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학습트랜스크립트
00:00메canical properties of metals
00:02핸드폰 how to studycraft
00:05Hello students.
00:07Today we will study mechanical properties of metals.
00:12Our plan is very simple and clear.
00:15First we will ask, we just ask, stress and strain.
00:21That's the very beginning of this whole chapter.
00:24And why do engineers use these words like stress or strain instead of just load or deformation.
00:33Load means how much force is applied to that object.
00:39And then we will see how they are deformed.
00:44And then we learn elastic behavior, elastic behavior and plastic behavior.
00:50We will see when a permanent deformation starts and we will define yield strength and tensile strength.
00:59So in this chapter we learn a lot of new words and they look very similar to each other.
01:05So we have to be very careful for the meaning of the words.
01:10And we will also talk about ductility and toughness and also like resilience and hardness.
01:22And we will learn how to measure all these properties with a standard tense.
01:29And then later we introduce true stress and true strain which are more accurate at large deformation.
01:37Finally, we will discuss why measured properties vary from sample to sample.
01:45And how engineers design safety when there is uncertainty.
01:51And I will try to speak very slowly and use simple words and a few examples if possible.
02:01And if a point is important, I will repeat it again and again.
02:08If you have any questions and if my explanation is not clear, then please just send me an email.
02:17And then I will prepare another presentation file to explain in detail.
02:22Okay.
02:23Okay.
02:24Okay.
02:25Okay.
02:26The second slide is elastic deformation.
02:31The word itself is kind of a confusing word.
02:35A little bit.
02:36Like elastic.
02:37Elastic is easier to keep it in mind.
02:40But next one, like the comparative word is plastic deformation.
02:47And when we think about like plastic, that's like a flexible and also the word, I don't think the word itself has some sort of like permanent deformation containing words.
03:08But we will see, like the elastic deformation is reversible, that's the most important thing, like elastic means reversible.
03:20When we apply a small load, small load, not like a huge load, like a small load to a metal.
03:27So we already learned like metals are organized in the quite ordered way.
03:35And when we apply this small load, then atomic bonds will like stretch a little, like see, like they are highly packed.
03:46But now they have some stretch, like some distance between them.
03:51So it's not like, what is that, like a boundary or a crack, something, but they just stretch, bonds stretch.
04:01And then let's say we remove the load, unload, then what's going to happen?
04:08The bonds will return and the shape returns to the original shape.
04:13So in this picture, this ordered structure should be the same as this ordered structure.
04:22They are the same.
04:24In this case, we say like elastic deformation.
04:29On a stress-strain graph, we have, if we apply this one, but this one is also quite weird.
04:36We will see some sort of the change is expressed as a delta.
04:43And when we apply the force, and then how this delta can be changed, that is expressed this way.
04:51But normally, let's say if you are like a force to make a graph for this, like a change, depending on the force applied to that object.
05:05I will draw like this way, like a force is located on the X axis, and then how much it has been extended, that could be Y.
05:16But they are using, in this whole chapter, they are using the other way, force.
05:23And then the normal, like Y scale goes to the X scale.
05:28I really want you to figure out why.
05:33I will explain a little bit at the end of this chapter, but before that, you focus on the manipulation way too.
05:43Okay, this is called like some, like a Hooke's law.
05:47We will discuss over that in detail in the later slides too.
05:52So, this, like this, what is that slope, is later we will see like a E, that's young modulus value.
06:05If E is large, this is quite important to understand why this F is located here.
06:12If E is larger, for the same stress, for the same stress, that means, like a, the, it's, mmm, the elastic strain is smaller.
06:27In other words, a material with a big E is stiffer, stiffer.
06:37Right?
06:38Like I think of a steel ruler, that's the, whatever you, like it's tweezers or, um, but some sort of like a longer one, which can be flexible.
06:54The, so, um, it bends just a little under a small load.
07:02Right?
07:03Like we have a, uh, steel ruler, and then we apply a, a little bit force load, and then there is just a bend.
07:11That small bending is elastic, because if we remove that load, it goes back, it comes back.
07:19One more idea, in elastic behavior, like there is no permanent change, right?
07:25After unloading, the length, width, and shapes are the same as before.
07:32That's elastic deformation.
07:34Relatively, the next one is, um, plastic deformation.
07:42Plastic deformation.
07:43Still, we are talking about metals, right?
07:47Remember that.
07:48Plastic deformation is permanent.
07:50So, this is a keyword, compared to the previous slides.
07:55So, like, um, maybe this word does not, like, come to you right away.
08:02Because when we use, like, a plastic, plastic is a, um, kind of vinyl bag, or, um, rubber band, or many things.
08:15So, sometimes when we, like, uh, pull it out, and then just, uh, unload my force, and then it goes back.
08:25Right?
08:26But, that's not the meaning of plastic deformation here.
08:32So, uh, after we, like, pass the elastic region.
08:36So, here, so, we just saw that elastic region.
08:40So, it's, it, would you go back to this, right here?
08:44Like, it's, like, a straight, right?
08:47So, um, if we, we go over this region, then planes of atoms shear and move here.
08:55We learned about this, like, there are many different kinds of shear, and then some sort of axis to move that way.
09:04And then move, and then dislocations move through the crystal.
09:09Direction, or plane.
09:11When we unload from the plastic region, only the elastic part recovers.
09:19The plastic part still remains.
09:23During the loading, we first see elastic behavior.
09:28Elastic behavior first.
09:31And then plastic plus the elastic together.
09:40During unloading from the plastic region, then we follow a line that is almost parallel.
09:47It looks, like, very parallel to each other, together.
09:52They're almost parallel to the elastic slope.
09:55The remaining strain is called plastic strain.
10:00The words, like, uh, we, we have many words in this chapter, like, you have to memorize.
10:07Like, this delta is a change that is called, like, a strain.
10:12Okay?
10:13So, we will use that words in the next slide or something.
10:18A little bit, little.
10:19More and more.
10:20More and more.
10:21So, uh, let's say we have, like, a metal bar.
10:26We stretch a metal bar.
10:28Here, this is the metal bar.
10:30A stretch.
10:31Beyond its elastic limit, and it becomes longer.
10:36The size has been changed.
10:39Then, although it comes back a little bit, but still we have some permanent changes here.
10:46That's plastic deformation.
10:50Okay?
10:52And then, uh, here, like, uh, we have stress.
10:58What's your stress?
11:00Studying, or, uh, professors, friends, and, uh, boyfriend, girlfriend.
11:09So, uh, and that's, that's stress.
11:13Everything is stress.
11:15We have to get money instead of stress by working hard or something.
11:22Get a job.
11:24So, that kind of stress is pressing something or do that kind of, uh, the pressure elongation
11:36to the G direction.
11:38So, here, we have many stress.
11:41Here, tensile stress and shear stress.
11:45And, uh, this stress is expressed as this one, sigma.
11:51And then, here, like, shear stress is expressed as, like, tau.
11:58So, let's take a look at the left one first.
12:01So, uh, they are doing some, uh, uh, the force out to the object.
12:08And then, that is a force.
12:11So, T is, like, a tensile force.
12:14So, that goes to up and down direction.
12:18And that is applied to a certain area.
12:22So, most cases of upper, uh, occur in this kind of situation, right?
12:30You have some specimen or any object.
12:34And then, you pull up and down.
12:37That's some sort of elongation way, right?
12:40And then, the, that, uh, this sigma equals F sub T over A knot.
12:50That's an area.
12:52So, that unit has a newton divided by a square meter.
12:57And, uh, for shear stress, so, uh, I don't know, the, this is easy to understand.
13:07So, let's say we have a certain, uh, what is that, like, a dice, whatever.
13:13And then, we force this, like, a shear direction.
13:18So, the, this is parallel to the, the surface face.
13:23And then, we, if we have, so, this is tensile sub.
13:28And then, this is a shear direction.
13:30So, they are perpendicular to each other.
13:33So, let's say we have, like, a tofu-dubu.
13:37You know, when we have this kind of tofu-dubu.
13:42Then, let's say you, uh, put your hands on top of this, like, a, the, the face, the, the upper face.
13:50And then, move to this direction.
13:54Then, what's gonna happen?
13:55The tofu-dubu will be like, you know, we have a picture that, in the later slides.
14:02So, we will see that.
14:04That's shear stress.
14:06So, how much you pressed onto the, um, the same direction to the surface.
14:11That's, like, a, uh, stress.
14:15So, here, remember that, the stress has been expressed as a sigma here, right?
14:21So, we have many different kinds of expression in this chapter.
14:26So, you have to be familiar with them.
14:29So, take a look at many times, uh, take a look at them very often.
14:35So, you should be very familiar with those to get a high score for your final exam.
14:42Or, midterm exam, whatever.
14:50So, uh, here, common states of stress.
14:53So, I just explained some sort of stress.
14:56So, that's, like, a force.
14:58Then, uh, let's say we have some, some cable here.
15:02So, here, you know what it is?
15:05It's, um, the cable.
15:08Cable car.
15:09The cable is moving.
15:11You know, if you take a look at that cable, that's quite thick.
15:15And, um, it's, uh, wired.
15:18It's twisted wires.
15:20And then, uh, when it moves, then the force will be acting like this.
15:26Right?
15:27That's why it's, like, sometimes it turned off.
15:31If it's pressurizing inside, I don't think they have chance to be broken down.
15:38Right?
15:39So, it, it obviously goes out.
15:43And, uh, like, this is a simple tension.
15:47That's the way we have to consider this kind of tension.
15:51And, um, like, uh, there are many different kinds of tension.
15:56Like, in the case of torsion, that's very similar to what I explained for, like, tofu.
16:02So, this, like, uh, the dark plane can be pressed in that way.
16:08Then, what's gonna happen?
16:10We will see that in the later slides.
16:14I'm sorry.
16:15This way.
16:16This, this goes.
16:18I'm sorry.
16:19I'm not good at drawing.
16:21So, uh, the tau can be expressed as, like, a force divided by the A0.
16:29A0.
16:30The same thing.
16:35And, uh, the other common stress state.
16:38So, um, uh, the real structure.
16:43Like, uh, in the previous one, we had a simple, like, a rod or some sort of a dice shape one.
16:52But that's not the real world structure.
16:55No.
16:56In the real world, we have this kind of the art.
17:00What is that?
17:01Like, a balanced rock.
17:03Arches.
17:04Like, a national park.
17:06And then, on the right side, it's a canyon bridge.
17:09Los Alamos.
17:10New Mexico.
17:11So, when we have this kind of structure, the real world has, uh, like, a very, many different
17:19kind of the combinations of stresses.
17:22So, let's take a look at each other.
17:25The bridge cable.
17:26Um, if we have a bridge, this could be, like, what is that name?
17:33Like, in, uh, California, they have, like, the, some sort of, um, many different, like, arched, the bridges.
17:48Then, San Francisco has, like, a, uh, what is that, like, 근문교?
17:54Then, they have some very, uh, I don't know how I can draw.
18:01So, it's, uh, the, what is it, hung?
18:06The bridge?
18:09How was it, like?
18:12Oh, whatever.
18:14Then, uh, we have some sort of, like, all the, uh, rubs, they have stretching down.
18:25Or, in this case, they have to pressing down.
18:30So, many different kinds of stress, right?
18:33So, which way?
18:35But, in, in the left side, we, we obviously see the, the gravity pressing down.
18:42That's the, the most, the, that's the most important thing in this structure.
18:50We do not have to consider the going up or going right or left.
18:55We don't care much about it.
18:57But, on the right side, it might be a little bit more complicated.
19:01This, it's not perpendicular to this, like, uh, uh, matching point.
19:08So, it's, it's quite complicated.
19:12So, uh, the, uh, bridge cable is in tension, while the towers feel compression.
19:18And, uh, large lock balance donor, like, uh, support feels compression, right?
19:23The, by the gravity.
19:25And, uh, may experience bending, depending on how it is supported.
19:31And, also, all the beams under gravity sees tension on one side and compression on the other side.
19:41That might happen.
19:42These simple pictures link the basic stress states to the real world.
19:48When you see a structure, try to ask, like, uh, where is tension?
19:54Where is compression?
19:55And, where is the shear?
19:57Why do we care?
19:59Right?
20:00And, uh, we will see why we do care.
20:03And, here, another, like, uh, the other common stress states.
20:09So, um, a thin world pressure vessel, it's called, like, a vessel,
20:15has two main tensile stresses in each wall.
20:19So, here, they express this one.
20:21So, uh, let's take, look at it in detail.
20:25So, it looks like it's going up and down.
20:29But, uh, which is the G.
20:34So, when we took one, uh, the piece over here, then, perpendicular to its, uh, this shape.
20:42And, also, it has, uh, some force along this, the, the face, the, uh, around this shape, whole things.
20:54Because, uh, inside, it has a pressurized gas that exists.
20:59So, that will push out.
21:01Right?
21:02So, this, the, the surface, that thin, uh, the paper-like wall, that will be pressurized to the outside.
21:15So, that will be expressed as, uh, either this one or this one.
21:20And, then, also, that the pressure will, uh, press the outside.
21:27And, this whole material will pressurize inside, too.
21:32Right?
21:33So, we have many different kinds of stress on, on one, on the same area or a spot, whatever.
21:43Right?
21:44So, um, the, the, the, it's called, like, circumferential or hoop stress.
21:56And, uh, longitudinal or axial stress.
21:59That's more obvious, the up and down.
22:02Then, both act at the same time.
22:04So, it is, like, a biaxial tension.
22:07It's not just simply one type of, like, tension to something.
22:11It, the, when we have, uh, any kind of object of interest.
22:17Then, we have to consider many different kinds of stress to, uh, explain that.
22:23Then, on the right side, the hydrostatic compression.
22:26Like, when we say hydro, it, it sounds like some, um, what is that?
22:33Like, water-related.
22:35Right?
22:36Right?
22:37Hydroxial group, hydro leak, or hydro something.
22:40But, here, hydrostatic means a totally different word.
22:44Um, I think they came from this water-related situation.
22:49Because, when we have water, they pressurize something in the, in the, all the same, um, direction.
22:59And, uh, the forces are very evenly distributed to that object.
23:05Right?
23:06So, let's say we have, like, a fish in the, the water.
23:10Then, all the water will press this fish from the top or from the bottom.
23:18or everything.
23:19But, you know, like, this water itself is already pressurized by gravity.
23:24And then, they are easily, um, movable.
23:28So, all the forces are, uh, connected to each other.
23:32So, although the bottom part, uh, is also, like, pressing to the upper part, to this fish.
23:43Right?
23:44It's pressurizing.
23:45So, um, the pressure itself is, like, some sort of, like, a negative way.
23:50Because, it's a pressing down.
23:52But, that's kind of some sort of factor expression.
23:56So, this means, like, pressure acts equally.
24:00So, hydrostatic is meaning, in this slide, like, equally from every direction.
24:08Stress is the same in all direction.
24:11Stress is the same in all direction.
24:14This case is very different from simple uniaxial tension.
24:19So, many real problems are multi-axial.
24:22And this is why we'll have to learn different stress states beyond simple tension.
24:28Okay?
24:30Okay.
24:31Okay.
24:32Okay.
24:33So, we just learned about, like, stress.
24:37So, when we apply the stress to the material, then that will change.
24:42That's, that was expressed as, like, deformation.
24:45Right?
24:46And then, how much?
24:48How much?
24:49How much is changing its original shape?
24:51That has been expressed as, here, like, um, epsilon.
24:56Epsilon.
24:57And then, how much has been changed?
25:00That's delta.
25:02And the original distance.
25:04Right?
25:05So, when we have this length, then that can be changed to this way, when we do some tensile strength.
25:16Then, if we have, like, a longer one, originally longer one, they might have the longer changes.
25:26Right?
25:27So, it, the, this delta, delta area, this, the size, is related to original size.
25:38So, we have to divide by the original size that makes, like, a unit distance or unit area, whatever.
25:48So, let's say we have, like, a black line, originally black, like, a square.
25:54And then, we do some tensile strength, tensile stress onto the upper and down direction.
26:06Then, they will change the, the length.
26:09And then, width, too.
26:11This length, length is defined as a tensile strain.
26:16And then, this, like, a, what is that, width.
26:21Change can be expressed like a lateral.
26:23Lateral means some sort of side or, um, it's not really side, you know.
26:33But it's, it's not like a G direction.
26:36It's like X direction.
26:39And, uh, when we apply this, obviously, uh, it's, it's, the, the length has been positively changed.
26:52But width has been negatively changed.
26:54Right?
26:55So, the, the, the delta L is the absolute value.
27:00So, we have to put negative.
27:02Otherwise, it becomes like a positive value.
27:05It's like a, the width is increasing.
27:08That's not the way.
27:09Right?
27:10So, we have to show that's decreasing.
27:13So, we put negative there.
27:15And, uh, this is a shear strain.
27:17That's the, the, the, the tofu drawing.
27:20I would like to draw, but actually, I couldn't.
27:23So, here, this is the tofu shape.
27:28And then, upper part, we are pressing this one.
27:31And this one, that's like a shear.
27:34I don't know what Korean word is for the shear.
27:38But, you know, like, you can put the hands on top and then press that way.
27:44To, uh, like a, what is that, like a screw or move this kind of, the, the angle changes.
27:53So, delta x is divided by original, like a y direction.
27:59If we have the, uh, lower, the, the object, then they may change very, uh, small amount.
28:11So, that's, uh, it's related to tangent theta.
28:17Strain is always dimensionless.
28:20Because, uh, the original distance and the changing distance.
28:26So, that's the kind of a ratio.
28:28Right?
28:29So, it's dimensionless.
28:32Okay, this is how we measure the stress and strain testing.
28:41So, this is the force and then the corresponding change, delta.
28:47Okay?
28:48So, how do we measure this properties?
28:52We use a standard tensile test machine.
28:57The specimen is often a dog bun, like a K-Piota-ki shape.
29:03We grip the ends and then pull at a constant, the, uh, rate here.
29:09So, we have, like, uh, some sort of a screw.
29:12It's moving.
29:13And then, uh, we have, like, a load cell to connect this one.
29:18And then, the, how much load will be applied.
29:22Or, how much, like, uh, the tensile strength will be applied to this direction.
29:28Or, down direction.
29:30Whatever.
29:31In this case, maybe, uh, they might explain, like, some sort of fracture.
29:37Or, upping, the, up moving is also, like, uh, cause some sort of friction at the end.
29:45So, um, let's say we are doing the tensile strength to the, uh, the up and down.
29:53Because here, the, the arrow is, uh, showing us.
29:56It's, uh, pressing.
29:59What is that?
30:00Like, uh, it's not pressing.
30:02It's, like, uh, uh, pulling out, out direction.
30:06And then, here, each word.
30:10So, that, that specimen is going here.
30:13And then, we have extensometer.
30:16Extensometer.
30:17So, this one is measuring how this specimen is changing.
30:22Like, uh, so we can put some, some, the position.
30:27And then, that'll move this way or this way.
30:30That change can be detected.
30:32Right?
30:33And, um, that, that, very simple one.
30:38But, it should be very accurate to, uh, measure the force.
30:43And then, how it has been, the, the delta, how much delta is changing.
30:49Right?
30:51From this single test, we can find Young's modulus, which, uh, briefly explained as, uh, e-value in the previous slide.
31:01Right?
31:02Like, uh, force and then delta can be, the, um, drawn in the graph.
31:10And then, this slope is e.
31:12Right?
31:13And, during, uh, by this experiment test, we can find Young's modulus, yield strength, and tensile strength, ductility, and toughness.
31:23So, it's very, um, powerful method to measure every, um, the force related to, um, related values.
31:35A tensile test is usually destructive.
31:38Right?
31:39Because it's, uh, the deformation occurs.
31:44So, the speed spin often fractures at the end.
31:51Even when it does not fracture, it may undergo large plastic, plastic deformation.
31:57So, it cannot be reused in the same, uh, state.
32:04Obviously.
32:07So, here, finally, we came to this, uh, the value.
32:11The initial reason, that's, uh, what we saw, like, uh, the stress is proportional to, uh, stress is proportional to, uh, this strain value.
32:20Then, this, uh, this is the Hooke's law.
32:24Right?
32:25Hooke's law.
32:26And then, sigma equals e times epsilon.
32:30A large e means small elastic stretch for the same stress.
32:36So, let's do a tiny example.
32:38Let's do a tiny example.
32:39Like, suppose e equals 200 gigapascal, and, uh, sigma equals 200 megapascal.
32:49Then, e must be, what?
32:53Like, something.
32:55So, uh, it's very, like, easy to measure.
33:00So, um, did you get a hunch for the, the graph shape?
33:06Why we are doing force is located on the y-axis, and then it's changing is on the, uh, the x-axis?
33:14So, let's say we have, uh, a new graph here, force and, uh, uh, delta changing.
33:25Right?
33:26So, when we apply high force, very, like, strong force, then we expect a large change.
33:35Right?
33:36So, uh, when you apply high force, we, uh, we expect large, larger change.
33:48But, if it doesn't go that way, then how can we draw the second one?
33:55For example, when you apply large, large force, then it's not moving that much.
34:02It's, it's, it's, it's change is very small.
34:05Then how do we, when they draw that graph?
34:08That is drawn is here.
34:13Right?
34:14So, um, then can you see what's changing here?
34:19So, it's, then if it's like a, the delta is, the changing is very serious, then it'll go down.
34:31Up here.
34:32When you apply small force, it's already changing a lot.
34:36So, this is, uh, the, some sort of, what, um, aluminum or silver.
34:46Right?
34:47They are very soft, and then we can, copper, we can also, um, extend it with easier way.
34:58And then this could be, uh, what is that?
35:03Other metal, like an iron.
35:07Then, at high force, it's changing very small.
35:13That could be like a tungsten or a titanium or something like that.
35:17They can use, now do you see what's happening here?
35:22So, the, the strong metals have a higher value.
35:29That's what we would like to have.
35:31Like a strong metal has a low value.
35:35That's easy to understand.
35:37So, if we have a high young modulus, that means the metal is quite strong and stiff.
35:46That's easier to compare.
35:48Right?
35:49So, that's why they put the graph this way, not the other way.
35:54And then, uh, also we have another word, like a poisson ratio.
36:00How do we read this?
36:01Like a poison?
36:03United States people, most likely, they read like a poison something.
36:12But this guy is maybe from, uh, France.
36:17Then, like Poisson, Poisson's ratio.
36:22So, we just saw, um, the, the value, how they, uh, like elongated some sort of epsilon value.
36:33So, um, that's lateral value.
36:37So, would you go back?
36:39Would you like to go back here?
36:41Here.
36:42So, uh, it's kind of a delta.
36:46Per unit distance, right?
36:50That's epsilon.
36:51So, actually to change the, what is that?
36:55It's a changing distance.
36:58So, lateral value and, uh, the elongation, like a, the straight value.
37:07That has been the compared.
37:10When we stretch a bar, right?
37:13It gets longer and thinner.
37:16Poisson's ratio describes the relative, uh, uh, way, like a relationship between actual strain
37:24and lateral strain.
37:26That's called like a new.
37:28So, uh, for most metals, new values are around 0.33 and ceramics 0.25 and polymers and 0.40.
37:41So, uh, the values are, uh, uh, not like, uh, we don't have to memorize these values.
37:51If needed, uh, I will give that values.
37:54And also like, um, the, if this value is greater than 0.5, then density increases.
38:03Otherwise, uh, decreases.
38:05Voids forms.
38:07And here, like a mechanical properties.
38:12Why does the E differ from metal to metal?
38:18And then that, um, that's not easy, uh, way to explain.
38:24We already learned about some crystal structure and then density and also like a crystal plane
38:31direction, everything.
38:33So, it's quite complicated.
38:35So, uh, it's not easy to define some words to explain, like, um, why the young modulus
38:46are different, but we can simply say, like, uh, that's because atomic bond's strength and
38:55bond's stiffness are totally different to each other.
38:59Strong, stiff bonds give a, like, steeper slope in the elastic region, right?
39:05And the high, uh, the young modulus.
39:09We can, uh, connect this macroscopic stiffness to atomic scale to see, like, strongly bonded
39:18or weakly bonded cases.
39:21So, the, the, this, like, separation is kind of a distance.
39:27So, here, to make the, almost the same direction, how much force is required.
39:36So, strongly bonded and weakly bonded.
39:41That's not that, uh, difficult to understand.
39:46And there are many different kinds of elastic properties.
39:50Some, the shear modulus is, uh, also expressed as, uh, the, the G value.
39:57And, uh, instead of the F, they use, like, a tau value here, and it's changing.
40:04And, uh, this way, it's not easy to, uh, approach in our case.
40:10So, just stay away from, um, this, this slide.
40:15But, the, the textbook explains a little bit.
40:18So, I will just briefly say this one, but you don't have to, uh, go in detail.
40:23But here, what they want to say is, uh, you know, like, there are many different kinds of,
40:30some, the bulk modulus, or, uh, this way, right?
40:35It's, like, a pressurizing, or whatever.
40:38We, we can simply see this kind of condition.
40:41And then, all the, these values are related to each other, here.
40:46So, uh, this specific, special relations, uh, for isotropic materials.
40:52So, if we know some other values, and then we can guess, uh, the, um, design and, uh, analysis approach.
41:04So, here is, uh, Young's moduli, uh, the table.
41:12So, uh, so, if you take a look at the Young modulus for, the value for, like, a kappa alloy.
41:19And, uh, where, where, where is it?
41:22Like, aluminum.
41:23That's what I explained in the, in the previous slide.
41:26Uh, here, yes.
41:28The aluminum and silver.
41:30They, they have, like, 80 values.
41:33And then, iron.
41:35Where is the iron?
41:36Ah, steel.
41:37And tungsten.
41:38Yeah, that's what I explained, like, in that order, right?
41:42So, uh, silver is, I know, like, silver is quite strong, but tungsten and titanium.
41:49I don't see titanium here, but, oh, sorry, yeah, titanium is lower here.
41:56I forget about it.
41:59And, uh, diamond is quite, like, a strong material.
42:04We know that.
42:06Then, silicon carbide, aluminum oxide.
42:09So, when something is oxidized or nitride, then they become, uh, stronger, right?
42:18The, um, but that's it.
42:21See, this is kind of low scale.
42:23But here, in the low, quite low value here, we see, like, polymer.
42:28You know, the, we can extend that, the plastic, the binet bag by your hands, by your force.
42:37But, you know, like, this diamond, it cannot be changed by your, uh, own force.
42:44So, that's the way.
42:49Okay, um, so, um, uh, I will stop in this page.
42:56Then, the next page slide will be explained in the next class material.
43:03Thank you.
43:04Thank you.
43:05감사합니다.
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