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학습트랜스크립트
00:00다음 영상에서 만나요.
00:10We have talked about some words and also many equations which show the metals, the length
00:23change or width change and also some kind of area change the according to the force applied
00:33to that specimen or any material.
00:37And also like a simple tension and delta, what's delta?
00:43Remember that?
00:44So it's like it's change, delta is kind of change all the time, right?
00:49The final minus initial.
00:52So force applied and the original length and the young modulus and also the area knot,
01:04the original area.
01:09And then like a lateral one is minus mu f width.
01:15So that's the equation.
01:19We can just simply think about that easily, it's changing, right?
01:25So when we apply this force, like tension, then obviously it's moving that's positive way.
01:34But in the case of width, it's negative way.
01:39And also like a simple torsion, it's like a torque.
01:43So the angle, that angle of twist is related to this equation, like a moment which we are
01:52not familiar with.
01:54So maybe some major students might be interested in this kind of extension, but they are just showing this kind of expression, but actually we do not go that far with this kind of application numbers.
02:10So that material and geometric and loading parameters all contribute to deflection and larger elastic moduli minimize elastic deflection.
02:25It goes that way.
02:27It goes that way.
02:29Textbook says that.
02:31We are more interested in this kind of deformation, like a plastic deformation, and that we already
02:39learned about the word plastic.
02:40Do you remember the another word which is different from this plastic?
02:47This is plastic means permanent, but if it goes back to the original position, that's elastic, right?
02:56So that plastic deformation, when we talk about this deformation, we always saw this kind of graph.
03:04This is the stress, engineering stress.
03:07So you should be familiar with this word like engineering stress and sigma and the engineering
03:14strain epsilon.
03:17So just keep them in mind, like sigma and epsilon.
03:22So when we see this straight line, remember that this slope is young modulus, and then that's
03:34going to change when we give the higher stress like this.
03:42So it's not like a straight any longer.
03:45It's changing a little bit.
03:47It says it's yield.
03:48Do you remember the word yield?
03:51What is it?
03:52It's in Korean like hangbo.
03:57So currently it has elastic part and also plastic part at larger stress, like higher stress.
04:07So that's depending on the plane that they slide down and screwed away.
04:20So it shows.
04:21And then let's see what's happening.
04:24So when we unload the stress, then it should go to the original position.
04:32No.
04:33No.
04:34Because it showed like this yielding point.
04:39In that case, it's not straight any longer.
04:42So in that part, we do not have only elastic components in the metal structure.
04:52It already showed some plastic structure changes.
04:57So it doesn't go to the original position and it comes to a certain point.
05:05That's plastic strain, the word plastic strain.
05:14So we know like this epsilon is a strain.
05:19And then P is a plastic strain.
05:25I mentioned that the yield is occurring, but I didn't define the yield yet.
05:31So let's define the words in the next slide here.
05:36Yield strength, it's a stress, right?
05:41But still stress is a certain amount that is called as like yield strength.
05:47The yield strength is the stress where permanent deformation begins.
05:55Noticeable plastic deformation, right?
05:58Noticeable.
05:59What's the noticeable?
06:02It's so like, it's not very clear, depending on the people.
06:09I might say, oh, that's noticeable.
06:12But some people have like a dull eyes, then they say, oh, I don't know if it's really changing
06:21or not.
06:22But they say they have a certain, you know, like in science, if we do not have numbers
06:28or explain in numbers, then that's not a science, okay?
06:37That's what I learned for the whole science classes.
06:41So everything should be transformed to numbers to communicate with others.
06:50So that epsilon, plastic epsilon, plastic strain is like a 0.002.
06:57That's percent at the relative value.
07:00So here, when this epsilon value is 0.002, that is called noticeable.
07:08So we have to measure that.
07:09We just do not look at them to figure out it's noticeable or not.
07:15So that stress is called yield strength, okay?
07:22Many metals do not show a perfectly sharp yield point.
07:28So we have to use the offset method.
07:31It's like offset changing method all the time.
07:35Draw a line parallel to the elastics.
07:40So it's very important.
07:42And then this line and this line, they are parallel to each other in that area.
07:54And then where that line meets the line meets the stress somewhere.
08:05So here is an example, note that for a 2-inch sample, if we had a, you know, the textbook
08:14is written in the United States, they are using inch.
08:17So the sample is also shown in inch.
08:20So epsilon is 0.002 and delta z over z.
08:27So delta z is, this is 2-inch, right?
08:31So delta z should be 0.004 inches.
08:36Then that's noticeable change, right?
08:41So designers, like all the science designers use this value to set safe limits so that parts
08:51do not undergo permanent deformation in service.
08:56A small elastic check is very necessary, right?
09:01In this way, to see where this like a yielding strength is occurring.
09:13We will see why this point is very important in the latter part.
09:19Here are a few examples, like yield strength varies widely.
09:22See, like from 10 to like a 2,000 and unhealed aluminum, where is an aluminum here and some
09:34other kind of what, like the aged aluminum and then also a unhealed aluminum.
09:46So when we, we unhealed the aluminum, that yield strength is only this way.
09:54But if we age that, I don't know how we can age that, like keeping it in some storage with
10:03special condition or something, and maybe aging normally occurs at low temperature rather
10:09than high temperature, right?
10:12Then that makes like a triple or more than triple, like if we choose like 60 and that's
10:21five times or almost five times.
10:25So you know, that's very important, the phenomena.
10:31So the same material, but that's changing like up to five or even more than that.
10:39So see here, like a kappa shows the HR, what's HR, hot world.
10:44And then the kappa, CW, cold, worked.
10:49So if we do in hot condition and, or if we do some cold condition, they show totally different
10:57value for yield strength.
11:01That means, you know, they are the same kappa, they look the same, right?
11:09So we have to be very careful when we treat like our own experimental material.
11:15They might be showing totally different characteristics depending on that handlers idea or handlers condition
11:26for the experiments.
11:28So very small change you make can make the quite large different result.
11:37So that's very important for your future experiment or current experiment too.
11:46See like the processing is very powerful, like cold working or heat treatment can raise yield
11:52strength, but there is some kind of trade off we are going to talk about in the later slides.
12:01So here are another words that like every slide has different words.
12:07So we have to be very careful to understand this tensile strength.
12:11It's very important too.
12:14The tensile strength, often called like ultimate strength, is the maximum, maximum engineering
12:21stress on the stress-strain curve, you know, this is like, I explained this specimen, the test
12:35in the previous class, and then we have certain, what is that, like a area for this specimen,
12:46and then like this tensile strength, it says it's near this point, necking begins, here you see necking, it's the, what is that, the area is a shrink down,
13:02right, so necking begins in a tensile test, after necking starts, the engineering stress drops, engineering stress drops, why?
13:22So we cannot go that much like strength, because it's, it's, the elongation occurs, right?
13:37But in this case, although this area has been changed, we started like the original area, during this whole calculation, we use that area value,
13:51for this, for this whole thing, and then the tensile strength is going down, because we can, if the necking occurs, we cannot apply that much, the high stress, because it's, it's, it's elongating.
14:08So, I hope you understand what I'm talking about. So, after the necking, once it starts, like engineering stress drops, because the cross-section area shrinks very quickly.
14:23Inside the neck, inside the neck, true stress can still rise, during uniform plastic flow, until instability, we are going to talk about that in the, the following, maybe a few slides later, not right away, we will see that part very soon.
14:42We almost never designed parts to reach the tensile strength, right? Because we, we use that part at this tensile stress, then necking may occur, then that'll change that, that part's shape, then that's not gonna work as, as it was supposed to work.
15:09So, you know, like at that point, plastic deformation is already very large, and unsuitable for service.
15:20So here, like necking starts, so here, like necking starts, and for the polymers, the polymer backbone chains are aligned, and about the break.
15:30So, the, I know you have some experience, or expertise on the polymer material.
15:40So, the polymer materials are like, the, the, all entangled, and then when we apply tensile strength, and they are stretched to, uh, the both sides, and then that's like a polymer backbone chains.
15:57Polymer backbone chains are aligned, like stretched out.
16:02Polymer backbone chains are aligned, and then torn down, like break down.
16:09Okay, here is some tensile strength comparison.
16:13Like a typical values have with intuition, so, you know, if you are familiar with these values, then you don't have to look up this table all the time.
16:27So, your brain will have the picture of the table, so, that, um, that may help to, um, choose what kind of material you need for certain applications.
16:44Like a, for, we, previously we saw like aluminum is, uh, like changing a lot.
16:52But here, the tensile strength change is smaller than the previous one.
16:57But still, like a silicon, a diamond, and, um, graphite, they are all carbon material, but they are totally different.
17:06That diamond is very, um, high, uh, it shows high tensile strength.
17:12That graphite doesn't.
17:14And, uh, polymer is located right here.
17:18And then, in the case of, like, composite fibers, they have, like, the various, the values.
17:27Like red, in the case of wood, you know, you can just break that.
17:32You can just, uh, um, tear it down.
17:37But if they are, like, um, the, covered with the fiber in parallel way, then its strength is increasing a lot.
17:50But that's, like, interesting change.
17:54So, uh, all these numbers illustrate that materials differ not only in stiffness, but also in their maximum load-bearing capacity before failure.
18:09So, we have to choose what's the best material for our own purpose.
18:15If we need, like, a very strong material, everyone can use, like, tungsten or titanium steel.
18:23But they are quite expensive compared to, like, other materials, such as in the low density polyethylene.
18:30And that's very cheap material, right?
18:33But, you know, they show only very low, like, tensile strength.
18:38And also ductility again.
18:44Uh, you know the word ductility?
18:47Have you heard about this word in, in your, um, regular life?
18:52Ductile.
18:54Uh, ductile is, uh, the, um, I learned this word in this class, in, in, in this textbook.
19:05So, I, I have never had a chance to use, uh, the word, like, ductile.
19:11So, I don't know this can be used for, uh, like, human beings, like, people, for their characteristics.
19:20It's, uh, but if you look up the words, that it's, like, some sort of, like, You Soon Han.
19:30Um, so, if this is the truth, maybe we can still use this word for people.
19:37Because, um, I don't think we use this word for, uh, only materials.
19:43So, um, if we, uh, but here it's quite interesting.
19:50Like, ductility tells us how much plastic strain a material can take before fracture.
19:57So, here, it's, it's a fracture occurs.
20:00That's why they cannot measure that any longer.
20:03So, that tensile strain, strain, you know the strain, right?
20:08The how much it, it's changing, like, some sort of delta value.
20:13So, um, it changes only small, uh, the value, and then fracture occurs.
20:24And then large elongation occurs.
20:26The percent elongation is measured as, uh, like, this way.
20:30Final value and the initial value, that's original value.
20:34That's difference.
20:36And then hundred times to make the percent.
20:41And also, there is, uh, another way, like, uh, ductility.
20:46We, in this case, we, we used just the length.
20:49Although, it's two-dimensional the way.
20:53It could be plate or whatever.
20:55But we can also measure that area, original area, and then final area.
21:10Whatever.
21:11Whatever we, you would like to use.
21:14But that, that's the way.
21:16And, um, you know, like, we, we just saw, like, some, the, the, uh, stress.
21:26Yield strength.
21:27Yield strength.
21:28And, uh, that's quite important.
21:30We understand that the, the parts should be very, uh, hard and steep.
21:35When we run a, the car or bike, whatever.
21:40That we don't expect they, uh, the parts are ductile.
21:45We want them very strong and steep and hard.
21:50But, uh, like, the ductile, ductility is, uh, also very important for forming processes and for energy absorption before fracture.
22:03So, uh, I mentioned that ductile means, like, Yul Sun Han.
22:07So, let's say we have ductile material.
22:10Then when we, uh, we apply the, the force on, on, on outside way.
22:16Then it may, uh, have my energy to, uh, to resist the fracture.
22:25So, large, larger energy absorption.
22:28And, uh, smaller energy absorption.
22:31Um, and toughness.
22:36Here, like, uh, what's toughness?
22:39You know that, right?
22:40Oh, you look tough.
22:42Do I, uh, look that way?
22:46But, but that's toughness, right?
22:48But here, it says it's energy in this class, in this textbook, or in this, like, field, area.
22:56They are used, they are using the word toughness as a kind of energy, uh, energy term.
23:06Energy to break a unit volume of material.
23:09We just saw that, uh, what is that?
23:13Like, um, the, this ductility, right?
23:17So, the, how much it can absorb the energy.
23:22But that value, the number value is considered as a toughness.
23:28Okay?
23:29So, uh, this is a still stress.
23:32And then the strain and the fractures here, here, and here.
23:37And that's the, uh, uh, kind of, uh, the toughness.
23:42Small toughness and large toughness.
23:45And, uh, and also small toughness.
23:48And, um, you know, the ductile, I mentioned that ductile is kind of, uh, the soft or, uh,
23:58uh, euthunan something, right?
24:00But brittle is, uh, the opposite word.
24:03It's, um, very stiff.
24:07And, uh, some sort of, like, a fragile.
24:10Do you know this word, fragile?
24:13Like, glassware is, uh, fragile.
24:17Uh, 부서지기 시운, 부러지기 시운, ductile 유순한.
24:22So, you know, you can see the difference.
24:26Glasses are easily, and they, easily, they broken down.
24:31And that's fragile.
24:33But, let's say we have, like, eraser or any kind of plastic cup.
24:38But that's, like, uh, that's not fragile that much.
24:43That's, uh, more like a ductile fracture.
24:47So, uh, when, uh, brittle fracture occurs.
24:52So, originally we had this kind of shape.
24:57Then brittle fracture is this way.
25:01Or many different pieces.
25:07You know what I'm talking about, right?
25:18So, this is the, uh, brittle fracture.
25:22But ductile fracture looks quite different.
25:26We had the same thing, and then...
25:36It doesn't have, like, a sharp angle.
25:40I'm not good at drawing, but you figured it out.
25:43So, um, that's the difference.
25:46You know, like, you are breaking a cup, like, glass cup.
25:49You already saw how they, uh, they break down.
25:54And also, let's say, it's not plastic cup.
25:58But if you have some bread or, uh, the rice cake,
26:06duck, and then you drop it.
26:09How do they, uh, break down?
26:12And we will see, that's, uh, the energy.
26:18And also, resilience.
26:20Resilience.
26:21And this, this word is also a famous word in this day.
26:26Because, um, the, the society has to have, like, some sort of resilience.
26:32It's kind of a bubble.
26:35So, um, the ability of material to store energy.
26:42So, um, it can have, absorb the energy and then release energy later.
26:48Resilience is the energy.
26:50So, it's, you know, that word doesn't have the meaning of energy for our, uh, physical chemistry
27:00or chemical physics, the, the classes.
27:05So, um, I don't know.
27:07It's very, uh, the accepted words or common for every scientist.
27:13But, resilience is, uh, kind of, uh, ability of materials to store energy.
27:19So, the resilience may, um, that, so, it's, it's ability of the,
27:29the stored energy.
27:30So, that resilience should be expressed as, uh, energy.
27:36Right?
27:37So, energy is stored best in an elastic region.
27:41So, that's important, elastic region.
27:44Remember that, if we measure this one, that's what?
27:49In the previous slide, like, toughness.
27:51Right?
27:52But, if we, uh, focus on only this part, that's resilience.
27:58Right?
27:59That's, uh, the, if we do the math, maybe that looks the same as, uh, this, like, a triangle
28:11value.
28:12Okay, um, this one is quite important, too.
28:19So, uh, let's say the same thing.
28:24We, we, we already saw this kind of, uh, the, the phenomena many times.
28:30But the whole slide is this, discussing this way.
28:34So, we have stress.
28:36Remember that?
28:37What is this region?
28:39Is it plastic or elastic?
28:42Elastic.
28:43Elastic.
28:44And then, deformation will, like, elastic and also here, plastic E and P.
28:52So, if we go back at this point, then it will go back to the original point.
28:58Once it passes this point, it never goes back to the, this point.
29:03So, it will go to, if we go here, then that'll go this way, a little bit changing and or changing.
29:12Uh, I don't know how, like, what's the slope for returning part.
29:18Uh, but the, we described that in the previous slides, most likely that's parallel to this
29:27original, the elastic graph.
29:29So, it should be like this way.
29:34If we, uh, stop at this point, it will come back this way.
29:39But, that's not, uh, like, um, the, yield strength.
29:46So, we have to wait until this becomes a 0.002, right?
29:52So, uh, let's, let's go.
29:56Um, but we are not talking about this one at this moment, but this way.
30:01And then, and, um, at certain point D, we have to remove that load.
30:09It comes back, uh, the stress is removed, but it doesn't go back to the original, uh, the length.
30:19So, let's say we started at this distance, and then at certain point, maybe it's longer than this way.
30:31And then, once we unload that, the force, this part is this way.
30:41Uh, it's not to scale for this width, but you know, this length.
30:46And then, it's elongated this way, but it's, it's a little bit go back, but, but still we have a certain amount.
30:55That's like, uh, uh, plastic strain.
31:04Then that's elastic strain.
31:07And then, let's go for that stress again.
31:12So, let's see what's gonna happen.
31:15So, that's the same material, right?
31:17So, if we have, if we apply the stress on the, on this material.
31:23So, you know, like, A, B, C.
31:28So, A is somewhere, uh, A is right here.
31:32And then, B is, the, B is here.
31:37I'm sorry, but that's D, but the B is here.
31:41And then, C is here, right?
31:44And then, what's gonna happen when we apply the stress again?
31:49So, it'll go up.
31:51Stress is going up, going up, going up.
31:53And then, we saw, like, a plastic strain over here.
31:56So, this may go to this way or something?
32:00No, that's what the textbook says.
32:03I didn't do this kind of experiment ever before.
32:07But that's what they say.
32:09And then, the textbook says, if we do this kind of experiment, it doesn't go this way.
32:15And then, let me show that one.
32:19Next one.
32:20Reapply road.
32:21See, it goes up to this part.
32:25And then, it changes.
32:28So, if we originally do that, maybe that, that's continuous to this point.
32:36Isn't it weird?
32:37Isn't it weird?
32:38Because the same material, but it has a higher stress to, or it's overcome.
32:48We need a higher stress to show that deformation for the same material.
33:01So, it's cold, like the material has a strain hardened.
33:06Dislocation density increases, increased, and further motion requires a higher stress.
33:15Isn't it interesting?
33:18It looks very interesting to me, right?
33:22In practice, this means a previously plastically deformed part can resist higher stress before yielding again.
33:35And it has like a reduced ductility compared to the original state.
33:41So, I hope you understand this part.
33:51And then, also, if you can explain this one in detail, that might be very appreciated for the test.
34:06Okay, let's move on to the next one, like hardness, resistance to permanently indenting the surface.
34:13Identing the surface.
34:15But this picture shows everything, right?
34:18Hardness.
34:19We have the ball, which has like a very strong, surface is quite strong.
34:27And 10 mm sphere.
34:30That's almost 10 mm is like 1 cm, right?
34:34And then, the applied dome force, the weight.
34:42And then, after removing this force, we will see what's...
34:49This is real diameter.
34:51But if we chose only a certain amount, then if it's soft, then this may go up to this way.
35:03But if it's hard enough, then it shows only limited distance.
35:10Here shows like increasing hardness.
35:13We already know about those.
35:14Like aluminum aloes are not that much hard.
35:18But like steel, steel man, like file hard.
35:22And cutting tool, nitride steel.
35:25And diamond, like carbon, the interstitial treatment is iron or something.
35:33Right?
35:34Increasing hardness.
35:35The hardness tests are very easy to perform.
35:46I will show that.
35:47So they are widely used for quality control and for estimating strengths in the field when tensile tests are not convenient.
35:57For the tensile strength, we saw that test equipment with like specimen.
36:07And for the specimen, we need a very specific design for that material.
36:15And also, quite large scale machine for the test.
36:25But for this hardness, it's easier.
36:28But you know, when we have hard material, then we can expect higher yield strength or related value.
36:38So if we have a soft one, they might have like a higher the ability and the higher resilience.
36:49But that's the simply we can guess.
36:53So if we do the test for the hardness, that information can be extended to the other characteristics we have discussed all over these slides.
37:08So there are like two ways, Raguel and Brunel hardness.
37:15Actually, I saw many hardness measurements in the research article.
37:23But all of them in our research field, I saw like HB rather than Raguel values.
37:33So no major sample damage.
37:37You know, in the previous that fracture test, that specimen, like a dog bone.
37:44Remember that?
37:46I can go back to the slides, but you can check.
37:49So in that case, we apply the tensile strength and then that shows a certain lacking or elongation that breaks down the sample.
38:02Right?
38:03But here, Raguel, we can put small, like the dent over there.
38:09So that no major sample damage.
38:12That sample still can be used for this tensile strength test.
38:18Each scale runs to 130 kg, but only useful in range 20 to 100 kg.
38:26Minor load 10 and major load.
38:29That will be discussed in the next table very soon.
38:33And then also like Brunel hardness HB.
38:37I don't know why they are like using this HB.
38:43Maybe somebody's initial.
38:48And then tensile strength can be expressed this way.
38:53Here, like Brunel and then Raguel.
38:59Here, we can use the ball or certain shape.
39:04This, the very sharp and very diamond, very strong one.
39:11And then apply this 60 kg, 100 kg or 150 kg in the Raguel.
39:23Or Brunel, the 10 mm sphere of steel or tungsten carbide.
39:34And true stress.
39:38That's what I explained in that, do you remember this one?
39:42Let me show you where, what I'm going to, this one.
39:47This one, the, we saw like a tensile strength is, tensile stress is going down.
39:54The tensile, this is the engineering stress is going down.
40:01But you know, but that's not the way, the actual value.
40:06So you have to understand this one.
40:08I obviously, most likely, I put this, the graph for the test.
40:14Most likely.
40:17So true engineering and true stress and engineering stress.
40:23And then when we apply the force, the force cannot go higher because it's releasing and the necking occurs.
40:36And then the length is changing in higher dimension, higher, the longer way.
40:43So the force looks like a decreasing, but actually, you know, the area is shrinking down, it gets smaller.
40:54So if we put this, like the area changes, then, you know, stress is, you know, all the time, the stress is area related, the function, right?
41:10Force divided by area.
41:12But if we put this A value the same, then the force is like a distracted.
41:19So it goes down.
41:21It looks like it going down, but actually the area is also decreasing.
41:26So the, the, the, the, the true stress is increasing.
41:34That hardening that we already mentioned this one.
41:41So once it goes high and then comes back and then when we go, it doesn't go, it doesn't move this way.
41:49So it's like a, the, the, the, the, the yielding stress is increasing due to like plastic deformation.
42:01So it's when we do like this stress part before the fracture occurs, then it's the, it gets hard, hardened and hard.
42:14But, but I, but I don't know if this is really a hardening or not, because, you know, for the, the stress, it's still like the strain across the same trend.
42:29So that has been, uh, calculated in, uh, the, this number.
42:35We don't care much.
42:36Right.
42:37And then the, uh, depending on the sample, sample to sample, they look quite different, the values.
42:47So measure the properties always shows some scatter.
42:51That's why we need like a mean or standard deviation to show some statistics, right?
43:00Like a sample to sample differences, the microstructural variation, impurities.
43:06Surface finish, then test method, machine calibration, environment, and the temperature.
43:13That's what textbook says.
43:15For the reason why, uh, they have this variable for the experiment results.
43:25So, uh, we describe data with a simple statistics.
43:32The mean average value and the standard deviation, which represents the scatter around the average.
43:42Right.
43:43We all do this for our own experiments and everything.
43:47And, uh, we go for design or safety factor.
43:54Because the loads and, uh, properties are uncertain, then we use the safety factors in design.
44:03So here, the one common method uses like a working stress.
44:10The working stress is like a wielding stress divided by certain number.
44:18You know, let's say, uh, I have, uh, the, I have, uh, the part rod here.
44:25It can survive like a hundred Pascal.
44:28Then do you want to use it up to one hundred Pascal?
44:33Or certain amount lower than this.
44:37That's the safety factor.
44:39If we put like a four there, then four, that's 25 Pascal.
44:45It can survive up to a hundred Pascal.
44:48But our design, uh, allows only 25 Pascal for this whole sample.
44:56So if we have higher number, like one, two, three, four, four, if it goes one, that's quite, uh, it's not safe at all.
45:06But if we go over like a two or three, then that makes quite safe.
45:12Here, calculate diameter.
45:14Here, the, the yield does not occur in that one, uh, 1045 carbon steel rod below.
45:21They have a lot of information here we see.
45:25Um, the, it says like, uh, the safety factor of five.
45:36They are very scared.
45:39They can use a little bit more.
45:42But, so, uh, the, this stress is also calculated by the area and then the force.
45:52So, uh, that, that can be calculated.
45:58And then, um, the, this one.
46:03Diameter.
46:04This is not one.
46:08This is 1.2.
46:10That's two, around like 20% lower.
46:14So if we put 1.2, I do not calculate it exactly, but that's around like 80 Pascal or low, even lower than that.
46:23Right?
46:24Right?
46:25Yes.
46:26Okay.
46:27Um, we, we've come a long way.
46:32I guess.
46:33Today, we defined the stress and strain and learned like how to measure them with a tensile test.
46:41And, uh, in elastic behavior, we, uh, we saw like a Hooke's law.
46:50Remember that like a Sigma equal is, uh, the, the, uh, young modulus times the epsilon.
46:58We used the Poisson ratio, new, something, something, right?
47:03And then also elastic behavior and then plastic behavior.
47:08That's quite obvious to discuss over.
47:12And then toughness and ductility.
47:15What else?
47:16We, we, we just saw like a resilience and, uh, some other factors too, like hardness and, uh,
47:27then some safety factor.
47:29Right?
47:30So, uh, I, I don't know why they, um, do not have those ones.
47:36I, I could put things like that.
47:39I'm sorry.
47:41So, um, that's the end of like a chapter six.
47:46Um, here, although we do not have that many, like, uh, the digitized, the expression,
47:56but I, I hope you understand a lot of things for the material characteristic.
48:05Okay.
48:06Thank you.
48:07We will see for chapter seven.
48:10Stephen.
48:12Stephen.
48:14Stephen.
48:15Stephen.
48:16Stephen.
48:17Stephen.
48:18John.
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