1 00:00:00,030 --> 00:00:02,470 The following content is provided under a Creative 2 00:00:02,470 --> 00:00:04,000 Commons license. 3 00:00:04,000 --> 00:00:06,320 Your support will help MIT OpenCourseWare 4 00:00:06,320 --> 00:00:10,680 continue to offer high quality educational resources for free. 5 00:00:10,680 --> 00:00:13,300 To make a donation or view additional materials 6 00:00:13,300 --> 00:00:17,025 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,025 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:26,570 --> 00:00:28,070 LORNA GIBSON: I think, last time, we 9 00:00:28,070 --> 00:00:31,210 got as far as talking about processing of foams 10 00:00:31,210 --> 00:00:33,960 and we talked a bit about processing of polymer foams. 11 00:00:33,960 --> 00:00:36,420 And today, I want to pick up where we left off. 12 00:00:36,420 --> 00:00:38,850 And I was going to talk about processing metal foams. 13 00:00:38,850 --> 00:00:42,040 We'll talk a little bit about carbon foams, ceramic foams, 14 00:00:42,040 --> 00:00:43,530 and glass foams. 15 00:00:43,530 --> 00:00:45,630 We'll finish this section on processing today 16 00:00:45,630 --> 00:00:47,630 and then we'll start talking about the structure 17 00:00:47,630 --> 00:00:48,870 of cellular materials. 18 00:00:48,870 --> 00:00:50,870 And hopefully-- we won't finish that today, 19 00:00:50,870 --> 00:00:53,866 but we'll finish it the start of tomorrow's lecture. 20 00:00:53,866 --> 00:00:55,990 And then, we'll start doing mechanics of honeycombs 21 00:00:55,990 --> 00:00:56,590 tomorrow. 22 00:00:56,590 --> 00:00:57,720 OK? 23 00:00:57,720 --> 00:00:59,571 So that's the scheme. 24 00:00:59,571 --> 00:01:02,070 I thought what I'd do-- I have a whole series of slides that 25 00:01:02,070 --> 00:01:05,519 show, schematically, a variety of different processes 26 00:01:05,519 --> 00:01:07,220 for making metal foams. 27 00:01:07,220 --> 00:01:09,440 So I thought I would just go through the slides- 28 00:01:09,440 --> 00:01:11,360 and I think I did this really quickly last time-- but I would 29 00:01:11,360 --> 00:01:13,900 write down a little bit of notes on each of the slides 30 00:01:13,900 --> 00:01:16,740 so that you've got some notes on it, too. 31 00:01:16,740 --> 00:01:18,710 This is the first method here. 32 00:01:18,710 --> 00:01:21,950 And many of these methods were developed for aluminum foams. 33 00:01:21,950 --> 00:01:24,920 But you could, in principle, use them for other types of foams, 34 00:01:24,920 --> 00:01:26,020 as well. 35 00:01:26,020 --> 00:01:27,800 This first method here-- let me see 36 00:01:27,800 --> 00:01:29,540 if I can get my little pointer. 37 00:01:29,540 --> 00:01:32,850 [INAUDIBLE] The idea here is that you take molten aluminum. 38 00:01:32,850 --> 00:01:35,620 Down in this bath here, you've got molten aluminum. 39 00:01:35,620 --> 00:01:38,860 And they put, into the aluminum, silicon carbide particles. 40 00:01:38,860 --> 00:01:40,700 And the silicon carbide particles 41 00:01:40,700 --> 00:01:42,750 adjust the viscosity of the melt. 42 00:01:42,750 --> 00:01:44,260 They make it more viscous. 43 00:01:44,260 --> 00:01:47,500 And then they just have a-- I've got this thing here-- 44 00:01:47,500 --> 00:01:50,934 they've got a tube here that they blow gas in with. 45 00:01:50,934 --> 00:01:52,600 And if you go to the bottom of the tube, 46 00:01:52,600 --> 00:01:56,390 there's an impeller, or a little paddle, that stirs the gas up. 47 00:01:56,390 --> 00:01:59,764 And so the gas just forms in the molten aluminum here. 48 00:01:59,764 --> 00:02:01,180 And then they have conveyors which 49 00:02:01,180 --> 00:02:07,110 pull off the molt-- or the metal foam, and then it cools. 50 00:02:07,110 --> 00:02:09,060 The idea is that if you just had the aluminum, 51 00:02:09,060 --> 00:02:11,268 you couldn't really do this because the bubbles would 52 00:02:11,268 --> 00:02:14,260 collapse before they cooled down and became a solid. 53 00:02:14,260 --> 00:02:17,520 But adding the silicon carbide particles increases 54 00:02:17,520 --> 00:02:19,400 the viscosity of the melt. It helps 55 00:02:19,400 --> 00:02:21,040 prevent drainage of the foam. 56 00:02:21,040 --> 00:02:23,352 Normally, if you have a liquid foam, just from gravity, 57 00:02:23,352 --> 00:02:24,810 you're going to have some drainage. 58 00:02:24,810 --> 00:02:27,510 It's going to tend to-- some of the liquid is going to tend 59 00:02:27,510 --> 00:02:30,060 to sink, just from gravity. 60 00:02:30,060 --> 00:02:32,330 By putting the silicon carbide particles in, 61 00:02:32,330 --> 00:02:33,690 you increase the viscosity. 62 00:02:33,690 --> 00:02:35,430 It helps prevent the drainage. 63 00:02:35,430 --> 00:02:38,890 And you can get the foam bubbles to be stable. 64 00:02:38,890 --> 00:02:41,810 Let me just write one little note here. 65 00:02:41,810 --> 00:02:47,630 The first method here involves just bubbling gas 66 00:02:47,630 --> 00:02:49,030 into the molten aluminum. 67 00:02:55,350 --> 00:02:59,730 And that molten aluminum is stabilized 68 00:02:59,730 --> 00:03:01,640 by silicon carbide particles. 69 00:03:01,640 --> 00:03:12,190 Sometimes people use aluminum particles and the particles 70 00:03:12,190 --> 00:03:29,240 increase the viscosity of the melt. 71 00:03:29,240 --> 00:03:42,924 And that reduces the drainage and it stabilizes the foam. 72 00:03:59,810 --> 00:04:03,340 That process was developed at Alcan in Canada 73 00:04:03,340 --> 00:04:06,930 and at Norsk Hydro in Norway. 74 00:04:06,930 --> 00:04:10,780 And this foam here is an example of the foam that they've made. 75 00:04:10,780 --> 00:04:12,880 And you can kind of see-- there's a density 76 00:04:12,880 --> 00:04:13,967 gradient in this foam. 77 00:04:13,967 --> 00:04:14,800 I'll pass it around. 78 00:04:14,800 --> 00:04:15,530 You can see it. 79 00:04:15,530 --> 00:04:18,360 But the bubbles are smaller down here and there's fewer of them 80 00:04:18,360 --> 00:04:19,630 than there are up here. 81 00:04:19,630 --> 00:04:21,630 And that's partly from the drainage. 82 00:04:21,630 --> 00:04:23,290 The molten aluminum is draining down 83 00:04:23,290 --> 00:04:24,860 and you get more liquid at the bottom 84 00:04:24,860 --> 00:04:26,609 and then you get more solid at the bottom. 85 00:04:26,609 --> 00:04:28,190 So that's the Alcan foam. 86 00:04:31,080 --> 00:04:31,580 OK. 87 00:04:31,580 --> 00:04:33,621 Another-- there's half a dozen of these processes 88 00:04:33,621 --> 00:04:34,810 for metal foams. 89 00:04:34,810 --> 00:04:39,350 Another version of the process involves taking metal powder 90 00:04:39,350 --> 00:04:42,317 and combining it with titanium hydride powder. 91 00:04:42,317 --> 00:04:44,150 And then you consolidate it and you heat it. 92 00:04:44,150 --> 00:04:48,149 So if I can show through the schematics here. 93 00:04:48,149 --> 00:04:50,690 In the first step, you take the two powders, you mix them up. 94 00:04:50,690 --> 00:04:53,880 So the second thing down here is mixing the powders up. 95 00:04:53,880 --> 00:04:55,520 And then you press them together. 96 00:04:55,520 --> 00:04:57,530 There's a dye here that you press it, 97 00:04:57,530 --> 00:04:58,950 and then you get pieces. 98 00:04:58,950 --> 00:05:01,230 And then you can heat that up. 99 00:05:01,230 --> 00:05:03,540 And the way that this works is that the titanium 100 00:05:03,540 --> 00:05:06,490 hydride decomposes at a temperature of about 101 00:05:06,490 --> 00:05:09,530 300 degrees C. And if the other powder is something 102 00:05:09,530 --> 00:05:12,800 like aluminum-- aluminum melts at something like 660 degrees 103 00:05:12,800 --> 00:05:16,670 C-- the aluminum has become soft at 300 degrees C, 104 00:05:16,670 --> 00:05:18,710 but it's not molten. 105 00:05:18,710 --> 00:05:20,920 And the titanium hydride-- when it decomposes-- 106 00:05:20,920 --> 00:05:22,320 forms hydrogen gas. 107 00:05:22,320 --> 00:05:24,000 So the hydrogen gas forms the bubbles 108 00:05:24,000 --> 00:05:25,940 that you need to make the foam. 109 00:05:25,940 --> 00:05:27,550 Are you riding your bicycle? 110 00:05:27,550 --> 00:05:31,300 You are tough. 111 00:05:31,300 --> 00:05:32,369 Very tough. 112 00:05:32,369 --> 00:05:34,410 I ride my bike, but I gave up a couple weeks ago. 113 00:05:34,410 --> 00:05:35,701 Well, three weeks ago, I guess. 114 00:05:35,701 --> 00:05:38,150 When it started snowing, I gave up. 115 00:05:38,150 --> 00:05:42,430 The idea with this process is you can use titanium hydride 116 00:05:42,430 --> 00:05:45,070 powder with aluminum and the aluminum becomes 117 00:05:45,070 --> 00:05:48,690 soft at the temperature that the titanium hydro decomposes. 118 00:05:48,690 --> 00:05:50,310 And when it forms the hydrogen gas, 119 00:05:50,310 --> 00:05:52,290 that gives you the bubbles, and so you get 120 00:05:52,290 --> 00:05:55,010 the foam made by that process. 121 00:05:55,010 --> 00:05:58,560 And that was developed by a place called Fraunhofer. 122 00:05:58,560 --> 00:06:00,330 And I have one of their little foams here. 123 00:06:00,330 --> 00:06:04,390 This is an example of their foam made by that powder metallurgy 124 00:06:04,390 --> 00:06:05,434 process there. 125 00:06:08,800 --> 00:06:09,340 OK. 126 00:06:09,340 --> 00:06:11,190 Let me just write a little note about that. 127 00:06:16,630 --> 00:06:21,460 So you can mix up titanium hydride powder with a metal 128 00:06:21,460 --> 00:06:27,286 powder and then heat that up. 129 00:07:04,950 --> 00:07:08,010 When you do this, you need to have a metal powder that's 130 00:07:08,010 --> 00:07:12,360 going to be deforming by, say, high temperature creep 131 00:07:12,360 --> 00:07:15,100 at the temperature that the decomposition of the titanium 132 00:07:15,100 --> 00:07:15,920 hydride happens. 133 00:07:15,920 --> 00:07:17,650 And for aluminum, that works. 134 00:07:17,650 --> 00:07:20,780 So you need to have the metal material be 135 00:07:20,780 --> 00:07:22,370 able to deform fairly easily, in order 136 00:07:22,370 --> 00:07:25,029 to get these bubbles to form a nice foam. 137 00:07:25,029 --> 00:07:26,570 But that's another way you can do it, 138 00:07:26,570 --> 00:07:29,410 is by consolidating these two powders. 139 00:07:29,410 --> 00:07:31,800 Here's another way to do it. 140 00:07:31,800 --> 00:07:34,800 You can also make use of this property of the titanium 141 00:07:34,800 --> 00:07:37,060 hydride-- that it'll decompose and form 142 00:07:37,060 --> 00:07:39,930 hydrogen gas-- by just putting it into molten aluminum. 143 00:07:39,930 --> 00:07:44,260 And in this example here, you've got an aluminum melt in here. 144 00:07:44,260 --> 00:07:47,730 And this time, they've added 2% calcium to it. 145 00:07:47,730 --> 00:07:50,230 Again, to adjust the viscosity. 146 00:07:50,230 --> 00:07:52,882 And then they add the titanium hydride in this step here 147 00:07:52,882 --> 00:07:54,590 and they've got a little mixer thing here 148 00:07:54,590 --> 00:07:56,440 that's spinning around and will mix it. 149 00:07:56,440 --> 00:08:00,100 And then they'll put a lid on it to control the pressure 150 00:08:00,100 --> 00:08:02,880 and the titanium hydride will decompose, 151 00:08:02,880 --> 00:08:04,690 the hydrogen gas will evolve, and you'll 152 00:08:04,690 --> 00:08:07,550 get the foam made by that method, too. 153 00:08:07,550 --> 00:08:10,890 So you can stir titanium hide right into a molten metal, 154 00:08:10,890 --> 00:08:11,496 as well. 155 00:08:45,540 --> 00:08:46,040 OK. 156 00:08:46,040 --> 00:08:47,710 So that's another method. 157 00:08:47,710 --> 00:08:52,240 And I think that was made by something called the Alporas 158 00:08:52,240 --> 00:08:52,890 process. 159 00:08:52,890 --> 00:08:54,765 And this is an example of one of their foams. 160 00:08:54,765 --> 00:08:58,150 I'm pretty sure that's an Alporas foam there. 161 00:08:58,150 --> 00:08:59,002 Yep. 162 00:08:59,002 --> 00:08:59,877 AUDIENCE: [INAUDIBLE] 163 00:09:03,770 --> 00:09:06,000 LORNA GIBSON: They can't really control it perfectly. 164 00:09:06,000 --> 00:09:08,130 In that first example that's going around-- maybe 165 00:09:08,130 --> 00:09:10,390 you might have missed it-- there's this drainage. 166 00:09:10,390 --> 00:09:13,630 The first one's made by a molten process and you get drainage. 167 00:09:13,630 --> 00:09:15,600 And you get different sized bubbles. 168 00:09:15,600 --> 00:09:17,500 And you get different-- you get a density 169 00:09:17,500 --> 00:09:19,280 gradient in the thing, as well. 170 00:09:19,280 --> 00:09:21,710 So you can't control these things perfectly. 171 00:09:24,420 --> 00:09:24,920 OK. 172 00:09:24,920 --> 00:09:28,130 Here's another method for the metal foams. 173 00:09:28,130 --> 00:09:30,820 This one here involves replication. 174 00:09:30,820 --> 00:09:33,010 In this method here, what you do is you start out 175 00:09:33,010 --> 00:09:35,700 with an open-cell polymer foam. 176 00:09:35,700 --> 00:09:39,340 In this step up here, there's an open-cell polymer foam. 177 00:09:39,340 --> 00:09:41,180 You fill that with sand. 178 00:09:41,180 --> 00:09:44,960 So you fill up all the open parts of the cells with sand. 179 00:09:44,960 --> 00:09:47,560 Then you burn off the polymer. 180 00:09:47,560 --> 00:09:49,520 And so you've got a little channels 181 00:09:49,520 --> 00:09:51,180 where the polymer used to be. 182 00:09:51,180 --> 00:09:55,790 And then you infiltrate those channels with the molten metal 183 00:09:55,790 --> 00:09:56,820 that you want to use. 184 00:09:56,820 --> 00:09:59,870 So you replicate the polymer foam structure. 185 00:09:59,870 --> 00:10:02,350 This is the infiltration process here. 186 00:10:02,350 --> 00:10:04,012 This little thing here is your furnace. 187 00:10:04,012 --> 00:10:05,720 And then you get rid of the sand and then 188 00:10:05,720 --> 00:10:12,380 you're left with a metal replica of the-- a replica 189 00:10:12,380 --> 00:10:13,960 of the original polymer foam. 190 00:10:13,960 --> 00:10:16,450 And this example here is one of these things that's made 191 00:10:16,450 --> 00:10:18,200 by this replication process. 192 00:10:18,200 --> 00:10:19,844 So that's an open-celled aluminum. 193 00:10:22,165 --> 00:10:24,540 I think the-- if you look at the density of these things, 194 00:10:24,540 --> 00:10:25,480 they're fairly low. 195 00:10:25,480 --> 00:10:28,100 And so there's quite a large volume of pores 196 00:10:28,100 --> 00:10:29,480 and they're all interconnected. 197 00:10:29,480 --> 00:10:31,420 So it's not that hard to get the sand out. 198 00:10:52,410 --> 00:10:54,460 This method would involve replication 199 00:10:54,460 --> 00:10:57,930 of the open-cell foam-- the polymer foam-- by casting. 200 00:10:57,930 --> 00:11:07,805 So you fill the open-cell polymer foam with sand. 201 00:11:12,030 --> 00:11:13,095 You burn off the polymer. 202 00:11:19,710 --> 00:11:22,000 And then you infiltrate the metal into that. 203 00:11:36,860 --> 00:11:39,630 And then you remove the sand. 204 00:11:39,630 --> 00:11:41,500 OK? 205 00:11:41,500 --> 00:11:45,640 Then, another process involves just using vapor depositions. 206 00:11:45,640 --> 00:11:48,420 So you take an open-cell polymer foam again. 207 00:11:48,420 --> 00:11:50,100 Here-- let me use my little arrow. 208 00:11:50,100 --> 00:11:52,690 Here's the open-cell polymer foam up here. 209 00:11:52,690 --> 00:11:57,490 And you have a furnace here with a vapor deposition system. 210 00:11:57,490 --> 00:12:01,730 And they use a nickel CO4 system to do this. 211 00:12:01,730 --> 00:12:04,680 You then burn out the polymer. 212 00:12:04,680 --> 00:12:07,480 You're left with a metal foam with hollow cell walls, 213 00:12:07,480 --> 00:12:08,739 where the polymer used to be. 214 00:12:08,739 --> 00:12:10,780 And then usually, what they do is they center it. 215 00:12:10,780 --> 00:12:14,070 They heat it up again to try to densify the walls. 216 00:12:14,070 --> 00:12:16,720 The only teeny weeny problem with this process 217 00:12:16,720 --> 00:12:19,780 is that the gas they use this incredibly toxic. 218 00:12:19,780 --> 00:12:24,099 And so it's not cheap and it's got health hazards, as well, 219 00:12:24,099 --> 00:12:24,890 associated with it. 220 00:12:24,890 --> 00:12:26,023 But you can do it. 221 00:12:28,641 --> 00:12:31,140 That gives you a nickel foam when you're finished with that. 222 00:12:37,820 --> 00:12:40,755 And you could also use an electrodeposition technique 223 00:12:40,755 --> 00:12:41,380 that's similar. 224 00:13:13,180 --> 00:13:15,690 OK. 225 00:13:15,690 --> 00:13:18,440 That's another method. 226 00:13:18,440 --> 00:13:22,040 Another method is shown here. 227 00:13:22,040 --> 00:13:25,000 This is the entrapped gas expansion method. 228 00:13:25,000 --> 00:13:28,600 And what they do in this method is they have a can 229 00:13:28,600 --> 00:13:30,450 and the can has a metal powder in it. 230 00:13:30,450 --> 00:13:32,810 It's whatever metal you want to make the foam out of. 231 00:13:32,810 --> 00:13:35,060 In this example here-- it's probably too small for you 232 00:13:35,060 --> 00:13:38,360 to read in the seats-- but it's titanium. 233 00:13:38,360 --> 00:13:40,690 They've taken a titanium alloy. 234 00:13:40,690 --> 00:13:42,690 They've got a powder of titanium alloy. 235 00:13:42,690 --> 00:13:44,127 They then evacuate the can. 236 00:13:44,127 --> 00:13:45,460 They take all the air out of it. 237 00:13:45,460 --> 00:13:47,880 And then they back fill it with argon gas. 238 00:13:47,880 --> 00:13:49,990 They put in an inert gas in there. 239 00:13:49,990 --> 00:13:52,370 And then what they do is they pressurize and heat 240 00:13:52,370 --> 00:13:55,820 the thing up and so the gas is internally 241 00:13:55,820 --> 00:13:58,110 pressurized by doing that. 242 00:13:58,110 --> 00:13:59,780 And then, sometimes when they do this, 243 00:13:59,780 --> 00:14:03,210 they want to have a skin on the two faces. 244 00:14:03,210 --> 00:14:05,110 So in this next little image here, 245 00:14:05,110 --> 00:14:08,500 it's done where they roll the can 246 00:14:08,500 --> 00:14:12,350 and produce a panel that's got solid faces. 247 00:14:12,350 --> 00:14:14,880 And then when you heat it up, the gas expands 248 00:14:14,880 --> 00:14:17,220 and you end up with a sandwich panel by doing this. 249 00:14:17,220 --> 00:14:19,446 So this bottom figure down here-- 250 00:14:19,446 --> 00:14:21,430 I'm not having much luck with the pointer. 251 00:14:21,430 --> 00:14:24,240 This bottom figure down here, they've heated it up. 252 00:14:24,240 --> 00:14:26,860 The gas expands and you've got this solid skin 253 00:14:26,860 --> 00:14:30,130 on the thing, which is from where the can use to be. 254 00:14:30,130 --> 00:14:32,815 So that's trapping of a gas. 255 00:15:37,420 --> 00:15:38,480 OK? 256 00:15:38,480 --> 00:15:41,910 There's a couple more methods for the metal foams. 257 00:15:41,910 --> 00:15:45,310 One involves centering hollow metal spheres together. 258 00:15:45,310 --> 00:15:48,150 And the trick there is to make the hollow spheres. 259 00:15:48,150 --> 00:15:52,670 And the way that can be done is by taking titanium hydride 260 00:15:52,670 --> 00:15:55,170 again, if you want to make titanium spheres. 261 00:15:55,170 --> 00:15:57,440 You put it in an organic binder-- in a solvent-- 262 00:15:57,440 --> 00:15:59,530 so you've got a slurry here. 263 00:15:59,530 --> 00:16:02,240 And you've got a tube that you blow gas through. 264 00:16:02,240 --> 00:16:05,390 And as you do that, you get hollow titanium hydride 265 00:16:05,390 --> 00:16:06,004 bubbles. 266 00:16:06,004 --> 00:16:08,420 And then you can do the same thing where you heat that up. 267 00:16:08,420 --> 00:16:11,510 The hydrogen gas evolves off, and you're left with titanium. 268 00:16:11,510 --> 00:16:13,020 You're left with titanium spheres 269 00:16:13,020 --> 00:16:14,210 down at the bottom here. 270 00:16:14,210 --> 00:16:15,840 And then you can pack those together 271 00:16:15,840 --> 00:16:19,810 and press those and form a cellular material that way. 272 00:16:19,810 --> 00:16:22,865 You can also center hollow metal spheres. 273 00:16:34,540 --> 00:16:38,139 And the last method I've got for the metal foams 274 00:16:38,139 --> 00:16:39,680 is that you can use a fugitive phase. 275 00:16:48,510 --> 00:16:51,620 With the fugitive phase, you would take some material 276 00:16:51,620 --> 00:16:54,930 that you could get rid of at the end of the process. 277 00:16:54,930 --> 00:16:57,500 Say, something like salt, that you could leach out. 278 00:16:57,500 --> 00:17:00,330 Here, we have our bed filled with salt. 279 00:17:00,330 --> 00:17:02,660 And then you would infiltrate that with a liquid metal, 280 00:17:02,660 --> 00:17:04,270 typically under pressure. 281 00:17:04,270 --> 00:17:07,180 And then, after the metals cooled, you leech out the salt. 282 00:17:07,180 --> 00:17:08,560 You get rid of that. 283 00:17:08,560 --> 00:17:14,349 You can pressure infiltrate a leachable bed of particles, 284 00:17:14,349 --> 00:17:16,863 and then leach the particles out. 285 00:17:56,220 --> 00:17:57,700 OK. 286 00:17:57,700 --> 00:17:59,430 We have a whole variety of methods 287 00:17:59,430 --> 00:18:01,840 that have been developed to make metal foams. 288 00:18:01,840 --> 00:18:04,230 And most of these have been developed, probably, 289 00:18:04,230 --> 00:18:05,210 in the last 20 years. 290 00:18:05,210 --> 00:18:05,810 Something like that. 291 00:18:05,810 --> 00:18:07,726 Some of them are a little bit older than that. 292 00:18:07,726 --> 00:18:10,730 But there's been a lot of interest in this recently. 293 00:18:10,730 --> 00:18:12,754 Those are all methods to make metal foams. 294 00:18:12,754 --> 00:18:15,170 I wanted to talk just a little bit about a few other types 295 00:18:15,170 --> 00:18:16,250 of foams. 296 00:18:16,250 --> 00:18:17,760 People make carbon foams. 297 00:18:17,760 --> 00:18:19,260 And they use the same kind of method 298 00:18:19,260 --> 00:18:21,990 as they do to make those bio carbon templates 299 00:18:21,990 --> 00:18:23,055 I told you about. 300 00:18:23,055 --> 00:18:25,555 When you take wood and you heat it up in an inert atmosphere 301 00:18:25,555 --> 00:18:27,660 and it turns into a carbon template, 302 00:18:27,660 --> 00:18:30,180 you can do the same thing where you take a polymer foam, 303 00:18:30,180 --> 00:18:32,440 you heat it up in an inert atmosphere, 304 00:18:32,440 --> 00:18:34,482 and everything except the carbon is driven off. 305 00:18:34,482 --> 00:18:35,940 And you're left with a carbon foam. 306 00:18:35,940 --> 00:18:39,080 It's the same process they used to make carbon fibers. 307 00:18:39,080 --> 00:18:40,200 There's carbon foams. 308 00:19:36,050 --> 00:19:38,940 There's also ceramic foams that you can make. 309 00:19:38,940 --> 00:19:41,170 I brought the little sample of ceramic foaming again. 310 00:19:41,170 --> 00:19:42,530 You can pass that around. 311 00:19:42,530 --> 00:19:45,280 And those are typically made by taking an open-cell polymer 312 00:19:45,280 --> 00:19:49,420 foam and passing a ceramic slurry through the polymer foam 313 00:19:49,420 --> 00:19:51,280 so that you coat the cell walls. 314 00:19:51,280 --> 00:19:55,210 And then you fire it so that you bond the ceramic together 315 00:19:55,210 --> 00:19:56,730 and you burn the polymer off. 316 00:19:56,730 --> 00:19:59,560 And you're left with a foam that's got hollow cell walls. 317 00:19:59,560 --> 00:20:02,410 You can also make ceramic foams by doing a CVD process 318 00:20:02,410 --> 00:20:04,090 on the carbon foam that you could 319 00:20:04,090 --> 00:20:05,563 make by the previous process. 320 00:21:07,305 --> 00:21:10,670 And people also make glass foams. 321 00:21:10,670 --> 00:21:12,330 And to make glass foams, they use 322 00:21:12,330 --> 00:21:14,180 some of the same kinds of processes 323 00:21:14,180 --> 00:21:16,720 as people use for polymer foams. 324 00:21:16,720 --> 00:21:21,285 I'll just say similar processes to polymer foams. 325 00:21:29,600 --> 00:21:31,280 OK. 326 00:21:31,280 --> 00:21:33,640 That covers making the foams, and I 327 00:21:33,640 --> 00:21:35,950 think we talked about the honeycombs last time. 328 00:21:35,950 --> 00:21:38,390 I wanted to talk a little bit about making 329 00:21:38,390 --> 00:21:40,880 what are called 3D lattice materials, or 3D 330 00:21:40,880 --> 00:21:43,170 truss materials, as well. 331 00:21:43,170 --> 00:21:45,533 Let me [? strip ?] that up there. 332 00:21:59,660 --> 00:22:00,376 Yeah? 333 00:22:00,376 --> 00:22:01,250 AUDIENCE: [INAUDIBLE] 334 00:22:01,250 --> 00:22:02,916 LORNA GIBSON: Chemical vapor deposition. 335 00:22:09,189 --> 00:22:11,997 AUDIENCE: [INAUDIBLE] use this for metal foams? 336 00:22:11,997 --> 00:22:14,580 LORNA GIBSON: Well, people were quite interested in using them 337 00:22:14,580 --> 00:22:17,490 for sandwich panels-- the cores of sandwich panels-- 338 00:22:17,490 --> 00:22:18,840 lightweight panels. 339 00:22:18,840 --> 00:22:21,620 There was interest in using them for energy absorption, 340 00:22:21,620 --> 00:22:22,932 say, car bumpers. 341 00:22:22,932 --> 00:22:25,140 The automotive industry was quite interested in this, 342 00:22:25,140 --> 00:22:28,110 in terms of trying to make components with sandwich 343 00:22:28,110 --> 00:22:29,960 structures that would be lighter weight, 344 00:22:29,960 --> 00:22:31,930 or energy absorption for bumpers. 345 00:22:31,930 --> 00:22:35,120 Or filling up-- if you take-- say you take a metal tube. 346 00:22:35,120 --> 00:22:38,740 If you think of a car chassis and it's made of tubes, 347 00:22:38,740 --> 00:22:41,352 if you fill those tubes with a foam-- 348 00:22:41,352 --> 00:22:43,310 especially if you fill them with a metal foam-- 349 00:22:43,310 --> 00:22:45,900 you can increase the energy absorption quite substantially. 350 00:22:45,900 --> 00:22:49,040 So when you have a tube in a chassis, 351 00:22:49,040 --> 00:22:51,480 if it's loaded axially, it will fold up 352 00:22:51,480 --> 00:22:54,170 and you get all these wavelengths of buckling. 353 00:22:54,170 --> 00:22:55,770 And if you've put a foam in there, 354 00:22:55,770 --> 00:22:57,380 it changes the buckling wavelength 355 00:22:57,380 --> 00:23:00,410 and it increases the amount of energy you can absorb. 356 00:23:00,410 --> 00:23:02,740 So not only is the energy absorbed by the foam 357 00:23:02,740 --> 00:23:06,460 itself, it actually changes the buckling of the tube 358 00:23:06,460 --> 00:23:08,130 so you can absorb more energy. 359 00:23:08,130 --> 00:23:09,842 So there was a lot of interest in that. 360 00:23:09,842 --> 00:23:11,300 There was an interest in using them 361 00:23:11,300 --> 00:23:17,490 for cooling devices for, say, electronic components. 362 00:23:17,490 --> 00:23:19,100 The idea was you would take, say, 363 00:23:19,100 --> 00:23:21,430 an aluminium open-cell foam and you 364 00:23:21,430 --> 00:23:23,190 would flow air through that. 365 00:23:23,190 --> 00:23:26,180 And say you have your device that's generating heat, 366 00:23:26,180 --> 00:23:27,880 you'd have a foam underneath it. 367 00:23:27,880 --> 00:23:31,020 And the aluminum conducts the heat fairly well. 368 00:23:31,020 --> 00:23:32,644 And then you would blow air through it 369 00:23:32,644 --> 00:23:33,560 to try to cool it off. 370 00:23:33,560 --> 00:23:35,330 So there were a bunch of different applications 371 00:23:35,330 --> 00:23:36,704 people have had in mind for them. 372 00:23:36,704 --> 00:23:38,052 AUDIENCE: What about glass? 373 00:23:38,052 --> 00:23:39,510 LORNA GIBSON: Glass foams, I think, 374 00:23:39,510 --> 00:23:41,610 are largely used for insulation in buildings, 375 00:23:41,610 --> 00:23:42,360 believe it or not. 376 00:23:42,360 --> 00:23:45,220 I think, actually, one of the dorms at MIT-- maybe 377 00:23:45,220 --> 00:23:48,995 the Simmons dorm-- has a glass foam insulation. 378 00:23:48,995 --> 00:23:51,296 AUDIENCE: [INAUDIBLE] 379 00:23:53,644 --> 00:23:55,560 LORNA GIBSON: Well, I think because the foam-- 380 00:23:55,560 --> 00:23:59,510 because the cells are closed, the gas is trapped in the cell. 381 00:23:59,510 --> 00:24:03,240 Whereas with a fiberglass, gas could move through the fibers 382 00:24:03,240 --> 00:24:04,560 more easily. 383 00:24:04,560 --> 00:24:06,600 So I think that's partly how it works. 384 00:24:06,600 --> 00:24:07,100 OK. 385 00:24:07,100 --> 00:24:09,558 Well, let me talk a little bit about the lattice materials, 386 00:24:09,558 --> 00:24:11,260 too, and how we make those. 387 00:24:11,260 --> 00:24:13,550 We're going to start talking about the modeling 388 00:24:13,550 --> 00:24:15,290 of honeycombs and foams. 389 00:24:15,290 --> 00:24:17,850 And when we do that, we're going to see that if we have 390 00:24:17,850 --> 00:24:21,120 a structure that deforms by bending, 391 00:24:21,120 --> 00:24:24,010 the properties vary with the amount of material, 392 00:24:24,010 --> 00:24:25,180 in a certain way. 393 00:24:25,180 --> 00:24:29,400 But if we have materials where the deformation is controlled 394 00:24:29,400 --> 00:24:32,360 by axial deformation, the stiffness and the strength 395 00:24:32,360 --> 00:24:35,110 are going to be higher at the same density. 396 00:24:35,110 --> 00:24:37,832 People made these lattice-type materials 397 00:24:37,832 --> 00:24:39,290 to try to get something with a more 398 00:24:39,290 --> 00:24:40,950 regular structure, and especially 399 00:24:40,950 --> 00:24:42,210 a triangulated structure. 400 00:24:42,210 --> 00:24:44,520 You see how these things are like little trusses? 401 00:24:44,520 --> 00:24:45,950 Triangulated? 402 00:24:45,950 --> 00:24:47,570 Triangulated structures, when you 403 00:24:47,570 --> 00:24:49,570 load them-- say I load this like this-- 404 00:24:49,570 --> 00:24:52,350 there's just axial components-- axial forces 405 00:24:52,350 --> 00:24:53,365 in each of the members. 406 00:24:53,365 --> 00:24:54,740 And so, theoretically, this would 407 00:24:54,740 --> 00:24:58,030 be higher stiffness and strength for a given weight 408 00:24:58,030 --> 00:24:59,464 than, say, a foam would be. 409 00:24:59,464 --> 00:25:01,630 So people were interested in these lattice material. 410 00:25:01,630 --> 00:25:03,269 This one here is made of aluminum. 411 00:25:03,269 --> 00:25:05,060 And I wanted to talk a little bit about how 412 00:25:05,060 --> 00:25:06,970 you can make these things. 413 00:25:06,970 --> 00:25:10,300 One way you can do it is by injection molding. 414 00:25:10,300 --> 00:25:14,450 And this here is just the centerpiece of something 415 00:25:14,450 --> 00:25:15,860 that would look like this. 416 00:25:15,860 --> 00:25:17,840 So there would be a-- I didn't bring it, 417 00:25:17,840 --> 00:25:20,790 but there's a top face and a bottom face that fit onto this. 418 00:25:20,790 --> 00:25:23,140 And they would be injection molded 419 00:25:23,140 --> 00:25:25,990 as three different pieces, and then assembled together. 420 00:25:25,990 --> 00:25:30,450 So you can make a mold in this complicated geometry, 421 00:25:30,450 --> 00:25:35,190 and you can make a lattice material by injection molding. 422 00:25:35,190 --> 00:25:40,363 We'll start with polymer lattices first. 423 00:25:45,280 --> 00:25:46,856 One way is injection molding. 424 00:25:50,330 --> 00:25:54,820 Another way to do it is by 3-D printing. 425 00:25:54,820 --> 00:25:58,170 You can generate a structure like that by 3-D printing. 426 00:25:58,170 --> 00:26:03,600 You can also make trusses in 2D and you 427 00:26:03,600 --> 00:26:07,630 can make them so that you can snap fit those together. 428 00:26:07,630 --> 00:26:12,299 So you can make little 2D trusses. 429 00:26:12,299 --> 00:26:13,840 Here's a little truss here and here's 430 00:26:13,840 --> 00:26:16,040 a little piece of a truss here. 431 00:26:16,040 --> 00:26:19,750 And you can make a little snap fit joints. 432 00:26:19,750 --> 00:26:23,710 Do you see how these ones have little divots in them? 433 00:26:23,710 --> 00:26:26,170 And you can make it so that these things will fit together. 434 00:26:26,170 --> 00:26:29,640 I think these guys-- can I do it? 435 00:26:29,640 --> 00:26:30,457 No. 436 00:26:30,457 --> 00:26:31,540 You'd have to take-- oops. 437 00:26:31,540 --> 00:26:32,123 Wait a minute. 438 00:26:32,123 --> 00:26:34,740 No, it's not that way. 439 00:26:34,740 --> 00:26:36,280 There we go. 440 00:26:36,280 --> 00:26:39,600 So you can snap them together like that. 441 00:26:39,600 --> 00:26:40,100 OK. 442 00:26:40,100 --> 00:26:43,229 I can't get it to-- there we go. 443 00:26:43,229 --> 00:26:44,020 So you can do that. 444 00:26:44,020 --> 00:26:45,600 And you do that over and over again. 445 00:26:45,600 --> 00:26:46,640 And if you do it over and over again, 446 00:26:46,640 --> 00:26:48,400 you get something that looks like that. 447 00:26:48,400 --> 00:26:49,450 OK? 448 00:26:49,450 --> 00:26:51,210 You can make a snap fit thing. 449 00:26:51,210 --> 00:26:52,790 Let me pass all these guys around 450 00:26:52,790 --> 00:26:54,105 and you can play with those. 451 00:26:56,805 --> 00:26:58,180 That's the injection molding one. 452 00:26:58,180 --> 00:27:01,770 This is the snap-fit one. 453 00:27:01,770 --> 00:27:02,270 Got that? 454 00:27:06,270 --> 00:27:06,940 Let's see. 455 00:27:06,940 --> 00:27:08,481 I think I have a little picture here. 456 00:27:08,481 --> 00:27:11,430 This is an example of the snap fit truss here. 457 00:27:11,430 --> 00:27:14,520 It's the thing that's getting passed around. 458 00:27:14,520 --> 00:27:17,180 And another clever way that was developed 459 00:27:17,180 --> 00:27:21,140 was by taking a monomer that's sensitive to light. 460 00:27:21,140 --> 00:27:23,490 You take a photo sensitive monomer. 461 00:27:23,490 --> 00:27:27,410 And you put a mask on top of it and the mask has holes in it. 462 00:27:27,410 --> 00:27:29,710 And then you shine collimated light on it. 463 00:27:29,710 --> 00:27:31,550 You shine, say, a laser on it. 464 00:27:31,550 --> 00:27:35,030 And the light goes through the holes in the mask. 465 00:27:35,030 --> 00:27:37,660 And it starts to polymerize the polymer 466 00:27:37,660 --> 00:27:39,330 because it's photosensitive. 467 00:27:39,330 --> 00:27:43,970 And then, as the polymer-- as it polymerizes and becomes solid, 468 00:27:43,970 --> 00:27:47,120 it then acts as a waveguide and draws the light down 469 00:27:47,120 --> 00:27:49,200 deeper into the monomer. 470 00:27:49,200 --> 00:27:51,720 And so the polymer acts as a wave guide. 471 00:27:51,720 --> 00:27:54,080 It brings the light down. 472 00:27:54,080 --> 00:27:58,280 And this is a schematic over here. 473 00:27:58,280 --> 00:28:00,340 This is a schematic showing the set up. 474 00:28:00,340 --> 00:28:02,960 And these are some examples of some 3D trusses 475 00:28:02,960 --> 00:28:05,500 that they've made using this technique. 476 00:28:05,500 --> 00:28:07,050 And one of the nice things about this 477 00:28:07,050 --> 00:28:09,160 is you can get a very small size cell size. 478 00:28:09,160 --> 00:28:13,141 So this is-- I think that bar-- it says 1,500 microns. 479 00:28:13,141 --> 00:28:13,640 That's what? 480 00:28:13,640 --> 00:28:14,765 One and a half millimeters. 481 00:28:14,765 --> 00:28:18,480 So you can get a nice, small cell size if you want that. 482 00:28:18,480 --> 00:28:19,753 Let me write that down. 483 00:28:46,700 --> 00:28:52,900 You take a photosensitive monomer 484 00:28:52,900 --> 00:28:55,200 and then you have it in a mold beneath a mask. 485 00:29:00,020 --> 00:29:07,130 And then you shine collimated light on it. 486 00:29:15,910 --> 00:29:19,375 And as the light shines on it, it polymerizes the monomer. 487 00:29:31,620 --> 00:29:34,770 So then it solidifies and then it guides the light deeper 488 00:29:34,770 --> 00:29:35,890 into the monomer. 489 00:30:02,564 --> 00:30:04,080 OK. 490 00:30:04,080 --> 00:30:05,300 That's that. 491 00:30:05,300 --> 00:30:08,360 And then finally, there's metal lattices, as well. 492 00:30:15,030 --> 00:30:17,670 And so this is, obviously, a metal lattice here. 493 00:30:17,670 --> 00:30:19,140 It's an aluminum alloy. 494 00:30:19,140 --> 00:30:21,280 And the metal lattice is made by taking 495 00:30:21,280 --> 00:30:25,310 that polymer lattice that was made by the injection molding 496 00:30:25,310 --> 00:30:26,300 technique. 497 00:30:26,300 --> 00:30:28,620 You coat that with a ceramic slurry. 498 00:30:28,620 --> 00:30:30,130 You burn off the polymer, and then 499 00:30:30,130 --> 00:30:34,110 you infiltrate the metal where the polymer used to be. 500 00:31:16,030 --> 00:31:17,250 OK. 501 00:31:17,250 --> 00:31:20,150 That's the section on processing of the honeycombs 502 00:31:20,150 --> 00:31:21,872 and the foams and the lattices. 503 00:31:21,872 --> 00:31:23,705 So there's a variety of different techniques 504 00:31:23,705 --> 00:31:25,730 that people have developed for making 505 00:31:25,730 --> 00:31:27,590 these kinds of materials. 506 00:31:27,590 --> 00:31:30,990 And I thought it'd be useful to just describe 507 00:31:30,990 --> 00:31:32,140 some of the techniques. 508 00:31:32,140 --> 00:31:34,455 As I think I said last time, this isn't comprehensive. 509 00:31:34,455 --> 00:31:36,060 This doesn't cover every technique. 510 00:31:36,060 --> 00:31:38,039 But it gives you a flavor of what 511 00:31:38,039 --> 00:31:39,830 techniques people have developed for making 512 00:31:39,830 --> 00:31:41,990 these kinds of materials. 513 00:31:41,990 --> 00:31:42,940 OK? 514 00:31:42,940 --> 00:31:44,100 Are we good? 515 00:31:44,100 --> 00:31:44,900 We're good. 516 00:31:44,900 --> 00:31:45,740 OK. 517 00:31:45,740 --> 00:31:48,220 The next part, I want to do on the structure 518 00:31:48,220 --> 00:31:50,360 of cellular materials. 519 00:31:50,360 --> 00:31:53,877 And I have a little overview. 520 00:31:53,877 --> 00:31:55,460 I don't think we'll finish this today, 521 00:31:55,460 --> 00:31:57,090 but we'll finish it tomorrow. 522 00:32:50,480 --> 00:32:50,990 Yeah? 523 00:32:50,990 --> 00:32:53,811 AUDIENCE: [INAUDIBLE] 524 00:32:53,811 --> 00:32:54,810 LORNA GIBSON: Down here? 525 00:32:54,810 --> 00:32:57,010 AUDIENCE: What happens to the ceramic? 526 00:32:57,010 --> 00:32:58,760 LORNA GIBSON: They get rid of the ceramic. 527 00:32:58,760 --> 00:33:01,320 Typically, the ceramic is not very strong 528 00:33:01,320 --> 00:33:04,075 and it's just fired enough so they can infiltrate it 529 00:33:04,075 --> 00:33:04,700 with the metal. 530 00:33:04,700 --> 00:33:08,300 And then they-- yeah, I think with mechanical smushing 531 00:33:08,300 --> 00:33:11,280 around, you can get rid of the ceramic. 532 00:33:11,280 --> 00:33:13,880 And the ceramic's brittle, so if you break the ceramic, 533 00:33:13,880 --> 00:33:15,530 you're not going to break the metal. 534 00:33:15,530 --> 00:33:17,030 AUDIENCE: I'm wondering if you could 535 00:33:17,030 --> 00:33:19,678 make a type of metal lattice [INAUDIBLE] 536 00:33:19,678 --> 00:33:21,625 with reducing [? the ?] oxides? 537 00:33:21,625 --> 00:33:24,000 LORNA GIBSON: I guess you could, if you could-- but you'd 538 00:33:24,000 --> 00:33:25,958 have to then make the oxide in that shape, too. 539 00:33:25,958 --> 00:33:28,869 You've always got to make something in that shape. 540 00:33:28,869 --> 00:33:29,744 AUDIENCE: [INAUDIBLE] 541 00:33:35,640 --> 00:33:37,640 LORNA GIBSON: Yeah, maybe you could make a foam. 542 00:33:37,640 --> 00:33:40,210 But to make these lattices, you need this really regular kind 543 00:33:40,210 --> 00:33:43,290 of structure and be able to control the structure. 544 00:33:43,290 --> 00:33:44,680 OK. 545 00:33:44,680 --> 00:33:48,820 Let me scoot out of this set of slides and get the next set up. 546 00:33:51,800 --> 00:33:54,370 OK. 547 00:33:54,370 --> 00:33:57,270 We want to talk about the structure of cellular solids. 548 00:33:57,270 --> 00:34:01,410 And we classify cellular materials into two main groups. 549 00:34:01,410 --> 00:34:03,460 One's called honeycombs. 550 00:34:03,460 --> 00:34:05,660 This thing down here is a honeycomb. 551 00:34:05,660 --> 00:34:09,389 And honeycombs have polygonal cells that fill a plane 552 00:34:09,389 --> 00:34:11,730 and then they're prismatic in the third direction. 553 00:34:11,730 --> 00:34:15,120 So you can think of them as just being a prismatic-- 554 00:34:15,120 --> 00:34:17,239 and they can be hexagons, they can be squares, 555 00:34:17,239 --> 00:34:19,365 they can be triangles-- but you can think 556 00:34:19,365 --> 00:34:21,100 of them as prismatic cells. 557 00:34:21,100 --> 00:34:24,020 And the cells are just in a 2D plane. 558 00:34:24,020 --> 00:34:25,389 And then we also have foams. 559 00:34:25,389 --> 00:34:29,060 All of these ones over here are foamed materials. 560 00:34:29,060 --> 00:34:31,120 And they're made up of polyhedral cells. 561 00:34:31,120 --> 00:34:34,469 The cells themselves are three-dimensional polyhedra. 562 00:34:34,469 --> 00:34:36,659 And this slide here shows a number 563 00:34:36,659 --> 00:34:37,889 of different types of foams. 564 00:34:37,889 --> 00:34:39,790 These ones are polymers up here. 565 00:34:39,790 --> 00:34:41,159 These are two metals. 566 00:34:41,159 --> 00:34:42,550 These are two ceramics. 567 00:34:42,550 --> 00:34:44,699 This is a glass foam down here. 568 00:34:44,699 --> 00:34:47,080 And this is another polymer foam down here. 569 00:34:47,080 --> 00:34:48,376 OK? 570 00:34:48,376 --> 00:34:49,810 AUDIENCE: [INAUDIBLE] 571 00:34:49,810 --> 00:34:50,600 LORNA GIBSON: No. 572 00:34:50,600 --> 00:34:51,520 I just know that. 573 00:34:51,520 --> 00:34:52,300 AUDIENCE: OK. 574 00:34:52,300 --> 00:34:54,567 LORNA GIBSON: I took those pictures so I know that. 575 00:34:54,567 --> 00:34:56,150 No, you can't tell by looking at them. 576 00:34:56,150 --> 00:34:58,250 In fact, that's one of the things about how we 577 00:34:58,250 --> 00:35:00,710 model the cellular materials. 578 00:35:00,710 --> 00:35:03,000 The fact that their structure is so similar 579 00:35:03,000 --> 00:35:04,810 is what gives them similar properties. 580 00:35:04,810 --> 00:35:06,768 And they behave in similar ways because they've 581 00:35:06,768 --> 00:35:09,751 got similar structures. 582 00:35:09,751 --> 00:35:10,251 OK. 583 00:35:25,110 --> 00:35:34,310 We've got 2D honeycombs, where we have polygonal cells 584 00:35:34,310 --> 00:35:35,700 that pack to fill a plane. 585 00:35:41,650 --> 00:35:44,110 And then they're prismatic in the third direction. 586 00:35:56,080 --> 00:36:00,290 And then we have what we call 3D cellular materials, which 587 00:36:00,290 --> 00:36:02,805 are foams, which have polyhedral cells. 588 00:36:07,560 --> 00:36:08,950 And then they pack to fill space. 589 00:36:16,350 --> 00:36:19,200 The properties of all of these materials 590 00:36:19,200 --> 00:36:21,062 depend, essentially, on three things. 591 00:36:24,922 --> 00:36:27,380 They're going to depend on the solid that you make it from. 592 00:36:27,380 --> 00:36:30,182 If you make the material from a rubber or from an aluminum, 593 00:36:30,182 --> 00:36:31,890 you're going to get different properties. 594 00:36:31,890 --> 00:36:33,806 So they depend on the properties of the solid. 595 00:36:45,300 --> 00:36:46,860 And some of the properties that we're 596 00:36:46,860 --> 00:36:52,137 going to use that are important for this type of modeling 597 00:36:52,137 --> 00:36:54,470 are a density of the solid-- which I'm going to call rho 598 00:36:54,470 --> 00:36:56,990 s-- a Young's modulus of the solid-- which I'm going to call 599 00:36:56,990 --> 00:36:59,580 es-- and some sort of strength of the solid-- 600 00:36:59,580 --> 00:37:02,390 which I'm going to call sigma ys for now. 601 00:37:02,390 --> 00:37:03,890 And you could think of other things. 602 00:37:03,890 --> 00:37:05,973 There could be a fractured toughness of the solid. 603 00:37:05,973 --> 00:37:07,920 There could be other kinds of things. 604 00:37:07,920 --> 00:37:10,800 One thing that the properties of the cellular material depend on 605 00:37:10,800 --> 00:37:12,560 is the properties of the solid. 606 00:37:12,560 --> 00:37:18,840 Another is the relative density of the cellular material. 607 00:37:18,840 --> 00:37:21,110 And that's the density of the cellular thing divided 608 00:37:21,110 --> 00:37:22,810 by the density of the solid. 609 00:37:22,810 --> 00:37:26,295 And that's equivalent to the volume fraction of solids. 610 00:37:36,109 --> 00:37:38,150 So it makes sense that the more solid you've got, 611 00:37:38,150 --> 00:37:40,370 the stiffer and stronger the material's going to be. 612 00:37:40,370 --> 00:37:43,180 So it's going to depend on how much material you've got. 613 00:37:43,180 --> 00:37:45,570 And it also depends-- the properties also 614 00:37:45,570 --> 00:37:46,972 depend on the cell geometry. 615 00:38:06,280 --> 00:38:09,370 The cell shape can control things like whether or not 616 00:38:09,370 --> 00:38:12,460 the honeycomb or the foam is isotropic or anisotropic. 617 00:38:12,460 --> 00:38:14,520 You can imagine, if you have a foam, 618 00:38:14,520 --> 00:38:16,320 and you've got equiaxed cells, you 619 00:38:16,320 --> 00:38:18,820 might expect to have the same properties in all directions. 620 00:38:18,820 --> 00:38:21,300 But if you had cells that were elongated in some way, 621 00:38:21,300 --> 00:38:23,300 you might expect you'd have different properties 622 00:38:23,300 --> 00:38:25,300 in the direction that they're elongated relative 623 00:38:25,300 --> 00:38:26,640 to the other plane. 624 00:38:26,640 --> 00:38:28,280 So cell shape can lead to anisotropy. 625 00:38:33,530 --> 00:38:36,560 For the foams, you can also have what 626 00:38:36,560 --> 00:38:39,375 we call open-cell and closed-cell foams. 627 00:38:48,570 --> 00:38:51,620 If you look at this slide here, and we 628 00:38:51,620 --> 00:38:55,840 look at this top right images-- these two up here-- 629 00:38:55,840 --> 00:38:59,690 the one on the left in the top is an open-celled foam. 630 00:38:59,690 --> 00:39:01,440 There's just material in the edges. 631 00:39:01,440 --> 00:39:02,330 There's no faces. 632 00:39:02,330 --> 00:39:05,515 And so a gas can flow between one cell and another. 633 00:39:05,515 --> 00:39:07,390 And then if you look at the one on the right, 634 00:39:07,390 --> 00:39:08,750 this is a closed-celled foam. 635 00:39:08,750 --> 00:39:09,500 There's faces. 636 00:39:09,500 --> 00:39:11,041 If you think of the polyhedra, you've 637 00:39:11,041 --> 00:39:14,412 got solid faces covering the faces of the polyhedra. 638 00:39:17,510 --> 00:39:21,430 For an open-cell foam, you've only got solid 639 00:39:21,430 --> 00:39:23,065 in the edges of the polyhedra. 640 00:39:27,840 --> 00:39:31,190 And the voids are continuous, so they're connected together. 641 00:39:35,230 --> 00:39:36,930 And for a closed-cell foam, you've 642 00:39:36,930 --> 00:39:38,765 got solid in the edges and the faces. 643 00:39:43,210 --> 00:39:46,270 And then the voids are separated off from each other. 644 00:39:46,270 --> 00:39:49,830 So we'll say, the cells are closed off from one another. 645 00:39:58,210 --> 00:40:01,840 Another feature of the cell geometry is the cell size. 646 00:40:05,470 --> 00:40:07,690 And the cell size can be important for things 647 00:40:07,690 --> 00:40:09,790 like the thermal properties of foams. 648 00:40:09,790 --> 00:40:11,540 It's important for things like the surface 649 00:40:11,540 --> 00:40:12,776 area per unit volume. 650 00:40:12,776 --> 00:40:14,650 But typically, for the mechanical properties, 651 00:40:14,650 --> 00:40:15,650 it's not that important. 652 00:40:23,867 --> 00:40:25,950 And we'll see why that is when we do the modeling. 653 00:40:59,135 --> 00:40:59,635 OK. 654 00:41:06,100 --> 00:41:08,300 Yes? 655 00:41:08,300 --> 00:41:12,070 AUDIENCE: For the closed-cell foams-- because we can't really 656 00:41:12,070 --> 00:41:17,580 see it without cutting it, is it that all of the faces 657 00:41:17,580 --> 00:41:19,260 are closed? 658 00:41:19,260 --> 00:41:22,300 Or is it like some fraction of the faces are closed? 659 00:41:22,300 --> 00:41:25,180 LORNA GIBSON: If you look at this one on the top right here, 660 00:41:25,180 --> 00:41:26,550 they're pretty much all closed. 661 00:41:26,550 --> 00:41:28,300 But the reason we have this little picture 662 00:41:28,300 --> 00:41:30,660 down here is some of them are closed and some of them 663 00:41:30,660 --> 00:41:31,160 are open. 664 00:41:31,160 --> 00:41:32,880 So you can get ones that are in between. 665 00:41:32,880 --> 00:41:34,820 But typically-- this is kind of unusual. 666 00:41:34,820 --> 00:41:36,778 Usually, they're either all open or all closed. 667 00:42:14,500 --> 00:42:16,240 If we look at the mechanical properties 668 00:42:16,240 --> 00:42:19,460 of cellular materials, typically the cell geometry 669 00:42:19,460 --> 00:42:20,960 doesn't have that much of an effect. 670 00:42:20,960 --> 00:42:23,370 The relative density is much more important. 671 00:42:23,370 --> 00:42:25,420 The relative density, we define as the density 672 00:42:25,420 --> 00:42:27,020 of the cellular solid. 673 00:42:27,020 --> 00:42:30,650 And when I use a parameter like rho or e or something, 674 00:42:30,650 --> 00:42:32,650 if it's got a star, it's for the cellular thing 675 00:42:32,650 --> 00:42:35,017 and if it's got an s, it's for the solid. 676 00:42:35,017 --> 00:42:36,600 So rho star is going to be the density 677 00:42:36,600 --> 00:42:37,770 of the cellular material. 678 00:42:46,590 --> 00:42:48,680 And rho s is going to be the density of the solid 679 00:42:48,680 --> 00:42:49,440 it's made from. 680 00:43:01,570 --> 00:43:05,282 And so the relative density is just rho star over rho s. 681 00:43:05,282 --> 00:43:06,990 And I just wanted to show you how this is 682 00:43:06,990 --> 00:43:08,920 the volume fraction of solids. 683 00:43:08,920 --> 00:43:11,800 So rho star is going to be the mass of solid 684 00:43:11,800 --> 00:43:13,047 over the total volume. 685 00:43:13,047 --> 00:43:15,380 Imagine you've got a honeycomb or a foam and you've got, 686 00:43:15,380 --> 00:43:17,350 say, a unit cube of it, the sum total 687 00:43:17,350 --> 00:43:19,375 volume of the whole thing-- the density 688 00:43:19,375 --> 00:43:20,750 of the cellular material is going 689 00:43:20,750 --> 00:43:22,775 to the mass of the solid over the whole volume. 690 00:43:22,775 --> 00:43:24,150 The density of the solid is going 691 00:43:24,150 --> 00:43:28,130 to be the mass of the solid over the volume of the solid. 692 00:43:28,130 --> 00:43:30,937 This is really just equivalent to the volume fraction 693 00:43:30,937 --> 00:43:32,520 of solids, how much solids you've got. 694 00:43:41,610 --> 00:43:43,980 And that's also n equal to 1 minus the porosity. 695 00:43:51,720 --> 00:43:54,820 Typical values for cellular materials-- 696 00:43:54,820 --> 00:43:59,350 I think last time I passed around one of those collagen 697 00:43:59,350 --> 00:44:01,300 scaffolds-- those tissue enineering scaffolds. 698 00:44:01,300 --> 00:44:03,680 It was in a little plastic bag. 699 00:44:03,680 --> 00:44:09,920 That collagen scaffold has a relative density of 0.005, 700 00:44:09,920 --> 00:44:14,290 so its 0.5% solid and 99.5% air. 701 00:44:14,290 --> 00:44:20,950 And if we look at typical polymer foams, 702 00:44:20,950 --> 00:44:22,510 the relative density is typically 703 00:44:22,510 --> 00:44:25,505 between about 2% and 20%. 704 00:44:31,920 --> 00:44:34,610 And if we look at something like softwoods-- wood 705 00:44:34,610 --> 00:44:36,510 is a cellular material. 706 00:44:36,510 --> 00:44:39,210 And we look at softwoods, the relative density 707 00:44:39,210 --> 00:44:43,860 is usually between about 15% and about 40%. 708 00:44:43,860 --> 00:44:44,711 Something like that. 709 00:44:44,711 --> 00:44:45,210 OK? 710 00:44:49,550 --> 00:44:51,370 As the relative density increases, 711 00:44:51,370 --> 00:44:53,410 you get more material on the cell edges, 712 00:44:53,410 --> 00:44:56,310 and if it's closed-cell foam, on the cell faces. 713 00:44:56,310 --> 00:44:58,480 And the pore volume decreases. 714 00:44:58,480 --> 00:45:00,550 And you can think of some limit. 715 00:45:00,550 --> 00:45:03,100 If you keep increasing the relative density more and more 716 00:45:03,100 --> 00:45:05,550 and more, eventually you've got-- it's not really 717 00:45:05,550 --> 00:45:06,950 a cellular material anymore. 718 00:45:06,950 --> 00:45:10,380 It's more like a solid with little isolated pores in it. 719 00:45:10,380 --> 00:45:11,991 And so there's two bounds. 720 00:45:11,991 --> 00:45:14,490 And the density has to be less than a certain amount for you 721 00:45:14,490 --> 00:45:16,740 to consider it a cellular material in the models 722 00:45:16,740 --> 00:45:19,690 that we're going to derive to be valid. 723 00:45:19,690 --> 00:45:23,040 And if the relevant density is more than a certain amount, 724 00:45:23,040 --> 00:45:25,373 people model it as a solid with isolated holes. 725 00:46:06,450 --> 00:46:10,627 If I have a unit square of material, 726 00:46:10,627 --> 00:46:12,210 if it's a cellular material, you might 727 00:46:12,210 --> 00:46:15,390 expect that you've got pores that would look like this. 728 00:46:15,390 --> 00:46:18,850 And you've got relatively thin cell walls, 729 00:46:18,850 --> 00:46:21,360 relative to the length of the material. 730 00:46:21,360 --> 00:46:25,730 And for a cellular material, typically, the relative density 731 00:46:25,730 --> 00:46:31,290 is less than about 0.3. 732 00:46:31,290 --> 00:46:34,220 And when we come to the modeling for the honeycombs 733 00:46:34,220 --> 00:46:38,410 and the foams, we're going to see that the cell walls deform, 734 00:46:38,410 --> 00:46:40,610 in many cases, by bending. 735 00:46:40,610 --> 00:46:42,260 And that you can model the deformation 736 00:46:42,260 --> 00:46:43,780 by modeling the bending. 737 00:46:43,780 --> 00:46:46,340 And that the bending dominates the behavior 738 00:46:46,340 --> 00:46:48,870 if the density is less than about that. 739 00:46:48,870 --> 00:46:52,230 And at the other extreme, you can 740 00:46:52,230 --> 00:46:54,110 imagine if you had just little teeny pores. 741 00:46:54,110 --> 00:46:55,760 I have a little pore here and one here 742 00:46:55,760 --> 00:46:58,620 and one there and one there. 743 00:46:58,620 --> 00:47:00,350 That's not really a cellular material. 744 00:47:00,350 --> 00:47:02,750 It's just got a teeny weeny little bit of pores. 745 00:47:02,750 --> 00:47:07,900 And that could be modeled as isolated pores in a solid. 746 00:47:07,900 --> 00:47:09,704 Each one is acting independently. 747 00:47:12,760 --> 00:47:16,510 And people have found that that is appropriate 748 00:47:16,510 --> 00:47:19,440 if the relative density is greater than about 0.8. 749 00:47:19,440 --> 00:47:21,430 And then, in between, there's a transition 750 00:47:21,430 --> 00:47:23,670 in behavior between the cellular solid 751 00:47:23,670 --> 00:47:26,830 and the isolated pores in the solid. 752 00:47:26,830 --> 00:47:28,020 OK? 753 00:47:28,020 --> 00:47:28,691 Are we OK? 754 00:48:04,512 --> 00:48:06,720 The next thing I wanted to talk about was unit cells. 755 00:48:09,310 --> 00:48:12,440 Especially for honeycombs, people often use unit cells. 756 00:48:12,440 --> 00:48:14,450 A hexagonal cell is an obvious one 757 00:48:14,450 --> 00:48:18,150 to use to model this kind of behavior. 758 00:48:18,150 --> 00:48:20,880 For honeycomb materials, you can have unit cells 759 00:48:20,880 --> 00:48:22,420 and you can have different ones. 760 00:48:22,420 --> 00:48:25,190 On the left here, we've got triangles, in the middle, 761 00:48:25,190 --> 00:48:26,610 I've got squares. 762 00:48:26,610 --> 00:48:28,850 On the right-hand side, I've got hexagons. 763 00:48:28,850 --> 00:48:31,130 And you can see, even if you have a certain unit cell, 764 00:48:31,130 --> 00:48:32,920 there's also different ways to stack it. 765 00:48:32,920 --> 00:48:36,920 So the number of edges that meet at a vertex 766 00:48:36,920 --> 00:48:40,200 is different for, say, this example on the top left 767 00:48:40,200 --> 00:48:42,950 and this example on the bottom left. 768 00:48:42,950 --> 00:48:46,510 Here, we've got six members coming into each vertex, 769 00:48:46,510 --> 00:48:48,040 and here, we've got four. 770 00:48:48,040 --> 00:48:51,440 And again, this stacking for the two square cells 771 00:48:51,440 --> 00:48:53,700 is also different. 772 00:48:53,700 --> 00:48:58,070 So you can have different numbers of edges per vertex. 773 00:48:58,070 --> 00:49:00,800 Another thing to note that's kind of interesting-- 774 00:49:00,800 --> 00:49:03,730 if you look at the honeycomb cells here, 775 00:49:03,730 --> 00:49:06,660 this one on the top left-- this equilateral triangle 776 00:49:06,660 --> 00:49:10,040 one with the stacking-- and this one on the top right-- 777 00:49:10,040 --> 00:49:13,790 the regular hexagonal cells-- those two are isotropic 778 00:49:13,790 --> 00:49:16,500 for linear elastic behavior, whereas all the other ones are 779 00:49:16,500 --> 00:49:18,650 not. 780 00:49:18,650 --> 00:49:22,890 So we have 2D honeycomb unit cells. 781 00:49:26,960 --> 00:49:38,550 We can have triangles, squares, and hexagons. 782 00:49:38,550 --> 00:49:40,656 They can be stacked in more than one way. 783 00:49:49,670 --> 00:49:53,377 And that gives different numbers of edges per vertex. 784 00:50:01,110 --> 00:50:04,370 And in that figure, a and e are isotropic, 785 00:50:04,370 --> 00:50:06,160 for linear elasticity. 786 00:50:16,730 --> 00:50:17,300 OK. 787 00:50:17,300 --> 00:50:19,160 When we come to modeling the honeycombs, 788 00:50:19,160 --> 00:50:21,780 we're going to focus on the hexagonal cells. 789 00:50:21,780 --> 00:50:24,300 We'll talk a little bit about the square and triangular 790 00:50:24,300 --> 00:50:26,490 cells, as well. 791 00:50:26,490 --> 00:50:28,371 And then, for foams, when you look 792 00:50:28,371 --> 00:50:30,120 at the structure of a foam, it's obviously 793 00:50:30,120 --> 00:50:33,080 not a unit cell that repeats over and over again. 794 00:50:33,080 --> 00:50:36,450 But people started off trying to model the mechanical behavior 795 00:50:36,450 --> 00:50:40,950 of foams by looking at periodic repeating polyhedral cells. 796 00:50:40,950 --> 00:50:43,540 And there's three cells here that are prismatic. 797 00:50:43,540 --> 00:50:46,050 We're not really going to talk about those beyond this. 798 00:50:46,050 --> 00:50:49,800 So they're not really physically realistic or interesting. 799 00:50:49,800 --> 00:50:53,310 But people would use these two cells here in initial attempts 800 00:50:53,310 --> 00:50:54,630 to model foams. 801 00:50:54,630 --> 00:50:58,220 And this one here is called the rhombic dodecahedra. 802 00:50:58,220 --> 00:50:59,990 Rhombic because each of the faces 803 00:50:59,990 --> 00:51:05,770 has four sides and dodecahedra because each polyhedra has 12 804 00:51:05,770 --> 00:51:07,770 faces. 805 00:51:07,770 --> 00:51:10,640 I forget if I've bored you with my Latin already. 806 00:51:10,640 --> 00:51:14,160 Hedron means face in-- oh, this is Greek, I think. 807 00:51:14,160 --> 00:51:15,870 Hedron means face. 808 00:51:15,870 --> 00:51:18,600 Do is two, deca is 10. 809 00:51:18,600 --> 00:51:20,530 So dodeca is two plus 10. 810 00:51:20,530 --> 00:51:21,930 It's got 12 faces. 811 00:51:21,930 --> 00:51:22,700 OK? 812 00:51:22,700 --> 00:51:25,870 So that's the rhombic dodecahedra over here. 813 00:51:25,870 --> 00:51:29,536 And then this bottom one down here is a tetrakaidecahedra. 814 00:51:29,536 --> 00:51:30,410 It's a similar thing. 815 00:51:30,410 --> 00:51:32,930 Tetra's four, kai mean and. 816 00:51:32,930 --> 00:51:37,000 Four and 10-- tetra kai deca-- it's got 14 faces. 817 00:51:37,000 --> 00:51:37,910 OK? 818 00:51:37,910 --> 00:51:40,310 And those two pack to fill space. 819 00:51:40,310 --> 00:51:44,320 I think those are the only uniform polyhedra 820 00:51:44,320 --> 00:51:47,900 that pack to fill space. 821 00:51:47,900 --> 00:51:51,545 Here is the 3D foams. 822 00:51:54,910 --> 00:52:02,640 We have the rhombic dodecahedron and the tetrakaidecahedron. 823 00:52:34,510 --> 00:52:38,920 And the tetrakaidecahedron packs in a bcc packing. 824 00:52:56,020 --> 00:53:00,030 Initial models for foams-- they took these two unit cells. 825 00:53:00,030 --> 00:53:02,760 And what they would do is have an infinite array of them 826 00:53:02,760 --> 00:53:04,060 to make up the whole material. 827 00:53:04,060 --> 00:53:05,900 And then they would isolate a unit cell. 828 00:53:05,900 --> 00:53:08,900 And they would apply loads-- some say compressive stress, 829 00:53:08,900 --> 00:53:09,860 for example. 830 00:53:09,860 --> 00:53:12,420 And then they would figure out what the load, or force, was 831 00:53:12,420 --> 00:53:15,360 in every single member, and how much that member deformed. 832 00:53:15,360 --> 00:53:17,024 And they would figure out the component 833 00:53:17,024 --> 00:53:18,690 of the deformation in the same direction 834 00:53:18,690 --> 00:53:19,820 that they were putting the load on. 835 00:53:19,820 --> 00:53:22,153 And they would figure out things like a Young's modulus, 836 00:53:22,153 --> 00:53:24,870 or they would figure out when there was some failure of one 837 00:53:24,870 --> 00:53:26,620 of these struts, and they would figure out 838 00:53:26,620 --> 00:53:27,690 a strength for the foam. 839 00:53:27,690 --> 00:53:30,070 But you can kind of imagine, geometrically, 840 00:53:30,070 --> 00:53:31,740 not that easy to keep straight. 841 00:53:31,740 --> 00:53:33,630 A little bit complicated. 842 00:53:33,630 --> 00:53:36,590 So one way to model foams is by using these unit cells. 843 00:53:36,590 --> 00:53:38,530 But we're going to talk about a different way 844 00:53:38,530 --> 00:53:40,610 to do it, as well. 845 00:53:40,610 --> 00:53:41,340 OK. 846 00:53:41,340 --> 00:53:42,375 So those are unit cells. 847 00:53:47,770 --> 00:53:50,930 When they make foams, as we just talked about, 848 00:53:50,930 --> 00:53:54,380 one way to make a foam is by blowing a gas into a liquid. 849 00:53:54,380 --> 00:53:57,040 And if you blow a gas into a liquid, 850 00:53:57,040 --> 00:53:58,720 then the surface tension is going 851 00:53:58,720 --> 00:54:00,420 to have an effect on the cell geometry 852 00:54:00,420 --> 00:54:02,430 and on the shape of the cells. 853 00:54:02,430 --> 00:54:04,890 And if the surface tension is isotropic-- 854 00:54:04,890 --> 00:54:08,700 if it's the same in all directions-- then the structure 855 00:54:08,700 --> 00:54:10,940 that you get is one that minimizes the surface 856 00:54:10,940 --> 00:54:12,920 area per unit volume. 857 00:54:12,920 --> 00:54:15,560 And so people were interested in what sort of cell shape 858 00:54:15,560 --> 00:54:18,440 minimizes the surface area per unit volume. 859 00:54:18,440 --> 00:54:21,530 And Lord Kelvin, in the 1800s, was 860 00:54:21,530 --> 00:54:22,890 the person who worked this out. 861 00:54:22,890 --> 00:54:26,550 And this is called the Kelvin tetrakaidecahedron. 862 00:54:26,550 --> 00:54:29,310 And it's not just a straight tetrakaidecahedron. 863 00:54:29,310 --> 00:54:33,160 There's a slight curvature to the cells here, to the faces. 864 00:54:33,160 --> 00:54:35,990 And you can kind of see it in some of the edges here. 865 00:54:35,990 --> 00:54:37,820 Like if we-- let me get my little pointer. 866 00:54:37,820 --> 00:54:39,979 If you look at that edge, it's not straight. 867 00:54:39,979 --> 00:54:41,270 This edge here is not straight. 868 00:54:41,270 --> 00:54:43,120 It's got a little bit of a curvature to it. 869 00:54:43,120 --> 00:54:47,360 But this minimizes the surface area per unit volume. 870 00:54:47,360 --> 00:54:49,800 And then more recently, in the 1990's, there 871 00:54:49,800 --> 00:54:53,840 were two people-- Dennis Weaire and Robert Phelan-- discovered 872 00:54:53,840 --> 00:54:57,030 that this structure here-- which isn't a single polyhedron, 873 00:54:57,030 --> 00:55:00,410 but it's made up of a few polyhedra. 874 00:55:00,410 --> 00:55:03,560 That has a slightly smaller surface area per unit volume. 875 00:55:03,560 --> 00:55:05,790 Smaller by 0.3%. 876 00:55:05,790 --> 00:55:07,580 So, a tiny bit smaller. 877 00:55:07,580 --> 00:55:09,810 OK. 878 00:55:09,810 --> 00:55:10,370 Let's see. 879 00:55:10,370 --> 00:55:15,360 What I'll say here is that foams are often made 880 00:55:15,360 --> 00:55:17,115 by blowing a gas into a liquid. 881 00:55:33,190 --> 00:55:40,600 And if the surface tension controls and it's isotropic, 882 00:55:40,600 --> 00:55:42,960 then the structure will minimize the surface area 883 00:55:42,960 --> 00:55:43,680 per unit volume. 884 00:57:55,190 --> 00:57:55,690 OK. 885 00:58:09,430 --> 00:58:12,480 That's relevant if the foam is made 886 00:58:12,480 --> 00:58:16,820 by blowing a gas into a liquid and surface tension 887 00:58:16,820 --> 00:58:18,430 is the controlling factor. 888 00:58:18,430 --> 00:58:21,620 Sometimes foams are made by supersaturating a liquid 889 00:58:21,620 --> 00:58:23,720 with a gas, and then you nucleate bubbles, 890 00:58:23,720 --> 00:58:25,020 and then the bubbles grow. 891 00:58:25,020 --> 00:58:26,811 So there's a nucleation and growth process. 892 00:58:26,811 --> 00:58:28,400 So that's a little bit different. 893 00:58:28,400 --> 00:58:31,050 And if you have a nucleation and growth process, 894 00:58:31,050 --> 00:58:34,700 you get a structure that is similar to something 895 00:58:34,700 --> 00:58:36,940 called a Voronoi structure. 896 00:58:36,940 --> 00:58:38,810 In an idealized case, imagine that you 897 00:58:38,810 --> 00:58:42,090 have random points that are nucleation points 898 00:58:42,090 --> 00:58:45,180 and that you start to grow bubbles 899 00:58:45,180 --> 00:58:47,880 at those nucleation points. 900 00:58:47,880 --> 00:58:49,850 So you start off with these random points. 901 00:58:49,850 --> 00:58:52,150 And the bubbles all start to grow at the same time 902 00:58:52,150 --> 00:58:54,460 and they all grow at the same linear rate. 903 00:58:54,460 --> 00:58:57,110 If you have that situation, then you 904 00:58:57,110 --> 00:58:59,280 end up with this Voronoi kind of structure. 905 00:58:59,280 --> 00:59:00,660 And I've shown a 2D version of it 906 00:59:00,660 --> 00:59:02,810 here just because it's easier to see in 2D, 907 00:59:02,810 --> 00:59:05,320 but you can imagine a 3D system. 908 00:59:05,320 --> 00:59:08,060 And in order to make one of these Voronoi honeycombs, 909 00:59:08,060 --> 00:59:11,571 you can imagine-- if you have random points-- here, 910 00:59:11,571 --> 00:59:14,070 say that little point there is one of the nucleation points, 911 00:59:14,070 --> 00:59:15,850 and here's another point here-- you 912 00:59:15,850 --> 00:59:19,910 form the structure by drawing the perpendicular bisectors 913 00:59:19,910 --> 00:59:21,430 between each pair of points. 914 00:59:21,430 --> 00:59:23,840 This is the bisector between these two points. 915 00:59:23,840 --> 00:59:26,100 Here's a bisector between those two points. 916 00:59:26,100 --> 00:59:29,260 And then you form the envelope of those lines 917 00:59:29,260 --> 00:59:31,490 around each nucleation point. 918 00:59:31,490 --> 00:59:33,660 And that, then, gives you that structure. 919 00:59:33,660 --> 00:59:36,770 And you can see, this structure here is kind of angular. 920 00:59:36,770 --> 00:59:39,430 It doesn't look that representative of something 921 00:59:39,430 --> 00:59:41,230 like a foam. 922 00:59:41,230 --> 00:59:43,450 But if you have an exclusion distance, 923 00:59:43,450 --> 00:59:46,250 where you say that you're not going to allow the nucleation 924 00:59:46,250 --> 00:59:49,660 points to be closer than some given distance-- your exclusion 925 00:59:49,660 --> 00:59:51,920 distance-- then you get this structure here. 926 00:59:51,920 --> 00:59:53,530 And this starts to look a lot more 927 00:59:53,530 --> 00:59:55,340 like a foamy kind of structure. 928 00:59:55,340 --> 00:59:58,140 So these Voronoi structures are representative 929 00:59:58,140 --> 01:00:00,730 of structures that are related to nucleation 930 01:00:00,730 --> 01:00:02,990 and growth of the bubbles, or nucleation and growth 931 01:00:02,990 --> 01:00:04,340 processes. 932 01:00:04,340 --> 01:00:07,375 Let me write down something about Voronoi things. 933 01:00:44,000 --> 01:00:46,470 And these Voronoi structures were first 934 01:00:46,470 --> 01:00:49,164 developed to look at grain growth in metals. 935 01:00:49,164 --> 01:00:51,080 They weren't developed for cellular materials. 936 01:00:51,080 --> 01:00:54,170 But you can use them to model cellular materials, 937 01:00:54,170 --> 01:00:57,426 as well, as long as it's a nucleation and growth process. 938 01:00:59,954 --> 01:01:01,370 We'll say that foams are sometimes 939 01:01:01,370 --> 01:01:24,030 made by supersaturating a liquid with a gas, 940 01:01:24,030 --> 01:01:26,590 and then reducing the pressure so that the bubbles nucleate 941 01:01:26,590 --> 01:01:27,340 and grow. 942 01:01:46,824 --> 01:01:48,990 So initially, the bubbles are going to form spheres. 943 01:01:57,360 --> 01:01:59,410 But as the spheres grow, they start 944 01:01:59,410 --> 01:02:02,315 to intersect with each other and form polyhedral cells. 945 01:02:29,060 --> 01:02:30,480 And you get the Voronoi structure 946 01:02:30,480 --> 01:02:34,480 by thinking about an idealized case in which you randomly 947 01:02:34,480 --> 01:02:38,760 nucleate the-- you have nucleation points at a randomly 948 01:02:38,760 --> 01:02:40,542 distributed space. 949 01:02:40,542 --> 01:02:42,000 They start to grow at the same time 950 01:02:42,000 --> 01:02:43,720 and they grow at the same linear rate. 951 01:04:00,750 --> 01:04:01,250 OK. 952 01:04:01,250 --> 01:04:13,570 The Voronoi honeycomb, or the foam-- 953 01:04:13,570 --> 01:04:16,680 you can form that by drawing the perpendicular bisectors 954 01:04:16,680 --> 01:04:17,775 between the random points. 955 01:05:22,125 --> 01:05:24,530 So each cell contains the points that 956 01:05:24,530 --> 01:05:30,050 are closer to the nucleation point than any other point-- 957 01:05:30,050 --> 01:05:31,490 or any other nucleation point. 958 01:06:06,162 --> 01:06:13,070 And if we just do this process as I've described here, 959 01:06:13,070 --> 01:06:15,530 you end up with a Voronoi structure, 960 01:06:15,530 --> 01:06:17,850 where the cells appear kind of angular. 961 01:06:17,850 --> 01:06:19,920 And if you specify an exclusion distance, 962 01:06:19,920 --> 01:06:22,140 where you say the nucleation points can't be closer 963 01:06:22,140 --> 01:06:24,890 than a certain distance, then the cells 964 01:06:24,890 --> 01:06:27,905 become less angular, and of more similar size. 965 01:07:19,201 --> 01:07:19,700 OK. 966 01:07:19,700 --> 01:07:22,830 So are we good with the Voronoi honeycomb nucleation and growth 967 01:07:22,830 --> 01:07:23,330 idea? 968 01:07:26,124 --> 01:07:26,624 Alrighty. 969 01:08:42,778 --> 01:08:43,630 All right. 970 01:08:43,630 --> 01:08:46,100 If we think about cell shape-- if we start with honeycombs 971 01:08:46,100 --> 01:08:50,000 and we just think about it hexagonal honeycombs, if I have 972 01:08:50,000 --> 01:08:53,120 a regular hexagonal honeycomb so that all the edges are 973 01:08:53,120 --> 01:08:58,140 the same length and this angle here is 30 degrees, 974 01:08:58,140 --> 01:09:01,319 then that is an isotropic material 975 01:09:01,319 --> 01:09:03,483 in the plane in the linear elastic regime. 976 01:09:26,342 --> 01:09:27,800 One of the things we're going to do 977 01:09:27,800 --> 01:09:30,279 is calculate-- if I loan it this way on, 978 01:09:30,279 --> 01:09:31,430 what's the Young's modulus? 979 01:09:31,430 --> 01:09:33,660 If I load it that way on, what's the Young's modulus? 980 01:09:33,660 --> 01:09:35,300 And we're going to find they're the same, in fact, no matter 981 01:09:35,300 --> 01:09:36,399 which way on I loaded it. 982 01:09:36,399 --> 01:09:37,560 It would be the same. 983 01:09:37,560 --> 01:09:41,109 But if I now have my honeycomb, and imagine that I stretched it 984 01:09:41,109 --> 01:09:43,670 out-- and I'm kind of exaggerating how much we 985 01:09:43,670 --> 01:09:45,370 might stretch it out. 986 01:09:45,370 --> 01:09:47,100 But if we did something like that, 987 01:09:47,100 --> 01:09:49,220 it wouldn't be too surprising to think that the properties are 988 01:09:49,220 --> 01:09:51,220 going to be different if I loaded it this way on 989 01:09:51,220 --> 01:09:53,080 and that way on. 990 01:09:53,080 --> 01:09:55,810 And in terms of the cell geometry, 991 01:09:55,810 --> 01:10:00,520 I'm going to call that vertical cell edge length h. 992 01:10:00,520 --> 01:10:04,860 And I'm going to call this one-- the inclined one-- of length l. 993 01:10:04,860 --> 01:10:08,140 I'm going to say that angle is the angle theta. 994 01:10:08,140 --> 01:10:11,160 And the cell shape can be defined by the ratio of h 995 01:10:11,160 --> 01:10:13,070 over l and that angle theta. 996 01:10:18,030 --> 01:10:18,840 OK. 997 01:10:18,840 --> 01:10:21,770 When we derive equations for the mechanical properties 998 01:10:21,770 --> 01:10:24,250 of the honeycombs, we're going to find that they depend 999 01:10:24,250 --> 01:10:25,970 on some solid properties. 1000 01:10:25,970 --> 01:10:27,880 Say, the modulus of the honeycombs 1001 01:10:27,880 --> 01:10:29,615 can depend on the modulus of the solid. 1002 01:10:29,615 --> 01:10:31,740 It's going to depend on the relative density raised 1003 01:10:31,740 --> 01:10:32,490 to some power. 1004 01:10:32,490 --> 01:10:34,100 And we're going to figure out what that is. 1005 01:10:34,100 --> 01:10:35,599 And then it's going to depend, also, 1006 01:10:35,599 --> 01:10:37,910 on some function of h over l and theta. 1007 01:10:37,910 --> 01:10:40,210 And that function really represents the contribution 1008 01:10:40,210 --> 01:10:44,680 of the cell geometry to the mechanical properties. 1009 01:10:44,680 --> 01:10:45,180 OK. 1010 01:10:45,180 --> 01:10:47,300 That's the honeycombs. 1011 01:10:47,300 --> 01:10:51,230 It's fairly straightforward to characterize the shell shape 1012 01:10:51,230 --> 01:10:53,420 for the honeycombs. 1013 01:10:53,420 --> 01:11:00,000 It's a little more involved to do it for the foams. 1014 01:11:00,000 --> 01:11:02,880 And the technique that's used is called the mean intercept 1015 01:11:02,880 --> 01:11:03,380 length. 1016 01:11:03,380 --> 01:11:05,545 At least, that's one technique that's used. 1017 01:11:05,545 --> 01:11:06,920 Let me wait until you've finished 1018 01:11:06,920 --> 01:11:08,300 writing because I want you to see 1019 01:11:08,300 --> 01:11:11,270 the picture as I talk about it. 1020 01:11:11,270 --> 01:11:13,410 OK? 1021 01:11:13,410 --> 01:11:13,910 OK. 1022 01:11:13,910 --> 01:11:14,770 Here's-- whoops. 1023 01:11:14,770 --> 01:11:16,730 My pointer keeps disappearing. 1024 01:11:16,730 --> 01:11:20,850 This top left picture here shows an SEM image of a foam. 1025 01:11:20,850 --> 01:11:23,770 And you can see, you've got some big cells and little cells 1026 01:11:23,770 --> 01:11:28,530 and there's no obvious way to characterize the cell shape. 1027 01:11:28,530 --> 01:11:31,620 And what people do to calculate this mean intercept length 1028 01:11:31,620 --> 01:11:34,170 is they would take an image. 1029 01:11:34,170 --> 01:11:38,090 They would then sketch out just the cell edges 1030 01:11:38,090 --> 01:11:39,780 that touch a plane's surface. 1031 01:11:39,780 --> 01:11:42,210 So all these black lines are just the-- 1032 01:11:42,210 --> 01:11:44,620 if you took your-- if you put ink on your foam 1033 01:11:44,620 --> 01:11:47,810 and you just put it on a pad and put it on a piece of paper, 1034 01:11:47,810 --> 01:11:50,600 you would get this outline of the edges of the cells, where 1035 01:11:50,600 --> 01:11:52,300 they intersect that plane. 1036 01:11:52,300 --> 01:11:54,480 And then what people do is they draw test circles. 1037 01:11:54,480 --> 01:11:56,680 Here's the test circle here. 1038 01:11:56,680 --> 01:12:01,870 And they draw parallel equiaxed, or equidistant lines. 1039 01:12:01,870 --> 01:12:03,420 So the lines here are parallel. 1040 01:12:03,420 --> 01:12:05,050 They're all at, say, zero degrees. 1041 01:12:05,050 --> 01:12:07,110 And they're all the same distance apart. 1042 01:12:07,110 --> 01:12:09,970 And then they count the number of intercepts. 1043 01:12:09,970 --> 01:12:13,060 They count-- say we went out here. 1044 01:12:13,060 --> 01:12:14,530 The cell wall intercepts here. 1045 01:12:14,530 --> 01:12:16,157 There's one that intercepts here. 1046 01:12:16,157 --> 01:12:17,240 And then, it'd go up here. 1047 01:12:17,240 --> 01:12:18,330 Here's another intercept. 1048 01:12:18,330 --> 01:12:19,371 Here's another intercept. 1049 01:12:19,371 --> 01:12:22,470 So they count the number of intercepts of the cell wall 1050 01:12:22,470 --> 01:12:23,830 with the lines. 1051 01:12:23,830 --> 01:12:26,150 And then they get a mean intercept length, 1052 01:12:26,150 --> 01:12:30,177 which is characteristic of the cell dimension. 1053 01:12:30,177 --> 01:12:32,010 And then what they do-- because this is just 1054 01:12:32,010 --> 01:12:34,240 in one orientation-- you would then 1055 01:12:34,240 --> 01:12:37,289 rotate those parallel lines by, say, 5 degrees 1056 01:12:37,289 --> 01:12:38,330 and do it all over again. 1057 01:12:38,330 --> 01:12:40,121 And get another length at 5 degrees and one 1058 01:12:40,121 --> 01:12:41,760 at 10 degrees one at 15. 1059 01:12:41,760 --> 01:12:44,290 And so you get different lengths for the intercepts 1060 01:12:44,290 --> 01:12:46,860 as you rotate your parallel lines around. 1061 01:12:46,860 --> 01:12:48,610 And then you make a polar plot, and that's 1062 01:12:48,610 --> 01:12:50,680 what the thing is down at the bottom here. 1063 01:12:50,680 --> 01:12:53,240 And so you plot your mean intercept length 1064 01:12:53,240 --> 01:12:56,480 as a function of the angle that you measured it at. 1065 01:12:56,480 --> 01:12:58,399 And you can fit it to an ellipse. 1066 01:12:58,399 --> 01:12:59,940 And if you do it in three dimensions, 1067 01:12:59,940 --> 01:13:01,890 you fit it to an ellipsoid. 1068 01:13:01,890 --> 01:13:06,660 And the major and minor axes of that ellipse, or ellipsoid, 1069 01:13:06,660 --> 01:13:09,816 are characteristic of how elongated the cell is 1070 01:13:09,816 --> 01:13:10,982 in the different directions. 1071 01:13:10,982 --> 01:13:13,000 And the orientation of that ellipsoid 1072 01:13:13,000 --> 01:13:16,450 is characteristic of the orientation of the cells. 1073 01:13:16,450 --> 01:13:19,490 Those of you who took 303, too, you remember Mohr's circles? 1074 01:13:19,490 --> 01:13:21,200 Is this beginning to look familiar? 1075 01:13:21,200 --> 01:13:23,810 It's the same kind of idea as Mohr's circles. 1076 01:13:23,810 --> 01:13:26,340 Same way we have principal stresses and orientation 1077 01:13:26,340 --> 01:13:29,160 of principal stresses, now we have principal dimensions 1078 01:13:29,160 --> 01:13:31,160 and the orientation of the principal dimensions. 1079 01:13:31,160 --> 01:13:32,830 So it's the same kind of idea. 1080 01:13:32,830 --> 01:13:35,230 OK? 1081 01:13:35,230 --> 01:13:36,230 Let's see. 1082 01:13:36,230 --> 01:13:39,410 I feel like I'm getting to the end here. 1083 01:13:39,410 --> 01:13:42,300 Maybe I'll stop there for today. 1084 01:13:42,300 --> 01:13:44,840 But next time, I'll write down the whole technique 1085 01:13:44,840 --> 01:13:48,030 about how we get these mean intercepts 1086 01:13:48,030 --> 01:13:49,770 and get this ellipsoid. 1087 01:13:49,770 --> 01:13:54,524 And I'm going to write the mean intercepts down as a matrix. 1088 01:13:54,524 --> 01:13:56,190 But you could also write it as a tensor. 1089 01:13:56,190 --> 01:13:57,815 And there's something called the fabric 1090 01:13:57,815 --> 01:14:00,860 tensor, which characterizes the shape of the cells. 1091 01:14:00,860 --> 01:14:03,280 And as you might imagine, the same is with the honeycomb. 1092 01:14:03,280 --> 01:14:05,770 If you have equiaxed cells in the foams, 1093 01:14:05,770 --> 01:14:09,010 you might expect you would get isotropic properties. 1094 01:14:09,010 --> 01:14:12,650 If you have cells that are stretched out in some way-- 1095 01:14:12,650 --> 01:14:16,930 so you've got different principal dimensions for them-- 1096 01:14:16,930 --> 01:14:19,130 then you've got anisotropic material. 1097 01:14:19,130 --> 01:14:21,730 And you can relate how much anisotropy to the shape 1098 01:14:21,730 --> 01:14:22,681 of the cells. 1099 01:14:22,681 --> 01:14:23,180 OK. 1100 01:14:23,180 --> 01:14:26,040 I'm going to stop there for today. 1101 01:14:26,040 --> 01:14:27,100 I'll see you tomorrow. 1102 01:14:27,100 --> 01:14:29,110 Seems very sudden. 1103 01:14:29,110 --> 01:14:30,820 I'll see you tomorrow. 1104 01:14:30,820 --> 01:14:34,010 I'll pick up and I'll finish this section on the structure. 1105 01:14:34,010 --> 01:14:35,159 We've got a bit more to do. 1106 01:14:35,159 --> 01:14:37,450 And then we'll start looking at honeycombs and modeling 1107 01:14:37,450 --> 01:14:38,480 honeycombs. 1108 01:14:38,480 --> 01:14:39,950 The honeycombs are simpler to model 1109 01:14:39,950 --> 01:14:42,480 just because they have this nice simple unit cell. 1110 01:14:42,480 --> 01:14:44,490 So we'll start with that, and then we'll 1111 01:14:44,490 --> 01:14:46,000 move from there to the foams. 1112 01:14:46,000 --> 01:14:47,550 OK?