and it's small enough in diameter for me to break it, I get a brittle fracture, okay. No deformation. That's a brittle fracture. So Silly Putty is very strain rate dependent. At slow strain rates it's a super plastic material. At high strain rates it's a brittle material.

So metals are not so complex. Metals are either brittle or ductile, unless you're at ballistic velocities. Actually metals do start behaving like that at ballistic velocities, speed of sound. But Silly Putty does it at a lot lower speed. Yes?

Well, that's an interesting philosophical point among materials people. Some definitions will say, if you're familiar — don't have, pay attention — let me put it up. [Tom draws at the board.] Some people will look at a stress-strain curve, and they're used to being metallurgists, and they say, okay, we'll have a yield point and then it becomes plastic at the yield point. So this is stress versus strain. And if you're familiar, that at 0.2 strain, which is 0.2 percent strain, okay, they define that as the yield point of the material. Because usually this sort of curves over gently, and what do you call the yield point if it's curving over gently? They come back down here. So some people say it's two-tenths of a percent strain is the limit of brittle material, and brittle is everything where you have elastic strain, just like Griffith — kind of, what's the elastic strain energy, and then thing snaps. Some people say it's 0.5 percent, okay, 0.05 — I've seen some textbooks try to say five percent. Well, if you're present way out here, okay, and way out here you've got a lot of stored energy. The energy stored, if this is where you actually fracture, the energy storage is the area under the curve, okay.

So some people say brittle is anything below 0.2 percent, which is the yield point of a metal. Some people, and this is in the pipeline business, will say the yield point is defined at 0.5 percent, which is two and a half times as great. Some people will say you need to have five percent ductility to be ductile. In fact, let's just say anything above one percent is ductile and means the thing has stretched. And I didn't bring the sample, but I passed a sample around the last time, my brittle centrifuge, and if you look very carefully, just a little bit of stretch before the thing snapped, okay. So something — it's a continuous spectrum of materials. Something is very brittle like glass, depending on the flaw size, could fracture here anywhere along that elastic limit. Things that fail out here above five percent strain are clearly ductile. They stretch like this, the Silly Putty. Things that are in between are sort of beauty in the eye of the beholder, okay.

But most design engineers would not like to design with something with less than five percent strain capacity, because they know that I'm going to have holes and things like that, stress concentrations. I want to have something that's going to give before it snaps. Glass doesn't give before it snaps. Diamond doesn't give before it snaps, okay. So to a designer, five percent is probably the minimum ductility he would want, okay. To a laboratory technician, he would define ductile-brittle transition as 0.2 percent, maybe 0.5 percent. Where is it? It's somewhere between 0.2 and five percent, okay. So is that confusing enough for the answer? It depends on who you're talking to and what their purpose is. You really want something that's going to stretch a little bit. Most metals — aluminums and steels and coppers and nickels — most of them, unless they're really high strength, are going to have more than ten percent strain. Many will have twenty or thirty percent strain. You don't usually get fifty or sixty percent strain, but you sometimes do.

And I'll pass that around. I've got some tensile tests here in copper, okay. [Tom picks up a copper tensile bar.] Here's a copper tensile bar. This is actually material from the wire right on the Acela between New Haven and Boston. This is a piece of the material for the conductors overhead. They're carrying the current to the train. It's really ductile material. I mean, the — if you look how much that has necked down, it's tremendous. I mean, this has got — it's probably more than 75 percent reduction in area on this specimen, okay. And that's a lot. Copper is a very ductile metal, and that's a very pure copper, very fine grain size in the stuff they finally used. [Tom passes tensile bars around.] Here's some tensile bars. Pass each other — if I can just show these.

This one's kind of interesting in that the amount of stretch you get — again, it's not just beauty in the eye of the beholder, beauty is the geometry of the specimen, okay. This is just a strip tensile specimen. And it turns out, if you pull it, you can see these were the original length before — the black lines were the gauge length — and right here you can see it has started to neck down. It's ductile. And that is a 55 degree angle. If you take my course on deformation, we can prove from theory why that's true. This is a similar tensile bar — that was the original length, and you can see it's now, the one on the right is a little bit longer, you may not be able to see it, but there's a necking down right in here. And this one is just a tensile specimen. It shows what we call a cup-cone fracture. And you get a cup-cone fracture when, because of, depending on the size of the specimen, the ductility of the specimen, you actually have plane stress on the outside and you have plane strain on the inside. We don't have to get into that in this course, but you'll get a different type of fracture, 45 degree fracture, on the outside surface. And the size of that 45 degree fracture, the plane stress area, is another measure of the ductility and the toughness — indirect measure of the toughness of the steel. I have seen big fractures and explosions and things where I have shear lips that are three or four inches wide, okay. That's some of the best material that's up here, with a four-inch wide shear lip in plane stress, is going to be really tough material, okay. It's not a measure of fracture toughness, but there is a correlation, okay. Other questions on this?

So if you spend 30 or 40 years — you know, they say it takes 10,000 hours to become an expert at anything, 10,000 hours of practice. So I have spent 10,000 hours looking at fractures. Who'd of thought I went to college to look at things that were broken, right? But I did, and put seven kids through college, you know, helping to raise grandchildren. But this is, you know, we'll post this on Stellar, but this is out of the Metals Handbook, and it talks about Fracture Mode Identification Chart. Instantaneous failure can be ductile or brittle, we've been talking about that. Necking or distortion, I just passed around some samples to show necking, and the necking is different in a flat specimen than in a round specimen. It's geometry dependent. And the way you measure it depends on the length of the specimen, the size of the specimen.

I remember as a sophomore, Professor Backofen said the longer you think about our tensile tests, the less you understand it. Tensile test is a very complex test. But brittle fractures, little or no distortion, they occur in the elastic regime. Ductile failure occurs in the plastic regime. One of the first things I do when I go look at a fracture — sometimes I only go look at it, someone sends me a photo — I'm looking to see if there's any stretch to the metal, okay. So out in Arizona, a year ago, some guy — can't remember what they were — they had some big forklift machine lifting, I guess if they were pipes for some pipeline. And the thing that was holding all these pipes, so they're lifting up 50 tons of pipe, and the container on the forklift broke, and, you know, did a lot of damage, millions of dollars of damage. And someone said, well, why did it fail? I looked at the photos, and the steel bent before it broke. So the steel is ductile. I knew right there, it was an overload failure, duh, okay. I didn't even have to go see it. I sent someone else to go look at it.

But in any case, if it had been brittle and there had been no distortion, if it broke like a teacup so that you could glue it back together with Krazy Glue — that's brittle, and there is no way to predict the load it failed at, unless you know the size of the flaw, in which case I got to get in there and start measuring the fracture surface and look and see how big the flaw is. But if it's ductile, I don't need to know the size of the flaw. It failed above the yield point. Who designs anything above the yield point? People design things typically at one-third to one-half the yield point of the material, whether it's aluminum or steel or anything else. You have safety factors. And if it failed above the yield point, it got overloaded, and the question is, who put so much load on, why was there so much load on there, okay.

So a metallurgist could look at it just a photo of it, and often tell you whether it's ductile or brittle. Then they can go — that's macroscopically visual — they can go to the scanning electron microscope from 20 to 10,000 X. Why would you ever look at the fracture 10,000 X? I don't know, it can go that high, but anyway. And we can start looking at features there. We can do a metallographic polishing section, and we can look at features. And these are some of the features someone would look at. You don't have to worry about all these details over here. That's instantaneous fracture. We have progressive failures by fatigue, corrosion, wear, and creep. Fatigue is bending the paperclip back and forth — doesn't break the first time, doesn't break the second time, might break the 10,000th time of the stress cycle. We can predict fatigue. We have fatigue failures all the time. Aircraft are flying fatigue machines, okay. Corrosion — now we have environmental degradation of the material. General wastage, roughening, stress corrosion cracking. Where — mechanical rubbing — so here's chemical wear. Fatigue is cyclical, where cyclical stresses, corrosion is chemical, wear is mechanical wear, and creep is high temperature degradation of the material. And there are particular features we can look at, and we can tell why something fractures.

And there are entire books written about fracture analysis, and it helps to have someone who's been looking at it for 10 or 15 years show you how to do it. I remember Professor Pelloux, who passed away, but Professor Pelloux came from France, got his PhD in this department, went to work at Boeing, came back after three or four years, became a faculty member here, and taught fatigue and fracture, okay. And I remember in the mid '80s I had a tail shaft fracture on a liquid natural gas carrier, one of these same ships that was built down here in Quincy, that I worked on the steel for their skirts 15 years before — or 12 years before. They had a tail shaft fail in the middle of the Philippine Sea. They were going from Indonesia to Japan, full of LNG. When you've got a container ship full of, you know, a hundred thousand tons of LNG, that LNG is going to be boiling off, and you would like to have power so that it doesn't blow up something. Well, they had to offload it on a ship that was coming back from Japan that was empty, and they had Learjets flying halfway around the world with the right type of fittings. They did the transfer in an out-of-the-way harbor in the middle of the Philippines, and nobody got hurt. Took them a couple of days to offload the cargo. But they wanted to know why the tail shaft fractured. And I can remember bringing in Professor Pelloux because he had a lot more experience.

And it was a very interesting fatigue failure, and one of my courses, one of my modules, I actually talk about that failure and give you the details. But it's an interesting story about how the flaw was there. It was a casting flaw. It was found by the inspector. The steel company in Seattle was losing their shirt on this job. They were rejecting shafts because they shouldn't have ever been on this job — it was too big for them. And the manager threw him out of his office when the guy found the defect. And so they shipped the shaft with a defect, and five years later, the fatigue crack grew from the defect, and the shaft broke in two, and they lost all power in a critical application.

So anyway, it's — we know how to analyze fatigue, we know how to analyze brittle fracture, we actually know how to analyze most these things, but people don't always apply what they know. In fact, metallurgists think they can go in the laboratory and look at it in scanning electron microscope, take pictures, and understand everything about it. Mechanical engineers, on the other hand, think that they can calculate the fracture strength and things like that, except they often don't do the fracture mechanics. They just say, well, what's the cross sectional area, what are the loads on it, where there bending loads and stuff. And I would say that virtually 99.5 percent of all metallurgists refuse to do the fracture mechanics calculations, and only ten percent of most mechanical engineers do the fracture mechanics calculations to find out whether their hypothesis makes any sense, okay. And in fact, most of the time, well, some of the time it makes sense, sometimes it doesn't.

So just give you an example. This was an article — last time I taught this course, this is in Science magazine in 2014. Guy Rob Ritchie, used to be a faculty member in Mechanical Engineering here, now he's at Berkeley, wrote this article on a fracture is this high entropy alloy for cryogenic applications. It's working at Lawrence Berkeley Lab. And they used a five-component alloy, equiatomic chromium, manganese, iron, cobalt, nickel. Equiatomic, so it's not equal weight percent, it's equal atomic percent. And they say this is a high entropy alloy. Well, this is basically using a term to make it sound like it's not scientific, because many people don't know what entropy is. But in any case, what do they have in Science magazine? Here's the Ashby plot of strength versus the toughness, okay, same type of thing. Here are those plots. This one is a thousand millimeters — they're claiming that would be a 40 inch critical flaw size, okay. And here's their high entropy alloys. Nothing comes up there. I mean, this — even these things, if this pink area is non-existent materials, I mean, they just drew a big bubble around the actual metals, and most of the metal is about four inches — about is the largest of critical flaws you can get.

And anyway, so people are always trying for tougher and tougher steels or other materials. This is a complex one — alloyed steel. There's your compact tension specimen. Here's the energy versus crack extension. And you'd be measuring — you could measure a CTOD at the opening right there. But it's just, you pull on it and that starts to open up. And eventually this one will not shatter. This is one of the toughest materials ever measured. This is called the J-integral. And the J-integral is what you do when you can't do a fracture toughness specimen. We actually use things called K-one for a tensile fracture — K Roman numeral one. We have K Roman numeral two, K Roman numeral three, depending on whether you're doing tensile loading, shear loading. There's two types of shear, in and out of the plane. But in any case, the J-integral was developed by a guy named Jim Rice at Lehigh University as part of his doctoral thesis back in the early '70s, late '60s. Rice went on to Brown University, he's been at Harvard for the last 30 or so years in the area of fracture of materials. Jim Rice is up here, and the next best person in the world is several steps down, okay. Jim Rice is the god of fracture. He's about 70 or 75 now, but he's still at Harvard. And he's looked at a lot of the fracking that's done. Jim Rice was looking at earthquakes and fracture of rock 25 years ago, and a lot of the fracking that's done to make oil today is because Jim Rice basically decided to start thinking about the problem and coming up with ways to fracture rock, which were then applied in situ and whatnot, okay. Questions?

In case you're really interested in fracture mechanics, here's a little book you might want to buy. [Tom holds up a reference book.] The Stress Analysis of Cracks Handbook. I'm sure you all want this on your bookshelf. It's on my bookshelf. Okay, Stress Analysis of Cracks Handbook, third edition, published by, I think, ASME and ASM — yeah, ASME Press. Mechanical engineers and materials engineers got together. And it's written by the guy who did the work, Pas de — Paul Paris, who is a professor at Ohio State, and came up with the Paris equation of fatigue. He is also one of the most arrogant people you will ever meet, okay. And then George Irwin. George Irwin was at the Naval Research Lab, worked with Pellini on some of the fracture toughness stuff. He's known as the father of fracture mechanics. Not the — Irwin wasn't really, maybe Irwin's the non-Irwin, but not the — Griffith wasn't the grandfather. But Irwin basically came up with a lot of the math. And this is just pages and pages of formula for looking at different geometries of cracks and different types of, you know, different shaped specimens. Just an encyclopedia of analysis of the stress-strain relationships when you're pulling on that Griffith specimen.

You're not always using a simple little specimen. You've got a pressure vessel, or you've got some — you got some spherical vessel or cylindrical vessel, you've got edge cracks, you got embedded cracks. Every solution that anyone's ever come up with is in here. And so the solutions look something like crack opening profile — this is the crack tip opening displacement formula, okay. People have spent careers working these out. How exciting — just think what you could do. Well, you can't do this, someone's already done it. Think of something else that you could — that is utterly boring that you can do for your career, okay. Any questions? But it's important. I mean, I pull that off the shelf about once every three years and use it when I have to.