§1. Course logistics and review of property limits [00:00]
Before we get started — Dr. Belmar wants to have a day in between when he finishes and you have to present your presentations, and he'll be back to talk about that next week. The presentations will not begin until October 19th. I was working on the schedule this morning, and I should finish up by the end of that next week, which is like October 28th. So we should be able to be done by Halloween, at least for the planned portion. If you're taking these two modules together, you only have to do one other module, and you can do that whenever you want. As far as when I have to have the grades in — the registrar doesn't make me have the grades in until mid-December, because they think this class runs all the way to mid-December. And it does, if you don't watch the third module and turn in your assignments until then. But you could be done before then.
Okay. Does anybody have any questions? Brian did all right with you on material substitution? You never thought about drink boxes that way before, right? Everybody just keeps competing with each other.
We talked about material property limits. This is just bringing us back to where we were, and how fundamentals of the atoms — chemical bonding — determine material properties. You can look at the melting point of all materials and see how it's related to the strength of that chemical bond, which is the enthalpy of the chemical reaction from the elements to form whatever compound we're talking about. The boiling point actually has even less scatter on the plot, because that's when you have to break all the bonds. So the melting point or the boiling point is directly related to the strength of the bonds, and that limits the properties we can have in different materials.
§2. Stiffness, geometry, and Charpy testing [02:33]
We can talk about the modulus, which is a measure of the stiffness. There are two ways to get stiffness. You can get stiffness by the inherent strength of the chemical bond. If I have a round rod or a square rod, I can measure the stiffness of that material. If I want to measure it in bending, it's basically how much that diving board will flex when I put a certain weight on it. But there's another way to get stiffness in an object — anybody know what that is? Mechanical engineers? You can do it with geometry. I could take the same mass of material and make it into a tube rather than a small rod. With the same amount of material I could make a larger tube, and that will be much stiffer.
For example, the propeller shafts of submarines are hollow, because the stiffness in torsion is all carried by the outside fibers. If you look at the mathematics of stiffness in the moment of inertia, it's all the outer fibers at the farthest radii — the stuff in the center really doesn't do much for you. You're weight-critical on a submarine; you don't want it to sink to the back with a great big heavy propeller shaft, so they hollow it out. We don't do that on commercial shipping because it costs money to drill the shaft out, and we don't care about the weight on most ships. But we do on submarines. So that's two ways to get stiffness: geometry, and the inherent strength of the bond — melting temperature.
We talked about toughness. There are some metals — steels don't go quite this high, but some of the superalloys will get up to 300 megapascals square root of meter. We don't produce any of these in large quantities; it's sort of a laboratory curiosity. You can get 200 megapascals square root of meter in large quantities in steels and superalloys without too much difficulty — some expense, but not too much difficulty. And the cost goes from just picking up gravel out of the ground to unlimited costs that people pay for some things. Generally if you look in Ashby's plots, you'll find these properties vary by about a factor of 10 to the 5th.
Now I want to talk about the difference between our different types of strength. Strength measured by force is something Galileo worked out back in 1638. He was following Leonardo da Vinci in 1493. Galileo worked out the mathematics for beam theory. The stiffness of that beam goes as the thickness H cubed and the width linearly.
Today we can do all kinds of fancy things in a finite element analysis. In the computer you can take a complex beam and put a uniform load on it, and you'll see how it will bend more on this end than that end, and get curvatures to it. You can put stiffeners on, you can start seeing waviness. This is all magnified so you can see it better. We can do tremendous things in measuring the force on a material in terms of the tensor properties of force. Galileo really wasn't dealing with tensors. He was just saying how much weight can I hang on the end of a beam. Nowadays we recognize that stress is a tensor — it's not just a vector quantity. And there are not just nine components, there are 81 components of stress and strain. But the computer can handle all that. We have to do it, and we help to understand how the computer does it.
But there's another measure of strength, and that's the energy — not the force of fracture, but the energy of fracture. The Charpy test was developed in France by a guy named Charpy in 1901. So it's over a hundred years old. All you do is take a little sample, one centimeter square by 10 centimeters long, with a 2-millimeter notch. That notch has to be very precise. In fact we broach it — anybody know what broaching is? You take a tool — basically a linear tool that cuts the thing, rather than trying to machine it with an end mill. The broach can have exactly the right radius at the tip of that crack. You put it in a machine, the specimen down here; you take a calibrated hammer and you drop it by gravity and let the pendulum swing. Typically one of these things will put out 264 foot-pounds. That may not mean too much to you, but 264 foot-pounds is like dropping 130 pounds from two feet. That's a fair amount, that's a pretty good hit.
[Tom holds up two Charpy bar halves.] Here I have half of a brittle Charpy bar and half of a tough Charpy bar that stopped the machine. You take your Charpy bar, machined, and after you hit it, if you have a really good steel, you can stop the Charpy bar — which the guys who run the test hate. When I worked at Bethlehem Steel forty-some years ago I was working on high-toughness steels, and I would stop the Charpy bar on a fairly regular basis. They have to recalibrate the machines, about five hundred dollars every time. They actually ran my samples at the end and wouldn't recalibrate — they'd just break my samples and give me the results, and who cared. But stopping the machine means you have a very tough steel. So that's a way to measure — it's not really the energy of fracture, but we measure it in foot-pounds.
§3. Liberty ships and the discovery of fracture toughness [09:40]
This turns out — we knew about Galileo and the force of fracture 400 years ago, and by the 1880s engineers were designing bridges and buildings and calculating beam theory and saying what the force was on a building. But it really wasn't until World War Two that we learned we should also be worried about the energy of fracture. In World War Two we had to mobilize and build lots of things, and so we built almost 5,000 Liberty ships. This is the report at the end of the war of what happened to some of those Liberty ships. This is an island off the coast of Washington state where Henry Kaiser — you can see all these Liberty ships lined up — basically took Henry Ford's ideas of an assembly line and produced lots of ships for World War Two, and they were called Liberty ships.
[Tom holds up the Navy report.] There's the report from the US Navy. That's the MIT copy. They were throwing it out in the library, selling it for two bucks, and one of my graduate students saw it and bought it for me. It has the pictures of what happened after the war. The famous picture, in most of the fracture books, is of the USS Schenectady. Brand new, sitting at dry dock — I can't remember the location, but it was cold, it was winter, and it just brittle-fractured. One of the problems with steel is that as it gets colder, below 32 degrees, it starts to become more brittle. It's called the ductile-brittle transition. The middle of the ship just broke right in two. No one got hurt there. This is the SS Esso Manhattan — it happened in the middle of the North Atlantic in the middle of winter, and that's not a good thing.
The Navy was very concerned about this. Hollywood was excited about this in more recent times — The Finest Hours, about the Coast Guard. In 1952 one of these — actually it wasn't one of the Liberty ships, it was a T2 tanker. When we talk about the Liberty ships, the oil tankers were T2 tankers and the Liberty ships were classed together. One of these tankers that was only seven or eight years old, off Cape Cod in 1952, broke in two. The people were stuck on half a ship. It completely broke in two, and nearly everyone survived — you can watch the movie. It's a true story of what happened to these ships. The Navy was concerned, so they commissioned this report that's going around.
This problem resulted in the formation of the Welding Institute in Great Britain, which is one of the world's premier welding research centers today, and the development of fracture mechanics by George Irwin, who was head of the mechanics division in the Naval Research Lab. George Irwin is now called the father of fracture mechanics. The report actually said: 4,694 welded steel merchant vessels were built by the Maritime Commission in World War Two. 970, nearly twenty percent, suffered casualties involving fractures. By casualties they mean ship casualties. 24 vessels had sustained a complete fracture of the strength deck, like the Schenectady and the Esso Manhattan. One vessel sustained a complete fracture of the bottom. Eight vessels were lost, 26 lives were lost. Incidence of fracture occurs under a combination of low temperatures and heavy seas being high stress.
§4. Griffith, Irwin, and the mathematics of fracture [13:59]
The solution was started in 1925 by a guy, Alan Griffith. Griffith was a British scientist interested in the fracture of glass, trying to understand the energy of fracture of glass. He worked out a formula for the stress concentration. Has anyone ever cut glass, or seen glass being cut? You can take a flat sheet of glass and make a swirl shape with a diamond tool or a carbide tool. You can't do it with a steel tool, because glass is harder than steel — you can't scratch glass with a steel tool. But with a carbide or diamond tool you can put a fancy shape on it, put it over the edge, whack it with the butt of your hand, and it will fracture exactly where you put the scratch. The theory of fracture mechanics that Griffith came up with — he went on to do entirely different things with the rest of his career, but he was the guy who first started it.
Everyone thought that what he did only applied to brittle materials. Then Irwin came along in 1946, heading up the mechanics group of the Naval Research Laboratory — obviously they were interested in why these ships were failing — and he found that you could apply it to ductile materials if you knew what you were doing. Then a guy, Alan Wells, in Britain in the '50s and '60s worked out some of the mathematics for crack-tip opening displacement measurements, which is what the British all use. He did it when he was at the British Welding Institute, then he went off to become a professor, then he came back as director general of the Welding Institute. He wrote a letter for my tenure. He didn't have a clue who I was — well, he knew who I was, he's a very gracious gentleman, but he talked about how I always attended the IIW, International Institute of Welding meetings. I'd never been. I went to one once when I had to give the Houdremont lecture, but that was before he wrote the letter. I read his letter — it was glowing. That tells you what tenure letters are worth.
[Tom holds up Irwin's handbook.] This is Irwin's book on the stress analysis of cracks handbook. If you don't have a copy, I'm sure you want to get one for your library. I'll pass it around. It's nothing but a bunch of mathematical formulas for stresses and different shape geometries, giving you fracture mechanics. Metallurgists like to think they can understand the fracture of a piece of steel. Mechanical engineers actually know how to use the fracture mechanics formulas, but they can't understand the metallurgy of the fractures. If you can actually do both, you will be an order of magnitude ahead of any of the other people.
The basic formula is: the stress intensity at the tip of the crack is equal to the stress applied times the square root of pi a. That comes out of Alan Griffith's formula, but Irwin showed how it could be related to ductile fracture and helped work out the math and the experiments to apply this. I'm going to show you some of the types of diagrams he came up with that give you an idea of what the critical flaw size is. I took a piece of paper the other day and ripped it in two, and showed you how a notch in a brittle material will lower the strength by ninety percent. It's the size of the flaws that determines the strength of the material.
Well, that's what happened in the Liberty ships. People were slugging welds. They were tired of welding, so they'd take a handful of welding electrodes, throw them in the groove, and weld over them.
I've only seen one slug-welded structure in my life. It was a guy in Nova Scotia who'd built a 40-foot yacht. He took it down to Newport, Rhode Island. He won the sailing yacht thing. He was driving up Route 24 going back to Nova Scotia, all pleased with his new award. He hears a pow, puts on his brakes, looks out the side window, and sees a trailer with a yacht that looks just like his passing him on the highway. Turns out the trailer he'd built — he put a bolt in to kind of bridge one of the V sections on the frame, and he welded over it. Big flaws, because he didn't really weld into the bolt. It was his own fault, but he ended up with a piece of junk for a sailboat.
§5. Modes of fracture and the Egyptian obelisk problem [19:22]
So fracture toughness gets fairly complex. It can be taken to mathematical extremes. People love to do it and prove that they know more math than the next person. Mode 1 fracture is when you're just pulling — like the piece of paper where I was pulling on it — you're pulling in two directions, putting the stress at the tip of the crack, and you've got two diving boards opposing each other. Mode 2 is when you're shearing it, and Mode 3 is shearing in the opposite direction. The toughness is also a function of the thickness of the material. We haven't put the thickness on here, because where it goes from plane stress of high toughness to plane strain of lower toughness is a function of the toughness of the material. If you have a low-toughness material, that transition will be at a lower thickness. You also get shear lips. In a tough ductile material the material will fracture at 45 degrees. In a brittle material it'll be a nice flat fracture.
[Tom produces a granite fracture toughness specimen.] This is a fracture toughness specimen I retrieved from Wendell W. Wilkening, doing his PhD thesis here in 1976 when I came back on the faculty. He was trying to understand why the Egyptian obelisks were able to be raised up. Obviously they didn't cut them to shape in the vertical position — they hauled them out of granite in the horizontal position, and they had to raise them up. In 1976, with our current knowledge of the toughness of stone — granite is a composite of three different types of minerals, and you can see them, white, gray, and black, in that particular granite — the current knowledge was that if you tried to raise it up like this it should fracture under its own weight with just the natural flaw sizes there. What he found was that you get micro-cracking ahead of the crack tip. That's got a slot cut in it; you grab it by the two holes and you pull it. We do the same thing with metal specimens.
But in a metal specimen — they've made specimens that are this tall and about a foot and a half wide, because in a very tough metal, in order to get out to the plane strain condition, you have to have huge dimensions. In something like granite you can be here. In something like glass you can do it with a thin sheet of glass. It just depends on the toughness of the material that's inherent to that material. So we've learned a lot about measuring fracture toughness. We have not learned how to educate students who understand both the materials science and the mechanics of fracture.
§6. Charpy specifications, safety factors, and LNG tankers [22:38]
Originally, if you look at that Navy report, they found that in most of the ships that failed, the plates where the fractures initiated had less than five foot-pounds Charpy energy. The recommendation of the 1946 report was: you'd better have ten foot-pounds of fracture energy in that Charpy bar in order to avoid the brittle fractures and catastrophic failures. In the 1950s, when they started writing the code, someone decided we'd better put a safety factor on, so they upped it to 15. By the 1960s the Coast Guard said we'd better have a bigger safety factor, so they upped it to 20. By the time I was an engineer at Bethlehem Steel and people were designing the Alaskan pipeline, they were saying we need fracture toughness that will stop a running brittle crack. Because there had been fractures in pipelines where the fracture ran for 30 miles in the pipeline once the brittle fracture started. That gets expensive. So they wanted something that would stop a running brittle fracture. They were looking for 70 foot-pounds of fracture toughness, which is one of the reasons I was working on trying to come up with higher-toughness steels.
Typical steel fracture toughness in the mid-'70s — I'll give you an example. Down here they were building LNG tankers at Quincy shipyard. Quincy shipyard is now an auto-import area — they bring in autos from Japan and Europe — but at the time they were still building ships. They were building these huge aluminum-sphere LNG tankers. You have to have a sphere held by a cylinder. The spheres were aluminum, and the skirt, the cylinder that was going to hold the sphere, was steel. I was working on a better steel for that, because the heat conduction would go down to lower temperatures, and we needed a better material with high toughness at lower temperatures, that was easy to weld. The Coast Guard requirement was 20 foot-pounds to get that toughness.
The only microstructure or composition that gives you both strength by force — increased tensile strength — and increased toughness is fine grain size. You can add nickel; it gives you more strength, but it's not necessarily going to give you everything you want. Fine grain size is what you want. So they were normalizing the steels, which means doing a heat treatment to get a fine grain size. About a third of the plates they had to do a second normalization heat treatment to get an even finer grain size, because they had to meet 20 foot-pounds. The plates that were shipped to Quincy from Sparrows Point, Maryland, had an average of 20.5 foot-pounds. They were happy — they were just barely making it.
But every now and then they'd find a plate that had 30 foot-pounds. So what did the shipyard do? They'd go cut that big plate up into a bunch of little test plates. The way you measure the quality control in the shipyard is you run a runoff tab on the weld — you take two of these little plates, put them onto the long weld you're making to put in the ship, and put these test plates there. When you're finished making the weld, you cut off the test plates and measure those. So all the measurements of the weld toughness were being done on 30 foot-pound test plates. The ones being put into production, going into the ship, were being done on things that had 20.5 foot-pounds. It's just a way to cheat. And that's why you have safety factors.
It didn't really matter, because they built five or six of these ships at a cost of, in the mid-'70s, one and a half billion dollars or whatever, all underwritten by US taxpayer dollars, insured. They found, when they put the foam insulation in the ships, they screwed up, and the Coast Guard wouldn't certify the ships. For a number of years you could go off Newport, Rhode Island — you could drive down by the highway and see these six ships sitting there, just sitting there, because there's no use for this billion dollars worth of ships, because they couldn't fix the insulation. I don't know what they finally did — probably used them to carry grain or something.
§7. Ratio analysis diagrams and the North Andover pressure vessel [27:42]
If we look at fracture toughness versus tensile strength — fracture toughness and the elastic limit — you'll find metals away up here, ceramics down here, polymers here, foams down here. Non-technical ceramics and things like concrete should be over here somewhere. You really want to be up in this corner: high fracture toughness and a reasonable elastic limit. These are the design lines. Here's an Ashby plot — you see in red and pink, metals are way ahead of everything else, and that's why metals are good as structural materials. We're going to talk later this week about how they're not the structural material. The structural materials are actually stone and concrete in terms of volume of use.
Irwin came up with something he called the ratio analysis diagram — a plot of fracture toughness versus strength. This is before the Ashby plot, and this is for steels. This is what he called the technological limit, the best steels you could make versus the strength of the steel. They had very high toughness until you got to about 180,000 pounds per square inch, and then it drops off precipitously. So things we make — aircraft landing gear or helicopter rotor masts — have tremendous strength, 300 ksi, but they don't have anywhere near the toughness of submarine steel. Submarine hull steels are way down here, and the Navy's very conservative about submarines.
Most of the steels we make today — not the 1970s, but compared to the 1960s — we've learned to improve steelmaking technology, so we generally can get very high toughness at the strengths we're interested in. There's something on here that's a little hard to see: low-quality practice, high-quality practice, as you go up in terms of steelmaking. If you're loading up to the yield strength of the material, the critical flaw size — going to K equals sigma square root of pi C, where C is the half crack length, or on an edge crack it's just the depth of that edge crack — that's C right there. K is what we use; it comes out of Griffith's formulation. If I'm at the yield strength of the material, which is as high as it can go, and I have a particular toughness, I've only got three parameters to define the fracture.
If you have something of this toughness, or something at the yield strength of the material along here, you can calculate the critical flaw size, and you'll have something on the order of one — the size of the flaw necessary to cause a brittle catastrophic fracture in good steel is going to be on the order of 1 inch. It could be three inches. I can give you an example. It was a 10-inch-thick pressure vessel, and they thought it was going to be a 12-inch critical flaw size. But because of manufacturing errors, they had a half-inch critical flaw size, and the thing, when it broke catastrophically, was up here in North Andover. It sent a 16-ton piece a quarter mile away, and it landed fortunately in an industrial site at 2 a.m. — no one was around. But some of the neighbors were distraught to think that there were 16-ton missiles that could land in their backyard.
§8. Rail steel, Northridge, and code lag [32:03]
Student: [inaudible question about rails]
I've worked on a lot of rail derailments, and one exception is — rail steel has very little fracture toughness in the specs. They don't put it in the spec, so they don't manufacture for it. From the steelmaking side, that's because the rail companies have not been forced to do it, and they don't want to go to the expense of making better-grade steel. A lot of the rail steel specs were developed in 1900 or 1920, and they don't want to modernize them.
We didn't have specifications for high toughness in buildings until the 1990 Northridge earthquake in southern California, which did five to ten billion dollars worth of damage because the steels didn't have a fracture toughness specification. 1990. Some of these buildings were built in the 1960s — we knew about this, and the Coast Guard was requiring it for some ships in the 1950s and 1960s. But no one was forcing the civil engineers to put those specifications into their requirements for buildings, in the '60s, '70s, or '80s. Then in the early '90s we have the Northridge earthquake, ten billion dollars worth of damage to buildings. By 2000 the civil engineers have a requirement for toughness in their buildings. But they don't on railroads. Until somebody decides they have a big enough problem, no one wants to write it into the spec, because it's going to cost money. So they keep living dangerously until something happens. There are lots of industries like that — we still haven't written it into a lot of other industries.
For steels, critical flaw size of one inch for the high-toughness, lower-strength steels. The higher-strength steels we could be talking about critical flaw sizes out here of one millimeter. That's not a very big flaw. The typical flaw size you can detect easily by non-destructive testing is about three millimeters. So out here, you've got to be real careful about how you inspect those helicopter rotor masts or those landing gears on aircraft. And in fact they do — they do extraordinary inspection, because very small flaws can cause failure.
§9. Aluminum, the Brazilian helicopter rotor, and titanium [34:38]
This is a ratio analysis diagram for aluminum. The strength levels, instead of 10,000, you've got 2,000 — one-fifth the strength of the toughness level. The strength levels are down by about a factor of five also. So this is sort of scrunched down by a factor of five vertically and horizontally. You still have a one-inch critical flaw size, but only at 40 ksi. If you're going to the high-strength 70 ksi, 80 ksi things we're making aluminum spars for aircraft wings out of now, we're talking about one-millimeter and three-millimeter critical flaw sizes in those wings. So we have to pay a lot more attention to the design in terms of fracture mechanics.
I had a helicopter rotor spar once that failed in Brazil. They initially said it was because people had put a little notch in the surface. The Brazilians didn't want to send the rotor spar back to a certified repair facility. Not everyone can — the aircraft manufacturers do not certify just anybody to start grinding on your rotor blades. Because if you lose a rotor blade, it's all over, folks — you're going to crash. Even the people from the helicopter company went out there and said, oh, these people were sanding on the rotor spar and repainted it, and they put a little notch in there. They didn't do the fracture mechanics.
I come along four years later — there's a lawsuit going on, and they asked me to explain what happened. I said, this is fracture mechanics, it's not a very complex formula, I can do this with pencil and paper, and I know approximately where the numbers are. It didn't make any sense. Fracture mechanics could not explain the failure with the typical flaw size you get from a grinding operation. I knew approximately what the stress was — rotor blades are fairly well known — and I know what the stiffness of aluminum is. So I calculated, and boy, they would have had to have an eighth-inch flaw. When you're sanding the surface of something, you don't get eighth-inch deep scratches.
I went back and looked at photos. I said, metallurgically, on the surface, it was stress corrosion cracking. The problem was not that they had sanded the surface — they hadn't repainted it well enough to protect it from stress corrosion cracking of a high-strength aluminum. They got a stress corrosion crack which was a three-millimeter-deep crack, which now fracture mechanics could explain. I gave my deposition. The plaintiffs were very unhappy, because the helicopter company had come out with an alert service bulletin saying you've got to be careful and inspect all this stuff. After I gave my deposition, the helicopter company went back, had their engineers look at what I had said, redid the calculations, and withdrew their service bulletins, because they got it wrong. People just say, oh, I had a scratch, and a scratch caused the whole thing to fail. Well, scratches don't cause a ductile metal to fail. They might cause a piece of glass to fail, but they don't cause a piece of metal to fail. And I see two people a year in some failure claiming that — oh, the scratches caused the failure. Not in metals, folks.
Titanium. The Navy was interested in titanium for submarines, so they did the same thing. Now we're up at about sixty percent of the strength of steel in terms of both toughness and strength, and you still have the one-inch critical flaw size. Ti-100 is the Navy alloy for titanium submersibles, which they've never had the money to build. You have this same analysis in terms of critical flaw size if you want to go to 180 ksi strength. Titanium sheets, if you go back, have a much higher toughness. The thin titanium sheets we put on fancy aircraft now have a much higher toughness than the plane strain fracture toughness. All these ratio-analysis diagrams are for the plane strain fracture toughness — thick stuff for building submarines, basically.
[Tom holds up a piece of silicon boule.] That's kind of the story of strength of materials in terms of both toughness and strength, and industry codes and standards that just don't keep up with it until they're forced to. You want to see what brittle material fracture looks like? This is a piece of silicon boule from a growing single crystal silicon. You can actually see the outside on the dark side, and how they spin the silicon. Just take a big hammer and whack it, and you can fracture it, because it's got plenty of critical flaws in it. Very brittle, more brittle than glass. A good example of what brittle fractures look like, and critical flaws that are extremely small. Any questions on fracture toughness?
§10. Class summary: materials by family [40:46]
This is strength versus maximum service temperature. You can see we have some ceramics here that now are competing with the metals, and actually go to even higher temperatures than the metals at very high strength. The difference is, these are ductile, these are brittle. If we're going to use these, we've got to do some other things. Polymers are way down here. Polymers are not really used in large structures. Who builds a polymer bridge, other than maybe some Cub Scouts building a very small bridge across a very small stream? No one's going to build a highway bridge out of polymers, because they just don't have the strength or the service temperature — because of the bonding, which is the secondary bonding between the chains.
If you look at the highest fracture toughness materials at a thousand versus things that are down here a hundred times lower at ten, you're going to find that, instead of a one-centimeter or one-inch-long flaw, you can only tolerate a one-thousandth-of-an-inch flaw. That's why you can cut glass with just a little scratch. Concrete's down here, it's a thousand times lower. Concrete has no strength to speak of in tension. When you're trying to bend a piece of concrete, we give zero strength to concrete in tension. So one of the things we do for concrete is make it into a composite material that has steel rebar in it — reinforcing bar — that takes the tension. Concrete's very good in compression, high strength, it's hard, and we build a lot of big buildings out of it, but only because we can use steel as a reinforcing structure inside. It takes about ten percent by weight, usually, of steel to the concrete, to balance the tensile strength to the compressive strength. Why ten percent? Because steel has about ten times the strength of the concrete, so you can get by with ten percent steel in concrete.
Let's review structural material selection, which we've been doing for a number of lectures. We start out with externalities. We started talking about cost and availability as two of the most important criteria. We've talked about strength, toughness, ductility. We've talked a very little bit about stiffness. We talked a fair amount about lightweight as some of the most important criteria. There's not a single criterion for the selection of a structural material. There are multiple criteria. That's why when people say, I've got the highest-strength material, or I've got the toughest material, or I've got the lowest-cost material — well, that's nice, what about the other properties? It's got to be a balance, and each application has a different balance.
You'll have this in your notes. Then I talked about the geometry of stiffness, and here's when you put things in the same plane. When you put the stiffeners in the other direction, things are not very stiff. Here's specific stiffness versus strength of different materials, which you can't even read — it's too small — but it gives you an idea.
So if I want to look at the classes of materials we're going to go over the next few days. Metals have moderate costs; they're not cheap — it takes a fair amount of energy. At four hundred dollars a ton compared to concrete at twenty to fifty dollars a ton, concrete's a lot cheaper. Ceramics are low cost. So metals are moderate cost, they have good strength, they have good toughness — they don't have the highest strength, they do have the highest toughness — they have good ductility, and we're going to talk about steel in some detail starting tomorrow.
Ceramics are low-cost, high-strength, low-toughness, and brittle. Low cost is such a driver that if I look at the billion-ton-per-year club — steel is 1.6 billion, concrete's 4.2 or something like that — low cost is the driver. We use concrete when we can, compared to steel. But steel has some of these other secondary things; we can use steel in applications where we wouldn't dare use concrete or ceramics. Ceramics have very high strength, they're very hard, very low toughness, and they're brittle, and that means we have to do some significant things. We're going to talk about concrete, and glass is a very interesting material if you want to talk about where people have taken a material that is so brittle that you really have to treat it with kid gloves. When you transport it down the highway you have to be careful, because it could just shatter.
We're going to show you some examples where glass can be as strong as steel. You have to look and see what's really controlling the strength. Glass in principle has very high strength; it just has very little toughness. If we can get rid of those defects, those little small flaws, and get them down to the nanometer size on the surface, and have favorable compressive stresses — we actually use ceramics in higher volumes than we do metals. I can tell you how wonderful steel is, but concrete's an even better material if I want to talk about volume of use.
Polymers — they're moderate cost. They're actually more expensive than metals, but not really on a per-volume basis, because they have low density. They're lightweight. They have inherently low strength — about one-tenth the value of strength of metals and ceramics — and that's because of their secondary bonds. The primary bonds can be very high strength. They're only good for low temperatures. You go above about 200 degrees centigrade, they start pooping out. There are some that go up to 400 centigrade, very few though, and they're very expensive. They have low stiffness. I was thinking about it this weekend — I cannot think of any large structure made out of polymers. You don't build big bridges out of polymers.
They can have very good corrosion resistance. Ceramics have better corrosion resistance than metals. Here's the Achilles' heel of metals: corrosion resistance. But ceramics — the concrete structures, the Roman aqueducts, are not corroding. And the polymers — well, no one wants to put polymers into the environment, because they'll be there a hundred years from now. So those two slides are sort of our summary, and Brian went through these other things on materials.
Anybody have any questions? We have 30 seconds. Okay. I'll be lecturing tomorrow. Brian is going to do glass — he gets to do glass on Wednesday — I have to go to Washington. Then I'll be here on Thursday and Friday, and then my module's done, and Dr. Belmar will be finishing up the next week.