WEBVTT 00:00:00.000 --> 00:00:16.308 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:16.308 --> 00:00:21.360 align:middle line:84% Well, Why the theoretical strength of glass materials 00:00:21.360 --> 00:00:24.000 align:middle line:84% is so much higher compared to what you would measure 00:00:24.000 --> 00:00:25.580 align:middle line:90% in a realistic glass sample? 00:00:25.580 --> 00:00:28.720 align:middle line:84% We attribute it to the presence of some kind of defects 00:00:28.720 --> 00:00:31.520 align:middle line:84% that actually are present in bulk glass materials that 00:00:31.520 --> 00:00:34.600 align:middle line:84% can actually compromise the fracture strength. 00:00:34.600 --> 00:00:38.360 align:middle line:84% So this is what is called the Griffith's theory. 00:00:38.360 --> 00:00:40.000 align:middle line:84% Essentially, what is proposed here 00:00:40.000 --> 00:00:41.920 align:middle line:84% is there are actually tiny little cracks 00:00:41.920 --> 00:00:44.960 align:middle line:84% inside the brittle materials, like glass. 00:00:44.960 --> 00:00:46.720 align:middle line:84% So what I'm showing you here, this 00:00:46.720 --> 00:00:50.947 align:middle line:84% is basically a slab of the material coming from the bulk. 00:00:50.947 --> 00:00:53.280 align:middle line:84% This is one little crack that goes through the thickness 00:00:53.280 --> 00:00:54.360 align:middle line:90% of the material. 00:00:54.360 --> 00:00:58.560 align:middle line:84% The length of the crack is customarily labeled as 2a. 00:00:58.560 --> 00:01:02.670 align:middle line:84% Now, this is what happens if the crack is embedded entirely 00:01:02.670 --> 00:01:03.710 align:middle line:90% inside the material. 00:01:03.710 --> 00:01:08.110 align:middle line:84% As you'll see later, in practice, for most glasses, 00:01:08.110 --> 00:01:10.910 align:middle line:84% the defects actually come from the surface. 00:01:10.910 --> 00:01:13.390 align:middle line:84% Some kind of surface cracks is usually the weak link. 00:01:13.390 --> 00:01:15.990 align:middle line:84% So if it's on the surface, you can think of it 00:01:15.990 --> 00:01:19.150 align:middle line:84% as you can cut this whole material into two pieces, two 00:01:19.150 --> 00:01:21.190 align:middle line:90% symmetric pieces. 00:01:21.190 --> 00:01:25.350 align:middle line:84% And effectively, the correct length would be a. 00:01:25.350 --> 00:01:28.110 align:middle line:84% So if it's on the surface, the correct length 00:01:28.110 --> 00:01:31.710 align:middle line:84% that needed to lead to the same level of strength decrease 00:01:31.710 --> 00:01:34.390 align:middle line:84% is essentially half the length compared to when 00:01:34.390 --> 00:01:36.990 align:middle line:90% the crack is in the bulk. 00:01:36.990 --> 00:01:39.310 align:middle line:84% So 2a for crack length in the bulk, 00:01:39.310 --> 00:01:42.510 align:middle line:84% a for crack length in the surface. 00:01:42.510 --> 00:01:46.310 align:middle line:84% The stress we applied, the macroscopic 00:01:46.310 --> 00:01:50.173 align:middle line:84% stress we applied, that's what we label as sigma infinity. 00:01:50.173 --> 00:01:51.590 align:middle line:84% Infinity essentially means that we 00:01:51.590 --> 00:01:53.510 align:middle line:84% are looking at essentially the average stress 00:01:53.510 --> 00:01:56.510 align:middle line:84% far away, very far away from the crack. 00:01:56.510 --> 00:01:58.515 align:middle line:84% If you look at the stress field distribution 00:01:58.515 --> 00:02:00.140 align:middle line:84% when plotting here-- these are actually 00:02:00.140 --> 00:02:03.220 align:middle line:84% the field lines that indicate the direction of the stress. 00:02:03.220 --> 00:02:04.980 align:middle line:84% And the density of these lines gives you, 00:02:04.980 --> 00:02:06.800 align:middle line:84% essentially, the level of stress. 00:02:06.800 --> 00:02:10.139 align:middle line:84% So you can clearly see that, near the tip of the crack, 00:02:10.139 --> 00:02:12.140 align:middle line:84% you have a concentration of the stress 00:02:12.140 --> 00:02:15.780 align:middle line:84% here so that effective stress you see at the crack tip 00:02:15.780 --> 00:02:20.700 align:middle line:84% is much higher than the applied stress sigma infinity. 00:02:20.700 --> 00:02:23.300 align:middle line:84% So quantitatively, people have gone in 00:02:23.300 --> 00:02:26.280 align:middle line:84% and solved this so-called stress concentration factor. 00:02:26.280 --> 00:02:30.040 align:middle line:84% Essentially, the level of stress increases at the crack tip. 00:02:30.040 --> 00:02:32.100 align:middle line:84% And that's actually given by this factor here, 00:02:32.100 --> 00:02:34.660 align:middle line:90% a divided by a0. 00:02:34.660 --> 00:02:40.740 align:middle line:84% Now, a0 is what we labeled as the atomic spacing. 00:02:40.740 --> 00:02:46.780 align:middle line:84% And a, in this case, this is the half length of a bulk crack 00:02:46.780 --> 00:02:50.220 align:middle line:90% or length of the surface crack. 00:02:50.220 --> 00:02:52.660 align:middle line:84% Now, because the length of the crack, 00:02:52.660 --> 00:02:54.300 align:middle line:84% it will be in the order of microns 00:02:54.300 --> 00:02:57.690 align:middle line:84% compared to interatomic spacing, which is like angstroms, 00:02:57.690 --> 00:03:00.350 align:middle line:84% this is many orders of magnitude higher. 00:03:00.350 --> 00:03:02.970 align:middle line:84% And that's why you can have significant stress 00:03:02.970 --> 00:03:04.930 align:middle line:90% concentration at a crack tip. 00:03:04.930 --> 00:03:06.490 align:middle line:84% So then it becomes the weakest link 00:03:06.490 --> 00:03:09.530 align:middle line:84% where material preferentially fails at the crack tip, 00:03:09.530 --> 00:03:11.090 align:middle line:84% leading to an essentially propagation 00:03:11.090 --> 00:03:14.650 align:middle line:84% of crack, which eventually leads to a catastrophic failure. 00:03:14.650 --> 00:03:17.770 align:middle line:84% So now, we can now use that to actually calculate 00:03:17.770 --> 00:03:20.610 align:middle line:84% what is the fracture strength of a material now containing 00:03:20.610 --> 00:03:21.810 align:middle line:90% a crack. 00:03:21.810 --> 00:03:25.170 align:middle line:84% So in the last lecture, we have already 00:03:25.170 --> 00:03:27.610 align:middle line:84% mentioned that the theoretical strength 00:03:27.610 --> 00:03:31.490 align:middle line:84% of a material, sigma m, this will be given 00:03:31.490 --> 00:03:38.850 align:middle line:90% by square root gamma E a0. 00:03:38.850 --> 00:03:44.650 align:middle line:84% So now, because of the presence of the defects here, 00:03:44.650 --> 00:03:47.370 align:middle line:84% the stress that's applied at the crack tip 00:03:47.370 --> 00:03:49.970 align:middle line:84% is effectively amplified by this factor. 00:03:49.970 --> 00:03:51.890 align:middle line:84% So the fracture strength will also 00:03:51.890 --> 00:03:53.930 align:middle line:84% be decreased by a factor corresponding 00:03:53.930 --> 00:03:56.600 align:middle line:84% to the stress concentration factor. 00:03:56.600 --> 00:03:59.760 align:middle line:84% So this will then give you the fracture strength 00:03:59.760 --> 00:04:01.740 align:middle line:90% of a flawed material. 00:04:01.740 --> 00:04:05.080 align:middle line:84% So let me put all the equations on the board here. 00:04:05.080 --> 00:04:14.900 align:middle line:84% Sigma f is 1/2 square root gamma E a, which now depends, 00:04:14.900 --> 00:04:19.800 align:middle line:84% of course inversely, on the length of the crack. 00:04:19.800 --> 00:04:24.000 align:middle line:84% So now, you can put in some actual numbers there. 00:04:24.000 --> 00:04:26.720 align:middle line:84% We know that, for a typical silica glass, 00:04:26.720 --> 00:04:29.645 align:middle line:84% its strength is about 110 megapascals. 00:04:29.645 --> 00:04:31.520 align:middle line:84% You plug in all the numbers, what you come up 00:04:31.520 --> 00:04:33.895 align:middle line:84% with is that they correspond to a correct length of about 00:04:33.895 --> 00:04:35.200 align:middle line:90% 5 microns. 00:04:35.200 --> 00:04:38.440 align:middle line:84% So what it tells you is that, even 00:04:38.440 --> 00:04:41.460 align:middle line:84% in the presence of tiny little defects, 00:04:41.460 --> 00:04:44.120 align:middle line:84% a crack of the length of only a few microns, 00:04:44.120 --> 00:04:46.400 align:middle line:84% that can already account for the vast gap 00:04:46.400 --> 00:04:49.200 align:middle line:84% between the theoretical strength and the actual measured strength 00:04:49.200 --> 00:04:52.580 align:middle line:90% in engineering materials. 00:04:52.580 --> 00:04:56.580 align:middle line:84% Now, the theory has been proposed for more than a couple 00:04:56.580 --> 00:04:58.760 align:middle line:90% of centuries. 00:04:58.760 --> 00:05:00.043 align:middle line:90% But seeing is believing. 00:05:00.043 --> 00:05:02.460 align:middle line:84% Of course, people will now have ways to actually visualize 00:05:02.460 --> 00:05:05.523 align:middle line:84% the presence of these cracks and confirm the Griffith's theory. 00:05:05.523 --> 00:05:06.940 align:middle line:84% So what I'm showing you here, this 00:05:06.940 --> 00:05:08.660 align:middle line:84% is actually experimental validation 00:05:08.660 --> 00:05:11.200 align:middle line:84% actually visualizing the presence of these cracks. 00:05:11.200 --> 00:05:14.020 align:middle line:84% So these are essentially a few different plots. 00:05:14.020 --> 00:05:16.540 align:middle line:84% On the top, these two, these are two plots 00:05:16.540 --> 00:05:20.320 align:middle line:84% of images collected using atomic force microscope. 00:05:20.320 --> 00:05:23.920 align:middle line:84% That shows the surface morphology near a crack. 00:05:23.920 --> 00:05:25.820 align:middle line:84% This is actually a little crack here. 00:05:25.820 --> 00:05:29.120 align:middle line:84% So this is actually before the crack propagation. 00:05:29.120 --> 00:05:30.560 align:middle line:90% This is after crack propagation. 00:05:30.560 --> 00:05:32.580 align:middle line:84% You see the crack actually gets longer. 00:05:32.580 --> 00:05:35.530 align:middle line:84% Now, from the difference of these two plots, 00:05:35.530 --> 00:05:37.780 align:middle line:84% you can actually get the displacement of the materials 00:05:37.780 --> 00:05:41.038 align:middle line:84% around the crack center after the crack propagation. 00:05:41.038 --> 00:05:43.580 align:middle line:84% So there's something you can actually theoretically calculate 00:05:43.580 --> 00:05:45.100 align:middle line:90% based on Griffith's theory. 00:05:45.100 --> 00:05:48.140 align:middle line:84% So the displacement field, the theoretical predicted 00:05:48.140 --> 00:05:50.940 align:middle line:84% displacement field, is actually plotted right here. 00:05:50.940 --> 00:05:53.970 align:middle line:84% So now, the last figure here, this 00:05:53.970 --> 00:05:56.930 align:middle line:84% is actually a difference between the theoretical prediction 00:05:56.930 --> 00:06:00.050 align:middle line:84% and what's actually measured experimentally. 00:06:00.050 --> 00:06:02.690 align:middle line:84% Now, if you look at the scale of this plot here, 00:06:02.690 --> 00:06:04.770 align:middle line:84% the maximum variation is probably 00:06:04.770 --> 00:06:07.930 align:middle line:84% of the order of about 0.2 nanometers-- basically, 00:06:07.930 --> 00:06:09.930 align:middle line:90% about 2 angstroms. 00:06:09.930 --> 00:06:12.730 align:middle line:84% That's comparable to one single atomic spacing. 00:06:12.730 --> 00:06:16.270 align:middle line:84% So bottom line is, within the accuracy of the measurement, 00:06:16.270 --> 00:06:19.450 align:middle line:84% which is atomic spacing, the Griffith's theory did 00:06:19.450 --> 00:06:22.490 align:middle line:84% predict very well the stress/strain distribution, 00:06:22.490 --> 00:06:26.710 align:middle line:84% the displacement field of the crack. 00:06:26.710 --> 00:06:32.420 align:middle line:84% So this really validates that this theory actually works. 00:06:32.420 --> 00:06:35.450 align:middle line:84% So besides the fact that you can actually 00:06:35.450 --> 00:06:37.473 align:middle line:84% amplify the stress at the crack tip, 00:06:37.473 --> 00:06:39.890 align:middle line:84% the other very important factor that also becomes relevant 00:06:39.890 --> 00:06:43.450 align:middle line:84% when it comes to glass materials is that these cracks can also 00:06:43.450 --> 00:06:45.650 align:middle line:90% lead to water condensation. 00:06:45.650 --> 00:06:49.410 align:middle line:84% So if you think about a little crack here, 00:06:49.410 --> 00:06:53.220 align:middle line:84% this will be like a surface crack. 00:06:53.220 --> 00:06:57.337 align:middle line:84% Now, most glass materials, they're actually hydrophilic. 00:06:57.337 --> 00:06:58.920 align:middle line:84% So if it's hydrophilic, it essentially 00:06:58.920 --> 00:07:01.365 align:middle line:84% means that water will tend to spread 00:07:01.365 --> 00:07:03.740 align:middle line:84% on the glass surface, which is basically your experience. 00:07:03.740 --> 00:07:05.400 align:middle line:90% You have seen windows. 00:07:05.400 --> 00:07:07.740 align:middle line:84% Raindrops falling on windows, they tend to spread. 00:07:07.740 --> 00:07:09.460 align:middle line:84% They essentially become in big bubbles. 00:07:09.460 --> 00:07:12.960 align:middle line:84% So to minimize the surface energy, essentially 00:07:12.960 --> 00:07:16.760 align:middle line:84% what happens here is that, if you have a little crack, 00:07:16.760 --> 00:07:20.920 align:middle line:84% then any water vapor will tend to condensate inside this crack 00:07:20.920 --> 00:07:23.200 align:middle line:90% here. 00:07:23.200 --> 00:07:25.480 align:middle line:84% And by doing so, you can essentially 00:07:25.480 --> 00:07:29.840 align:middle line:84% increase the maximum interface area 00:07:29.840 --> 00:07:33.520 align:middle line:84% between the water and the glass, while minimizing 00:07:33.520 --> 00:07:37.000 align:middle line:84% any free interface between the droplet and the air. 00:07:37.000 --> 00:07:40.000 align:middle line:84% So effectively, this is like this little droplet here 00:07:40.000 --> 00:07:42.440 align:middle line:84% is spreading effectively spreading on the glass 00:07:42.440 --> 00:07:46.680 align:middle line:90% surface around the crack. 00:07:46.680 --> 00:07:51.190 align:middle line:84% Now, water can be problematic, in this case 00:07:51.190 --> 00:07:53.590 align:middle line:84% here, because, of course, we mentioned 00:07:53.590 --> 00:07:58.030 align:middle line:84% that if it's SiO bond, SiOSi bond, if you put water 00:07:58.030 --> 00:08:03.190 align:middle line:84% in there, then this can lead to essentially a breaking 00:08:03.190 --> 00:08:06.490 align:middle line:90% of the SIO bond to become SiOH. 00:08:06.490 --> 00:08:12.150 align:middle line:90% 00:08:12.150 --> 00:08:15.150 align:middle line:84% So this will essentially accelerate this integration 00:08:15.150 --> 00:08:16.990 align:middle line:90% of the glass network. 00:08:16.990 --> 00:08:20.910 align:middle line:84% And if you have a soda lime glass or any alkaline silicate 00:08:20.910 --> 00:08:24.910 align:middle line:84% glass, the alkaline ion also tends to preferentially leach 00:08:24.910 --> 00:08:26.990 align:middle line:90% out into the aqueous solution. 00:08:26.990 --> 00:08:30.250 align:middle line:84% And when that happens, because you have OH here, 00:08:30.250 --> 00:08:32.549 align:middle line:84% if you have alkaline ion-- let's say sodium-- then 00:08:32.549 --> 00:08:36.130 align:middle line:84% what you end up having is you have a sodium hydroxide, 00:08:36.130 --> 00:08:38.510 align:middle line:84% which makes the whole solution becomes basic. 00:08:38.510 --> 00:08:41.510 align:middle line:84% And basic solution would significantly 00:08:41.510 --> 00:08:43.270 align:middle line:84% accelerate the chemical corrosion 00:08:43.270 --> 00:08:45.350 align:middle line:90% of the glass materials. 00:08:45.350 --> 00:08:51.020 align:middle line:84% So this is called a stress corrosion. 00:08:51.020 --> 00:08:53.220 align:middle line:84% And later on, we'll have a few slides 00:08:53.220 --> 00:08:55.820 align:middle line:84% to discuss about the importance of stress corrosion 00:08:55.820 --> 00:08:58.040 align:middle line:90% in subcritical crack growth. 00:08:58.040 --> 00:09:01.420 align:middle line:84% It essentially means that, even if the crack length is 00:09:01.420 --> 00:09:04.640 align:middle line:84% below the critical length that's predicted by Griffith's theory, 00:09:04.640 --> 00:09:07.500 align:middle line:84% leading to catastrophic failure, the crack will still slowly 00:09:07.500 --> 00:09:10.182 align:middle line:84% grow in length because of essentially this stress 00:09:10.182 --> 00:09:12.640 align:middle line:84% corrosion behavior, because of the presence of water vapor. 00:09:12.640 --> 00:09:17.420 align:middle line:90% 00:09:17.420 --> 00:09:22.500 align:middle line:84% So now, in order to characterize the material strength, what 00:09:22.500 --> 00:09:25.820 align:middle line:84% we are seeing here is that the fracture strength, this is 00:09:25.820 --> 00:09:27.632 align:middle line:90% no longer a material constant. 00:09:27.632 --> 00:09:29.340 align:middle line:84% It depends not only on material constants 00:09:29.340 --> 00:09:32.400 align:middle line:84% like gamma and E, surface energy and Young's modulus. 00:09:32.400 --> 00:09:34.460 align:middle line:84% It also depends on crack length, which 00:09:34.460 --> 00:09:37.300 align:middle line:84% is essentially a function of your sample quality. 00:09:37.300 --> 00:09:43.420 align:middle line:84% So to characterize the material quality using the material's 00:09:43.420 --> 00:09:46.450 align:middle line:84% ability to resist fracture, we then 00:09:46.450 --> 00:09:48.810 align:middle line:84% propose essentially this new term here 00:09:48.810 --> 00:09:50.690 align:middle line:90% called stress intensity factor. 00:09:50.690 --> 00:09:52.930 align:middle line:84% So stress intensity factor Ki is basically 00:09:52.930 --> 00:09:56.450 align:middle line:90% given as sigma infinity. 00:09:56.450 --> 00:09:58.450 align:middle line:84% This is basically the stress you applied 00:09:58.450 --> 00:10:00.730 align:middle line:90% to your macroscopic sample. 00:10:00.730 --> 00:10:06.530 align:middle line:84% You also have a factor of square root a here, which means, 00:10:06.530 --> 00:10:12.930 align:middle line:84% then it normalizes out, the dependence of the fracture 00:10:12.930 --> 00:10:15.930 align:middle line:90% strength, only crack length. 00:10:15.930 --> 00:10:19.530 align:middle line:84% So when the Ki, the stress intensity factor, 00:10:19.530 --> 00:10:22.050 align:middle line:84% exceeds this critical stress intensity 00:10:22.050 --> 00:10:28.330 align:middle line:84% factor, which is labeled as K1c here, so once it exceeds K1c, 00:10:28.330 --> 00:10:31.050 align:middle line:84% then it effectively means that sigma-- 00:10:31.050 --> 00:10:34.770 align:middle line:84% the failure criteria will be when 00:10:34.770 --> 00:10:38.330 align:middle line:84% the sigma infinity, your applied stress, 00:10:38.330 --> 00:10:41.750 align:middle line:84% becomes greater than the fracture strength. 00:10:41.750 --> 00:10:44.400 align:middle line:90% That's when the material fails. 00:10:44.400 --> 00:10:49.560 align:middle line:84% Equivalently, that translates to your K1 00:10:49.560 --> 00:10:51.580 align:middle line:90% becomes greater than your K1c. 00:10:51.580 --> 00:10:56.320 align:middle line:90% 00:10:56.320 --> 00:11:03.260 align:middle line:84% Now, for K1c, we can by definition plug in the terms 00:11:03.260 --> 00:11:03.760 align:middle line:90% here. 00:11:03.760 --> 00:11:05.640 align:middle line:84% K1c is basically the fracture strength 00:11:05.640 --> 00:11:07.640 align:middle line:90% times the square root of pi a. 00:11:07.640 --> 00:11:11.840 align:middle line:84% So you have your fracture strength here. 00:11:11.840 --> 00:11:20.680 align:middle line:84% So if you put in a square root pi a, 00:11:20.680 --> 00:11:22.760 align:middle line:84% this will be the expression for K1c. 00:11:22.760 --> 00:11:25.017 align:middle line:90% 00:11:25.017 --> 00:11:26.600 align:middle line:84% Now, by looking at this equation here, 00:11:26.600 --> 00:11:29.200 align:middle line:84% you understand why people like K1c rather than sigma 00:11:29.200 --> 00:11:31.780 align:middle line:84% f as the criteria to gauge material failure. 00:11:31.780 --> 00:11:35.560 align:middle line:84% Because, if you look at K1c, it depends on surface energy 00:11:35.560 --> 00:11:37.120 align:middle line:90% and Young's modulus. 00:11:37.120 --> 00:11:39.160 align:middle line:90% And both are material constants. 00:11:39.160 --> 00:11:42.340 align:middle line:84% So therefore, K1c itself is also a material constant. 00:11:42.340 --> 00:11:44.050 align:middle line:84% It does not depend on crack length. 00:11:44.050 --> 00:11:47.230 align:middle line:90% 00:11:47.230 --> 00:11:50.030 align:middle line:84% So then K1c can be used essentially 00:11:50.030 --> 00:11:52.630 align:middle line:84% as a way to gauge the material's ability 00:11:52.630 --> 00:11:56.370 align:middle line:84% to resist fracture and resist crack propagation. 00:11:56.370 --> 00:12:02.630 align:middle line:90% 00:12:02.630 --> 00:12:06.290 align:middle line:84% So K1c is formulated in terms of a stress and essentially 00:12:06.290 --> 00:12:08.310 align:middle line:84% the stress at the crack tip exceeding 00:12:08.310 --> 00:12:11.910 align:middle line:90% the theoretical stress. 00:12:11.910 --> 00:12:15.330 align:middle line:84% You can also define an equivalent quantity. 00:12:15.330 --> 00:12:17.470 align:middle line:84% Let's look at energy instead of stress. 00:12:17.470 --> 00:12:20.950 align:middle line:84% This is basically defined in this vector here G1 and G1c. 00:12:20.950 --> 00:12:24.250 align:middle line:84% So it's basically K1 squared divided by the Young's modulus. 00:12:24.250 --> 00:12:26.650 align:middle line:84% This gives you essentially a strain energy release rate. 00:12:26.650 --> 00:12:28.450 align:middle line:84% And the failure criteria is the same. 00:12:28.450 --> 00:12:30.710 align:middle line:84% When G1 becomes greater than G1c, 00:12:30.710 --> 00:12:32.630 align:middle line:90% then the material will fail. 00:12:32.630 --> 00:12:34.750 align:middle line:84% The crack will now propagate, and then 00:12:34.750 --> 00:12:37.830 align:middle line:90% eventually lead to failure. 00:12:37.830 --> 00:12:41.820 align:middle line:84% So key takeaway message here is that K1c as a material constant 00:12:41.820 --> 00:12:43.300 align:middle line:90% is independent of crack length. 00:12:43.300 --> 00:12:47.060 align:middle line:84% So the criteria to tell whether or not a material will actually 00:12:47.060 --> 00:12:50.020 align:middle line:84% fail becomes K1 will have to be greater than K1c 00:12:50.020 --> 00:12:53.460 align:middle line:84% instead of directly comparing the strength. 00:12:53.460 --> 00:12:54.000 align:middle line:90% All right. 00:12:54.000 --> 00:12:57.940 align:middle line:84% So the Griffith's crack theory essentially 00:12:57.940 --> 00:12:59.660 align:middle line:90% applies to brittle materials. 00:12:59.660 --> 00:13:01.860 align:middle line:84% One of the underlying assumptions 00:13:01.860 --> 00:13:05.500 align:middle line:84% is that there is no plastic deformation when 00:13:05.500 --> 00:13:06.660 align:middle line:90% the crack opens. 00:13:06.660 --> 00:13:09.180 align:middle line:84% That's what Griffith assumes in his theory. 00:13:09.180 --> 00:13:17.140 align:middle line:84% So the assumption is a better assumption 00:13:17.140 --> 00:13:18.980 align:middle line:90% in the case of glass materials. 00:13:18.980 --> 00:13:21.180 align:middle line:84% I did not say it's a perfect assumption because, 00:13:21.180 --> 00:13:24.260 align:middle line:84% turns out, even for oxide glasses, which 00:13:24.260 --> 00:13:27.000 align:middle line:84% is a very brittle material, when they actually deform, 00:13:27.000 --> 00:13:28.700 align:middle line:84% when they actually break, there's 00:13:28.700 --> 00:13:31.700 align:middle line:84% also some plastic deformation that actually takes place. 00:13:31.700 --> 00:13:34.100 align:middle line:84% Plastic deformation in oxide glass materials 00:13:34.100 --> 00:13:38.780 align:middle line:84% usually assumes the form of essentially condensation. 00:13:38.780 --> 00:13:40.520 align:middle line:84% The material essentially becomes-- 00:13:40.520 --> 00:13:41.740 align:middle line:90% I should say densification. 00:13:41.740 --> 00:13:44.040 align:middle line:84% The material, essentially, the density 00:13:44.040 --> 00:13:46.400 align:middle line:84% increases because of the compression. 00:13:46.400 --> 00:13:50.400 align:middle line:90% 00:13:50.400 --> 00:13:52.473 align:middle line:84% As a result of this kind of plastic deformation, 00:13:52.473 --> 00:13:54.640 align:middle line:84% it means that the Griffith's theory does not totally 00:13:54.640 --> 00:13:57.480 align:middle line:84% apply even in the case for oxide materials. 00:13:57.480 --> 00:14:00.560 align:middle line:84% Now, when it comes to other kinds of amorphous materials, 00:14:00.560 --> 00:14:06.760 align:middle line:84% like amorphous metal, amorphous metal, 00:14:06.760 --> 00:14:08.800 align:middle line:84% you have an even larger component 00:14:08.800 --> 00:14:10.800 align:middle line:90% in terms of plastic deformation. 00:14:10.800 --> 00:14:14.880 align:middle line:84% And this has to do with the nature of metallic bonds. 00:14:14.880 --> 00:14:17.820 align:middle line:84% In covalent bonds, if you have any kind of deformation, 00:14:17.820 --> 00:14:20.440 align:middle line:84% you essentially have one part of the material shifting 00:14:20.440 --> 00:14:22.060 align:middle line:90% with respect to the other part. 00:14:22.060 --> 00:14:26.470 align:middle line:84% This will involve breaking of the covalent bonds. 00:14:26.470 --> 00:14:28.445 align:middle line:84% And because a covalent bond is directional, 00:14:28.445 --> 00:14:29.820 align:middle line:84% once you break the covalent bond, 00:14:29.820 --> 00:14:31.237 align:middle line:84% it's very difficult to reestablish 00:14:31.237 --> 00:14:35.440 align:middle line:84% the chemical connection versus in the case of a metal. 00:14:35.440 --> 00:14:37.840 align:middle line:84% Metallic bond is non-directional. 00:14:37.840 --> 00:14:40.333 align:middle line:84% So even if you have some part of atom 00:14:40.333 --> 00:14:42.250 align:middle line:84% that's flipped with respect to the other part, 00:14:42.250 --> 00:14:44.710 align:middle line:84% you can still easily reestablish this kind of atomic level 00:14:44.710 --> 00:14:46.070 align:middle line:90% connection there. 00:14:46.070 --> 00:14:51.350 align:middle line:84% So what this suggests is that amorphous metal can accommodate 00:14:51.350 --> 00:14:54.230 align:middle line:84% significantly larger plastic deformation compared 00:14:54.230 --> 00:14:55.990 align:middle line:90% to oxide glasses. 00:14:55.990 --> 00:15:00.630 align:middle line:84% So this is manifested in the fracture behavior 00:15:00.630 --> 00:15:01.710 align:middle line:90% of amorphous metal here. 00:15:01.710 --> 00:15:04.043 align:middle line:84% That's why I have a few slides specifically highlighting 00:15:04.043 --> 00:15:06.030 align:middle line:84% the unique behavior of amorphous metal 00:15:06.030 --> 00:15:07.650 align:middle line:90% when it comes to a failure. 00:15:07.650 --> 00:15:14.230 align:middle line:84% So depending on how you do the post-fabrication thermal 00:15:14.230 --> 00:15:16.390 align:middle line:84% treatment, you can change essentially this kind 00:15:16.390 --> 00:15:19.550 align:middle line:84% of plasticity of amorphous metal here. 00:15:19.550 --> 00:15:23.350 align:middle line:84% This is usually called intrinsic plasticity or local plasticity. 00:15:23.350 --> 00:15:25.985 align:middle line:84% So one example here, what I'm showing here, 00:15:25.985 --> 00:15:27.610 align:middle line:84% this is essentially a fracture surface, 00:15:27.610 --> 00:15:32.910 align:middle line:84% SEM an image of a fracture surface for an as-cast amorphous 00:15:32.910 --> 00:15:34.602 align:middle line:90% metal, bulk amorphous metal. 00:15:34.602 --> 00:15:36.310 align:middle line:84% If you look at the fracture surface here, 00:15:36.310 --> 00:15:38.080 align:middle line:84% unlike glass, when they fracture, 00:15:38.080 --> 00:15:41.180 align:middle line:84% you have essentially-- unless it has a smooth surface. 00:15:41.180 --> 00:15:45.860 align:middle line:84% If you look at the cross-section here, what you end up getting 00:15:45.860 --> 00:15:47.440 align:middle line:90% is something like this. 00:15:47.440 --> 00:15:51.330 align:middle line:84% You get a bunch of surface corrugation. 00:15:51.330 --> 00:15:55.500 align:middle line:84% So these little ridges is what you observe on the SEM image 00:15:55.500 --> 00:15:56.460 align:middle line:90% here. 00:15:56.460 --> 00:16:00.820 align:middle line:84% So the presence of these ridges is actually a signature 00:16:00.820 --> 00:16:04.420 align:middle line:90% of local plastic deformation. 00:16:04.420 --> 00:16:08.785 align:middle line:84% And the reason you have this kind of a angle in the fracture 00:16:08.785 --> 00:16:10.660 align:middle line:84% surface here is because shear stress actually 00:16:10.660 --> 00:16:12.480 align:middle line:90% gets maximum at 45 degrees. 00:16:12.480 --> 00:16:15.060 align:middle line:84% That's why locally you see a lot of ridges 00:16:15.060 --> 00:16:17.660 align:middle line:84% with an angle that's close to 45 degrees. 00:16:17.660 --> 00:16:20.660 align:middle line:84% So if you see this kind of fracture surface, 00:16:20.660 --> 00:16:27.080 align:middle line:84% this is actually indicative of a local plastic deformation. 00:16:27.080 --> 00:16:31.460 align:middle line:90% 00:16:31.460 --> 00:16:35.530 align:middle line:84% Now, you can tune this level of plasticity by essentially-- yes? 00:16:35.530 --> 00:16:38.650 align:middle line:84% STUDENT: So the SEM on the left is the fracture surface? 00:16:38.650 --> 00:16:40.290 align:middle line:90% JUEJUN HU: The fracture surface. 00:16:40.290 --> 00:16:42.530 align:middle line:90% STUDENT: OK. 00:16:42.530 --> 00:16:44.490 align:middle line:84% JUEJUN HU: If you induce essentially breakage 00:16:44.490 --> 00:16:46.958 align:middle line:84% of an amorphous metal, you then examine the surface, 00:16:46.958 --> 00:16:47.750 align:middle line:90% what it looks like. 00:16:47.750 --> 00:16:48.417 align:middle line:90% STUDENT: Gotcha. 00:16:48.417 --> 00:16:50.209 align:middle line:84% And then compared to the one on the right-- 00:16:50.209 --> 00:16:51.959 align:middle line:84% JUEJUN HU: That's also a fracture surface. 00:16:51.959 --> 00:16:53.030 align:middle line:90% It's a different process. 00:16:53.030 --> 00:16:56.470 align:middle line:84% So what's on the left here is as-cast. 00:16:56.470 --> 00:16:58.730 align:middle line:84% So essentially, you have the metal, liquid metal. 00:16:58.730 --> 00:17:02.750 align:middle line:84% You then just put it into the mold, put it into cast, 00:17:02.750 --> 00:17:03.610 align:middle line:90% let it cool down. 00:17:03.610 --> 00:17:04.950 align:middle line:84% That's what you get on the left-hand side. 00:17:04.950 --> 00:17:05.950 align:middle line:90% That's the material. 00:17:05.950 --> 00:17:12.050 align:middle line:84% Now, on the right-hand side, if you anneal this metal for some 00:17:12.050 --> 00:17:12.895 align:middle line:90% time-- 00:17:12.895 --> 00:17:14.770 align:middle line:84% anneal above the glass transition temperature 00:17:14.770 --> 00:17:15.849 align:middle line:90% for some time. 00:17:15.849 --> 00:17:17.410 align:middle line:84% So what we have mentioned before is 00:17:17.410 --> 00:17:21.410 align:middle line:84% that this annealing can lead to thermal embrittlement. 00:17:21.410 --> 00:17:23.089 align:middle line:84% If you anneal it, essentially you 00:17:23.089 --> 00:17:24.670 align:middle line:90% lead to a structural relaxation. 00:17:24.670 --> 00:17:26.790 align:middle line:84% It relaxes towards the supercooled liquid state, 00:17:26.790 --> 00:17:29.370 align:middle line:84% which means that free volume actually decreases. 00:17:29.370 --> 00:17:31.430 align:middle line:84% For metal, once you decrease the free volume, 00:17:31.430 --> 00:17:34.320 align:middle line:84% it essentially means that you have less wiggle room 00:17:34.320 --> 00:17:35.820 align:middle line:90% for the atoms to move around. 00:17:35.820 --> 00:17:38.760 align:middle line:84% This decreases its capacity for plastic deformation. 00:17:38.760 --> 00:17:40.640 align:middle line:84% And therefore, it becomes more brittle. 00:17:40.640 --> 00:17:42.920 align:middle line:84% So that's why, after annealing, you 00:17:42.920 --> 00:17:44.520 align:middle line:84% see the fracture surface appear more 00:17:44.520 --> 00:17:48.260 align:middle line:84% like essentially the fracture surface for brittle material. 00:17:48.260 --> 00:17:50.880 align:middle line:84% It becomes essentially smooth and flat. 00:17:50.880 --> 00:17:55.980 align:middle line:84% So the key takeaway point here is that, in amorphous metal, 00:17:55.980 --> 00:17:59.040 align:middle line:84% we can essentially tune this level of plasticity. 00:17:59.040 --> 00:18:01.840 align:middle line:84% And that's why they can exhibit different kinds of fracture 00:18:01.840 --> 00:18:03.720 align:middle line:84% behavior compared to oxide glasses, which 00:18:03.720 --> 00:18:06.560 align:middle line:90% is a lot more brittle. 00:18:06.560 --> 00:18:08.240 align:middle line:84% STUDENT: Can you explain the picture 00:18:08.240 --> 00:18:12.120 align:middle line:84% on the left, how that's also displaying this pyramidal-- 00:18:12.120 --> 00:18:14.000 align:middle line:84% JUEJUN HU: This is like a cross-section. 00:18:14.000 --> 00:18:14.560 align:middle line:90% STUDENT: OK. 00:18:14.560 --> 00:18:15.660 align:middle line:84% JUEJUN HU: These are not pyramidal. 00:18:15.660 --> 00:18:16.800 align:middle line:90% These are like ridges. 00:18:16.800 --> 00:18:17.800 align:middle line:90% Think of it like ridges. 00:18:17.800 --> 00:18:18.420 align:middle line:90% STUDENT: Running-- 00:18:18.420 --> 00:18:19.753 align:middle line:90% JUEJUN HU: Yeah, running around. 00:18:19.753 --> 00:18:22.340 align:middle line:84% And these are essentially ridges we're seeing here. 00:18:22.340 --> 00:18:24.008 align:middle line:84% This is like the tip of the ridges. 00:18:24.008 --> 00:18:24.800 align:middle line:90% STUDENT: Oh, I see. 00:18:24.800 --> 00:18:25.140 align:middle line:90% OK. 00:18:25.140 --> 00:18:26.580 align:middle line:84% JUEJUN HU: Yeah, so these are lines. 00:18:26.580 --> 00:18:28.440 align:middle line:84% If you look at the cross-section here, each of these lines 00:18:28.440 --> 00:18:30.232 align:middle line:84% would essentially have something like this. 00:18:30.232 --> 00:18:32.350 align:middle line:84% STUDENT: So those are like lots of little pits? 00:18:32.350 --> 00:18:33.610 align:middle line:90% JUEJUN HU: Yes, almost. 00:18:33.610 --> 00:18:35.070 align:middle line:90% Yes, yeah. 00:18:35.070 --> 00:18:36.390 align:middle line:90% And that's what happens. 00:18:36.390 --> 00:18:39.050 align:middle line:84% If it's a glass, brittle glass, when the crack opens, 00:18:39.050 --> 00:18:40.450 align:middle line:90% it just simply opens there. 00:18:40.450 --> 00:18:42.390 align:middle line:84% And we're going to talk a little bit more 00:18:42.390 --> 00:18:43.770 align:middle line:90% later about stability of crack. 00:18:43.770 --> 00:18:45.650 align:middle line:84% But basically, the crack elongates. 00:18:45.650 --> 00:18:47.150 align:middle line:84% So when it elongates, it essentially 00:18:47.150 --> 00:18:49.350 align:middle line:84% creates this fresh, smooth surface. 00:18:49.350 --> 00:18:51.733 align:middle line:84% But for metallic glass, as it opens, 00:18:51.733 --> 00:18:53.650 align:middle line:84% there's a lot of pressure deformation happens. 00:18:53.650 --> 00:18:55.025 align:middle line:84% So it means that the two surfaces 00:18:55.025 --> 00:18:57.630 align:middle line:84% don't want to separate from each other simply. 00:18:57.630 --> 00:19:00.430 align:middle line:84% So as it deforms, essentially some part of the surface 00:19:00.430 --> 00:19:01.932 align:middle line:90% gets stretched. 00:19:01.932 --> 00:19:04.390 align:middle line:84% And then eventually, they break because of the shear stress 00:19:04.390 --> 00:19:06.105 align:middle line:90% at the 45-degree angle. 00:19:06.105 --> 00:19:08.230 align:middle line:84% So that's what happens, if you think of it like two 00:19:08.230 --> 00:19:09.450 align:middle line:90% parts trying to stick together. 00:19:09.450 --> 00:19:10.950 align:middle line:84% And as you separate, essentially you 00:19:10.950 --> 00:19:13.758 align:middle line:84% pull this material from its original surface, 00:19:13.758 --> 00:19:15.050 align:middle line:90% leading to plastic deformation. 00:19:15.050 --> 00:19:17.790 align:middle line:84% STUDENT: So the points were the last contact 00:19:17.790 --> 00:19:21.163 align:middle line:90% points before fracture? 00:19:21.163 --> 00:19:21.830 align:middle line:90% JUEJUN HU: Yeah. 00:19:21.830 --> 00:19:23.870 align:middle line:84% I mean, these are the surfaces where essentially eventually 00:19:23.870 --> 00:19:25.350 align:middle line:90% you have developed large slip. 00:19:25.350 --> 00:19:27.750 align:middle line:84% And then eventually, it fractures, yeah. 00:19:27.750 --> 00:19:30.705 align:middle line:90% 00:19:30.705 --> 00:19:32.580 align:middle line:84% So this is just a different fracture behavior 00:19:32.580 --> 00:19:35.600 align:middle line:84% between bulk metallic glass and oxide glass. 00:19:35.600 --> 00:19:36.680 align:middle line:90% So it's a bit special. 00:19:36.680 --> 00:19:38.403 align:middle line:84% That's why I want to highlight that. 00:19:38.403 --> 00:19:39.820 align:middle line:84% Now, empirically, people have also 00:19:39.820 --> 00:19:41.407 align:middle line:90% developed this criteria here. 00:19:41.407 --> 00:19:43.740 align:middle line:84% Essentially, you can take the ratio of the shear modulus 00:19:43.740 --> 00:19:45.048 align:middle line:90% and bulk modulus. 00:19:45.048 --> 00:19:47.340 align:middle line:84% What empirically people found is that, if this ratio is 00:19:47.340 --> 00:19:50.620 align:middle line:84% less than this threshold number, this bulk metallic glass tends 00:19:50.620 --> 00:19:52.620 align:middle line:90% to be essentially a plastic. 00:19:52.620 --> 00:19:55.020 align:middle line:84% Above the number, it becomes brittle. 00:19:55.020 --> 00:19:57.900 align:middle line:84% And here are some experimental data 00:19:57.900 --> 00:20:01.220 align:middle line:84% that actually plots the fracture energy as a function 00:20:01.220 --> 00:20:02.660 align:middle line:90% of this ratio here. 00:20:02.660 --> 00:20:07.300 align:middle line:84% What you clearly see is that, when the material is brittle, 00:20:07.300 --> 00:20:10.020 align:middle line:84% the energy required to actually create a fracture 00:20:10.020 --> 00:20:14.020 align:middle line:84% is much less, which makes sense because this plastic deformation 00:20:14.020 --> 00:20:17.500 align:middle line:84% absorbs lots of energy, which makes the material more 00:20:17.500 --> 00:20:20.180 align:middle line:90% resistant to fracturing. 00:20:20.180 --> 00:20:25.460 align:middle line:84% So that's why this kind of a microscopic plastic behavior 00:20:25.460 --> 00:20:31.770 align:middle line:84% is what leads to a very high fracture toughness 00:20:31.770 --> 00:20:34.330 align:middle line:90% of bulk metallic glasses. 00:20:34.330 --> 00:20:35.890 align:middle line:84% This is different for oxide glass. 00:20:35.890 --> 00:20:38.290 align:middle line:84% Oxide glass can have very high strength, 00:20:38.290 --> 00:20:40.090 align:middle line:84% as we have shown in the previous data. 00:20:40.090 --> 00:20:42.350 align:middle line:84% But the problem is that oxide glasses, 00:20:42.350 --> 00:20:45.730 align:middle line:84% because they are so brittle, it doesn't absorb a lot of energy. 00:20:45.730 --> 00:20:48.370 align:middle line:84% It has high strength, but low toughness. 00:20:48.370 --> 00:20:50.150 align:middle line:84% Bulk metallic glasses, on the other hand, 00:20:50.150 --> 00:20:56.650 align:middle line:84% they can have high strength and also a large toughness 00:20:56.650 --> 00:20:59.170 align:middle line:84% because you can actually create-- essentially 00:20:59.170 --> 00:21:01.770 align:middle line:84% accommodate a lot of local plastic deformation 00:21:01.770 --> 00:21:04.772 align:middle line:84% that absorbs a lot of energy and resists crack propagation. 00:21:04.772 --> 00:21:06.730 align:middle line:84% So that's a key difference in terms of behavior 00:21:06.730 --> 00:21:08.850 align:middle line:84% here for these two classes of materials, which 00:21:08.850 --> 00:21:10.410 align:middle line:90% is what I'm plotting here. 00:21:10.410 --> 00:21:12.110 align:middle line:84% Horizontal axis is yield strength. 00:21:12.110 --> 00:21:13.790 align:middle line:84% Vertical axis is fracture toughness. 00:21:13.790 --> 00:21:16.930 align:middle line:84% That's why you see bulk metallic glasses reside in this top right 00:21:16.930 --> 00:21:21.490 align:middle line:84% corner here, which is what we desire for engineering material. 00:21:21.490 --> 00:21:24.833 align:middle line:84% And specifically, for the material, 00:21:24.833 --> 00:21:26.750 align:middle line:84% this particular material I'm showing you here, 00:21:26.750 --> 00:21:31.190 align:middle line:84% this little star, this is one of the materials-- 00:21:31.190 --> 00:21:34.350 align:middle line:84% one of the bulk metallic glasses with very high fracture 00:21:34.350 --> 00:21:35.710 align:middle line:90% toughness. 00:21:35.710 --> 00:21:38.150 align:middle line:84% This is actually an SEM image showing 00:21:38.150 --> 00:21:40.130 align:middle line:90% what happens at the crack tip. 00:21:40.130 --> 00:21:42.830 align:middle line:84% So this is actually a little surface crack in this material. 00:21:42.830 --> 00:21:45.350 align:middle line:84% And you can see that, as the crack opens, 00:21:45.350 --> 00:21:47.830 align:middle line:84% you see a lot of these shear lines. 00:21:47.830 --> 00:21:51.510 align:middle line:84% Essentially, these lines shows essentially they are essentially 00:21:51.510 --> 00:21:55.210 align:middle line:84% a shear deformation taking place near those locations. 00:21:55.210 --> 00:21:58.830 align:middle line:84% And you can clearly see this very large amount of deformation 00:21:58.830 --> 00:22:01.150 align:middle line:90% occurring at the crack tip. 00:22:01.150 --> 00:22:03.472 align:middle line:84% That's why this material can be very, very tough 00:22:03.472 --> 00:22:05.430 align:middle line:84% because all this shear deformation can actually 00:22:05.430 --> 00:22:08.790 align:middle line:84% absorb lots of energy, all the plastic deformation. 00:22:08.790 --> 00:22:11.470 align:middle line:90% 00:22:11.470 --> 00:22:11.970 align:middle line:90% All right. 00:22:11.970 --> 00:22:15.850 align:middle line:84% So that's a short detour talking about bulk metallic glasses. 00:22:15.850 --> 00:22:19.070 align:middle line:84% Now, let's come back to oxide glasses. 00:22:19.070 --> 00:22:21.790 align:middle line:84% One of the questions that I think was actually 00:22:21.790 --> 00:22:24.470 align:middle line:84% asked during the demo session in the glass lab 00:22:24.470 --> 00:22:28.780 align:middle line:84% is how fast does a crack propagate in the glass material. 00:22:28.780 --> 00:22:32.480 align:middle line:84% So I actually have a little quick video here. 00:22:32.480 --> 00:22:34.272 align:middle line:90% I'm going to click Play here. 00:22:34.272 --> 00:22:35.480 align:middle line:90% Let's see, hopefully, no ads. 00:22:35.480 --> 00:22:36.620 align:middle line:90% It's a very short video. 00:22:36.620 --> 00:22:37.120 align:middle line:90% All right. 00:22:37.120 --> 00:22:38.080 align:middle line:90% It's very, very fast. 00:22:38.080 --> 00:22:39.665 align:middle line:84% So now, let me try to do it again. 00:22:39.665 --> 00:22:41.540 align:middle line:84% Now, a couple of things to look at here-- one 00:22:41.540 --> 00:22:43.360 align:middle line:84% is where does the crack initiate. 00:22:43.360 --> 00:22:47.318 align:middle line:90% 00:22:47.318 --> 00:22:48.360 align:middle line:90% This is a bit more clear. 00:22:48.360 --> 00:22:53.380 align:middle line:84% You can see where the crack initiates, from right there. 00:22:53.380 --> 00:22:57.398 align:middle line:84% This is a clear example of essentially a surface defect, 00:22:57.398 --> 00:22:59.940 align:middle line:84% as where the crack essentially nucleates, and then propagates 00:22:59.940 --> 00:23:01.420 align:middle line:90% through the glass material. 00:23:01.420 --> 00:23:05.780 align:middle line:84% By the way, this is taken at more than 200,000 frames per 00:23:05.780 --> 00:23:06.568 align:middle line:90% second. 00:23:06.568 --> 00:23:08.860 align:middle line:84% And we have to slow it down by another factor of 4 just 00:23:08.860 --> 00:23:10.280 align:middle line:90% to see where it originates. 00:23:10.280 --> 00:23:13.380 align:middle line:84% So from that video, you can actually 00:23:13.380 --> 00:23:16.280 align:middle line:84% infer the speed of crack propagation in glass. 00:23:16.280 --> 00:23:19.500 align:middle line:84% Any of you want to guess what the speed is? 00:23:19.500 --> 00:23:22.820 align:middle line:84% STUDENT: The speed of sound inside glass. 00:23:22.820 --> 00:23:24.540 align:middle line:90% JUEJUN HU: Very good guess-- 00:23:24.540 --> 00:23:27.890 align:middle line:90% close, not exactly. 00:23:27.890 --> 00:23:28.430 align:middle line:90% Let me see. 00:23:28.430 --> 00:23:32.610 align:middle line:90% Why is it not moving forward? 00:23:32.610 --> 00:23:33.990 align:middle line:90% This is the correct velocity. 00:23:33.990 --> 00:23:36.770 align:middle line:84% You can actually calculate from this plot there. 00:23:36.770 --> 00:23:42.250 align:middle line:84% This is about 1/3 to 1/2 of the velocity of sound in glass. 00:23:42.250 --> 00:23:43.870 align:middle line:90% You may wonder why is that. 00:23:43.870 --> 00:23:47.570 align:middle line:84% It turns out, if glass is a perfectly brittle material, 00:23:47.570 --> 00:23:49.810 align:middle line:84% then your assumption would be correct. 00:23:49.810 --> 00:23:53.850 align:middle line:84% As soon as an elastic wave propagates at the crack tip, 00:23:53.850 --> 00:23:56.450 align:middle line:84% then the material will immediately 00:23:56.450 --> 00:23:58.670 align:middle line:84% exceed its fracture strength at the crack tip, 00:23:58.670 --> 00:23:59.650 align:middle line:90% then it will open up. 00:23:59.650 --> 00:24:01.530 align:middle line:84% If it's perfectly brittle, that's 00:24:01.530 --> 00:24:03.810 align:middle line:90% exactly what's going to happen. 00:24:03.810 --> 00:24:05.610 align:middle line:84% However, you may recall that I mentioned 00:24:05.610 --> 00:24:09.570 align:middle line:84% glass is not perfectly brittle, even for oxide glass, which 00:24:09.570 --> 00:24:11.290 align:middle line:90% is very brittle. 00:24:11.290 --> 00:24:13.970 align:middle line:84% It can still create plastic deformation 00:24:13.970 --> 00:24:19.490 align:middle line:84% in the form of a compression or densification. 00:24:19.490 --> 00:24:21.530 align:middle line:84% So this plastic deformation is then 00:24:21.530 --> 00:24:24.380 align:middle line:84% going to slow down the crack propagation. 00:24:24.380 --> 00:24:27.160 align:middle line:84% And that's why the crack propagation velocity is 00:24:27.160 --> 00:24:30.480 align:middle line:84% typically about 1/3 or maybe up to 1/2 of the sound velocity 00:24:30.480 --> 00:24:34.000 align:middle line:84% in glass materials because essentially it has 00:24:34.000 --> 00:24:36.668 align:middle line:84% to essentially overcome the plastic deformation, 00:24:36.668 --> 00:24:38.460 align:middle line:84% energy absorbed by the plastic deformation. 00:24:38.460 --> 00:24:41.960 align:middle line:84% So it takes more energy to actually open up the crack. 00:24:41.960 --> 00:24:44.400 align:middle line:84% So two things to take away here-- one 00:24:44.400 --> 00:24:47.350 align:middle line:84% is that surface is usually the Achilles heel. 00:24:47.350 --> 00:24:49.600 align:middle line:84% That's where glass tends to break because some surface 00:24:49.600 --> 00:24:50.720 align:middle line:90% defects. 00:24:50.720 --> 00:24:53.760 align:middle line:84% And that's why, later on in the next section, when 00:24:53.760 --> 00:24:55.807 align:middle line:84% we talk about how to strengthen glass materials, 00:24:55.807 --> 00:24:57.640 align:middle line:84% pretty much all the strengthening techniques 00:24:57.640 --> 00:25:01.400 align:middle line:84% are centered around how to minimize the surface defect 00:25:01.400 --> 00:25:04.240 align:middle line:84% density or find ways to prevent the surface 00:25:04.240 --> 00:25:05.920 align:middle line:90% defects from propagating. 00:25:05.920 --> 00:25:12.360 align:middle line:84% Second takeaway message is that glass is not totally brittle. 00:25:12.360 --> 00:25:14.800 align:middle line:84% It can still accommodate plastic deformation 00:25:14.800 --> 00:25:16.500 align:middle line:90% in the form of densification. 00:25:16.500 --> 00:25:19.240 align:middle line:90% 00:25:19.240 --> 00:25:19.780 align:middle line:90% All right. 00:25:19.780 --> 00:25:22.020 align:middle line:84% So I mean, here is a little YouTube video. 00:25:22.020 --> 00:25:23.810 align:middle line:84% I'm not going to play it because of time. 00:25:23.810 --> 00:25:27.090 align:middle line:84% But basically, now, people get better videos, better cameras. 00:25:27.090 --> 00:25:28.510 align:middle line:84% So they were able to actually redo 00:25:28.510 --> 00:25:30.990 align:middle line:84% the process over large panes of glasses. 00:25:30.990 --> 00:25:31.650 align:middle line:90% It's fun. 00:25:31.650 --> 00:25:33.067 align:middle line:84% You can take a look at this video. 00:25:33.067 --> 00:25:34.710 align:middle line:84% There's also a link on here that links 00:25:34.710 --> 00:25:36.495 align:middle line:84% to an article on ceramic tech today. 00:25:36.495 --> 00:25:38.870 align:middle line:84% It's essentially talking about this particular experiment 00:25:38.870 --> 00:25:42.350 align:middle line:84% that people have done using high speed cameras. 00:25:42.350 --> 00:25:42.990 align:middle line:90% All right. 00:25:42.990 --> 00:25:45.492 align:middle line:84% So what we are going to do instead, 00:25:45.492 --> 00:25:46.950 align:middle line:84% we're going to talk about something 00:25:46.950 --> 00:25:48.630 align:middle line:90% that I think is more fun. 00:25:48.630 --> 00:25:50.470 align:middle line:90% It's called fractography. 00:25:50.470 --> 00:25:52.470 align:middle line:90% What is fractography? 00:25:52.470 --> 00:25:56.830 align:middle line:84% Essentially, it's a branch of forensic science. 00:25:56.830 --> 00:26:00.110 align:middle line:84% It's about getting-- in our context here, 00:26:00.110 --> 00:26:02.430 align:middle line:84% it's about getting a piece of broken glass. 00:26:02.430 --> 00:26:05.670 align:middle line:84% And you have to infer why it breaks, 00:26:05.670 --> 00:26:08.310 align:middle line:84% how it breaks, essentially answering 00:26:08.310 --> 00:26:12.550 align:middle line:84% the question about what actually happened before it breaks. 00:26:12.550 --> 00:26:17.117 align:middle line:84% So this is used a lot in things like crime scene investigation. 00:26:17.117 --> 00:26:18.950 align:middle line:84% You'll see some of the references I actually 00:26:18.950 --> 00:26:19.730 align:middle line:90% quoted from books. 00:26:19.730 --> 00:26:22.272 align:middle line:84% I actually specifically talk about crime scene investigation. 00:26:22.272 --> 00:26:24.500 align:middle line:90% That's what people use this for. 00:26:24.500 --> 00:26:28.500 align:middle line:84% If a glass pane is broken by a projectile, then 00:26:28.500 --> 00:26:29.800 align:middle line:90% what's that projectile? 00:26:29.800 --> 00:26:30.560 align:middle line:90% Where does it hit? 00:26:30.560 --> 00:26:31.240 align:middle line:90% What does it look like? 00:26:31.240 --> 00:26:32.000 align:middle line:90% Where does it nucleate? 00:26:32.000 --> 00:26:33.042 align:middle line:90% All those kind of things. 00:26:33.042 --> 00:26:36.420 align:middle line:84% Now, I also want to mention that this fractography is important 00:26:36.420 --> 00:26:38.360 align:middle line:84% not just to a crime scene investigation, 00:26:38.360 --> 00:26:42.153 align:middle line:84% this is also critical to people who live in the Stone Age, 00:26:42.153 --> 00:26:43.820 align:middle line:84% when they are actually trying to process 00:26:43.820 --> 00:26:45.900 align:middle line:90% all kinds of stone tools. 00:26:45.900 --> 00:26:48.580 align:middle line:84% They essentially leverage this very unique breaking behavior 00:26:48.580 --> 00:26:50.900 align:middle line:84% of glass materials to actually create 00:26:50.900 --> 00:26:54.187 align:middle line:84% the tool of the specific geometry they need. 00:26:54.187 --> 00:26:56.020 align:middle line:84% You probably have the experience that when-- 00:26:56.020 --> 00:26:59.642 align:middle line:84% any of you have broken glasses, glassware at home? 00:26:59.642 --> 00:27:00.600 align:middle line:90% All of you have, right? 00:27:00.600 --> 00:27:02.160 align:middle line:90% Yeah, exactly. 00:27:02.160 --> 00:27:04.300 align:middle line:84% So have you actually looked at the cross-section 00:27:04.300 --> 00:27:05.440 align:middle line:90% of broken piece of glass? 00:27:05.440 --> 00:27:10.100 align:middle line:84% You notice that seashell pattern, that kind of texture? 00:27:10.100 --> 00:27:13.260 align:middle line:84% That's quite unique to brittle materials like glass. 00:27:13.260 --> 00:27:16.420 align:middle line:84% That's called a conchoidal fracture. 00:27:16.420 --> 00:27:18.920 align:middle line:84% It's actually a useful behavior if you look at, 00:27:18.920 --> 00:27:20.850 align:middle line:84% for example-- in this case, this is actually 00:27:20.850 --> 00:27:22.650 align:middle line:84% arrowheads made of obsidian, which 00:27:22.650 --> 00:27:24.090 align:middle line:90% is basically a natural glass. 00:27:24.090 --> 00:27:26.370 align:middle line:84% You clearly see these kind of patterns there. 00:27:26.370 --> 00:27:29.170 align:middle line:84% This is actually the way the ancient people have actually 00:27:29.170 --> 00:27:31.010 align:middle line:84% mastered the technique to leverage 00:27:31.010 --> 00:27:33.910 align:middle line:84% this conchoidal fracture to create the desired breakage 00:27:33.910 --> 00:27:36.790 align:middle line:84% and to shape things into the target geometry. 00:27:36.790 --> 00:27:40.405 align:middle line:90% 00:27:40.405 --> 00:27:41.910 align:middle line:84% Now, what we're going to do next, 00:27:41.910 --> 00:27:43.410 align:middle line:84% we're going to explain what actually 00:27:43.410 --> 00:27:45.890 align:middle line:84% happens, how do you actually look at the fractured glass 00:27:45.890 --> 00:27:46.530 align:middle line:90% surface. 00:27:46.530 --> 00:27:50.788 align:middle line:90% 00:27:50.788 --> 00:27:52.330 align:middle line:84% Instead of the black and white image, 00:27:52.330 --> 00:27:53.630 align:middle line:84% I like to show you this one here. 00:27:53.630 --> 00:27:55.010 align:middle line:84% This is probably a bit more clear. 00:27:55.010 --> 00:27:56.427 align:middle line:84% So what I'm showing you here, this 00:27:56.427 --> 00:27:59.590 align:middle line:84% is a microscopic image of a piece of a broken glass. 00:27:59.590 --> 00:28:03.170 align:middle line:84% This is actually a glass rod that was shattered. 00:28:03.170 --> 00:28:05.490 align:middle line:84% Now, when you're looking at the fracture surface 00:28:05.490 --> 00:28:09.570 align:middle line:84% here, what you want to do, you want to look for a region-- 00:28:09.570 --> 00:28:10.910 align:middle line:90% it's a flat region here. 00:28:10.910 --> 00:28:14.010 align:middle line:90% That's called a mirror. 00:28:14.010 --> 00:28:16.927 align:middle line:84% A mirror is next to the origin of the defect. 00:28:16.927 --> 00:28:18.760 align:middle line:84% So in this particular case, you can actually 00:28:18.760 --> 00:28:22.680 align:middle line:84% see right here this is where the surface crack eventually 00:28:22.680 --> 00:28:24.072 align:middle line:90% leads to catastrophic failure. 00:28:24.072 --> 00:28:25.780 align:middle line:84% So if you look at the glass surface here, 00:28:25.780 --> 00:28:27.155 align:middle line:84% you see essentially large regions 00:28:27.155 --> 00:28:29.200 align:middle line:84% with essentially a lot of surface undulation. 00:28:29.200 --> 00:28:30.920 align:middle line:84% If you trace it back, you usually 00:28:30.920 --> 00:28:34.320 align:middle line:84% see a small region where it's actually smooth and flat. 00:28:34.320 --> 00:28:35.700 align:middle line:90% It reflects light like a mirror. 00:28:35.700 --> 00:28:38.242 align:middle line:84% That's why it's called a mirror, this particular region here. 00:28:38.242 --> 00:28:40.540 align:middle line:84% Now, in the center of the mirror region, 00:28:40.540 --> 00:28:45.040 align:middle line:84% you usually find where the crack initiates. 00:28:45.040 --> 00:28:47.920 align:middle line:84% Now, the reason you have a mirror region-- mirror 00:28:47.920 --> 00:28:51.240 align:middle line:84% is where the crack starts to propagate. 00:28:51.240 --> 00:28:53.180 align:middle line:84% So when the crack starts to propagate, 00:28:53.180 --> 00:28:56.760 align:middle line:84% its velocity is relatively small. 00:28:56.760 --> 00:28:59.702 align:middle line:84% And as a result, the crack propagation is quite stable. 00:28:59.702 --> 00:29:01.160 align:middle line:84% Essentially, say this is the crack. 00:29:01.160 --> 00:29:04.040 align:middle line:84% It essentially opens up, like that. 00:29:04.040 --> 00:29:07.760 align:middle line:84% So this then leaves behind a well-defined flat surface 00:29:07.760 --> 00:29:08.780 align:middle line:90% after it fractures. 00:29:08.780 --> 00:29:10.780 align:middle line:84% This is what a mirror surface looks like. 00:29:10.780 --> 00:29:13.712 align:middle line:90% 00:29:13.712 --> 00:29:17.070 align:middle line:84% Now, as the crack gets longer, we 00:29:17.070 --> 00:29:21.430 align:middle line:84% know that the stress at the crack tip 00:29:21.430 --> 00:29:22.870 align:middle line:90% actually gets amplified. 00:29:22.870 --> 00:29:26.830 align:middle line:84% The stress concentration factor scales with the correct length. 00:29:26.830 --> 00:29:28.870 align:middle line:84% So as the correct length gets longer, 00:29:28.870 --> 00:29:32.470 align:middle line:84% the stress at the crack tip actually increases. 00:29:32.470 --> 00:29:36.390 align:middle line:84% This increasing stress means that the energy release 00:29:36.390 --> 00:29:38.710 align:middle line:90% rate increases. 00:29:38.710 --> 00:29:42.910 align:middle line:84% And as a result, the crack propagation becomes less stable. 00:29:42.910 --> 00:29:46.090 align:middle line:84% It will start to essentially create micro-branches. 00:29:46.090 --> 00:29:49.130 align:middle line:84% The crack starts to branch out as it propagates. 00:29:49.130 --> 00:29:50.850 align:middle line:84% Now, once it starts to branch out, 00:29:50.850 --> 00:29:53.510 align:middle line:84% the surface is no longer smooth and flat. 00:29:53.510 --> 00:29:56.510 align:middle line:84% You start to get lots of surface roughness. 00:29:56.510 --> 00:29:59.310 align:middle line:84% So that's when you transition from this mirror region 00:29:59.310 --> 00:30:01.470 align:middle line:90% into this called mist region. 00:30:01.470 --> 00:30:03.870 align:middle line:84% So around it, you see this region here 00:30:03.870 --> 00:30:06.150 align:middle line:84% where it becomes start to become foggy. 00:30:06.150 --> 00:30:07.690 align:middle line:90% This is called mist region. 00:30:07.690 --> 00:30:10.870 align:middle line:84% This is essentially at the onset of unstable propagation 00:30:10.870 --> 00:30:11.690 align:middle line:90% of the crack. 00:30:11.690 --> 00:30:14.470 align:middle line:90% 00:30:14.470 --> 00:30:17.790 align:middle line:84% So if that continues, then you enter the region, 00:30:17.790 --> 00:30:20.267 align:middle line:90% so-called the hackle. 00:30:20.267 --> 00:30:21.350 align:middle line:90% I also have this one here. 00:30:21.350 --> 00:30:22.017 align:middle line:90% This is similar. 00:30:22.017 --> 00:30:23.430 align:middle line:90% This is a black and white image. 00:30:23.430 --> 00:30:25.370 align:middle line:84% But you see these are actually hackles. 00:30:25.370 --> 00:30:28.570 align:middle line:84% Hackles are essentially these ridges 00:30:28.570 --> 00:30:33.850 align:middle line:84% that go along the radial direction that traces back. 00:30:33.850 --> 00:30:36.170 align:middle line:84% They point towards the origin of the failure. 00:30:36.170 --> 00:30:40.170 align:middle line:84% So this hackle, the reason you have so much surface roughness, 00:30:40.170 --> 00:30:43.130 align:middle line:84% is because you now have a very high energy release rate. 00:30:43.130 --> 00:30:45.750 align:middle line:84% Then to accommodate this very high energy release rate, 00:30:45.750 --> 00:30:48.670 align:middle line:84% the glass will try to create more fracture surfaces. 00:30:48.670 --> 00:30:52.250 align:middle line:90% 00:30:52.250 --> 00:30:55.130 align:middle line:84% And this is done through essentially creating a lot 00:30:55.130 --> 00:30:58.890 align:middle line:90% of this surface corrugation. 00:30:58.890 --> 00:31:02.710 align:middle line:84% So that's why you see this large surface roughness. 00:31:02.710 --> 00:31:04.530 align:middle line:84% These are essentially the hackle regions. 00:31:04.530 --> 00:31:07.850 align:middle line:90% 00:31:07.850 --> 00:31:10.870 align:middle line:84% Now, this hackle region continues to propagate. 00:31:10.870 --> 00:31:13.580 align:middle line:84% And then if you move even further, 00:31:13.580 --> 00:31:15.568 align:middle line:84% you start to see these lines here. 00:31:15.568 --> 00:31:16.860 align:middle line:90% These are called Wallner lines. 00:31:16.860 --> 00:31:18.280 align:middle line:90% These are ridges. 00:31:18.280 --> 00:31:20.080 align:middle line:84% The Wallner lines is what actually 00:31:20.080 --> 00:31:22.720 align:middle line:84% forms the seashell pattern you see on a fractured glass 00:31:22.720 --> 00:31:23.560 align:middle line:90% surface. 00:31:23.560 --> 00:31:27.040 align:middle line:84% Those lines essentially are actually tiny little ridges. 00:31:27.040 --> 00:31:29.040 align:middle line:90% Those are called Wallner lines. 00:31:29.040 --> 00:31:31.520 align:middle line:84% Now, Wallner lines is formed because 00:31:31.520 --> 00:31:34.640 align:middle line:84% of the velocity difference between the correct propagation 00:31:34.640 --> 00:31:37.360 align:middle line:84% and the sound velocity in the glass. 00:31:37.360 --> 00:31:39.640 align:middle line:84% So the sound wave velocity, this is also 00:31:39.640 --> 00:31:41.900 align:middle line:84% velocity where the elastic deformation propagates. 00:31:41.900 --> 00:31:45.680 align:middle line:84% Elastic wave propagates essentially with sound velocity. 00:31:45.680 --> 00:31:48.320 align:middle line:84% Now, that's actually faster than the crack propagation 00:31:48.320 --> 00:31:50.720 align:middle line:84% velocity because of the elastic deformation. 00:31:50.720 --> 00:31:52.920 align:middle line:84% So what that means is that this elastic wave is 00:31:52.920 --> 00:31:57.600 align:middle line:84% going to propagate through the material before the crack tip. 00:31:57.600 --> 00:32:00.120 align:middle line:84% And then this elastic wave can get reflected 00:32:00.120 --> 00:32:03.025 align:middle line:84% or get scattered because any kind of non-uniformity-- 00:32:03.025 --> 00:32:05.400 align:middle line:84% for example, you have some kind of surface non-uniformity 00:32:05.400 --> 00:32:06.880 align:middle line:84% or whatever-- they can essentially 00:32:06.880 --> 00:32:11.790 align:middle line:84% serve as a secondary source that then scatters this elastic wave. 00:32:11.790 --> 00:32:16.270 align:middle line:84% This irregular scattering of elastic waves 00:32:16.270 --> 00:32:18.270 align:middle line:84% would then actually cause essentially reflection 00:32:18.270 --> 00:32:19.250 align:middle line:90% of secondary waves. 00:32:19.250 --> 00:32:20.750 align:middle line:84% These secondary waves, they interact 00:32:20.750 --> 00:32:22.710 align:middle line:84% with the propagating crack tip leading 00:32:22.710 --> 00:32:24.090 align:middle line:90% to instability of crack tip. 00:32:24.090 --> 00:32:25.548 align:middle line:84% So essentially, it create this kind 00:32:25.548 --> 00:32:27.950 align:middle line:90% of waviness, periodic waviness. 00:32:27.950 --> 00:32:30.070 align:middle line:84% So this periodic waviness is what then 00:32:30.070 --> 00:32:32.990 align:middle line:90% generates these Wallner lines. 00:32:32.990 --> 00:32:34.590 align:middle line:84% In fact, what people have found is 00:32:34.590 --> 00:32:37.550 align:middle line:84% that, from the period or the spacing between the Wallner 00:32:37.550 --> 00:32:40.258 align:middle line:84% lines, you can determine the crack opening velocity. 00:32:40.258 --> 00:32:42.050 align:middle line:84% There are tons of papers looking into this. 00:32:42.050 --> 00:32:45.410 align:middle line:84% In general, if you have a faster crack opening velocity, 00:32:45.410 --> 00:32:48.650 align:middle line:84% the spacing between the Wallner lines gets smaller. 00:32:48.650 --> 00:32:49.810 align:middle line:90% That's a rule of thumb. 00:32:49.810 --> 00:32:58.350 align:middle line:90% 00:32:58.350 --> 00:33:03.670 align:middle line:84% The shape and the orientation of the Wallner lines 00:33:03.670 --> 00:33:08.410 align:middle line:84% also has a lot to do with where the defect is initiated. 00:33:08.410 --> 00:33:13.337 align:middle line:90% 00:33:13.337 --> 00:33:16.140 align:middle line:84% So if you look at-- this is what I quoted from this reference 00:33:16.140 --> 00:33:18.980 align:middle line:90% here, Criminal Investigation. 00:33:18.980 --> 00:33:23.580 align:middle line:84% Now, what it says is that if you essentially have a flat pane 00:33:23.580 --> 00:33:25.540 align:middle line:84% glass that's essentially fractured 00:33:25.540 --> 00:33:27.700 align:middle line:84% due to some kind of impact, you may 00:33:27.700 --> 00:33:32.100 align:middle line:84% want to decide which side the impact is coming from. 00:33:32.100 --> 00:33:35.140 align:middle line:84% So the way to do that is through this 4R rule. 00:33:35.140 --> 00:33:39.100 align:middle line:84% The 4R rule basically says ridge lines on radial fractures are 00:33:39.100 --> 00:33:41.140 align:middle line:90% at right angles to the rear. 00:33:41.140 --> 00:33:44.060 align:middle line:84% So the ridge lines, this is essentially 00:33:44.060 --> 00:33:48.860 align:middle line:84% the known scientific name for Wallner lines. 00:33:48.860 --> 00:33:51.040 align:middle line:84% Essentially, these are the Wallner lines. 00:33:51.040 --> 00:33:53.300 align:middle line:84% If you look at the Wallner line orientation 00:33:53.300 --> 00:33:55.740 align:middle line:84% on these flat pane glasses, you notice that they all 00:33:55.740 --> 00:33:57.620 align:middle line:90% come in this orientation here. 00:33:57.620 --> 00:34:00.340 align:middle line:84% And on this side, the Wallner lines 00:34:00.340 --> 00:34:03.540 align:middle line:84% essentially come in a surface normal direction. 00:34:03.540 --> 00:34:09.690 align:middle line:84% So this is the direction where the fracture propagates. 00:34:09.690 --> 00:34:12.850 align:middle line:84% You will see the origin of the defects on top here. 00:34:12.850 --> 00:34:17.850 align:middle line:84% And then this side, where the Wallner lines 00:34:17.850 --> 00:34:21.112 align:middle line:84% come in right angles with the surface, is the rear surface. 00:34:21.112 --> 00:34:22.570 align:middle line:84% So essentially, the point of impact 00:34:22.570 --> 00:34:23.929 align:middle line:90% is on this side of the surface. 00:34:23.929 --> 00:34:26.350 align:middle line:84% This is the front side, where the impact happens. 00:34:26.350 --> 00:34:28.927 align:middle line:90% This is actually the back side. 00:34:28.927 --> 00:34:30.969 align:middle line:84% So by just looking at essentially a cross-section 00:34:30.969 --> 00:34:33.594 align:middle line:84% of glass, you can tell where the impact-- which side the impact 00:34:33.594 --> 00:34:35.346 align:middle line:90% is actually coming from. 00:34:35.346 --> 00:34:37.330 align:middle line:90% STUDENT: [INAUDIBLE] 00:34:37.330 --> 00:34:39.250 align:middle line:90% JUEJUN HU: What is that? 00:34:39.250 --> 00:34:41.449 align:middle line:84% STUDENT: Time to pull up a crime scene. 00:34:41.449 --> 00:34:43.232 align:middle line:84% JUEJUN HU: Yeah, you can look at that. 00:34:43.232 --> 00:34:44.690 align:middle line:84% Actually, if you look online, there 00:34:44.690 --> 00:34:47.023 align:middle line:84% are actually people that actually make a living on this. 00:34:47.023 --> 00:34:49.165 align:middle line:84% There are people doing consulting just 00:34:49.165 --> 00:34:50.790 align:middle line:84% by looking at fractured glass surfaces. 00:34:50.790 --> 00:34:54.427 align:middle line:84% STUDENT: So these curved lines are the same Wallner lines? 00:34:54.427 --> 00:34:56.010 align:middle line:84% JUEJUN HU: They are the Wallner lines. 00:34:56.010 --> 00:34:57.468 align:middle line:84% They actually come from, as I said, 00:34:57.468 --> 00:34:59.910 align:middle line:84% the interaction of the elastic waves with the crack tip. 00:34:59.910 --> 00:35:00.410 align:middle line:90% STUDENT: OK. 00:35:00.410 --> 00:35:07.760 align:middle line:84% And then if you were to take a cross-section going this way-- 00:35:07.760 --> 00:35:09.768 align:middle line:84% JUEJUN HU: This way is which way? 00:35:09.768 --> 00:35:12.600 align:middle line:84% STUDENT: [INAUDIBLE] Yeah, parallel 00:35:12.600 --> 00:35:15.920 align:middle line:84% to the plane of the glass, perpendicular to this fracture 00:35:15.920 --> 00:35:16.900 align:middle line:90% that we're being shown. 00:35:16.900 --> 00:35:19.255 align:middle line:84% That's when you would get the circular-- 00:35:19.255 --> 00:35:20.380 align:middle line:90% JUEJUN HU: It's right here. 00:35:20.380 --> 00:35:22.100 align:middle line:90% So this is the glass pane. 00:35:22.100 --> 00:35:24.120 align:middle line:84% And then this is where the cross-section is. 00:35:24.120 --> 00:35:26.662 align:middle line:84% So you are seeing essentially these lines going like this. 00:35:26.662 --> 00:35:28.620 align:middle line:84% This is actually similar to this cross-section. 00:35:28.620 --> 00:35:31.720 align:middle line:84% STUDENT: But the point of impact face 00:35:31.720 --> 00:35:35.463 align:middle line:84% is how you would see this region and the mirror-- 00:35:35.463 --> 00:35:36.380 align:middle line:90% JUEJUN HU: Right here? 00:35:36.380 --> 00:35:37.643 align:middle line:90% Yeah, yeah. 00:35:37.643 --> 00:35:39.560 align:middle line:84% Near the point of impact is where you actually 00:35:39.560 --> 00:35:43.000 align:middle line:84% see the mirror, and then essentially the mist and hackle. 00:35:43.000 --> 00:35:46.140 align:middle line:84% And outside that, in larger macroscopic regions, 00:35:46.140 --> 00:35:49.740 align:middle line:84% that's where you actually start to see these Wallner lines. 00:35:49.740 --> 00:35:50.240 align:middle line:90% Yeah. 00:35:50.240 --> 00:35:52.620 align:middle line:84% I mean, if you look at the length scale here, 00:35:52.620 --> 00:35:54.400 align:middle line:90% so this is 200 microns. 00:35:54.400 --> 00:35:57.600 align:middle line:84% So the mirror region, the size of the mirror region 00:35:57.600 --> 00:36:00.480 align:middle line:84% actually depends on how much stress you apply. 00:36:00.480 --> 00:36:03.240 align:middle line:84% The higher stress you apply, the smaller mirror region 00:36:03.240 --> 00:36:04.420 align:middle line:90% is, which makes sense. 00:36:04.420 --> 00:36:07.370 align:middle line:84% The higher stress means that you have a high energy release rate. 00:36:07.370 --> 00:36:09.230 align:middle line:84% The crack easily becomes more stable-- 00:36:09.230 --> 00:36:10.790 align:middle line:90% sorry, it becomes more unstable. 00:36:10.790 --> 00:36:12.870 align:middle line:84% So that's why mirror region becomes smaller. 00:36:12.870 --> 00:36:16.990 align:middle line:84% But typically, the mirror region is of the order of a few hundred 00:36:16.990 --> 00:36:17.870 align:middle line:90% microns. 00:36:17.870 --> 00:36:21.010 align:middle line:84% So you can see it on the naked eye, this small region there. 00:36:21.010 --> 00:36:22.950 align:middle line:84% And then outside, this is typically 00:36:22.950 --> 00:36:25.730 align:middle line:84% of essentially like millimeter region, hackle and mist. 00:36:25.730 --> 00:36:27.830 align:middle line:84% And then beyond that, several macroscopic scale, 00:36:27.830 --> 00:36:30.330 align:middle line:84% you see Wallner lines coming out. 00:36:30.330 --> 00:36:30.830 align:middle line:90% Yeah. 00:36:30.830 --> 00:36:31.410 align:middle line:90% Yes? 00:36:31.410 --> 00:36:33.590 align:middle line:84% STUDENT: So back to the other slide, so 00:36:33.590 --> 00:36:42.470 align:middle line:84% how does the thickness of the glass affect the Wallner lines? 00:36:42.470 --> 00:36:44.390 align:middle line:90% Is it just a longer-- 00:36:44.390 --> 00:36:45.490 align:middle line:90% JUEJUN HU: It gets longer. 00:36:45.490 --> 00:36:46.110 align:middle line:90% STUDENT: Or-- 00:36:46.110 --> 00:36:47.510 align:middle line:90% JUEJUN HU: It gets longer. 00:36:47.510 --> 00:36:49.908 align:middle line:84% The Wallner lines, the main difference 00:36:49.908 --> 00:36:51.950 align:middle line:84% that actually impacts the Wallner line morphology 00:36:51.950 --> 00:36:53.408 align:middle line:84% is actually the velocity difference 00:36:53.408 --> 00:36:56.710 align:middle line:84% between the elastic wave and the crack propagation velocity. 00:36:56.710 --> 00:36:59.230 align:middle line:84% In fact, people have this empirical formula 00:36:59.230 --> 00:37:04.060 align:middle line:84% that basically says that the spacing d between the Wallner 00:37:04.060 --> 00:37:07.620 align:middle line:90% lines is roughly given by V-- 00:37:07.620 --> 00:37:09.700 align:middle line:90% let's see, elastic wave. 00:37:09.700 --> 00:37:12.660 align:middle line:90% Let's say Ve minus Vc. 00:37:12.660 --> 00:37:15.140 align:middle line:84% So Vc will be the crack velocity. 00:37:15.140 --> 00:37:17.475 align:middle line:84% And Ve is elastic wave propagation velocity, 00:37:17.475 --> 00:37:19.100 align:middle line:84% which is basically sound wave velocity. 00:37:19.100 --> 00:37:25.620 align:middle line:84% And f will be the frequency of elastic waves. 00:37:25.620 --> 00:37:27.540 align:middle line:90% So that's what I'm saying. 00:37:27.540 --> 00:37:29.980 align:middle line:84% Because Vc is always smaller than Ve, 00:37:29.980 --> 00:37:33.220 align:middle line:84% so you have a higher correct propagation velocity. 00:37:33.220 --> 00:37:34.740 align:middle line:84% The spacing between Wallner lines 00:37:34.740 --> 00:37:36.280 align:middle line:84% actually essentially gets bigger. 00:37:36.280 --> 00:37:39.840 align:middle line:90% 00:37:39.840 --> 00:37:40.340 align:middle line:90% Yeah. 00:37:40.340 --> 00:37:46.700 align:middle line:90% 00:37:46.700 --> 00:37:48.620 align:middle line:84% And then Vc also has to do with essentially, 00:37:48.620 --> 00:37:50.580 align:middle line:84% for example, intrinsic plasticity 00:37:50.580 --> 00:37:51.620 align:middle line:90% in the glass materials. 00:37:51.620 --> 00:37:53.780 align:middle line:84% It has to do with how much stress you apply. 00:37:53.780 --> 00:37:55.340 align:middle line:84% So there are lots of things you can infer just 00:37:55.340 --> 00:37:57.673 align:middle line:84% by essentially looking at the morphology of the fracture 00:37:57.673 --> 00:37:58.540 align:middle line:90% surfaces there. 00:37:58.540 --> 00:38:01.220 align:middle line:84% Now, one more thing I also want to mention here 00:38:01.220 --> 00:38:04.020 align:middle line:84% is that, for this particular kind of morphology, 00:38:04.020 --> 00:38:07.000 align:middle line:84% this only applies to essentially non-tempered glasses, 00:38:07.000 --> 00:38:08.717 align:middle line:90% so not strengthened. 00:38:08.717 --> 00:38:10.800 align:middle line:84% Temper is basically a process that you essentially 00:38:10.800 --> 00:38:13.240 align:middle line:84% do a fast annealing, fast quenching on the glass material 00:38:13.240 --> 00:38:15.380 align:middle line:84% to introduce surface compressive stress. 00:38:15.380 --> 00:38:16.900 align:middle line:84% We're going to talk about it later. 00:38:16.900 --> 00:38:19.320 align:middle line:84% But it just suffices to highlight 00:38:19.320 --> 00:38:22.760 align:middle line:84% that, if it's tempered glass, the cross-section looks 00:38:22.760 --> 00:38:23.460 align:middle line:90% quite different. 00:38:23.460 --> 00:38:24.960 align:middle line:84% This is actually what it looks like. 00:38:24.960 --> 00:38:26.980 align:middle line:84% So actually, this is a top surface. 00:38:26.980 --> 00:38:28.140 align:middle line:90% This is a bottom surface. 00:38:28.140 --> 00:38:31.160 align:middle line:84% This is essentially a tempered glass pane. 00:38:31.160 --> 00:38:35.120 align:middle line:84% When it fractures, you usually have center-- essentially, 00:38:35.120 --> 00:38:37.447 align:middle line:90% you have the mist hackle band. 00:38:37.447 --> 00:38:39.280 align:middle line:84% So in the center, this is where you actually 00:38:39.280 --> 00:38:41.560 align:middle line:90% have a lot of tensile stress. 00:38:41.560 --> 00:38:45.660 align:middle line:84% This is where usually the defect initiates in the tempered glass. 00:38:45.660 --> 00:38:48.360 align:middle line:84% This is unlike regular glass, where you usually 00:38:48.360 --> 00:38:49.840 align:middle line:90% have surface defects. 00:38:49.840 --> 00:38:53.680 align:middle line:84% In tempered glass, the defects usually initiate in the inside, 00:38:53.680 --> 00:38:56.440 align:middle line:84% in the interior, where you have large tensile stress that 00:38:56.440 --> 00:38:57.740 align:middle line:90% facilitates crack opening. 00:38:57.740 --> 00:39:00.480 align:middle line:84% So that's why you see the mist and the hackle 00:39:00.480 --> 00:39:03.192 align:middle line:84% actually in the center, rather than near the surface. 00:39:03.192 --> 00:39:04.650 align:middle line:84% And then you see the Wallner lines. 00:39:04.650 --> 00:39:06.608 align:middle line:84% You have two symmetric Wallner line propagation 00:39:06.608 --> 00:39:07.850 align:middle line:90% patterns on the outside. 00:39:07.850 --> 00:39:10.510 align:middle line:84% And then near the surface, you see this horizontal pattern. 00:39:10.510 --> 00:39:13.030 align:middle line:84% This is actually indicative of the high compressive 00:39:13.030 --> 00:39:14.070 align:middle line:90% stress on the surface. 00:39:14.070 --> 00:39:16.910 align:middle line:84% That's what leads to these horizontal lines. 00:39:16.910 --> 00:39:21.230 align:middle line:84% You can also look at the pattern of the breakage here. 00:39:21.230 --> 00:39:23.710 align:middle line:84% You essentially have these primary cracks 00:39:23.710 --> 00:39:25.275 align:middle line:84% that propagate in the radial pattern. 00:39:25.275 --> 00:39:27.150 align:middle line:84% And then you also have these secondary cracks 00:39:27.150 --> 00:39:28.630 align:middle line:90% that essentially branch out. 00:39:28.630 --> 00:39:31.650 align:middle line:84% You can always trace back to the center of defect, right here. 00:39:31.650 --> 00:39:34.270 align:middle line:84% You see this butterfly-like pattern? 00:39:34.270 --> 00:39:35.950 align:middle line:84% This is actually called a butterfly, 00:39:35.950 --> 00:39:37.665 align:middle line:90% if you look at the fractography. 00:39:37.665 --> 00:39:40.290 align:middle line:84% And the defect usually is right here, where I'm pointing there. 00:39:40.290 --> 00:39:42.370 align:middle line:84% That's where the initial defect actually happens. 00:39:42.370 --> 00:39:46.830 align:middle line:90% 00:39:46.830 --> 00:39:47.330 align:middle line:90% OK. 00:39:47.330 --> 00:39:50.030 align:middle line:84% So this really just scratches the surface of fractography 00:39:50.030 --> 00:39:52.630 align:middle line:84% that people actually spend decades essentially 00:39:52.630 --> 00:39:53.410 align:middle line:90% looking into this. 00:39:53.410 --> 00:39:55.310 align:middle line:84% But at least next time, if you do 00:39:55.310 --> 00:39:58.510 align:middle line:84% break any kind of glass materials or glass pieces, 00:39:58.510 --> 00:39:59.900 align:middle line:90% don't panic. 00:39:59.900 --> 00:40:01.453 align:middle line:90% Do your fractography. 00:40:01.453 --> 00:40:03.620 align:middle line:84% You can then go back to tell your parents or whoever 00:40:03.620 --> 00:40:06.140 align:middle line:84% that it's not your fault. Most likely, a surface defect 00:40:06.140 --> 00:40:08.920 align:middle line:84% is the culprit, 99% of the cases. 00:40:08.920 --> 00:40:11.820 align:middle line:90% 00:40:11.820 --> 00:40:12.320 align:middle line:90% OK. 00:40:12.320 --> 00:40:14.120 align:middle line:84% Any more questions about fractography? 00:40:14.120 --> 00:40:21.500 align:middle line:90% 00:40:21.500 --> 00:40:23.240 align:middle line:90% STUDENT: Yeah. 00:40:23.240 --> 00:40:27.140 align:middle line:84% Is this-- do these patterns only occur 00:40:27.140 --> 00:40:29.040 align:middle line:90% when there's total fracture? 00:40:29.040 --> 00:40:31.860 align:middle line:90% Or is it happening-- 00:40:31.860 --> 00:40:33.940 align:middle line:90% JUEJUN HU: It depends. 00:40:33.940 --> 00:40:35.580 align:middle line:84% STUDENT: Hackles and the Wallner lines 00:40:35.580 --> 00:40:39.340 align:middle line:84% when it's still just crack propagation but not yet 00:40:39.340 --> 00:40:39.840 align:middle line:90% fractured? 00:40:39.840 --> 00:40:41.590 align:middle line:84% JUEJUN HU: Well, it depends on which face. 00:40:41.590 --> 00:40:43.398 align:middle line:84% I mean, the problem with glass is 00:40:43.398 --> 00:40:45.440 align:middle line:84% that, once you get a crack starting to propagate, 00:40:45.440 --> 00:40:48.020 align:middle line:84% unless you very promptly terminate the stress, 00:40:48.020 --> 00:40:49.860 align:middle line:84% it's going to propagate very quickly. 00:40:49.860 --> 00:40:53.300 align:middle line:84% So it's hard to see a half open crack thing. 00:40:53.300 --> 00:40:55.740 align:middle line:84% You have to terminate it in a fraction of a second. 00:40:55.740 --> 00:40:59.213 align:middle line:84% STUDENT: You wouldn't really get to, oh, the hackle region-- 00:40:59.213 --> 00:41:00.130 align:middle line:90% JUEJUN HU: [INAUDIBLE] 00:41:00.130 --> 00:41:01.250 align:middle line:90% STUDENT: We saved it-- 00:41:01.250 --> 00:41:01.850 align:middle line:90% JUEJUN HU: You could. 00:41:01.850 --> 00:41:04.308 align:middle line:84% Think of it-- the propagation velocity is like 1,000 meters 00:41:04.308 --> 00:41:05.610 align:middle line:90% per second. 00:41:05.610 --> 00:41:08.695 align:middle line:84% And the width of the region is like a few hundred microns. 00:41:08.695 --> 00:41:11.070 align:middle line:84% So you'd have to stop it really at the microsecond level. 00:41:11.070 --> 00:41:12.150 align:middle line:84% If you can precisely control that, 00:41:12.150 --> 00:41:13.150 align:middle line:90% then you will actually see it. 00:41:13.150 --> 00:41:14.590 align:middle line:84% STUDENT: But they are sequential? 00:41:14.590 --> 00:41:15.882 align:middle line:90% JUEJUN HU: They are sequential. 00:41:15.882 --> 00:41:17.768 align:middle line:84% You start with mirror, mist, hackle, and then 00:41:17.768 --> 00:41:18.810 align:middle line:90% eventually Wallner lines. 00:41:18.810 --> 00:41:19.370 align:middle line:90% STUDENT: OK. 00:41:19.370 --> 00:41:21.290 align:middle line:90% JUEJUN HU: Yeah. 00:41:21.290 --> 00:41:22.710 align:middle line:84% So by looking at fracture surface, 00:41:22.710 --> 00:41:24.635 align:middle line:84% you're already tracing back in time. 00:41:24.635 --> 00:41:26.010 align:middle line:84% That's how it actually initiates. 00:41:26.010 --> 00:41:28.097 align:middle line:84% STUDENT: Even if it's a very short amount of time. 00:41:28.097 --> 00:41:29.930 align:middle line:84% JUEJUN HU: It's a very short amount of time. 00:41:29.930 --> 00:41:33.530 align:middle line:90% Exactly, yeah. 00:41:33.530 --> 00:41:35.930 align:middle line:84% Now, let's talk about crack propagation 00:41:35.930 --> 00:41:38.810 align:middle line:84% over a much longer period of time. 00:41:38.810 --> 00:41:43.650 align:middle line:84% So the Griffith's theory has one important limitation. 00:41:43.650 --> 00:41:46.630 align:middle line:84% It's that time is actually not a function in Griffith's theory. 00:41:46.630 --> 00:41:48.070 align:middle line:84% Griffith's theory is very simple. 00:41:48.070 --> 00:41:51.850 align:middle line:84% If the stress at the crack tip exceeds the material strength, 00:41:51.850 --> 00:41:53.150 align:middle line:90% crack is going to open. 00:41:53.150 --> 00:41:55.190 align:middle line:84% Once it starts to open, the crack gets longer. 00:41:55.190 --> 00:41:57.563 align:middle line:84% The stress actually gets more amplified. 00:41:57.563 --> 00:41:59.480 align:middle line:84% Then it means that essentially the crack opens 00:41:59.480 --> 00:42:00.760 align:middle line:90% at an even higher velocity. 00:42:00.760 --> 00:42:02.180 align:middle line:90% So it's a one-way street. 00:42:02.180 --> 00:42:06.120 align:middle line:84% It just quickly, immediately leads to catastrophic failure. 00:42:06.120 --> 00:42:11.040 align:middle line:84% However, what people observe in glass materials is, 00:42:11.040 --> 00:42:13.520 align:middle line:84% even if the stress, applied, stress, 00:42:13.520 --> 00:42:18.080 align:middle line:84% is below the fracture stress of glass, 00:42:18.080 --> 00:42:23.560 align:middle line:84% if you keep the load, over time, the glass will still fail, 00:42:23.560 --> 00:42:28.640 align:middle line:84% even if sigma infinity applied stress is less than sigma f. 00:42:28.640 --> 00:42:31.680 align:middle line:84% So the reason that happens is actually-- 00:42:31.680 --> 00:42:34.293 align:middle line:84% this is called essentially a fatigue in glass materials. 00:42:34.293 --> 00:42:36.460 align:middle line:84% And it actually has to do with the stress corrosion. 00:42:36.460 --> 00:42:38.760 align:middle line:84% It's because of water vapor getting condensed 00:42:38.760 --> 00:42:40.800 align:middle line:90% into the crack tip. 00:42:40.800 --> 00:42:43.920 align:middle line:84% So what I'm showing you here, essentially this 00:42:43.920 --> 00:42:45.060 align:middle line:90% is called static fatigue. 00:42:45.060 --> 00:42:46.560 align:middle line:84% Essentially, it means that you apply 00:42:46.560 --> 00:42:50.560 align:middle line:84% a static load, sigma infinity that's less than sigma f. 00:42:50.560 --> 00:42:51.960 align:middle line:84% And then you can measure the time 00:42:51.960 --> 00:42:53.880 align:middle line:90% to failure for glass pieces. 00:42:53.880 --> 00:42:56.890 align:middle line:84% And you can generate a plot like what I'm showing here. 00:42:56.890 --> 00:43:01.170 align:middle line:84% So the vertical axis is essentially the sigma infinity, 00:43:01.170 --> 00:43:03.550 align:middle line:84% which is the applied stress normalized to the fracture 00:43:03.550 --> 00:43:04.310 align:middle line:90% stress. 00:43:04.310 --> 00:43:06.163 align:middle line:90% You see that this is below 1. 00:43:06.163 --> 00:43:08.830 align:middle line:84% So it means that you are looking at another catastrophic failure 00:43:08.830 --> 00:43:09.650 align:middle line:90% of glass material. 00:43:09.650 --> 00:43:11.710 align:middle line:84% This is essentially a fatigue failure 00:43:11.710 --> 00:43:13.370 align:middle line:84% that takes a long, long period of time. 00:43:13.370 --> 00:43:15.430 align:middle line:84% So this is below the fracture stress. 00:43:15.430 --> 00:43:19.270 align:middle line:84% Horizontal axis, this is the time to failure. 00:43:19.270 --> 00:43:22.090 align:middle line:84% Now, this is a pretty messy plot with lots of different symbols, 00:43:22.090 --> 00:43:23.110 align:middle line:90% whatever. 00:43:23.110 --> 00:43:24.330 align:middle line:90% Let's don't worry about that. 00:43:24.330 --> 00:43:27.710 align:middle line:84% Let's just focus on one line here. 00:43:27.710 --> 00:43:30.150 align:middle line:84% Each of these lines essentially represents 00:43:30.150 --> 00:43:34.390 align:middle line:84% one type of glass sample with a specific surface preparation. 00:43:34.390 --> 00:43:38.150 align:middle line:84% These different symbols here, each of them 00:43:38.150 --> 00:43:40.630 align:middle line:84% represents a different level of abrasion. 00:43:40.630 --> 00:43:42.110 align:middle line:84% Now, abrasion, you can think of it 00:43:42.110 --> 00:43:44.248 align:middle line:84% as essentially trying to create surface defects. 00:43:44.248 --> 00:43:46.790 align:middle line:84% Different levels of abrasion give you different surface crack 00:43:46.790 --> 00:43:47.450 align:middle line:90% size. 00:43:47.450 --> 00:43:50.230 align:middle line:84% So these are essentially different glass materials 00:43:50.230 --> 00:43:52.790 align:middle line:84% with a different surface crack sizes. 00:43:52.790 --> 00:43:56.980 align:middle line:84% So if you focus on only one of the lines here, what you see 00:43:56.980 --> 00:44:02.060 align:middle line:84% is that, as you increase the applied load, the time 00:44:02.060 --> 00:44:05.060 align:middle line:84% to failure decreases, which makes sense. 00:44:05.060 --> 00:44:07.700 align:middle line:84% And it decreases in this logarithmic manner 00:44:07.700 --> 00:44:10.820 align:middle line:84% because this is actually an exponential, essentially 00:44:10.820 --> 00:44:12.840 align:middle line:84% a logarithmic axis in the horizontal axis. 00:44:12.840 --> 00:44:17.020 align:middle line:90% 00:44:17.020 --> 00:44:21.900 align:middle line:84% Essentially, the time to failure increases logarithmically 00:44:21.900 --> 00:44:25.420 align:middle line:84% with respect to the applied stress. 00:44:25.420 --> 00:44:28.340 align:middle line:84% STUDENT: But it still fails quite quickly. 00:44:28.340 --> 00:44:30.780 align:middle line:84% JUEJUN HU: Yeah, it's under a second. 00:44:30.780 --> 00:44:32.280 align:middle line:90% Under a second, essentially. 00:44:32.280 --> 00:44:34.100 align:middle line:84% Or it can be like hundredths or thousandths 00:44:34.100 --> 00:44:38.060 align:middle line:90% of seconds, either way. 00:44:38.060 --> 00:44:40.060 align:middle line:90% Yeah? 00:44:40.060 --> 00:44:42.235 align:middle line:90% STUDENT: [INAUDIBLE] 00:44:42.235 --> 00:44:42.860 align:middle line:90% JUEJUN HU: Yes. 00:44:42.860 --> 00:44:47.980 align:middle line:84% STUDENT: Even at, like, very less than, like, 00:44:47.980 --> 00:44:49.340 align:middle line:90% half [INAUDIBLE]. 00:44:49.340 --> 00:44:52.865 align:middle line:90% 00:44:52.865 --> 00:44:54.602 align:middle line:84% JUEJUN HU: So for these curves here, 00:44:54.602 --> 00:44:56.310 align:middle line:84% these are measured for different samples. 00:44:56.310 --> 00:44:58.610 align:middle line:84% What we can also do is we can try 00:44:58.610 --> 00:45:00.890 align:middle line:84% to normalize all the curves with respect 00:45:00.890 --> 00:45:03.990 align:middle line:84% to the intersection point with the horizontal line here. 00:45:03.990 --> 00:45:05.810 align:middle line:84% So this horizontal line corresponds 00:45:05.810 --> 00:45:08.932 align:middle line:84% to when the applied stress is half of the fracture stress. 00:45:08.932 --> 00:45:10.890 align:middle line:84% So if you normalize all the curves with respect 00:45:10.890 --> 00:45:13.730 align:middle line:84% to their cross-section points with the horizontal line here, 00:45:13.730 --> 00:45:17.690 align:middle line:84% then turns out all of them collapse into one single line. 00:45:17.690 --> 00:45:22.570 align:middle line:84% This is called a universal static fatigue curve. 00:45:22.570 --> 00:45:25.970 align:middle line:84% It gives you a way to predict how long the glass sample will 00:45:25.970 --> 00:45:30.110 align:middle line:84% last under different levels of applied stress. 00:45:30.110 --> 00:45:35.210 align:middle line:90% 00:45:35.210 --> 00:45:36.830 align:middle line:84% STUDENT: I don't think I understand. 00:45:36.830 --> 00:45:37.413 align:middle line:90% JUEJUN HU: OK. 00:45:37.413 --> 00:45:39.830 align:middle line:84% The way it works, the horizontal axis, 00:45:39.830 --> 00:45:42.030 align:middle line:90% this is t divided by t 0.5. 00:45:42.030 --> 00:45:45.170 align:middle line:84% Now, t 0.5 is basically the intersection point of one 00:45:45.170 --> 00:45:47.650 align:middle line:84% of the curves with this line here. 00:45:47.650 --> 00:45:51.820 align:middle line:84% So this line corresponds to essentially the time to failure 00:45:51.820 --> 00:45:54.880 align:middle line:84% if you apply a stress that's half of the fracture stress. 00:45:54.880 --> 00:45:59.567 align:middle line:84% You then normalize the time to failure to that t 0.5. 00:45:59.567 --> 00:46:00.900 align:middle line:90% And then you take the logarithm. 00:46:00.900 --> 00:46:04.600 align:middle line:84% What you end up getting is this mostly linear relation. 00:46:04.600 --> 00:46:11.000 align:middle line:84% So it says that essentially the stress scales the logarithm of t 00:46:11.000 --> 00:46:13.600 align:middle line:90% basically. 00:46:13.600 --> 00:46:18.105 align:middle line:84% So with this plot, essentially if you know your-- 00:46:18.105 --> 00:46:20.895 align:middle line:90% 00:46:20.895 --> 00:46:24.440 align:middle line:84% if you know your t 0.5 and you know your load, 00:46:24.440 --> 00:46:26.440 align:middle line:84% you can then use it to actually predict the time 00:46:26.440 --> 00:46:28.500 align:middle line:90% to failure for your sample. 00:46:28.500 --> 00:46:29.000 align:middle line:90% Yeah. 00:46:29.000 --> 00:46:37.400 align:middle line:90% 00:46:37.400 --> 00:46:40.060 align:middle line:84% Now, what we want to do is let's take a look at, 00:46:40.060 --> 00:46:42.760 align:middle line:84% in more details, what exactly is the microscopic mechanism that 00:46:42.760 --> 00:46:44.340 align:middle line:84% lead to this kind of static fatigue. 00:46:44.340 --> 00:46:46.400 align:middle line:84% So as I've already mentioned, this 00:46:46.400 --> 00:46:49.380 align:middle line:90% has to do with stress corrosion. 00:46:49.380 --> 00:46:53.720 align:middle line:84% So what happens is that, inside a crack, surface crack, 00:46:53.720 --> 00:46:56.060 align:middle line:84% you always get condensation of water vapor. 00:46:56.060 --> 00:46:59.660 align:middle line:84% And this water vapor then leads to essentially a disintegration 00:46:59.660 --> 00:47:01.860 align:middle line:84% of the glass network through this chemical reaction 00:47:01.860 --> 00:47:04.420 align:middle line:84% there, which can also get further accelerated if you 00:47:04.420 --> 00:47:06.480 align:middle line:84% have alkaline present in glass network. 00:47:06.480 --> 00:47:08.780 align:middle line:84% They can preferentially reach out, go to the solution, 00:47:08.780 --> 00:47:13.460 align:middle line:84% form the hydroxide, lead to a basic solution that essentially 00:47:13.460 --> 00:47:17.100 align:middle line:84% attacks the glass network even faster. 00:47:17.100 --> 00:47:20.540 align:middle line:84% So what I'm showing on the right-hand side plot here, 00:47:20.540 --> 00:47:24.320 align:middle line:84% this is the crack velocity as a function of the applied stress. 00:47:24.320 --> 00:47:26.380 align:middle line:84% Basically, stress intensity factor basically 00:47:26.380 --> 00:47:30.740 align:middle line:84% is essentially a parameter that synthesizes both applied stress 00:47:30.740 --> 00:47:31.760 align:middle line:90% and the crack length. 00:47:31.760 --> 00:47:34.940 align:middle line:84% So what we are seeing here is that, for different kinds 00:47:34.940 --> 00:47:38.740 align:middle line:84% of glass materials, you have different crack velocity. 00:47:38.740 --> 00:47:41.540 align:middle line:90% You have essentially soda-lime. 00:47:41.540 --> 00:47:45.420 align:middle line:84% This line lies on top means it has the highest correct velocity 00:47:45.420 --> 00:47:48.610 align:middle line:84% under static load, which makes sense because soda-lime has 00:47:48.610 --> 00:47:50.370 align:middle line:90% lots of soda, lots of sodium. 00:47:50.370 --> 00:47:51.995 align:middle line:84% So the sodium essentially is what's 00:47:51.995 --> 00:47:53.370 align:middle line:84% causing this accelerated chemical 00:47:53.370 --> 00:47:58.210 align:middle line:84% attack due to this stress corrosion versus silica glass. 00:47:58.210 --> 00:48:00.030 align:middle line:84% This line at close to the bottom, 00:48:00.030 --> 00:48:01.530 align:middle line:84% it's a little more chemically stable 00:48:01.530 --> 00:48:03.890 align:middle line:84% because it doesn't contain these sodium ions. 00:48:03.890 --> 00:48:07.570 align:middle line:84% So this is one evidence showing that the presence of this sodium 00:48:07.570 --> 00:48:11.170 align:middle line:84% ions is the culprit that leading to stress corrosion. 00:48:11.170 --> 00:48:14.010 align:middle line:84% Now, more carefully, people also did more careful study 00:48:14.010 --> 00:48:16.870 align:middle line:84% looking into the kinetics of this process here. 00:48:16.870 --> 00:48:18.990 align:middle line:84% So again, this is a very messy plot. 00:48:18.990 --> 00:48:20.510 align:middle line:84% Let me try to explain what happens. 00:48:20.510 --> 00:48:22.970 align:middle line:84% So in this plot, what people are looking at 00:48:22.970 --> 00:48:24.430 align:middle line:90% is the crack velocity. 00:48:24.430 --> 00:48:26.250 align:middle line:84% This is the crack growth velocity 00:48:26.250 --> 00:48:29.810 align:middle line:84% under constant load as a function of the stress intensity 00:48:29.810 --> 00:48:30.770 align:middle line:90% factor. 00:48:30.770 --> 00:48:32.850 align:middle line:84% Now, the stress intensity factor, 00:48:32.850 --> 00:48:37.690 align:middle line:84% if you keep the load constant, then the stress intensity factor 00:48:37.690 --> 00:48:41.830 align:middle line:84% basically correlates with the length of the crack. 00:48:41.830 --> 00:48:44.290 align:middle line:84% The larger the length of the crack, the larger the stress 00:48:44.290 --> 00:48:45.910 align:middle line:90% intensity factor. 00:48:45.910 --> 00:48:48.440 align:middle line:84% So horizontal axis, you can treat it 00:48:48.440 --> 00:48:51.960 align:middle line:84% as the length of the crack or square root of the length 00:48:51.960 --> 00:48:53.360 align:middle line:90% of crack, to be exact. 00:48:53.360 --> 00:48:55.560 align:middle line:84% So then what we are seeing here is that there 00:48:55.560 --> 00:48:57.240 align:middle line:90% are different groups of curves. 00:48:57.240 --> 00:49:00.760 align:middle line:84% Each of these curves corresponds to a relative humidity 00:49:00.760 --> 00:49:03.080 align:middle line:90% level in the ambient air. 00:49:03.080 --> 00:49:06.520 align:middle line:84% So this is 100% relative humidity. 00:49:06.520 --> 00:49:10.080 align:middle line:84% This is 0.017% relative humidity. 00:49:10.080 --> 00:49:11.940 align:middle line:84% So in each curve, it goes like this. 00:49:11.940 --> 00:49:14.280 align:middle line:84% It starts to rise, plateaus, and then 00:49:14.280 --> 00:49:18.080 align:middle line:84% suddenly goes to this conversion single line there. 00:49:18.080 --> 00:49:22.400 align:middle line:84% So we can divide this behavior into three different regions 00:49:22.400 --> 00:49:22.900 align:middle line:90% here. 00:49:22.900 --> 00:49:28.080 align:middle line:84% Region 1 is this linear increased region. 00:49:28.080 --> 00:49:29.740 align:middle line:90% Region 2 is the plateau. 00:49:29.740 --> 00:49:32.280 align:middle line:84% And region 3, all the curves essentially 00:49:32.280 --> 00:49:34.360 align:middle line:90% collapsed into one single line. 00:49:34.360 --> 00:49:36.620 align:middle line:90% So now, let's see what happens. 00:49:36.620 --> 00:49:42.880 align:middle line:84% Region 1, this is where, if you have a larger stress or longer 00:49:42.880 --> 00:49:46.170 align:middle line:84% crack, you have a higher stress intensity factor. 00:49:46.170 --> 00:49:48.670 align:middle line:84% The crack opening actually becomes faster. 00:49:48.670 --> 00:49:49.530 align:middle line:90% That's what it says. 00:49:49.530 --> 00:49:51.990 align:middle line:84% Also, you clearly see that, if you 00:49:51.990 --> 00:49:56.070 align:middle line:84% have a higher relative humidity, you get more water condensation. 00:49:56.070 --> 00:49:58.970 align:middle line:84% Then the process actually gets expedited exponentially. 00:49:58.970 --> 00:50:01.710 align:middle line:90% 00:50:01.710 --> 00:50:04.310 align:middle line:84% This is clear evidence that water vapor actually 00:50:04.310 --> 00:50:09.350 align:middle line:84% plays a significant role in the subcritical crack growth. 00:50:09.350 --> 00:50:13.190 align:middle line:84% Now, if you come to region 2, what happens in region 2 00:50:13.190 --> 00:50:15.590 align:middle line:84% is that the crack growth rate becomes 00:50:15.590 --> 00:50:18.690 align:middle line:84% independent of the stress intensity factor-- 00:50:18.690 --> 00:50:21.910 align:middle line:84% or in other words, independent of the correct length. 00:50:21.910 --> 00:50:24.390 align:middle line:84% Now, normally, if you have a longer crack length, 00:50:24.390 --> 00:50:25.883 align:middle line:90% you should have a higher stress. 00:50:25.883 --> 00:50:28.050 align:middle line:84% You have more stress concentration at the crack tip. 00:50:28.050 --> 00:50:31.150 align:middle line:84% So you should have higher stress at the crack tip. 00:50:31.150 --> 00:50:34.270 align:middle line:84% So the reason that you have a-- now the crack propagation 00:50:34.270 --> 00:50:36.310 align:middle line:84% velocity becomes independent of crack length 00:50:36.310 --> 00:50:39.070 align:middle line:84% is because now the kinetics actually 00:50:39.070 --> 00:50:43.740 align:middle line:84% controlled not by the stress, but by the mass transport. 00:50:43.740 --> 00:50:47.420 align:middle line:84% If a longer crack, it takes longer time for the water vapor 00:50:47.420 --> 00:50:50.460 align:middle line:84% to diffuse into the crack and reach the crack tip. 00:50:50.460 --> 00:50:52.500 align:middle line:84% And water vapor needs to get to the crack tip 00:50:52.500 --> 00:50:55.900 align:middle line:84% in order to cause all the chemical reactions. 00:50:55.900 --> 00:51:01.860 align:middle line:84% So region 2 is basically a transport limited region. 00:51:01.860 --> 00:51:02.380 align:middle line:90% Yes? 00:51:02.380 --> 00:51:07.460 align:middle line:84% STUDENT: So technically, when people are making glass lenses 00:51:07.460 --> 00:51:13.580 align:middle line:84% and we use water around the drill, 00:51:13.580 --> 00:51:16.540 align:middle line:84% if it's not moving as fast as it is to not let 00:51:16.540 --> 00:51:19.400 align:middle line:90% the water enter the region-- 00:51:19.400 --> 00:51:20.457 align:middle line:90% JUEJUN HU: It will enter. 00:51:20.457 --> 00:51:21.040 align:middle line:90% It will enter. 00:51:21.040 --> 00:51:25.540 align:middle line:84% I mean, if you at it, this kind of a subcritical crack growth 00:51:25.540 --> 00:51:29.200 align:middle line:84% occurs even for relative humidity of like 0.017%. 00:51:29.200 --> 00:51:31.940 align:middle line:90% That's like extremely dry. 00:51:31.940 --> 00:51:34.260 align:middle line:84% So the problem is that glass surface 00:51:34.260 --> 00:51:36.260 align:middle line:90% is extremely hydrophilic. 00:51:36.260 --> 00:51:39.120 align:middle line:84% So even if there's only a tiny amount of water vapor, 00:51:39.120 --> 00:51:41.810 align:middle line:84% they will tend to condense at the crack tip. 00:51:41.810 --> 00:51:44.970 align:middle line:84% So it will get in there, regardless of what you do. 00:51:44.970 --> 00:51:50.050 align:middle line:84% [INAUDIBLE] Yeah, and so water is so-- 00:51:50.050 --> 00:51:52.770 align:middle line:84% STUDENT: Just basically, it's like, oh, 00:51:52.770 --> 00:51:56.510 align:middle line:84% people usually use water as some of cleaning 00:51:56.510 --> 00:52:00.230 align:middle line:90% [INAUDIBLE] for drilling. 00:52:00.230 --> 00:52:03.090 align:middle line:84% It's just like, oh, water is actually 00:52:03.090 --> 00:52:04.742 align:middle line:90% making it prone to cracking. 00:52:04.742 --> 00:52:05.450 align:middle line:90% JUEJUN HU: It is. 00:52:05.450 --> 00:52:06.810 align:middle line:90% Yeah, it is. 00:52:06.810 --> 00:52:07.770 align:middle line:90% It is, yeah. 00:52:07.770 --> 00:52:11.663 align:middle line:90% 00:52:11.663 --> 00:52:14.330 align:middle line:84% Yeah, that's why later on we're going to talk about some surface 00:52:14.330 --> 00:52:14.910 align:middle line:90% treatments. 00:52:14.910 --> 00:52:17.330 align:middle line:84% People do local firing and stuff, essentially 00:52:17.330 --> 00:52:18.690 align:middle line:90% trying to heal the cracks. 00:52:18.690 --> 00:52:21.970 align:middle line:84% So if you really want your piece to be strong, 00:52:21.970 --> 00:52:23.970 align:middle line:84% that's the surface treatment you have to do. 00:52:23.970 --> 00:52:25.750 align:middle line:84% Yeah, and glass lenses, it's usually OK. 00:52:25.750 --> 00:52:29.070 align:middle line:84% People don't care so much about the mechanical toughness. 00:52:29.070 --> 00:52:30.243 align:middle line:90% So it's OK. 00:52:30.243 --> 00:52:32.410 align:middle line:84% But in other cases, where you have that requirement, 00:52:32.410 --> 00:52:33.930 align:middle line:84% you have to do surface treatment. 00:52:33.930 --> 00:52:35.638 align:middle line:84% Yeah, you cannot just leave it like that. 00:52:35.638 --> 00:52:38.130 align:middle line:90% 00:52:38.130 --> 00:52:38.630 align:middle line:90% OK. 00:52:38.630 --> 00:52:40.440 align:middle line:84% And then the third region, this is 00:52:40.440 --> 00:52:43.560 align:middle line:84% when you have a sufficiently long crack, 00:52:43.560 --> 00:52:45.760 align:middle line:84% where you start to get essentially expedited crack 00:52:45.760 --> 00:52:47.080 align:middle line:90% opening. 00:52:47.080 --> 00:52:48.700 align:middle line:84% Once you get to the third region, 00:52:48.700 --> 00:52:52.240 align:middle line:84% the crack velocity essentially quickly grows. 00:52:52.240 --> 00:52:54.660 align:middle line:84% And this eventually leads to a catastrophic failure. 00:52:54.660 --> 00:52:58.680 align:middle line:84% Eventually, the fracture strength, the applied stress 00:52:58.680 --> 00:52:59.940 align:middle line:90% reaches the fracture stress. 00:52:59.940 --> 00:53:01.740 align:middle line:84% Then the crack immediately opens. 00:53:01.740 --> 00:53:04.700 align:middle line:84% It leads to a very high speed crack propagation. 00:53:04.700 --> 00:53:06.260 align:middle line:84% And then the material just fails. 00:53:06.260 --> 00:53:09.640 align:middle line:90% 00:53:09.640 --> 00:53:10.140 align:middle line:90% OK. 00:53:10.140 --> 00:53:13.100 align:middle line:84% So this is essentially what the three regions describes. 00:53:13.100 --> 00:53:17.560 align:middle line:84% So bottom line, glass material can 00:53:17.560 --> 00:53:19.720 align:middle line:84% fail even if the applied load is actually 00:53:19.720 --> 00:53:23.440 align:middle line:84% below the fracture stress because of stress corrosion. 00:53:23.440 --> 00:53:26.760 align:middle line:90% 00:53:26.760 --> 00:53:27.600 align:middle line:90% All right. 00:53:27.600 --> 00:53:31.468 align:middle line:84% So the last couple parts of the talk, 00:53:31.468 --> 00:53:33.760 align:middle line:84% I will describe a little bit about the characterization 00:53:33.760 --> 00:53:35.920 align:middle line:84% of fracture behavior in glass materials. 00:53:35.920 --> 00:53:40.150 align:middle line:84% So to measure the fracture toughness, 00:53:40.150 --> 00:53:41.848 align:middle line:84% people have established standards. 00:53:41.848 --> 00:53:43.390 align:middle line:84% Essentially, these are ASTM standards 00:53:43.390 --> 00:53:45.830 align:middle line:84% you have to follow to actually measure fracture toughness. 00:53:45.830 --> 00:53:48.910 align:middle line:84% To measure fracture toughness, because the definition 00:53:48.910 --> 00:53:51.470 align:middle line:84% of the fracture stress, it has to do 00:53:51.470 --> 00:53:55.230 align:middle line:84% with the length of the crack, so to precisely measure fracture 00:53:55.230 --> 00:53:59.030 align:middle line:84% toughness you need to find ways to actually generate cracks 00:53:59.030 --> 00:54:02.070 align:middle line:90% with a predefined length. 00:54:02.070 --> 00:54:05.990 align:middle line:84% And that's why people designed these specific sample geometries 00:54:05.990 --> 00:54:08.910 align:middle line:84% just to generate cracks with a specific length. 00:54:08.910 --> 00:54:10.910 align:middle line:84% So for example, if you look at this one here, 00:54:10.910 --> 00:54:12.490 align:middle line:90% it's a sample with a notch. 00:54:12.490 --> 00:54:14.510 align:middle line:84% You prepare this sample with a notch. 00:54:14.510 --> 00:54:16.630 align:middle line:84% And then at the tip of the notch, 00:54:16.630 --> 00:54:21.470 align:middle line:84% you then use static fatigue to generate a crack. 00:54:21.470 --> 00:54:23.750 align:middle line:84% You have to look at it under an optical microscope 00:54:23.750 --> 00:54:25.150 align:middle line:84% to essentially look at the correct length 00:54:25.150 --> 00:54:27.192 align:middle line:84% to ensure that when, you actually do the testing, 00:54:27.192 --> 00:54:31.230 align:middle line:84% the correct length is exactly at what we specified. 00:54:31.230 --> 00:54:34.550 align:middle line:84% So you can see that this is a pretty laborious process, just 00:54:34.550 --> 00:54:36.670 align:middle line:84% to do a fracture toughness testing, if you want 00:54:36.670 --> 00:54:39.340 align:middle line:90% to comply with ASTM standards. 00:54:39.340 --> 00:54:41.380 align:middle line:84% You have to essentially prepare a sample, 00:54:41.380 --> 00:54:44.015 align:middle line:84% wait 'til the crack goes to the desired length. 00:54:44.015 --> 00:54:46.140 align:middle line:84% And you also have to do active monitoring to ensure 00:54:46.140 --> 00:54:47.182 align:middle line:90% that's actually the case. 00:54:47.182 --> 00:54:48.900 align:middle line:84% Then once you have this sample, you 00:54:48.900 --> 00:54:50.320 align:middle line:84% can put it into a loading machine. 00:54:50.320 --> 00:54:52.140 align:middle line:84% You can measure the load displacement curve. 00:54:52.140 --> 00:54:54.390 align:middle line:84% From that, you can actually infer the stress toughness 00:54:54.390 --> 00:54:55.980 align:middle line:90% of the material here. 00:54:55.980 --> 00:54:58.680 align:middle line:84% Now, as I have already mentioned, 00:54:58.680 --> 00:55:00.797 align:middle line:84% this can be a pretty complicated process. 00:55:00.797 --> 00:55:02.880 align:middle line:84% It's quite difficult to comply with the standards. 00:55:02.880 --> 00:55:07.380 align:middle line:84% So that's why people have also come up with simpler methods 00:55:07.380 --> 00:55:10.420 align:middle line:84% to infer what is the fracture toughness of materials 00:55:10.420 --> 00:55:13.460 align:middle line:84% using techniques-- for example, as an indentation. 00:55:13.460 --> 00:55:18.420 align:middle line:84% So indentation essentially means that you have a stylus. 00:55:18.420 --> 00:55:20.380 align:middle line:90% The stylus has some kind of tip. 00:55:20.380 --> 00:55:22.660 align:middle line:84% You then press it against your material. 00:55:22.660 --> 00:55:24.500 align:middle line:90% And then you apply a load. 00:55:24.500 --> 00:55:26.660 align:middle line:84% Then this is going to press the stylus, which 00:55:26.660 --> 00:55:29.900 align:middle line:84% is made of some kind of hard material, into your material. 00:55:29.900 --> 00:55:31.840 align:middle line:84% And then once you remove the load, 00:55:31.840 --> 00:55:34.260 align:middle line:84% it's then going to cause some crack. 00:55:34.260 --> 00:55:35.975 align:middle line:84% From the crack propagation behavior, 00:55:35.975 --> 00:55:37.600 align:middle line:84% you can then use that to actually infer 00:55:37.600 --> 00:55:39.558 align:middle line:84% what is the fracture toughness of the material. 00:55:39.558 --> 00:55:42.512 align:middle line:90% 00:55:42.512 --> 00:55:45.460 align:middle line:84% The downside with this kind of indentation method, 00:55:45.460 --> 00:55:49.800 align:middle line:84% while being very simple, is that sometimes it's a bit more 00:55:49.800 --> 00:55:51.160 align:middle line:90% on the empirical side. 00:55:51.160 --> 00:55:55.000 align:middle line:84% The correlation of the data you collected using indentation 00:55:55.000 --> 00:55:56.760 align:middle line:84% does not correlate always very well 00:55:56.760 --> 00:56:00.100 align:middle line:84% with the data you get from the standard ASTM measurements. 00:56:00.100 --> 00:56:01.700 align:middle line:90% So take with a grain of sand. 00:56:01.700 --> 00:56:04.280 align:middle line:84% If you see people reporting fracture toughness values 00:56:04.280 --> 00:56:07.200 align:middle line:84% using these indentation samples, there 00:56:07.200 --> 00:56:10.880 align:middle line:84% can be considerable dispersion based on the specific details 00:56:10.880 --> 00:56:12.120 align:middle line:90% of the measurement. 00:56:12.120 --> 00:56:15.020 align:middle line:84% But just to show you one example here-- 00:56:15.020 --> 00:56:17.992 align:middle line:84% I mean, there can be different tip designs. 00:56:17.992 --> 00:56:20.200 align:middle line:84% This is a Hertziqan tip, which is basically a sphere. 00:56:20.200 --> 00:56:22.380 align:middle line:84% This is the more commonly used Vickers indenter tip. 00:56:22.380 --> 00:56:24.800 align:middle line:90% It has pyramidal geometry. 00:56:24.800 --> 00:56:27.280 align:middle line:84% So if you press one of these Vickers tips 00:56:27.280 --> 00:56:30.160 align:middle line:84% against a glass sample, let's see what happens. 00:56:30.160 --> 00:56:31.760 align:middle line:84% So what I'm showing you here, this 00:56:31.760 --> 00:56:35.690 align:middle line:84% is actually a few optical microscopic images showing you 00:56:35.690 --> 00:56:38.510 align:middle line:84% essentially this is the pit or the dent 00:56:38.510 --> 00:56:42.390 align:middle line:84% that's caused by this stylus on the glass surface. 00:56:42.390 --> 00:56:43.990 align:middle line:90% This is during loading. 00:56:43.990 --> 00:56:47.370 align:middle line:90% And this after unloading. 00:56:47.370 --> 00:56:50.090 align:middle line:84% So the first one, this is during loading cycle. 00:56:50.090 --> 00:56:52.630 align:middle line:84% This is 50% of the maximum force applied. 00:56:52.630 --> 00:56:54.510 align:middle line:90% This is at full load. 00:56:54.510 --> 00:56:58.730 align:middle line:84% This is when you start to essentially release the stylus. 00:56:58.730 --> 00:57:01.630 align:middle line:84% And this is after complete unloading. 00:57:01.630 --> 00:57:04.950 align:middle line:84% Now, what you notice here is that, during the loading cycle, 00:57:04.950 --> 00:57:08.670 align:middle line:84% the dent increases in size because the stylus essentially 00:57:08.670 --> 00:57:10.370 align:middle line:84% gets pressed against the sample wall. 00:57:10.370 --> 00:57:12.310 align:middle line:90% But there's no crack formation. 00:57:12.310 --> 00:57:16.430 align:middle line:84% The crack only starts to nucleate when 00:57:16.430 --> 00:57:19.830 align:middle line:90% you start to unload the stylus. 00:57:19.830 --> 00:57:21.950 align:middle line:84% This is quite typical for glass samples. 00:57:21.950 --> 00:57:24.070 align:middle line:84% Glass samples, typically, they don't fracture 00:57:24.070 --> 00:57:25.830 align:middle line:90% under compressive stress. 00:57:25.830 --> 00:57:28.930 align:middle line:84% They fracture when you have essentially a tensile stress. 00:57:28.930 --> 00:57:31.402 align:middle line:90% 00:57:31.402 --> 00:57:33.860 align:middle line:84% Now, you may wonder where the tensile stress is coming here 00:57:33.860 --> 00:57:35.240 align:middle line:84% in this kind of compressive test. 00:57:35.240 --> 00:57:38.740 align:middle line:84% So what actually happens is that a glass material, when 00:57:38.740 --> 00:57:40.440 align:middle line:84% you actually compress against it, 00:57:40.440 --> 00:57:44.860 align:middle line:84% it will deform both elastically and plastically. 00:57:44.860 --> 00:57:48.900 align:middle line:84% So when you start to unload, the part that deforms elastically 00:57:48.900 --> 00:57:51.660 align:middle line:84% is going to try to restore its original geometry. 00:57:51.660 --> 00:57:55.500 align:middle line:84% But the part that has deformed plastically, 00:57:55.500 --> 00:57:58.500 align:middle line:84% it will try to keep the original shape, the deformed shape. 00:57:58.500 --> 00:58:03.060 align:middle line:84% So then the mismatch between the plastic deformed regions 00:58:03.060 --> 00:58:05.300 align:middle line:84% and elastically deformed regions then 00:58:05.300 --> 00:58:08.100 align:middle line:84% will lead to essentially this fracture and the crack 00:58:08.100 --> 00:58:09.180 align:middle line:90% propagation. 00:58:09.180 --> 00:58:13.380 align:middle line:84% So that's why you see the crack formation during unloading cycle 00:58:13.380 --> 00:58:15.820 align:middle line:90% because of this mismatch here. 00:58:15.820 --> 00:58:17.680 align:middle line:84% And you can clearly see the crack propagate 00:58:17.680 --> 00:58:20.220 align:middle line:84% in this kind of a crisscross pattern corresponding 00:58:20.220 --> 00:58:22.320 align:middle line:84% to the four corners of the Vickers tip. 00:58:22.320 --> 00:58:24.060 align:middle line:84% This is where you have high stress there. 00:58:24.060 --> 00:58:27.180 align:middle line:84% And then from the size and shape of these cracks, 00:58:27.180 --> 00:58:28.980 align:middle line:84% you can use that to infer the fracture 00:58:28.980 --> 00:58:30.920 align:middle line:90% toughness of the material. 00:58:30.920 --> 00:58:32.750 align:middle line:84% So that's basically the idea there. 00:58:32.750 --> 00:58:36.185 align:middle line:90% 00:58:36.185 --> 00:58:38.810 align:middle line:84% One thing I also want to mention about this kind of measurement 00:58:38.810 --> 00:58:42.410 align:middle line:84% here is that, because the glass's fracture toughness 00:58:42.410 --> 00:58:45.770 align:middle line:84% depends on the length of the crack. 00:58:45.770 --> 00:58:48.690 align:middle line:84% So it means that any kind of fracture toughness measurement 00:58:48.690 --> 00:58:51.970 align:middle line:90% is inherently statistical. 00:58:51.970 --> 00:58:53.850 align:middle line:84% For different glass samples, even 00:58:53.850 --> 00:58:56.690 align:middle line:84% if they are prepared normally using the same technique, 00:58:56.690 --> 00:59:00.650 align:middle line:84% the distribution of the defect size is statistical. 00:59:00.650 --> 00:59:01.930 align:middle line:90% It's random. 00:59:01.930 --> 00:59:04.970 align:middle line:84% And the ultimate strength of a glass sample 00:59:04.970 --> 00:59:09.610 align:middle line:84% actually is determined by the longest crack, the longest crack 00:59:09.610 --> 00:59:11.730 align:middle line:84% corresponding to the weakest link. 00:59:11.730 --> 00:59:17.290 align:middle line:84% Now, the maximum crack length is a statistical parameter 00:59:17.290 --> 00:59:19.930 align:middle line:84% in different glass samples, even if they are prepared nominally 00:59:19.930 --> 00:59:21.810 align:middle line:90% using identical conditions. 00:59:21.810 --> 00:59:24.690 align:middle line:84% So that's why, when you actually try 00:59:24.690 --> 00:59:27.370 align:middle line:84% to measure fracture toughness, you should not only just measure 00:59:27.370 --> 00:59:28.670 align:middle line:90% one single glass sample. 00:59:28.670 --> 00:59:31.360 align:middle line:84% You should always measure a large group of glass samples 00:59:31.360 --> 00:59:33.760 align:middle line:84% and look at the statistical distribution of the fracture 00:59:33.760 --> 00:59:35.700 align:middle line:90% toughness. 00:59:35.700 --> 00:59:37.040 align:middle line:90% So that's the way to go. 00:59:37.040 --> 00:59:40.280 align:middle line:84% And that's why people have also developed all kinds of fracture 00:59:40.280 --> 00:59:45.320 align:middle line:84% statistics methods looking into the distribution of fracture 00:59:45.320 --> 00:59:46.700 align:middle line:90% toughness in glass samples. 00:59:46.700 --> 00:59:49.800 align:middle line:84% So the most commonly used distribution, this 00:59:49.800 --> 00:59:51.720 align:middle line:84% is called the Weibull distribution. 00:59:51.720 --> 00:59:54.960 align:middle line:84% What this function describes is the so-called cumulative failure 00:59:54.960 --> 00:59:56.560 align:middle line:90% probability. 00:59:56.560 --> 00:59:59.960 align:middle line:84% Essentially, what it says is that F gives you 00:59:59.960 --> 01:00:02.080 align:middle line:84% the fraction of samples that fractures 01:00:02.080 --> 01:00:04.800 align:middle line:90% at stresses below sigma. 01:00:04.800 --> 01:00:07.520 align:middle line:84% So now, if you think about the ideal case, 01:00:07.520 --> 01:00:09.680 align:middle line:84% if there's no distribution, there's 01:00:09.680 --> 01:00:11.520 align:middle line:84% no statistical distribution, all the samples 01:00:11.520 --> 01:00:13.840 align:middle line:84% are exactly identical, they should all 01:00:13.840 --> 01:00:15.880 align:middle line:90% fail under the same stress. 01:00:15.880 --> 01:00:19.760 align:middle line:84% So in that case, in the ideal scenario, 01:00:19.760 --> 01:00:25.000 align:middle line:84% then the curve will basically be a step function. 01:00:25.000 --> 01:00:28.430 align:middle line:84% Below the fracture strength, nothing is going to break. 01:00:28.430 --> 01:00:32.070 align:middle line:84% Above it, all, your pieces are going to break. 01:00:32.070 --> 01:00:33.510 align:middle line:84% That would be the ideal scenario. 01:00:33.510 --> 01:00:37.310 align:middle line:84% Now, obviously, because of the statistical nature 01:00:37.310 --> 01:00:39.750 align:middle line:84% of a glass failure, what you end up 01:00:39.750 --> 01:00:42.550 align:middle line:84% getting is this kind of sloped function there. 01:00:42.550 --> 01:00:45.570 align:middle line:84% And this function here, this so-called Weibull modulus, 01:00:45.570 --> 01:00:48.150 align:middle line:84% the exponent here, and then characterizes 01:00:48.150 --> 01:00:50.310 align:middle line:90% how steep this diffusion is. 01:00:50.310 --> 01:00:52.110 align:middle line:84% A larger Weibull modulus corresponds 01:00:52.110 --> 01:00:53.990 align:middle line:90% to a more tighter distribution. 01:00:53.990 --> 01:00:56.230 align:middle line:84% So a large Weibull modulus essentially 01:00:56.230 --> 01:01:00.270 align:middle line:84% means that you have a better control over the quality 01:01:00.270 --> 01:01:00.930 align:middle line:90% of your sample. 01:01:00.930 --> 01:01:02.430 align:middle line:84% You have a more tighter distribution 01:01:02.430 --> 01:01:06.330 align:middle line:90% of its fracture strength. 01:01:06.330 --> 01:01:08.270 align:middle line:84% So that's one way to characterize 01:01:08.270 --> 01:01:12.190 align:middle line:84% this kind of statistical behavior of glass fracturing. 01:01:12.190 --> 01:01:14.850 align:middle line:84% Alternatively, you can also use a probability density. 01:01:14.850 --> 01:01:17.550 align:middle line:84% You take the derivative of F with respect to sigma. 01:01:17.550 --> 01:01:19.950 align:middle line:84% What it gives you is then the probability of sample 01:01:19.950 --> 01:01:22.390 align:middle line:84% to fracture at a particular stress level. 01:01:22.390 --> 01:01:25.510 align:middle line:84% So if you go to your ideal sample, 01:01:25.510 --> 01:01:27.660 align:middle line:84% then what you have here for this probability 01:01:27.660 --> 01:01:29.460 align:middle line:90% is going to be a delta function. 01:01:29.460 --> 01:01:32.980 align:middle line:84% All the samples should break right at the fracture stress. 01:01:32.980 --> 01:01:36.020 align:middle line:84% So if you have a statistical distribution, 01:01:36.020 --> 01:01:38.240 align:middle line:84% then the delta function broadens into a peak. 01:01:38.240 --> 01:01:40.260 align:middle line:84% Same thing, higher Weibull modulus 01:01:40.260 --> 01:01:41.760 align:middle line:84% gives you a tighter distribution. 01:01:41.760 --> 01:01:43.180 align:middle line:84% It means that you have a better control 01:01:43.180 --> 01:01:44.520 align:middle line:90% over the quality of the sample. 01:01:44.520 --> 01:01:47.500 align:middle line:90% 01:01:47.500 --> 01:01:49.980 align:middle line:84% So now, if you actually go and do a project 01:01:49.980 --> 01:01:53.160 align:middle line:84% and try to measure the statistics of glass fracturing, 01:01:53.160 --> 01:01:54.960 align:middle line:84% how would you actually process the data? 01:01:54.960 --> 01:01:57.660 align:middle line:84% So what you do is you essentially 01:01:57.660 --> 01:02:00.020 align:middle line:84% prepare a large number of samples 01:02:00.020 --> 01:02:02.220 align:middle line:84% nominally under the same condition. 01:02:02.220 --> 01:02:05.440 align:middle line:84% You subject all of them under this tensile stress test 01:02:05.440 --> 01:02:08.220 align:middle line:84% and recall what the stress they feel. 01:02:08.220 --> 01:02:11.260 align:middle line:84% Then from that, you can then try to fit this function here 01:02:11.260 --> 01:02:13.980 align:middle line:84% by essentially using essentially a slightly different form 01:02:13.980 --> 01:02:15.080 align:middle line:90% of this function. 01:02:15.080 --> 01:02:17.100 align:middle line:90% You try to fit this function. 01:02:17.100 --> 01:02:19.200 align:middle line:84% You essentially apply a double logarithm. 01:02:19.200 --> 01:02:21.980 align:middle line:84% You can transform it into this form here. 01:02:21.980 --> 01:02:26.090 align:middle line:84% Now, the beauty of using this form of the function 01:02:26.090 --> 01:02:32.610 align:middle line:84% is that now, if you plot this double logarithm of 1 minus F 01:02:32.610 --> 01:02:37.730 align:middle line:84% as a function of logarithm sigma, the slope of the curve 01:02:37.730 --> 01:02:40.010 align:middle line:90% will then give you m. 01:02:40.010 --> 01:02:43.410 align:middle line:84% And then the intersection of the curve with horizontal axis, 01:02:43.410 --> 01:02:46.510 align:middle line:84% this corresponds to essentially sigma equal to sigma 0, 01:02:46.510 --> 01:02:52.010 align:middle line:84% where sigma 0 gives you the average failure stress. 01:02:52.010 --> 01:02:55.210 align:middle line:84% So by plotting your theta on this curve here, 01:02:55.210 --> 01:02:58.330 align:middle line:84% you can then infer what is the Weibull modulus, as well 01:02:58.330 --> 01:03:00.970 align:middle line:84% as your average failure stress of the material. 01:03:00.970 --> 01:03:04.170 align:middle line:90% 01:03:04.170 --> 01:03:06.450 align:middle line:84% So in the bottom right corner here, 01:03:06.450 --> 01:03:09.450 align:middle line:84% I'm showing one example I quoted from literature. 01:03:09.450 --> 01:03:11.850 align:middle line:84% This is actually measurements for four different sets 01:03:11.850 --> 01:03:13.730 align:middle line:90% of samples here. 01:03:13.730 --> 01:03:16.470 align:middle line:84% You can see that, for three groups of samples, 01:03:16.470 --> 01:03:21.470 align:middle line:84% the first three groups, you get a reasonably good linear fit, 01:03:21.470 --> 01:03:24.110 align:middle line:84% which allows you to infer the Weibull modulus 01:03:24.110 --> 01:03:26.150 align:middle line:84% and the average fracture strength. 01:03:26.150 --> 01:03:30.790 align:middle line:84% Now, this last group, D here, is a bit peculiar 01:03:30.790 --> 01:03:33.030 align:middle line:84% because you see there's a very clear inflection 01:03:33.030 --> 01:03:36.830 align:middle line:84% point where the line essentially changes slope. 01:03:36.830 --> 01:03:39.590 align:middle line:84% So what this indicates is that you have essentially 01:03:39.590 --> 01:03:42.350 align:middle line:90% a bimodal diffusion of defects. 01:03:42.350 --> 01:03:45.390 align:middle line:84% In some samples, you see that, if you extend this line, 01:03:45.390 --> 01:03:47.710 align:middle line:84% you intersect with the horizontal axis 01:03:47.710 --> 01:03:49.210 align:middle line:90% with a different sigma 0. 01:03:49.210 --> 01:03:52.990 align:middle line:84% So different sigma 0 essentially means that these samples tend 01:03:52.990 --> 01:03:54.970 align:middle line:90% to have this bimodal behavior. 01:03:54.970 --> 01:03:56.830 align:middle line:84% You have two groups, two subgroups, 01:03:56.830 --> 01:04:02.270 align:middle line:84% where each of the groups has a distinctive average fracture 01:04:02.270 --> 01:04:02.890 align:middle line:90% strength. 01:04:02.890 --> 01:04:06.340 align:middle line:90% 01:04:06.340 --> 01:04:09.285 align:middle line:84% So that just means that you need to essentially look 01:04:09.285 --> 01:04:11.410 align:middle line:84% a little bit more in the processing of that sample. 01:04:11.410 --> 01:04:12.590 align:middle line:84% There's some kind of inconsistency 01:04:12.590 --> 01:04:14.298 align:middle line:84% there that generates-- possibly generates 01:04:14.298 --> 01:04:16.990 align:middle line:84% essentially larger defects in some subgroup of samples 01:04:16.990 --> 01:04:18.750 align:middle line:90% over the others. 01:04:18.750 --> 01:04:21.150 align:middle line:84% So this is also a good way for you 01:04:21.150 --> 01:04:23.660 align:middle line:84% to gauge about the consistency of your process 01:04:23.660 --> 01:04:25.680 align:middle line:84% and how reproducible your process is, 01:04:25.680 --> 01:04:28.680 align:middle line:84% in terms of generating a defect of certain size. 01:04:28.680 --> 01:04:32.460 align:middle line:90% 01:04:32.460 --> 01:04:33.920 align:middle line:90% Does that make sense? 01:04:33.920 --> 01:04:39.620 align:middle line:90% 01:04:39.620 --> 01:04:40.240 align:middle line:90% All right. 01:04:40.240 --> 01:04:44.400 align:middle line:84% So this is so much about the basic theory about fracturing. 01:04:44.400 --> 01:04:46.793 align:middle line:84% I'm not going to go through a bullet point list here. 01:04:46.793 --> 01:04:48.460 align:middle line:84% But the key point is that we essentially 01:04:48.460 --> 01:04:51.157 align:middle line:84% discussed about why the material strength is much lower 01:04:51.157 --> 01:04:52.240 align:middle line:90% than theoretical strength. 01:04:52.240 --> 01:04:53.782 align:middle line:84% We talked about the role of the crack 01:04:53.782 --> 01:04:56.620 align:middle line:84% in lowering the theoretical strength, as well 01:04:56.620 --> 01:05:00.100 align:middle line:84% as the role of stress corrosion that 01:05:00.100 --> 01:05:02.760 align:middle line:84% can play in the subcritical crack growth. 01:05:02.760 --> 01:05:08.940 align:middle line:84% The key takeaway point here is that the weakest 01:05:08.940 --> 01:05:13.180 align:middle line:84% link in glass material usually tends to be a surface. 01:05:13.180 --> 01:05:15.740 align:middle line:84% The surface is where you come into contact with all kinds 01:05:15.740 --> 01:05:17.100 align:middle line:90% of [? enemy ?] environments. 01:05:17.100 --> 01:05:19.180 align:middle line:84% You can have mechanical abrasion. 01:05:19.180 --> 01:05:21.665 align:middle line:84% You can have essentially water condensation. 01:05:21.665 --> 01:05:24.290 align:middle line:84% So you tend to have the highest density of defects on the glass 01:05:24.290 --> 01:05:25.250 align:middle line:90% surface. 01:05:25.250 --> 01:05:27.570 align:middle line:84% And when the glass fails, those surface defects 01:05:27.570 --> 01:05:30.330 align:middle line:84% are usually where the crack nucleates. 01:05:30.330 --> 01:05:32.970 align:middle line:84% So if you want to strengthen the glass material, what 01:05:32.970 --> 01:05:35.810 align:middle line:84% you have to do is try to find ways to essentially 01:05:35.810 --> 01:05:38.490 align:middle line:84% either eliminate those defects or to find 01:05:38.490 --> 01:05:41.970 align:middle line:84% ways to prevent the crack propagation from the surface. 01:05:41.970 --> 01:05:45.690 align:middle line:84% So that's what we are going to cover in this application 01:05:45.690 --> 01:05:47.930 align:middle line:84% section here where we talk about practical ways 01:05:47.930 --> 01:05:50.210 align:middle line:84% how people actually strengthen glass. 01:05:50.210 --> 01:05:55.370 align:middle line:84% So strengthened glasses, they have 01:05:55.370 --> 01:05:57.690 align:middle line:90% many practical applications. 01:05:57.690 --> 01:06:00.490 align:middle line:84% They can be applied in, for example, solar panels, which 01:06:00.490 --> 01:06:02.115 align:middle line:84% is the one good example where you 01:06:02.115 --> 01:06:04.490 align:middle line:84% need to have glass materials that's not only transparent, 01:06:04.490 --> 01:06:06.115 align:middle line:84% but also have good mechanical strength. 01:06:06.115 --> 01:06:10.410 align:middle line:84% They can withstand all kinds of natural weathering and even 01:06:10.410 --> 01:06:12.450 align:middle line:84% extreme weather conditions like hail. 01:06:12.450 --> 01:06:14.410 align:middle line:84% They cannot break under extreme conditions. 01:06:14.410 --> 01:06:15.870 align:middle line:90% Display is the same story. 01:06:15.870 --> 01:06:18.130 align:middle line:84% People are always looking for stronger display glass. 01:06:18.130 --> 01:06:20.160 align:middle line:84% And there's also a trade-off there. 01:06:20.160 --> 01:06:22.200 align:middle line:84% For display, people also like to use glasses 01:06:22.200 --> 01:06:24.640 align:middle line:84% with smaller thickness, which reduces weight. 01:06:24.640 --> 01:06:27.240 align:middle line:84% And smaller thickness obviously creates a compromise 01:06:27.240 --> 01:06:29.200 align:middle line:84% in the mechanical overall strength. 01:06:29.200 --> 01:06:32.200 align:middle line:84% So how to enhance the glass strength 01:06:32.200 --> 01:06:34.120 align:middle line:84% while reducing the weight is a big topic 01:06:34.120 --> 01:06:36.480 align:middle line:90% in that kind of applications. 01:06:36.480 --> 01:06:38.320 align:middle line:84% The glass material can be so strong 01:06:38.320 --> 01:06:42.040 align:middle line:84% that people even apply them for defense applications. 01:06:42.040 --> 01:06:44.643 align:middle line:84% The windows on tanks, for example, 01:06:44.643 --> 01:06:46.560 align:middle line:84% they are actually made of strengthened glasses 01:06:46.560 --> 01:06:49.360 align:middle line:84% so that they can actually be bulletproof. 01:06:49.360 --> 01:06:51.368 align:middle line:84% So we're going to discuss about strategies how 01:06:51.368 --> 01:06:53.660 align:middle line:84% to increase the mechanical strength of glass materials, 01:06:53.660 --> 01:06:58.240 align:middle line:84% so they can resist projectiles like bullets. 01:06:58.240 --> 01:06:58.880 align:middle line:90% OK. 01:06:58.880 --> 01:07:01.520 align:middle line:84% So this slide essentially summarizes, 01:07:01.520 --> 01:07:04.280 align:middle line:84% at a high level, what are the different strategies how 01:07:04.280 --> 01:07:08.160 align:middle line:84% you enhance the strength of glass materials. 01:07:08.160 --> 01:07:11.240 align:middle line:84% Three different ways-- you can look at 01:07:11.240 --> 01:07:15.480 align:middle line:84% essentially-- goes back and look at what we have here. 01:07:15.480 --> 01:07:23.790 align:middle line:84% So you want to maximize sigma F. What you can do, 01:07:23.790 --> 01:07:27.590 align:middle line:84% you can either increase your K1c-- 01:07:27.590 --> 01:07:30.750 align:middle line:84% if you increase your K1c, you improve your glass material 01:07:30.750 --> 01:07:34.870 align:middle line:84% so it inherently becomes more resistant to crack propagation. 01:07:34.870 --> 01:07:37.870 align:middle line:84% So you can change your glass chemical formulae 01:07:37.870 --> 01:07:40.510 align:middle line:84% to essentially enhance this ability 01:07:40.510 --> 01:07:41.810 align:middle line:90% to resist crack propagation. 01:07:41.810 --> 01:07:44.643 align:middle line:90% That's one way. 01:07:44.643 --> 01:07:49.870 align:middle line:84% What you can also do is that you can reduce the defect density 01:07:49.870 --> 01:07:51.270 align:middle line:90% or reduce defect severity. 01:07:51.270 --> 01:07:52.645 align:middle line:84% It essentially means that you try 01:07:52.645 --> 01:07:57.710 align:middle line:84% to minimize the generation of any long cracks on the surface. 01:07:57.710 --> 01:08:02.690 align:middle line:84% Because K1 scales with square root of the correct length, 01:08:02.690 --> 01:08:04.390 align:middle line:84% so effectively you are reducing K1 01:08:04.390 --> 01:08:07.930 align:middle line:84% and, therefore, enhancing the longevity of the glass material. 01:08:07.930 --> 01:08:10.650 align:middle line:84% So you can eliminate surface defects. 01:08:10.650 --> 01:08:11.790 align:middle line:90% That's another way. 01:08:11.790 --> 01:08:19.060 align:middle line:84% The third way here is to prevent the crack propagation. 01:08:19.060 --> 01:08:21.540 align:middle line:84% Even if you try all the methods you 01:08:21.540 --> 01:08:23.460 align:middle line:84% talk about in the second example here, 01:08:23.460 --> 01:08:26.460 align:middle line:84% it's very difficult to still completely eliminate 01:08:26.460 --> 01:08:28.180 align:middle line:90% any kind of surface defects. 01:08:28.180 --> 01:08:30.180 align:middle line:84% So a very common way to enhance the strength 01:08:30.180 --> 01:08:33.260 align:middle line:84% is to introduce essentially a surface compressive stress. 01:08:33.260 --> 01:08:36.460 align:middle line:84% So even if there are some defects or cracks that's already 01:08:36.460 --> 01:08:39.300 align:middle line:84% happening on the surface, this compressive stress 01:08:39.300 --> 01:08:41.702 align:middle line:84% will try to keep the crack closed 01:08:41.702 --> 01:08:43.660 align:middle line:84% so that it doesn't propagate and, therefore, it 01:08:43.660 --> 01:08:44.700 align:middle line:90% doesn't lead to failure. 01:08:44.700 --> 01:08:46.979 align:middle line:84% So these are the three general strategies 01:08:46.979 --> 01:08:49.740 align:middle line:84% how to actually enhance the strength of glass materials. 01:08:49.740 --> 01:08:51.920 align:middle line:84% Now, for the first one, for example, 01:08:51.920 --> 01:08:53.859 align:middle line:90% you can do crystallization. 01:08:53.859 --> 01:08:57.060 align:middle line:84% Surface crystallization helps in several different ways. 01:08:57.060 --> 01:08:59.700 align:middle line:84% First of all is that the crystalline material, which 01:08:59.700 --> 01:09:01.899 align:middle line:84% is basically ceramics, they can mechanically 01:09:01.899 --> 01:09:03.399 align:middle line:90% be more stronger than glass. 01:09:03.399 --> 01:09:05.580 align:middle line:90% So that actually helps. 01:09:05.580 --> 01:09:09.140 align:middle line:84% And also, the material you crystallize in this manner 01:09:09.140 --> 01:09:11.180 align:middle line:84% here, starting from glass, this is actually 01:09:11.180 --> 01:09:12.500 align:middle line:90% called glass ceramics. 01:09:12.500 --> 01:09:15.470 align:middle line:84% Glass ceramics can also have superior mechanical properties 01:09:15.470 --> 01:09:17.270 align:middle line:84% sometimes, even compared to ceramics, 01:09:17.270 --> 01:09:19.489 align:middle line:84% you prefer using traditional methods, which 01:09:19.489 --> 01:09:21.177 align:middle line:90% is basically sintering. 01:09:21.177 --> 01:09:23.010 align:middle line:84% The advantage of this kind of glass ceramics 01:09:23.010 --> 01:09:25.410 align:middle line:84% is that you're starting from a completely dense matrix. 01:09:25.410 --> 01:09:28.529 align:middle line:84% Glass is essentially a pore-free matrix. 01:09:28.529 --> 01:09:29.550 align:middle line:90% It's not porous. 01:09:29.550 --> 01:09:32.265 align:middle line:84% Unlike the case of sintering, you start from a powder. 01:09:32.265 --> 01:09:33.890 align:middle line:84% Inevitably, there's always a little bit 01:09:33.890 --> 01:09:35.729 align:middle line:90% of air gap in your preform. 01:09:35.729 --> 01:09:39.410 align:middle line:84% So glass ceramics can give you a higher density compared 01:09:39.410 --> 01:09:42.170 align:middle line:84% to conventional sintering methods, which can sometimes 01:09:42.170 --> 01:09:44.890 align:middle line:84% translate to better mechanical properties. 01:09:44.890 --> 01:09:52.370 align:middle line:84% Also, crystallization can also change the surface stress. 01:09:52.370 --> 01:09:54.410 align:middle line:84% And this can be seen by essentially 01:09:54.410 --> 01:09:57.410 align:middle line:84% looking at the volume versus temperature curve. 01:09:57.410 --> 01:10:01.010 align:middle line:84% So if you think about this, the curve 01:10:01.010 --> 01:10:03.530 align:middle line:84% we have seen for many, many times-- this is temperature. 01:10:03.530 --> 01:10:05.150 align:middle line:90% This is volume. 01:10:05.150 --> 01:10:07.730 align:middle line:90% This is glass. 01:10:07.730 --> 01:10:12.010 align:middle line:84% This will be the corresponding ceramics. 01:10:12.010 --> 01:10:15.680 align:middle line:84% So if you heat up the material to some point 01:10:15.680 --> 01:10:18.600 align:middle line:84% here to crystallize it, the crystallization temperature 01:10:18.600 --> 01:10:20.120 align:middle line:90% will be above the TG. 01:10:20.120 --> 01:10:22.360 align:middle line:84% So then the volume change for glass 01:10:22.360 --> 01:10:25.280 align:middle line:84% will be given by essentially this vertical offset here. 01:10:25.280 --> 01:10:31.980 align:middle line:84% The volume change for ceramics, on the other hand, will be this. 01:10:31.980 --> 01:10:37.200 align:middle line:90% 01:10:37.200 --> 01:10:42.800 align:middle line:84% Sorry, the volume change for ceramics 01:10:42.800 --> 01:10:47.000 align:middle line:84% will be this one because, once you introduce crystallization, 01:10:47.000 --> 01:10:49.760 align:middle line:84% at high temperature, the stress will be relieved. 01:10:49.760 --> 01:10:54.520 align:middle line:84% So what's causing the ultimate change of volume, 01:10:54.520 --> 01:10:57.960 align:middle line:84% when you actually cool it down, will be the volume contraction 01:10:57.960 --> 01:10:59.800 align:middle line:90% due to the thermal expansion. 01:10:59.800 --> 01:11:04.080 align:middle line:84% Now, this volume change is actually smaller for ceramics as 01:11:04.080 --> 01:11:07.440 align:middle line:90% compared to glass. 01:11:07.440 --> 01:11:11.220 align:middle line:84% So that means, because if you introduce, for example, 01:11:11.220 --> 01:11:13.950 align:middle line:84% crystallization on the surface of the glass materials, 01:11:13.950 --> 01:11:17.150 align:middle line:84% then the interior will contract more. 01:11:17.150 --> 01:11:21.310 align:middle line:90% The surface will contract less. 01:11:21.310 --> 01:11:23.150 align:middle line:84% So as a result, the surface will then 01:11:23.150 --> 01:11:24.710 align:middle line:90% be under compressive stress. 01:11:24.710 --> 01:11:26.830 align:middle line:84% And compressive stress will help to prevent 01:11:26.830 --> 01:11:28.310 align:middle line:90% opening of the cracks. 01:11:28.310 --> 01:11:31.270 align:middle line:84% So that's also one way, by introducing a surface 01:11:31.270 --> 01:11:33.390 align:middle line:84% crystallization, you can actually also introducing 01:11:33.390 --> 01:11:36.710 align:middle line:84% surface compressive stress and therefore improve 01:11:36.710 --> 01:11:38.790 align:middle line:90% the stability of the material. 01:11:38.790 --> 01:11:42.210 align:middle line:84% So that's why crystallization can sometimes help. 01:11:42.210 --> 01:11:44.110 align:middle line:84% The downside of crystallization, obviously, 01:11:44.110 --> 01:11:46.630 align:middle line:84% is that you lose some of the desirable properties of glass, 01:11:46.630 --> 01:11:47.790 align:middle line:90% like transparency. 01:11:47.790 --> 01:11:51.090 align:middle line:84% You can also change essentially-- you 01:11:51.090 --> 01:11:52.870 align:middle line:90% can also go to composites. 01:11:52.870 --> 01:11:54.820 align:middle line:84% Instead of using one layer of glass, 01:11:54.820 --> 01:11:57.070 align:middle line:84% you can combine it with other materials-- for example, 01:11:57.070 --> 01:11:58.030 align:middle line:90% with polymers. 01:11:58.030 --> 01:11:59.730 align:middle line:84% So you can take the best of both worlds, 01:11:59.730 --> 01:12:02.790 align:middle line:84% both the high strength of glass, as well as 01:12:02.790 --> 01:12:04.710 align:middle line:84% the ductility of the polymer materials 01:12:04.710 --> 01:12:06.870 align:middle line:90% to give you a better durability. 01:12:06.870 --> 01:12:09.050 align:middle line:84% You can also engineer glass structures, 01:12:09.050 --> 01:12:11.050 align:middle line:84% which I'm going to talk about in the next slide. 01:12:11.050 --> 01:12:13.390 align:middle line:84% Now, second general strategy here, 01:12:13.390 --> 01:12:15.970 align:middle line:84% you want to reduce the defect density. 01:12:15.970 --> 01:12:18.510 align:middle line:84% A common way of doing it is so-called fire polishing. 01:12:18.510 --> 01:12:22.690 align:middle line:90% 01:12:22.690 --> 01:12:24.930 align:middle line:84% Now, what I'm showing you on this photo here, 01:12:24.930 --> 01:12:28.850 align:middle line:84% this is a photo of a test tube, glass test tube. 01:12:28.850 --> 01:12:32.330 align:middle line:84% You probably notice that, for the glass test tube, which 01:12:32.330 --> 01:12:35.230 align:middle line:84% is basically made from cut glass tubes, 01:12:35.230 --> 01:12:39.010 align:middle line:90% the edge is usually smooth. 01:12:39.010 --> 01:12:42.270 align:middle line:90% It's rounded. 01:12:42.270 --> 01:12:46.850 align:middle line:84% The reason it's rounded is because, once it's freshly cut, 01:12:46.850 --> 01:12:50.430 align:middle line:84% they usually essentially basically fire it, 01:12:50.430 --> 01:12:52.130 align:middle line:90% subject it to high temperature. 01:12:52.130 --> 01:12:54.430 align:middle line:84% When you subject the surface to high temperature, 01:12:54.430 --> 01:12:57.190 align:middle line:84% essentially it goes beyond the glass transition point. 01:12:57.190 --> 01:12:58.750 align:middle line:90% It becomes a viscous fluid. 01:12:58.750 --> 01:13:00.410 align:middle line:90% It starts to flow a little bit. 01:13:00.410 --> 01:13:02.610 align:middle line:84% And because in this flow process you're 01:13:02.610 --> 01:13:04.690 align:middle line:84% going to fill in any surface cracks 01:13:04.690 --> 01:13:07.570 align:middle line:90% and create a smooth surface. 01:13:07.570 --> 01:13:09.620 align:middle line:84% And under the action of surface tension, 01:13:09.620 --> 01:13:14.360 align:middle line:84% you can create this smooth surface finish free of cracks. 01:13:14.360 --> 01:13:17.280 align:middle line:84% So that's one way to reduce surface defect density, just 01:13:17.280 --> 01:13:21.640 align:middle line:84% simply by using a viscous flow property of glass materials. 01:13:21.640 --> 01:13:23.062 align:middle line:90% You can also do surface etching. 01:13:23.062 --> 01:13:24.020 align:middle line:90% That's straightforward. 01:13:24.020 --> 01:13:26.360 align:middle line:84% You just etch away the surface layer, which brings away 01:13:26.360 --> 01:13:27.740 align:middle line:90% any kind of surface defects. 01:13:27.740 --> 01:13:29.400 align:middle line:84% You can also do a surface coating. 01:13:29.400 --> 01:13:30.520 align:middle line:84% We already talked about one example 01:13:30.520 --> 01:13:32.820 align:middle line:84% when we talk about essentially making glass containers. 01:13:32.820 --> 01:13:35.200 align:middle line:84% When you make glass containers, there are two surface coating 01:13:35.200 --> 01:13:37.660 align:middle line:84% steps-- [? hardened ?] coating and [? coolant ?] coating. 01:13:37.660 --> 01:13:40.840 align:middle line:84% [? Hardened ?] coating is essentially putting a tin 01:13:40.840 --> 01:13:41.483 align:middle line:90% coating there. 01:13:41.483 --> 01:13:43.400 align:middle line:84% And tin oxide has a higher mechanical strength 01:13:43.400 --> 01:13:45.000 align:middle line:84% compared to glass materials, which 01:13:45.000 --> 01:13:48.270 align:middle line:84% is beneficial to increase this abrasion resistance. 01:13:48.270 --> 01:13:50.020 align:middle line:84% You then put in the [? coolant ?] coating, 01:13:50.020 --> 01:13:53.200 align:middle line:84% which is a polymer layer, which serves as a lubricant that 01:13:53.200 --> 01:13:55.760 align:middle line:84% minimizes any risk of generating the surface 01:13:55.760 --> 01:13:57.840 align:middle line:84% defects due to essentially wear and tear. 01:13:57.840 --> 01:13:59.960 align:middle line:84% So that's another strategy there. 01:13:59.960 --> 01:14:01.685 align:middle line:84% And finally, we'll spend also a lot 01:14:01.685 --> 01:14:03.560 align:middle line:84% of time talking about compressive stress, two 01:14:03.560 --> 01:14:05.162 align:middle line:84% ways of generating compressive stress, 01:14:05.162 --> 01:14:07.120 align:middle line:84% either through thermal tempering or through ion 01:14:07.120 --> 01:14:09.830 align:middle line:84% exchange, or so-called chemical tempering process. 01:14:09.830 --> 01:14:11.805 align:middle line:84% Now, let me come back a little bit, 01:14:11.805 --> 01:14:13.430 align:middle line:84% start by talking a little bit about how 01:14:13.430 --> 01:14:16.030 align:middle line:90% to actually tailor the-- 01:14:16.030 --> 01:14:17.530 align:middle line:84% in fact, we are running out of time. 01:14:17.530 --> 01:14:19.815 align:middle line:90% So we'll probably stop here. 01:14:19.815 --> 01:14:21.190 align:middle line:84% In the next lecture, we are going 01:14:21.190 --> 01:14:23.050 align:middle line:84% to discuss about the specific strategies, 01:14:23.050 --> 01:14:25.110 align:middle line:84% how to follow through with three different ways 01:14:25.110 --> 01:14:28.330 align:middle line:84% to enhance the strength of glass materials. 01:14:28.330 --> 01:14:31.930 align:middle line:84% Any more questions for the lecture here? 01:14:31.930 --> 01:14:32.830 align:middle line:90% OK. 01:14:32.830 --> 01:14:36.460 align:middle line:90% Then let's stop here. 01:14:36.460 --> 01:16:06.000 align:middle line:90%