Let's stop and we can collect your papers. So just to repeat a little bit what we were talking about earlier this week. On Tuesday, the strengthening mechanisms are basically

a mechanism whereby we introduce obstacles to dislocations, to the movement of dislocations,

so that we can increase the dislocation density in the material. And so the way you have to think about it is you have the dislocation, which is causing the plastic deformation,

moves through the material and meets an obstacle. We discussed just the fact that these obstacles

are not necessarily attractive. But let's assume that we followed a theory, one of the theories where the interaction is attractive. So the dislocation is prevented from moving here

at this obstacle. And so it will continue to move where it's not stuck, yes, under the influence of distress you apply. And so the obstacle will exert a force on this

dislocation. And the more I add force, the more I apply force, the more this dislocation

bulges out. The larger this force becomes, yes, why do I know it becomes larger? Because the, if F is the force exerted by the obstacle on the dislocation, then I can simply

draw the force that the dislocation has on the obstacles under the form of the line energies, yes, the line tension, if you want. So as I increase the bulge,

say the bulge is smaller here, the vectors T are oriented like this. So the sum of these

vectors become larger, yes. So at one point, the force is large enough and the dislocation is released when I reach this maximum force. That's basically what happens, yes.

So I can have strong obstacles, weak obstacles. And an obstacle usually is defined by a force

distance shape, yes. And depending on this obstacle and the particular interaction, you have a theory that describes this. And so we had seen that in the case of solid solution,

when you add, for instance, silicon, aluminum, other elements to a steel, yes, and the element is in solid solution, it doesn't form a precipitate, then the lattice distortion is the main cause of the interaction between dislocation and the substitutional or the

interstitial element, yes. And you can quantify this distortion by mean of this parameter delta, yes, which basically tells me how the lattice parameter changes with

the concentration of the solute. That's one thing. And then I also have a dependency on the concentration of the solute, yes. And usually, the available theory says it's

proportional to a certain power of this concentration. And so one of the theories says it's proportional to the square root of the carbon content. And, for example, we saw

some examples where the, for martensite, for instance, where the concentration, sorry, the strength of the martensite is proportional to the square root of the carbon content.

However, I've also told you that we don't have enough theory to work with in practice, so we usually go for the engineering solution, and that was shown here, yes. We basically say that we're going to use this empirical equation that the solute solution strengthening

is proportional to the concentration of a specific element, and we're going to use a lot of experimental data to know what is the strengthening per mass percent of an alloying element, yes.

And we have seen also that certain alloying elements such as phosphorus and silicon are very strong solid solution strengtheners, and that we like to use them, but that because of other reasons, in particular, the impact, the negative impact of these elements on

the toughness, we will not be able to use more than, say, I will say 700 ppm of phosphorus, less than that, and silicon, a max of 0.5, so mass percent or weight percent, if you

want to use that, because of toughness reasons. With manganese, we don't have the

toughness. Actually, it improves the toughness, but for most of the elements, you cannot add

very large amounts before you start other processes, you see other processes to occur. In particular, for instance, with manganese, as you add more manganese, yes, you add 2%, 2.5%, that's about the maximum people use for steels. For the, for instance, for

constructional steels, you rarely find compositions that are higher than that. Why is that? Well, as soon as you start adding 4, 3%, 3.5%, then the steel becomes very

hardenable. That means it becomes very easy to turn it into martensite. At 4%, the steel will be almost air hardenable. It means that any time you do a heat treatment, and

the cooling rate is a little bit high, you get martensite. Now, in many cases, you don't want martensite. That's a problem. With manganese, again, it's a good addition, but there you're limited by the fact that it makes the steel very hardenable. 2.5%

is about the maximum you will use. Otherwise, it becomes very hardenability. I had shown

you this graph to illustrate how difficult it was to, although it looks very simple

to check which theory applies, it's actually more complicated in practice, because we don't have, we can't have these very large ranges of sea, of concentrations in practice, and these different exponents apply in many cases. These were the examples we looked at.

This one phenomenon that is important for you to realize is when we talk about solid

solution hardening, we often forget that the properties of steel will vary with temperature.

That is the same with solid solution hardening. With solid solution hardening, you get temperature effects. In particular, when you go to higher temperatures, the solid solution effect is

less, is lower. Why would it be lower? Well, because I have two effects. First of all, my lattice distortion is less. Second, the elastic modulus becomes lower. Again,

that results in the fact that the solutes are less effective obstacles. That's one

special phenomenon that occurs, and that is a phenomenon that we call solute softening. It basically means that at lower temperatures, for certain alloying elements, we get an

alloy softening. Instead of having a yield strength increase, we get a yield strength decrease. You can measure what is the yield strength increase per mass percent for silicon.

You find that at lower temperature, it is reduced and it becomes zero. What does it mean? It means, for instance, if you have pure iron, this temperature, and you measure

the yield strength of pure iron as a function of temperature. This is about room temperature. This is what you find. As I said, there's very strong increase in the strength at lower

temperature because of the screw dislocation. Dislocation mobility is very low. If you add silicon, what I see is that at room temperature, I get solid solution strengthening.

The material is stronger, and it is so also at higher temperatures. As we reduce the temperature, this is what we find. The material here, this is actually softer than

if you hadn't put anything in it. The reason why this happens, for certain alloying element of others, it depends on the concentration of alloying element that you add, but it's

again, this is for BCC iron, not for austenitic. What this means, basically, is that something

else is happening here. What is happening here is simply the fact that these alloying elements will increase the screw dislocation mobility at low temperatures. They will do

this because the alloying element make double kink nucleation formation easier. That means

the dislocation mobility goes up. The screw dislocation mobility goes up. That's an important point to know that solid solution strengthening is a function of temperatures,

temperature dependent. Let's have a look at another strengthening phenomenon, a contribution

to strengthening. That is the dislocation density. There is a very well-known empirical

observation that the flow strength is proportional to the dislocation density squared. It basically means that when you measure a stress strain curve, you actually increase the dislocation

density. Dislocation density increases. If this is the strain, dislocation density

increases in a certain fashion. If you take this data together, and you plot the stress

as a function of the dislocation density squared, you find a straight line. This is very useful and very famous relation in strain hardening. It masks the number of points.

One of the things that happens is that the picture is not that you go from a homogeneous

distribution of dislocations with a certain density to a higher density of homogeneously distributed dislocations. What happens very quickly with the dislocations is that they

will form patterns. These patterns, we usually refer to them as cells. They form a cell structure. Let me show you a picture of the cell structure. This is a cell structure

here. This is ferrite, ferritic steel. You can see the dislocations of the black lines. The deformation here is 5%. That's not very much. You can still see the dislocation. This is 10% deformed. You can barely make out dislocations here. What you see

are very dark bands here, which we call cell walls, where all the dislocations seem to be confined, and then cell interiors, usually quite geometrical cell interiors,

where the dislocation density is very low. If you then, for instance, in a TM, make the analysis of the total dislocation density, what you'll find is that the dislocations

is that this total dislocation density consists of dislocations in the cell wall. You see most of the dislocations are in the cell wall. Then a small amount of dislocations in the cell interior. It is actually these dislocations that are responsible for the

plastic deformation, because these ones in the cell wall, they're basically immobile.

Now the interactions that we have between dislocations can be what we have already discussed on the left, which is what we call the forest dislocation interaction. You have a dislocation on one slip plane that comes across dislocations on another slip plane,

and it's prevented from moving because of what happens at the point where they meet. We've already seen that in certain cases, at the point where they meet, you can form

jogs. These jogs will act as a pinning point, literally. If it's a sessile edge jog on the screws, it's a very strong pinning point. We can make sense about the square root

dependence of the dislocation density simply by noticing that if you have a dislocation

density of rho, then the inter-dislocation distance is one over the square root of dislocation

density. And this is this equation here, right? It's a theoretical form. You've got stress is equal to a lattice friction, a solid solution contribution, and then you have your dislocation contribution. And your dislocation density contribution has a constant. The shear

modulus B is the Burgers factor of your dislocation and your dislocation density. And if for ferrite, you know what alpha is, about 0.3, 0.35, g is 80 gigapascal,

and B is about 0.25 nanometers, you can calculate this factor. And so you get this very simply, very simple dislocation density contribution to strength.

And if you need this, there are many people who have looked at the relation between strain and dislocation density. So you even have equations which will allow you to calculate

this contribution very simply. And this is an example here. What is this increase in dislocation density? Well, you typically go from 10 to the 12 meters of dislocations

per cube meters, yes? And then as you strain the material, the density goes up to, so if you have like 30% deformation, it goes to about close to 10 to the 15 meters

per cube meter of material. And you can then just basically using this here, calculate true stress as a function of true strain and plot N values, so strain hardening values,

that you obtain and then calculate even what the uniform strain will be. So that's very convenient. Now, and there's some example here of this calculation and a table that

gives you typical dislocation densities that you have. OK, so dislocations. Now, we usually don't use this, we don't usually deform our material

to get strength in products, yes? However, and the strengthening by dislocation is basically your standard work hardening. But what we can do and that gets a lot of attention

in technologies is reducing grain sizes. Because grain sizes, grain boundaries, excuse me, are very efficient in increasing the strength, yes? And in addition, the negative

impacts on other properties are minimal. And there's actually one very positive impact is this grain size reduction always leads to an increase in toughness, yes? And so that's in many applications, structural applications, in petroleum and gas industry, in the ship

building industry, wine pipe industry, it's very important to have very tough materials. So grain engineering, grain size engineering is very important for these products. So

you can see here what happens is that in your material, when you generate dislocations from a dislocation source, they will, dislocation will move and then they'll hit a grain boundary, yes? And then it's done, yes? In contrary to a single crystal, where as

you deform the single crystal, dislocation can move out of the single crystal. In this case, they're just stuck, stuck, literally stuck at the grain boundary, yes? And because the sources of dislocations emit always the same dislocation, you get pile ups, pile

ups. And these pile ups, in order to push more dislocations, yes, create more dislocations, it becomes increasingly harder to do this. And the reason it's very simple is because

these pile ups, the dislocation, all these dislocations exert a repulsive interaction on each other. So the more dislocations I have in the pile up, the larger the repulsive

interaction, yes? And the harder it is to make more dislocations, make the dislocation source create more dislocations. And you can see very nicely on this micrograph here that the stresses increase in the pile up because the distance between the dislocations

become gradually larger. So basically, these pile ups generate what are called back stresses. Yes, and these back stresses strengthen the material. And we're not going to go into

the theory, but you know that the strengthening from grain boundaries goes as the inverse of the grain size, the grain diameter. Now, what about the reason for the strengthening?

It would seem like I think the real interest in grain boundary, grain size engineering

dates from about 60 years ago. Then it was a big topic that people discovered and tried to work out in a big way. But there's still many things we don't know, yes? And it

certainly holds for seals about what is it actually that makes the grain boundaries so special in the strengthening effect. Because don't forget the square root dependence is

very easy to derive from a modeling point of view. A couple of models, four or five models out there that readily give this one over square root of D relation, yes? But they're very different models. One of the models is that, okay, you have these

huge pile ups at the grain boundaries, and these pile ups at the tip of the pile up, you have very high stresses. And these high stresses will propagate the slip from

one grain to the other grain. And so that's a very nice theory. And there are many, there are alloys, such as the one I showed you here, yes? Where you can see the pile ups, yes? And you say, well, that's a very reasonable theory. However, these pile ups,

you don't see them in steel. There are no pile ups in steels, yes? So it's the theory that you probably heard mentioned, Cottrell theory of grain size strengthening

is a very nice theory. But it's one of its basic elements that you need to have pile ups. You don't have pile ups in ferritic steels. The reason why you don't have pile ups is because of the dislocation properties. The dislocation properties are such that,

I've told you that when a dislocation in ferrite meets an obstacle, it just moves to another glide plane, yes? So you don't have buildup of these very high stresses, yes? And so what probably happens is the fact that the grain boundaries themselves

are active in the process of this strengthening effect, yes? And people have discovered this in this way, very simple way. They plot the yield strength of a steel as a function

of the inverse of the square root of the diameter. And they do this for different compositions, yes? In particular, they do this for different carbon contents, yes?

Zero carbon, 30 ppm carbon, 60 ppm carbon. And what you see is that you have an increased slope, yes? In other words, that for a specific diameter, grain size, you get a

higher strength, yes? So that points to the fact that, well, obviously if it was a pile up effect, you know, the grain boundary has nothing to do with it, yes? Here, we know that at this level of carbon concentration, the carbon is in grain boundaries, yes? Segregates

to grain boundaries and changes, well, we know it changes the cohesive strength of grain boundaries, for instance, yes? But it also changes apparently the emission of dislocations

by the grain boundaries. So the alternative theory says what happens is it's actually the grain boundaries that generate dislocations, yes? And, okay, so it's the grain boundaries

acts as dislocation sources and when they get stronger, it becomes more difficult to generate dislocations and you get increase in the flow stress, okay? Right, and these

are a number of examples here. I do want to point out that this, this equation, in

this equation here, this whole, this what we call the whole patch coefficient here, yes? It's not a universal constant, right? So if you, if you measure this, this is

the slope here for different steels. It will be different, yes? And it will also differ for, for instance, here, for instance, with the composition. Here we added phosphorus. Phosphorus is added, phosphorus is added, phosphorus is added. And you see that the

strength increases. The reason is because, you know, phosphorus is very efficient, solid solution strengthening, but the grain boundary strengthening becomes less efficient as I add more phosphorus, okay? So there are many people that have looked at this and there's

quite a variety of K values out there that you can find. But here, these are for a number of steels, actual steels. And you can see that, you know, for IF steels,

it's very low, yes? And for commercial quality steel, yes, basically a low carbon steel, it's much higher, about four times higher, yes? And what this basically means

is that this is a reflection, again, of the fact that in the commercial quality steel, you have carbon, yes? And the carbon can influence the strength of the grain boundary. Whereas in an IF steel, there's no free carbon, yes? So the grain boundaries are

very clean, yes? And apparently, it's very easy for them to emit dislocations, okay? And this is also for the Hall-Petch equation at higher strength. All right, so it's very,

again, so grain boundary, the more grain boundaries you have, the better for the strengthening. That's basically the word. So usually during thermal treatments, grain boundaries will

have a tendency to move, yes, so as to increase the grain size, yes? And so we prevent this by having particles in the way of the moving grain boundaries. Because if you have a grain

boundary that's moving, and it cuts a precipitate, now the precipitate is in the grain boundary, yes? Just this fact is enough to pin the grain boundary. And it pins the grain boundary

because you see the grain boundary energy is reduced by this surface, yes? And so this, you know, when the grain boundary wants to pass, it's got to increase the surface area

by this amount, yes? And that exerts a restraining force on the boundary, okay? And you can see here, for instance, this is a little particle at the grain boundary, yes? And

this is around the grain boundary here. It's not pinned, it has moved, whereas at the particle it stayed there, yes? So there is a very convenient equation, which we call the Zener equation, which relates the maximum grain diameter to very simple parameters,

the radius of the precipitate and the volume fraction of the precipitate, yes? The ratio of these two parameters times four divided by three. And this is called the Zener equation,

yes? Basically says that if I plot the diameter, yes, of the maximum diameter that I'll have in my microstructure, steel microstructure, over the radius of the precipitate, yes?

Yes, it will go down, yes, in a log-log plot via this linear relation, yes, with the amount, the volume fraction of the precipitate, yes? So having a lot of small particles

in your microstructure will prevent grain growth, yes? Now this equation, this theoretical equation is a little bit, doesn't actually apply for steels right away, but if you

replace this four-thirds by 0.17, yes, it applies perfectly. And this is an example here for a, so this would be that new equation, yes? And here you have the, for HSLA steel,

microalloyed steels, if I have precipitates of five nanometers, 50 angstroms, yes? The grain size, I can calculate the maximum grain size just by using this equation, yes?

The grain size will vary from five micron max to a half a micron, yes, for a density, a volume fraction that is not that large, yeah? 10 to the minus three, 10 to the minus four, okay? And this is actually what we do when we make HSLA steels, yes? Is

we control the grain size by adding carbides, yes, in the microstructure. Now the question

is, of course, if you can strengthen steels by reducing the grain size, yeah, note that you don't have to do anything with the chemistry, yes? Except maybe add a little bit, again,

the volume fraction is very small, a little bit of carbides in the microstructure. Why not go all the way, you know? Why not make extremely small grain sizes, much smaller than a micron or half a micron? What happens then? Well, the problem then is

that you get collapse in plasticity. If you take an IF steel, so that's an interstitial-free steel, yes, and you look at the strength of this steel as a function of the grain,

so one over the square root of the grain diameter, right? So what you expect to see, of course, is your Hall-Petch equation, right? And this is your Hall-Petch equation,

so that's fine, yes? And there is a Hall-Petch equation for the yield strength, and there is a Hall-Petch equation for the tensile strength. However, you can see here that

the two meet up, they meet. So what does this mean if you have a stress strain where the two meet up? Well, it's like, right, it's, there is no uniform deformation, yes? Because that's basically when you have a stress strain curve, so this is the yield strength,

and this is the tensile strength. When these two are one, there's no more, this is uniform elongation, right? There's no more uniform elongation, yes? The material will neck,

yes, will neck very quickly, and then break. So you lose all your plasticity. You have huge, I'm sorry, you have huge strengths because an IF steel will typically have, if it's well annealed, will have yield strengths less than 200 megapascal, yeah? You can increase the strength

up to a gigapascal, just by reducing the grain size. So that's an amazing value, but the material is, you cannot deform it anymore. There's no yield strength, there's no deformation. You can see here, so this is the unit, this is the total elongation.

You can see as soon as you hit one micron, you get a collapse of the elongation, yes? It doesn't go to zero, by the way, yes? There's still post-uniform elongation, yes? But if you concentrate on the uniform elongation, basically at, so this is one,

one micron, and this is a half a micron. So in the range of one to a half micron, you get no more uniform elongation, yes? So, right, you cannot really use this today.

We cannot use this method to make formable materials. We make, we can use this method to make extremely strong steels, but that's it. There are ways to address this problem,

but then you have to make more complex steels. Let me see, because I'm talking here, I'll come back to this, the small, very small grain size, and I'll also show you

that you do get increase in strength, yes? In general, you get a reduction in uniform elongation, but the other thing that's positive, of course, for reduction of grain sizes,

is the toughness. That usually improves as you reduce the grain size, and we'll talk about this in a moment. Precipitation strengthening in steels, usually that involves the following.

So, if the precipitates are softer, they can be cut, sheared by dislocations, yes? If they're very strong, they're bypassed by the dislocation, so they,

let me show you what bypassing means, yes? Say, this is an obstacle, yes? But now it's a very, very strong obstacle. It's an extremely strong obstacle, so that when the dislocation arrives here, yes, it will bulge out, yes?

It will bulge out, and typically in steels, these, for many steels, such as HSLA steels, these precipitates are very hard carbide particles, so there's no way the dislocations can shear them, yes? There's no way.

And so, the dislocation will just wrap around this precipitate, like this. And now, if this is a screw dislocation, yes, then the two arms

of this screw dislocation, yes, past the obstacle, have become two edge dislocations, yes? And if I look at these two edge dislocations, yes, from a point of view of the extra half plane,

then one of them looks like this, and the other one looks like this. So, they can annihilate each other, because they will, they attract each other, there is an attractive interaction, yes, and they can annihilate, simply move towards each other, and they form a perfect lattice again, yeah?

And this one needs this one, okay? So basically, the dislocation is pinched off, we say. So, this is before the pinch off, and this is after the pinch off.

After the pinch off, you have the obstacle, which has a small dislocation loop around, yes? And the dislocation here, which continues its motion. So, this interaction, which is very common in high strength steels,

with carbide precipitates, is called the R01 mechanism. Let me show you, this is an example here, from some TM images, you can see a dislocation close to a precipitate, here you can see it being pinned, yes?

Here you see the dislocation is pinned, and there are other dislocation pushing on it, yes? And this is a precipitate where dislocation, a few dislocations have passed it, and you can see it's surrounded by dislocation loops, yes? And every time you count the loop, that's the number of dislocations that have passed it, yeah?

Now, depending on the situation, if you can shear the precipitate, the relation between the strength, yes, the strength, and the precipitate radius is given by this equation.

This is for cutting, so-called precipitate can be cut, yes?

We don't encounter this situation in steels, most of the time. Most of the situations we encounter is this relation, yes? Where the strengthening is proportional to the density, or the volume fraction rather,

of the precipitates to the square root, and divided by the radius of the precipitate. So that means that if we have coarse precipitates, we get less strengthening. So we want to have very small precipitates, yes, and we want a certain density of it, yes?

Right, and again, this theory is worked out, and for instance, if you would want to calculate it for a particular situation that you have,

this would be it. The strengthening due to precipitation of carbides is ten times the square root of the volume fraction, so that would be, for instance, ten to the minus three, yes?

Precipitate volume fraction, dp here and here is the precipitate diameter in microns, yes? Okay, so this equation here can readily be put in a graph, yes?

Which shows you how much strengthening you can get from precipitates, yeah? So here is this equation that I just showed you, in terms of increase of the yield strength, and this is the size of the particles, yes, and the size decreases.

So we see that as the size of the particle decreases, I get the increase in the strength, yes? And that the volume fraction of these particles increases, I will get more strength too.

The same equation here you can present as the increase of the strength as a function of the precipitate fraction, yes? And in this case, you get these linear plots.

You have, of course, it has to be a log-log plot to get the linear equation, a linear plot, and the region for the HSLA steels is shown here. So we typically try to achieve particles that are 0.005 microns, so 5 nanometers, yes?

And so our density is typically 10 to the minus 3. The density should say volume fraction, 10 to the minus 3.

And so what can we expect in terms of strengthening, yes? We can expect about 100 megapascal, yeah? That is the contribution from the precipitation strengthening, yes?

Assuming all the particles are in the matrix, yes? At the same time, we've just seen that these carbide particles can also reduce the grain size, yes? So anytime you add niobium carbide in the microstructure of HSLA, you get two effects.

You get strengthening by grain size reduction and strengthening by precipitation hardening, okay? It's not the only system where we get precipitation hardening.

There's another system in steel where we use small copper particles, yes? Pure copper particles in our steel matrix, yes?

To obtain precipitation hardening, yes? This system of hardening is different from the one we just saw. Those particles, those copper particles, are actually soft particles, yes? And the hardening caused by these particles is not the oral one hardening.

You can cut the copper particles, yeah? The effect is actually, it's been studied in detail, but the effect, the strengthening effect,

is due to a difference in elastic modulus between the copper and the steel, okay? And copper precipitates are used in copper strengthens ferrite, but also in certain martensitic steels.

It's used to strengthen the ferrite. Now, again, the situation is a little bit more complicated, yes? Because if we look at the yield strength of a copper-added steel, yes?

So the yield strength as a function of the mass percent of copper, what we see is that copper does more than just increase the strength by precipitation hardening.

First of all, it leads to reduction of grain size, yes? And you can see here, the contribution of the reduction of grain size is actually considerable, yes? Second, copper, when you add copper to steel, it will form precipitates.

But some of the copper will remain in solid solution, and I will get a solid solution strengthening effect. And you can see here, this is the contribution here. It's a little bit less, a little bit over 50 MPa, depends of course on the amount of copper I've added.

And then you have the contribution of the precipitation hardening, yes? So the way you put the copper in is very simple. You can see here that copper at about 800 degrees C, yes?

You can easily dissolve up to about 1.5% of copper in ferrite, yes? And so you just, a typical copper strength in steel will contain about 1 mass percent of copper, yes?

And if you quench this, yes, you will keep it in solution. And then you do reheating at around 500 degrees C. That will precipitate out the copper that is in super saturation. And that's what gives you all these particles and the strengthening.

So going back to these precipitates, controlling the volume fraction is not really a big issue. You control the volume fraction of a precipitate by how much niobium and carbon you've added, or how much copper you've added.

It's basically concentration related. What's important is the distribution of the sizes. So for instance, here is an image of carbides in a niobium and titanium added steel.

These very large precipitates have no effect whatsoever, yes? Because they're way too large to impact the strength, yes?

So it's very important that the particles do not coarsen, yes? Do not coarsen to be efficient. In both situations of whether the particles can be sheared or whether they cannot be sheared,

it's important for them to be small, small enough. Right, so again, plenty of things.

we can get from theory and from experiments. For instance, if you know what the volume fraction is of your precipitate and what the size is of your precipitate, you can determine

what is the distance between the particles. And the strengthening is proportional to the inverse of the particle spacing. So the smaller the particle spacing,

so the larger the 1 over lambda, the larger the strength. That's what we expected. So in a nutshell, for ferrite, when

we look at the strength contribution, it's important to know that we are at room temperature. We are in a region where the strength properties of the steel

are temperature dependent. There are certain strengthening contributions which are not much temperature dependent. And which one are these? Well, so if you can see here, this curve here,

I can consider a temperature independent strength, part of the strength, and a temperature dependent part of the strength, this value. What parts are not temperature dependent?

Well, you don't have to worry about looking for a temperature dependence. Dislocation-dislocation interactions. Dislocation-solute interaction. So having said this, be aware of the fact

that there may be, you should check for solid solution softening, but that's for lower temperatures. And the parallel stress, that's the lattice friction. Yes?

Pretty much assume that's a constant value. And then we have the process of double kink formation, which is what we call the double kink formation, nucleation, which allows screw dislocations to move in BCC.

That is very much temperature dependent. And you cannot really ignore it, even at room temperature, because at room temperature, we're in the tail of this temperature dependent part of E.

Of course, that's the low temperature. On the high temperature part, what we see is that above 600 degrees C, we get a quick collapse.

If this is pure ion, you see a very quick collapse of the strength. And of course, that's because we are at the creep area of behavior.

Now, in, OK, so well, I think I'll stop here. What will.