DP_S2012_12

So I don't know what's going on. Let's talk a little bit about deep drawing. In deep drawing we actually have a situation where in the flange area of the draw we are in a condition of, uh, compressive or pure shear, I guess is what Backofen calls it. Okay, it's pure shear, you're squeezing equally on one side and pulling on the other side, and that's down in the fourth quadrant down here. So you get an extension in one direction and a shrinking in the other direction just because of the geometry of this pie-shaped slice going through here, which is just one piece of the whole 360-degree piece that you're trying to draw. Of course, you're not necessarily drawing something 360 degrees circular all the time, they can be rectangular draws and other things.

Down here on the wall you're in plane strain because there's no change in the circumference. And so there's no strain in the circumferential direction, and that's plane strain. That's up where your tangent, with zero strain in the two direction. That's a pure drawing operation. But in fact drawing operations get fairly complex. This is basically a nice schematic that should be in your text. This comes out of Hosford, although it's from my second edition, but anyway.

This is how you make a Coca-Cola can. Okay, you take a circular blank of aluminum, or in Japan you take a circular blank of steel, and you have some hold-down clamps which is part of the die coming down. And then you have two other dies in between, and the two center dies come down and draw a cup. And then this very center die, which is separate of the intermediate die, keeps on coming down and does a second draw. So you get two of your drawing operations in one stroke.

And then you have an ironing ring. This is a piece of hardened steel, or it could be carbide so far as that goes, particularly when you're doing aluminum, with the aluminum cans or something. That basically irons the thing, okay, just like an iron or a rolling pin will flatten something out and push metal ahead, or the dough ahead. This just pushes the metal ahead and thins down the wall. So if you measured a Coke can, the bottom of the Coke can might be nine-thousandths of an inch, the sidewall might today be three and a half thousandths. You'll get some of your thinning when you're making these first two draws, but that may only bring you down to six-thousandths of an inch. The final two and a half thousandths that you take off that original nine-thousandths blank is going to be the ironing operation, and that's when you really get the length, the height of that can. These first two draws, you got a little cup that's a third the height of the actual final can.

Okay, but this is all done in one stroke with a set of one or two million dollar dies. I mean these are not cheap dies, because, think of the tolerances on these things. If you're trying to iron something thirty-five-thousandths thick, it's got to be kept to dimensions that are within one or two ten-thousandths of a thousandth. So you're talking five microns type of tolerances on the diameters, otherwise you're going to end up with a can that's so flimsy that it's liable to explode on you. In fact, a soda can is worse than a beer can because the CO2 pressure is higher in a soda than it is in a beer can.

But you know, the easiest thing to see the importance of the internal pressure in stabilizing these cans is to just take a regular old plastic two-liter bottle of soda. You know, it's nice and rigid and feels nice and hard until you open the top, and then all of a sudden it's so flimsy you can barely hold it. Wants to fall out of your hands when it doesn't have the internal pressure to hold it together. So they actually design these cans on supercomputers, so far as that goes. So drawing, they're making automobile bodies, they're making Coca-Cola cans, they're making lots of things.

One of the things you have to worry about in all these drawing operations is necking. We know the stress-strain curve and we know that if you pull something far enough it'll start to neck down. And so the necking phenomena — I think Dr. Belmar went over what I'm going to go over here in a second — basically is when the material has geometric softening by thinning down faster than the rate of work hardening that you're getting by causing strain. So there's the math. Actually it's easier to see it out of Backofen's got it, and I'm sure Hosford got it, but Hertzberg's book has got it all on one page.

The extent that you can have of uniform strain is before you get necking. At necking, you basically have the rate of work hardening is equal to the rate of geometric softening, okay. And the geometric softening rate actually starts to expand or get faster, because you think of it, in a simple tensile bar the area is decreasing faster and faster as the radius gets smaller and smaller. So a little dr becomes bigger and bigger as you're shrinking. That same incremental dr.

Anyway, so pressure is equal stress times area, that's pretty simple. You take the complete derivative of that and you set dP is equal to zero, and you get d-sigma over sigma is equal to dA over — minus dA over A. You then write down the dA over A in terms of L, and you end up with — and say that dL over L is d-epsilon, which is your strain, and you get sigma is equal — when the stress is equal to the change in stress, the derivative of stress with respect to strain. Well what does that mean? Well geometrically, it means, if you want to try to figure it out from a graph, you can plot stress versus strain. This is the stress-strain curve. You can also plot d-sigma d-epsilon, which is the slope of this. And it's like, there's the slope of it, d-sigma d-epsilon is this dash line coming down, and when those two are equal, that is your necking strain, e-star or epsilon-star.

Okay, however, there's something called the Considère construction, which I mentioned once earlier but I haven't emphasized. But you take a stress-strain curve — this is an engineering stress-strain curve — and you can prove that the strain is the log of one plus the engineering strain. So this is one plus the engineering strain, and you take the tangency or the secant or whatever it is back here at a strain of minus one, draw a straight line, and that will give you your engineering strain when necking starts. If you want to do it in true strain, it turns out this is just a distance of one. So the other one down here was negative one. The distance from the necking strain to where you need to draw your secant is basically just a unit of one. And you can prove that by writing down transforming engineering strain to true strain. Both of these are called the Considère construction because some French mathematician or whatever came up with it once.

Or you basically can plot the log of stress versus strain, get the slope which is equal to n, and you can prove that your necking strain for a circular tensile bar, your necking strain is just equal to your strain hardening exponent. Again, anybody have an idea what the strain hardening exponent for steel or aluminum, low carbon steel or aluminum, might be? It's going to be something on the order of 0.2. Could be 0.15 for higher strength steel, could be 0.25 for a lower strength steel. For a martensitic stainless steel — oh, martensitic stainless steel, it can be 0.5 rather than 0.2, because this is a transformation-induced plasticity where it changes — remember I passed around the ferrite pot and the magnetism, and it changes crystal structure, and so you get increased plasticity. Your necking strain goes to much higher value. Instead of 20% strain it's going to go to 50% strain before you get necking, or even more.

And in fact today, this is the latest thing in the last couple of years in automotive steels, is to develop steels that are TRIP steels, transformation-induced plasticity, so you can get deeper draws with a single set of dies. It's an alternative if you will to super plasticity. It's not as dramatic as super plasticity but it can eliminate half your dies in some drawing operation, or you can successfully make a draw that otherwise wouldn't work.

Now there are, in the real world, stress-strain curves are not always so well behaved, and you sometimes — anybody know what type of material typically gives you a stress-strain curve that reaches a max, then drops and then increases?

Student: Polymer.

A lot of your polymers, polyethylene, polypropylene — polyethylene being this, okay — will typically have a stress-strain curve where it first yields, and then as everything's starting to move around it decreases, and then as you start getting all these chains aligned, now you're starting to get the modulus of the chain as opposed to the van der Waals bond in between the chains, and the thing will take off. So you get a dip.

Certain metals have this type of stress-strain curve. Anybody know what type of metals those are?

Student: [Reads off the sheet.]

Pardon me? Read it off the sheet? Oh, you can read it off the sheet. Yeah, mild steel. Is that where you got the polymer before? Oh, okay, you actually knew. Sorry.

Anyway, old mild steel is the answer. In the old days, before 1960 let's say, when we didn't know how to control the steel chemistry so well, we had nitrogen in the steels, a lot of nitrogen in the steels, and we would end up with something called the Lüders strain. And the mild steel, if you did a tensile test, it'd come up, you'd have the upper yield point, the lower yield point, the Lüders strain — which is this. Actually the Lüders strain would be a bunch of hash marks in here, it'd be kind of oscillating, but it's basically a constant strain. And then it would start work hardening.

And you could show — I remember as an undergraduate, you know, in the '70s, we had to do the little — you take a steel wire and you would turn it into a torsional pendulum, and you would measure the frequency as a function of temperature of this torsional pendulum, and from that you could calculate the diffusivity of nitrogen in the steel. A wonderful laboratory experiment, you just sit there go boop, and then you sit there and count the cycles, time it. I mean it's just really exciting. But back in the 1970s, you went to a steel research lab and they had, you know, million-dollar pieces of instruments to be able to measure this stuff, because this was an active area of research, to try to understand the Lüders strains.

Well, what happens when you have a polymer or a metal that have an upper and a lower yield point and you do a Considère construction? Well, you have the neck begin from Considère construction here, which is just a geometric softening versus material work hardening. And whenever the thing curves over, it's starting to get softer. When the work hardening goes negative, it's definitely getting softer. Negative the hardening becomes softening, and you get a strain, and that strain will propagate itself right through the material as a little thin-down region.

And in a polymer it actually looks like this. This is, I think, out of Hertzberg. That might be in your text. Cold drawing in polypropylene, polyethylene — polypropylene both behave basically the same with that same type of thing. If you took a tensile bar like this and you started pulling on it, you would see one region in here in the thin-down region that will start to neck down as soon as you get yielding. And then as you keep on pulling, you'll see nothing else deforms, but that band just grows until it consumes the whole thing in both directions. And then when it consumes the whole length, that's when the whole thing starts to go up again. And what you're doing in this region, you're basically aligning those polymer chains. So you're getting something it's more like Kevlar, okay. I mean, it turns out polypropylene and polyethylene, if you really get the polymer chains aligned, it's not quite as good as Kevlar, but it starts to approach the strength of one of these high strength fiber composites, because fundamentally it's just the primary bonds along the length of the polymer.

Well, you get the same thing in the steels. You'll get these bands — they used to call them stretcher strains, because you're doing a deep drawing operation and you'll get this band going right across your material. If you were to draw everything far enough you could get rid of the bands, you could stretch them all the way out. But in fact that's not the way a hood or a fender on a car works. You would leave these in, and it'd be a piece of junk, you'd have to throw it away, because when you painted it, all you'd have is these ugly looking stretcher strains in your sheet metal where it had locally necked down.

That's why the steel companies and all the researchers were spending so much money learning about this. Eventually as people learned that it was due to the nitrogen in the steel and the nitrogen changing sites in the BCC lattice — that's what we were doing with the pendulum, you basically were measuring a one lattice site, like a half a lattice unit cell dimension, as the nitrogen switched from one site to another site as you change the tension in the pendulum. The nitrogen was taking a one atom jump, and you measuring it back, that thing bouncing back and forth as you change the tension going from positive to negative in a simple torsion bar or pendulum bar.

Well, if you get the nitrogen out of the steel, which we now know how to do when you melt the steel, you don't get Lüders strains, you don't get a stress-strain curve that has this upper yield strength and lower yield strength. It just goes up nice and uniformly. And you end up getting a piece of sheet metal that you can sell. Okay, there's actually nothing wrong other than aesthetically. When you paint the car, you want the customer to see a nice smooth paint job. And in fact, the number one engineers, the most highly paid engineers in the automotive industry, are paint engineers, because that's what the customer sees.

Okay, and if you have problems in your paint line, you create scrap very quickly, because any types of flaws in that paint are unacceptable to the consumer. Not that it makes it less functional. If you go look at an army truck — the paint engineers are the not the most highly paid, and you look at that, in fact it's a lousy paint job, it's sort of dull matte and it's got these splotches of different colors. They call it camouflage. Okay, they don't care what it looks like. Actually they do care what it looks like, but in a different way, and not in terms of nice smooth reflectivity and things like that.

It turns out — I mentioned to you what Backofen told me 40 years ago, more than 40 years ago, that the longer you think about a tensile test, the more complex it gets. And it's a lot more complex than you realize. This is what Hertzberg talks about. In a simple necking in a tensile test, if you look at a little volume element inside the neck, you'll find it's got stresses in all three directions. You've got unyielding material basically on either side, and that means that you will induce Poisson's ratio giving you stresses in the other two directions, even though you're doing a uniaxial tensile test. In the neck region it's triaxial. And so he actually says that triaxial tensile stress distribution within the neck region.

Well, what difference does that make? Well, I had a debate with some people a few years ago, year and a half ago, about — we had some brittle-looking fractures in some steel welds that were down in a hole in the ground in a gas well. And the people said, oh, this proves that this is a brittle material that people put in the ground originally. So we just went and we bought some 1045 steel. 1045 steel is plain carbon steel, carbon-manganese steel. The actual bar we had was 46 rather than 45 carbon, but there's a range. It's just carbon, manganese, and some phosphorus and sulfur impurity. Garden variety steel.

And let me try to get this up. Made some tensile bars. We made two tensile bars. One was a regular tensile bar and it had some ductility, it had like 20% ductility, I guess I can look at the report. I don't know if we even reported it, but anyway, I'm sure we had the ductility somewhere — as a smooth tensile bar. We then made a notched tensile bar. And we just basically — there's a little machine bevel here, so it's larger in diameter, but the cross-sectional area at the root of the notch was exactly the same as the half-inch tensile bar. So this might have been 5/8 of an inch, this was a half inch, but the fracture surface was the same — half, 5/8 of an inch. But basically what we were doing is, we, by having a notched tensile bar, we were introducing the triaxiality that you get from a neck. We had unyielding material on either side, whereas in a smooth tensile bar everything's yielding.

So what happens? Well, what happens is — and you actually can read it in textbooks. This is what happens in my business, I have to explain undergraduate metallurgy to PhD metallurgists. Anyway. So let's see if I can get this to show up. This is the unnotched tensile bar fracture in the scanning electron microscope. It is ductile dimples. It's not the greatest ductile dimples, it's a medium carbon steel, but it has ductile dimples. That exact same steel — we've done nothing to it other than change the geometry of the tensile specimen by putting a notch in — at the same magnification, all of a sudden it goes from ductile dimples to cleavage fracture. All I did was change it from uniaxial tension to a triaxial state of stress at the fracture location.

Turns out the steel will change the fracture mode just by the stress state, whether it's triaxial or whether it's uniaxial. If you want, you can think of this as what happens in plane strain versus plane stress. Dr. Belmar kind of showed you some fracture, didn't you, must have shown them some fractures with plane stress versus plane strain. Out towards the edge you'll get plane stress, in the center you'll get plane strain. Plane strain is bad in terms of, it's the worst stress condition, or triaxial stress are the worst stress conditions in terms of the fracture behavior. The material will change the microscopic fracture mode depending on the stress state.

Then get the edge right. The sides of the cone in cup and cone are plane stress, and the flat part is plane strain, or essentially a region where you have a triaxial stress state. You get plane strain by a triaxial stress state. It's plane strain elongation, or it's plane strain — it's strain — but that means that the tensile stress is triaxial.

Okay, so that's a little bit about necking in general. Let's talk about necking with regard to our sheet metal drawing. In sheet metal drawing we're talking about flat sheets, and they can have either diffuse necking, where the whole sheet thins down, or they can have localized necking. The Lüders strains or the stretcher strains that you get by pulling polyethylene are localized necking. And there are some criteria for these localized necks. First of all, if you form a localized neck, it must be a state of plane stress or plane strain, because there's no strain in the x-prime-2 direction. It's not changing length because the material on either side is not deforming at the same rate.

So you can do a Mohr's circle diagram. If you draw a Mohr's circle diagram — and let's discuss the Mohr's circle diagram where e2 and e3 are Poisson's ratio times e1, and Poisson's ratio in elasticity might be 0.333 something like that. So this is not a plastic Mohr's circle where the Poisson's ratio is a half, it's an elastic Mohr's circle where the Poisson's ratio is like 0.3. And you draw to where you have a plane strain condition. A plane strain condition is where one of your strains is zero. So epsilon-i-j, which is either epsilon-2 or epsilon — it's either where your shear strains go to zero. Epsilon-1-2 goes to zero will be, if this is a unit strain and this is 0.33 times that unit strain, it turns out the plane strain condition will be at an angle of 55 degrees, because this is 2-theta.

We haven't gone over Mohr's circle constructions, so I apologize, but anyway, if you do the Mohr's circle on all this, which is the way people used to analyze strains 70 years ago, stresses and strains, you can prove that the angle of these Lüders bands or stretcher strains to the tensile pulling direction should be at 55 degrees. And lo and behold, if you go look at these nitrogenated steels, they were finding it. I remember as an undergraduate I think I got a question on a quiz before they had taught us all this, and said, what angle do you expect these? I figured, well, this is the pure shear direction or something, and I said 45 degrees. Uh-uh, it's 55 degrees, and if you go measure it, it is 55 degrees. And the way you explain it is in terms of plane strain necking behavior.

It turns out that you can prove for sheet metal — where you're getting zero extension in one direction but the other direction is not plane strain — you can prove that this criteria of d-sigma d-epsilon for local necking in sheet is sigma over 2. And so if you look at sheet metal and you do the Considère construction, you actually have will diffuse necking at epsilon is equal to n, and you'll have localized necking at 2n. So you can have localized and non-localized necks in sheet metal drawing, or diffuse necks and localized necks.

And if you look at an arbitrary — this is out of Backofen if I remember — an arbitrary biaxial stress-strain, Von Mises ellipse, not very elliptical, but Backofen wanted to point out it doesn't have to be, this is completely arbitrary. You will have regions depending on whether you're in pure shear down here, going all the way up through plane strain here, over to another pure shear. You will have changing angles of these localized necks. You cannot have any necking in compression back here, but you can have no local necking in balanced biaxial or on either side of it. So between plane strain and plane strain you have no local necking. In these regions over here you can get local necking, and it's all from geometric softening versus work hardening, Considère construction. But we can predict when these necks form. Now, anybody have any questions on any of that?

So you can predict the necking. If you go to think about super plasticity in necking and start looking at the strain rate in terms of these dA/dt — so it's a strain rate as a function of time — you can write down formulas, and it turns out that for a pure Newtonian liquid, with m is equal to one, has no strain rate dependence in terms of the rate at which you're pulling it. So it doesn't matter whether you're pulling it fast or whether you're pulling it slow, it will neck down the same. Or you can go to various m values, this is 3/4, 1/2, and 1/4. You can see that as the area gets smaller and smaller, the tendency to neck down gets greater and greater as you get to smaller m values. So even super plastic material which might be down here will eventually neck down and break.

But if you — and so you're basically looking at how fast will something, if you have some perturbation on the surface, how fast will the perturbation grow. It's a function of the cross-sectional area, because this is sort of cylindrical.

Now, why is this important? It's important if you think of the longest links that we form by — well, actually I shouldn't say that — by — well actually the longest links that we form by pure stretching are in a material that's not metallic. We've talked about it before. What? Glass. It's for making optical fibers. So anybody know how optical fibers are made? Corning has got all the basic patents on this, and this is what keeps Corning alive, is they really went after the optical fiber business.

They basically start on a lathe with a glass rod. It could be a half-inch or whatever glass rod. And they start plasma spraying on glass frit of different composition, so they make a functionally graded glass rod that might be two inches in diameter when they're all done. And they've functionally graded the composition for the optical properties you want. Something where the light going down the center of the glass hits different indices of refraction of glass because of the functionally graded composition, and bounces back to the center. You want to trap the light inside the fiber. You don't want it to get out of the fiber. If you made a uniform piece of glass, some of it would hit the walls at a certain angle and some of it would get out, and you'd leak photons. And you don't want to lose photons.

The original glass fibers which didn't have all this great functionally graded material, they might transmit light a couple hundred yards. Now we have glass fibers that will transmit light thousands of miles without losing more than half of its — and so when you're going to bury undersea cable, you don't want to have repeater stations very often. Okay, so Corning developed this process to make big rods with functionally graded glass composition that changes the index of refraction, so you always get internal reflections to keep the photons in the container of glass.

But then they had to draw that down. Well, turns out glass fortunately is the closest thing we know in the world to a Newtonian fluid. When you heat it up, it has an m value of one. So when they heat it up, they basically have something that heats this glass rod and they just pull a fiber out of it. And they pull it for thousands of miles, you know, they just keep coiling it and just keep pulling it, using temperature as a dieless drawing operation.

So if you basically have heat on one side and you're cooling on the other side, and you have the rod pulling through here, and you're basically propagating the neck if you will in that direction and pulling a fiber out this way, the temperature looks like this. You're using a dT/dx as your die. There is no physical material as a die, you're using temperature, a temperature gradient as your die material. And you're pulling it. The flow stress decreases, but it's a Newtonian material, it's the most super plastic of all super plastic materials, glass, hot glass. And you end up doing dieless drawing.

And people have tried to do this with metals, but the problem — what's the problem with metals? You don't have very big m values. You can use super plastic metals, but if you tried to do this very long time with super plastic metals, the grains would probably start growing and all kinds of other things, and then you lose your super plasticity. So you could probably do it, but it works really well with glass. And it is kept Corning a profitable company for all these many years — well, many years over the last 20 years.

Student: But no strain hardening there?

No, because it's all flowing. You're getting the glass so hot, it's basically flowing. Now, I take that back. You have to be careful when you make glass that you remove the residual stresses. There will be residual stresses. So it turns out there's lots of technology even if Corning didn't own the patents.

This is typical Corning. If you ever go to a Corning plant, they have more security than the federal government and most military installations, unless they have nuclear weapons. The tightest security I've ever seen is if they have nuclear material on site, and that's the tightest security I've ever had to go through. Now, they may have tighter security to go to the White House or something, but tightest I've ever seen is nuclear weapons. The second tightest is Corning. Corning has lost some very important technology to people who have stolen it from them, and as a result they are about as paranoid as you can be in terms of maintaining their intellectual property.

So if you go to the research labs, you know, they always have an escort, and that's not really any different. But you go into a manufacturing plant at Corning where they're making something like — the most recent one I've been to is where they're making the glass for your computer screens. Okay, that is basically — I can't tell you too much because I had to sign confidentiality, but it's not all that different than a sheet form of cold — of this hot drawing. Now they do some other things so they get perfect structures on both sides, both surfaces. I don't want to get into glass technology right now. I think I may have covered some of this in the lectures you're going to do on the casting. I may have talked about casting of glass and the Pilkington process and stuff, for making regular window glass.

But for making — Corning basically takes some of that same type of technology they use for optical fibers, and they sort of do it for these very thin screens for your computers. And so they sort of own the world's market on that too. But you go to that plant and they will be sort of nasty, okay. There's no compromise and say, oh well, we just want to take one picture. You couldn't take a picture of this wall at Corning. They're not going to let a camera into that facility other than their camera, and they're going to — anyway, never mind.

Actually, most military base security is not all that tight. Actually, it certainly wasn't when I was a kid growing up. I lived in Virginia Beach, and hey, most of my friends lived on military bases. You want to get on the base? You drive on, okay. I used to deliver mail at a military base, you can get — you know, was just as easy getting there as anywhere else in town. But then there was the Walker spy case in the mid '80s. That changed things a little bit.

Anyway, I thought I was going to — can't remember what story I was going to tell, but anyway. Okay, let's talk — if there are no other questions, I was going to say something about the whole glass technology business. But oh, I was going to tell you about light bulbs. Maybe I'll finish that before I start the friction hill.

And by the way, we will have — I need to tell you, we will have class on Monday and Tuesday. My trip to Florida got cancelled, actually got postponed, until the beginning of April. Dr. Belmar will give his last lecture, he was actually here yesterday. I guess I screwed things up, I thought he was going to be out of town this week. So he'll be here Monday and he'll lecture, which will be his last lecture. And then I will lecture on Tuesday of next week, which will probably be my last lecture, unless we decide to do Thursday or Friday. I'll let you know whether we're going to do anything else, but we may finish by Tuesday, we certainly should finish by Thursday or Friday.

We will finish next week with the lectures, which means we will be starting the presentations. And not everybody signed up — I just put this together this morning, and there's 20 students, so we're going to have 10 days somewhere between April 2nd and April 20th. I put in eight names to be ready that first week, and I recognize some people can only do it on certain days, and we'll accommodate those things, but I'll have my secretary email this around. I filled in blanks that other people didn't fill in, but you should be planning on a presentation. Hopefully we can finish all this in the first three weeks of April. I don't know if I'm going to get four days in that week or four days this week, but we only need 10 days total in about a three-week period. So if I can be in town two-thirds of those days we'll get it all done. If not, we'll go to the end of April, but I don't expect to have to go into May.

Okay, so what was I going to tell you? I was going to tell you about light bulbs, and getting rid of those residual stresses. Glass has to be annealed. If you can form glass — whatever glass, and I'm going to tell the story, I'll tell you, is about light bulbs, regular old incandescent light bulbs. But after you form it, you're forming at a temperature where it flows easily, and you can blow-mold a light bulb basically.

Corning had the business for light bulbs, and kind of their patents expired and everybody else started competing with them. And then they sort of had the business for the big old cathode ray tubes for televisions and computer monitors of the old days before we had flat screen monitors. And they sort of controlled that because they had the most productive technology equipment. But eventually patents expired, and they lost some of the technology through theft and other things.

But in any case, the old light bulbs, the old simple old incandescent light bulbs, had to be formed and then annealed before you use them, and the reason is they would have some significant residual stresses. Now, I'm sure that when Corning makes that optical fiber, they may have even designed in a geometry like that, favorable compressive stresses on the outside and you have tensile stresses on the inside. And that can make glass very fracture resistant.

Professor Owen [?] when I was a student had a piece of chemically tempered glass that had compressive residual stresses. It was bowed like that, it was an eighth of an inch thick, and he could put it on the table, and he could flatten it with his hand, three inches over about 15 inches, and it wouldn't break. Because it had favorable compressive residual stresses. I'd love to have that sample. I frankly would probably wear a pair of glass — gloves when I did it, because one day it's liable to have a defect in it and a scratch or something, and all of a sudden it's going to shatter, and you know, cut my hand. But anyway, nonetheless, you don't want to have any residual stresses, or if you do have residual stresses, you want to have favorable residual stresses that are compressive on the surface, so you have to overcome the compressive stress when you're doing bending of the glass.

So one time I got a call from some attorney in Southern California, and he had some kid, 14, 15-year-old teenager, whose parents had given him a black light for his birthday or Christmas or Hanukkah or whatever it was. And he had just taken a shower, and he came out of the shower, and he wanted to see if the soap or whatever would radiate. I don't know, maybe he had incandescent soap that would, you know, light him up with black light. But he was standing over the black light, and a drop of soapy water hit the light bulb and shattered the light bulb, and he lost an eye.

So they wanted me to look at this and figure out, well, why did this light bulb shatter? And so they sent me the light bulb. Well, first of all I looked at it, and one — you make light bulbs by, well, in high-volume production, like when you're making hundreds of millions of them, like just regular white lights, you would make them by a blow-molding process, but in this proprietary Corning type of equipment that everything's absolutely controlled. But when you're making black lights, how many black lights do you sell? A few tens of thousands a year. So they were made in Korea, probably by hand.

And the first thing I saw on the fractured light bulb was I could see some drips of soap, okay, because the water had dried and I could see the drip. So it was true, I mean obviously some soapy water dropped onto the lit black light bulb, which is just like a regular old 100-watt incandescent light bulb. And on one side where it had fractured it was about six-thousandths of an inch thick, it was paper thin, like two sheets of paper thin. And the other side it was actually fairly thick, it was like ten sheets of paper thick. So obviously, whenever they blow-molded this, they didn't have the thing uniformly heated and it got thin on one side. Well, that's one explanation.

But then I thought, well, you know, when you have different thicknesses and you do the annealing process to soften the glass and get rid of the residual stresses, you form it at one temperature and an intermediate temperature you would anneal it to soften it and relieve the residual stresses, and then you cool it down. And then intermediate temperature, when you don't have uniform thickness, you may not get uniform cooling and therefore you may not have eliminated your residual stresses. So I said, I called up the people, I said, well if I can get some more of these bulbs, I'd like to do some tests. I'd like to drop some water on a hot light bulb — you know, hot light bulb meaning I just turned the light on and the filament's hot, right — and I want to drip some water on it and see what happens, because I think they got residual stresses.

Well, they decided — well, they didn't want me to do that, because if I did it and it wasn't successful, I'd have to say that didn't work. I do have to tell the truth, you know. So they decided to let — have me have some students do this test, and they weren't supposed to tell me the results. But I — so I'm walking through the lab one day, and I got a couple students there with a bunch of light bulbs, and they're dripping water on light bulbs and videotaping it. They saw me coming so they stopped. And I never did — the case settled before I ever found out what happened.

So I finally asked the students, well, what happened? It turns out, you could take a regular light bulb you buy at the store, a white light bulb, and you could drip water on that all day long, and it's a hot light bulb, but nothing happens because it has no residual stresses. You take one of those Korean-made hand light bulbs, for the black light bulbs, you put a drip of water on there — kaboom, just blew up, okay. And they had videotape of that. That's why the thing settled. So when you're making glass, you have to relieve residual stresses.

Okay, the other story on glass is freshly made glass, as it's blown, has a very perfect surface. And glass actually corrodes in the moisture in the air, it's a silicate, it forms silicate hydroxides. And the strength of glass will change dramatically within a few days after its manufacture. And one of the secrets of fiberglass is they draw the fibers and they coat them with epoxy or whatever plastic resin it is, and they keep the moisture away from attacking the surface of the glass, so those fibers maintain fantastic strength, 200 ksi if you actually could measure them.

Well, the story I know is, my old thesis advisor Bob Rose lives up on the North Shore. Sylvania had a glass light bulb manufacturing plant up there in Beverly. And he used to lecture 3.091 back in the days when I was a student, and he would stop and get freshly made light bulbs on the way in before his lecture, and he would take the light bulbs in 10-250 and throw them across the room, and they'd bounce. They wouldn't shatter, because they were freshly made. They did not have surface imperfections that caused them to fracture.

Those surface imperfections may only be a micron or two deep, but when you have a material that has a fracture toughness of less than one ksi square root of inch — Dr. Belmar will be able to, he should have given you the equations — you can prove that a few-micron-deep scratch on a piece of glass will destroy its fracture resistance, because it's such a brittle material. But if it's freshly formed and the moisture hasn't attacked the surface, you don't have those surface imperfections. And the light bulbs bounce when you throw them across the room. But don't do this test at home, okay. Thanks.