 So, welcome to the fifth lecture on cryogenic engineering under this NPTEL program. Just taking a view of what we have done in the earlier lectures, we had introduction to cryogenics as topic 1 and in the topic 2 what we had was the information regarding all the cryogens, the properties, temperature and entropy diagrams and we talked about various cryogens which are aragon, air, nitrogen, oxygen and then we went little bit in depth regarding hydrogen and we talked about ortho and para-hydrogen and its conversion and also we talked about helium. We talked about helium isotopes which is helium 3 and helium 4, also we talk about normal helium 1 which is helium at 4.2 k helium liquid and we talked about helium as super fluid which is helium 2. In this lecture, we will talk about material properties at low temperature. Ultimately all these cryogens are kept in some cryo containers which are made up of some material, metal and sometimes non-metal and therefore, it is very important to understand how these materials behave at low temperature wherein we will study the structure of matter. Also we will study stress strain relationship for this material and in this particular lecture, we will talk about mechanical properties of metals and plastics at low temperature. Where we studying all these things? We want to study this because the properties of material change when cooled to cryogenic temperatures and sometimes these changes are drastic. For example, we have seen a video earlier and we will see the experiment again. We can see from this experiment that rubber when it got quenched into liquid nitrogen, it turns hard and it broke like a brittle material which we just saw. We can also see sometimes in a another experiment which we have not done yet. We can see that the wires made of material like niobium titanium, it exhibits 0 resistance when subjected to liquid helium temperature that means, this wire becomes superconducting wire. It shows r is equal to 0, i square r is equal to 0 that is no joule heating. These are very important changes that happen in these materials and these examples therefore, show that the material becomes hard and brittle at low temperature. At the same time, the electrical resistance decreases as temperature decreases for certain materials. These two examples show that material property do change drastically. In addition to these two properties which were just shown to you as an example, we got several other properties like strength, ductility of material, thermal and electrical conductivity, specific heat capacity, thermal expansion. All these properties change at low temperature and therefore, the knowledge of this material property changes at low temperature is very important for proper design of a material which is going to subjected to low temperature and this is what we plan to do in this particular lecture. Before we study the property changes at low temperature, it is important to understand the structure of matter. Solids are composed of atoms which are bound together and arranged in regular arrays. We know this. Solids are broadly classified into two types metals and nonmetals and in cryogenics we use both metals as well as nonmetals. The nonmetals are further classified into plastics and classes. Any cryo container for example, or any cryogenic equipment, we can have metals, we can have plastics and we can have glasses also. Well, glasses make a very special case. Most of the places metals are used and plastics are also used sometimes to support this metal and therefore, I am keeping this lecture limited to discussion regarding metals and plastics and we will study the property variations of these materials at low temperature. So, from cryogenic perspective I will discuss metals and plastics only. As you know now we will come to metals. We know that metals have highly ordered structure. The atoms are arranged in symmetrical crystal lattices and the most common of these lattice structures are face centered cubic that is FCC material, body centered cubic that is BCC material and hexagonal close packed material that is HCP material. I think we have studied all these things in the material science, in the fundamentals of material science may be in the first year or second year of engineering. We will just revise those fundamentals and find out what exactly FCC, BCC or HCP mean. The face centered cubic structure has an one atom at each of the 8 corners and an atom at the center of each of the 6 faces. Here you can see an FCC structure where you have got 4 plus 4 8 atoms and atom at the center of each of the faces and there are 6 faces. So, 8 plus 6 makes 14 atoms for FCC structure. The BCC structure has an atom at each of the 8 corners and one atom at the center of the cube that means there are 8 corners plus one at the center which makes it 9 atoms in total for BCC material. As far as HCP material is concerned which is hexagonal close packed we have got hexagonal side now. We have got 2 hexagons one at the top one at the bottom and there is an atom at each of this corner and this makes 12 corners. So, we got atoms at 12 corners and an atom at the center of each of the 2 vertical hexagonal ends which are these 2 and then 3 atoms at the center of here. So, here we can see that we have got 3 atoms at the center of a prism which is formed by this triangular face. So, you got a 6 atoms on the top 6 atom at the bottom plus 2 at the faces over here and then 3 atoms at the center of the middle plane of this prism which joins the top hexagonal face and the bottom hexagonal face. All these make around 17 atom for HCP lattice structure. The above lattice structure decides the number of slip planes in the crystal and this slip plane is a very important concept. This slip plane will decide lot of properties for this material. The slip planes are the directions within the crystal in which the planes can slip or move easily one over the another. So, slip plane basically will decide in what direction the thing should move. The dislocation should move and this is what we are going to talk about. The real crystals do not have perfect lattice arrangement. The real crystal will have some kind of defect and dislocations and there exists always some dislocations like edge dislocations, screw dislocations, some imperfections like we got an additional atom called interstitial atom. We can have some atom absent which is called as vacancy etcetera and all the movement of this dislocation decides the properties of this material. The number of slip planes now the number of slip planes are governed by the lattice structure we talked about. The number of slip plane governs the movement of these dislocations and this governs the ductility and the impact strength of any material. Now this is all related the lattice structure. The atom structure in a lattice will determine how many slip planes are there and the number of slip planes will allow the dislocation to move in the structure. So, ultimately the lattice structure will decide whether a particular material allows the motion of dislocations or not. The FCC structure what we found was FCC structure has maximum number of slip planes while the BCC structure has the least. The SCP structure falls in between the above two lattices. What does this mean? It means that the FCC solids are more ductile as compared to the BCC and SCP. So, FCC we can call as a most ductile material followed by SCP followed by BCC based on the available slip planes in which direction the dislocations can move. With this background now we will try to study various properties of material which are mechanical properties, thermal properties, electrical properties, magnetic properties. So, there are several of these properties which we can study because this course is meant for mechanical engineers. I am going to talk about mechanical properties and thermal properties from mechanical engineering point of view. While there are several electrical properties, several magnetic properties which I think we will not bother about so much while I will cover these properties in terms of superconductivity. So, we will devote some more time to understand what are these mechanical properties, what are these thermal properties because that is what will govern the thermal design of any material, thermal design of any cryostat. At the same time thermal and mechanical design of any cryostat for example, or any cryogenic equipment. While I will not cover these properties in details the electrical magnetic properties, but I will instead talk about superconductivity in this case. The mechanical properties can be well understood once we understand the stress strain curve for any material where the stress is kept on the y axis while the strain is kept on the x axis. Now, when a ductile specimen is subjected to a tensile test, the stress strain relationship is shown as follows. So, you can see that in this case the stress is varying in relation with the strain and the variation is linear variation or we can see that the stress is directly proportional to strain in this case. Now, you could see that when the material is subjected to tensile loading the stress increase in a straight line up to the point called proportional limit or PL which is what I have written here. What is this PL? This PL is the limit in which the elongation of the specimen is directly proportional to the stress applied. So, we can say that during this period stress is directly proportional to strain. Most of you may have done all these things into details I am just trying to give you some fundamentals. So, that we can understand the variation of properties which we are going to discuss in the next slides. The slope of this line which is constant during this entire line is called as you know Young's modulus. So, stress upon strain is constant during this period. Now, if this elongating force is removed in this case the material will come back to its original shape and size and that is why we call that this particular behavior is nothing but elastic behavior of the material. Even if we remove the elongating force the material will come back to its original shape and size. However, if we apply the force beyond this particular strain or beyond this particular stress you can see lot of different things happen. We can see first at this point at point C that there is a tremendous increase in strain immediately by the application of very small stress and if we apply more stress or if we apply more force we can follow the behavior in this pattern and this is what a stress strain curve of any ductile material would be. What you can see from this is we can see the elastic region up to P L. We can see that the material yields during this space this is called yielding and the material shows plastic behavior at this point. Now, during this period if the stress or the elongating force is removed the material will not come to the original shape and size. You will find some deformation in the material. Now, there are various point which I have shown here C D E F G the F what we call as ultimate tensile stress. The point C is called as the yield point and the stress is called as yield stress. The value of the stress at this particular point is called as yield stress while the point F we called as ultimate tensile stress. If we increase the stress beyond this value we find this kind of behavior and at this particular point G the there is a breakage point. In principle the force at point G will be actually more than that of point F but as you go beyond this point the area of cross section goes on decreasing and therefore the force upon area or the stress starts coming down. However, the engineering diagram will show that the G is more than F. Now, this is what we call as a typical stress strain curve for any material and what is important to note here are the two properties one is a yield stress and other one is a ultimate tensile stress. We will study the behavior of these two properties at low temperature. This is typical diagram for a ductile material and we can see now the brittle material also has a stress strain curve and it will also have its proportionate limit. So, if I want to compute if I want to draw a stress strain curve for a brittle material let us say this is a brittle material it will have its own proportion limit now during which time this behavior is elastic behavior. If I increase the stress beyond this value this is the behavior and G is a breakage point and the material will break. So, a stress strain curve of brittle material is as shown over here and stress when exceeds the p l value it will break at this point G. So, in summary we have got two stress strain curve one is showing the ductile material and one is showing the brittle material. We will study these two properties more that is a yield strength and ultimate tensile strength what happens to this property at lower temperature. The mechanical properties which we want to study in this particular course are the yield and ultimate strength of which we just talked about. We talk about the fatigue strength of a material. We talk about the impact strength of a material. We talk about the hardness and ductility of the material and we talk about elastic model of the material. So, all these five properties in fact six property they are basically the mechanical properties. In the next lecture maybe we talk about the thermal properties and the electrical property and the magnetic properties. Now, these are the five mechanical properties which we will discuss in this particular lecture for different materials. First we will come to yield and ultimate strength of the material. Just to redefine those property which we just saw what is the yield stress? It is a stress at which the strain of a material shows a rapid increase with an increase in stress value when subjected to simple tensile test. We found that suddenly the strain increased by giving a small stress at a particular location and that is called as yield point and the stress is called yield stress. Ultimate stress it is the maximum nominal stress attained by a test specimen during a simple tensile test. So, ultimate stress is also a very important property, a very characteristic property of any material and also yield stress also is a characteristic of a characteristic of a any material. Now, we will study what happens to this properties at low temperature. This particular figure gives the variation of yield strength at low temperature. You can see the y axis is giving the yield strength while the x axis gives the temperature variation in the reverse direction. That means, what I am saying here is a 300 Kelvin is a room temperature and then I am coming down towards 0 Kelvin or towards cryogenic temperature. What you can see? I have shown different curves here they are meant for different materials. For example, this curve is meant for 304 stainless steel SS 304. The second curve is 9 percent nickel steel. The third curve is carbon steel CT 1020 and then we have got an aluminum alloy. All these materials are shown in this legend in the order of decreasing strength value. So, you can see that in all these cases the strength as you come down lower in temperature the strength has increased most of the cases in all the cases almost while the stainless steel shows maximum strength as compared to other materials. So, we can conclude from heat the yield strength of various commonly used material increases with decreasing temperature. This is what we see from this particular curve. These materials are normally alloys of iron and aluminum etcetera. When we saw the curve it was for yield strength and now see the similar kind of a curve for ultimate strength. So, again in this particular map what you see is a ultimate strength plotted on a y axis and again temperature on the x axis and again you can see that as the temperature is lowered from room temperatures to 0 Kelvin the ultimate strength of the material have increased the way it was shown for yield strength. So, we can see that in both the cases the yield strength and the ultimate strength increase as the temperature is lowered. At the same time what we again can see from this that the stainless steel shows maximum ultimate strength in these four materials followed by 9 percent nickel followed by carbon steel followed by aluminum as shown in the order in given in this legend. So, again we can conclude similar to the yield strength the ultimate strength of the material also increases with decreasing temperature. This is a very important thing at the same time what it shows is the room temperature is actually the unsafe thing. If the material is safe at room temperature that means it is definitely safe in the cryogenic temperature. So, for any design your reverse design will be at room temperature because your ultimate strength or the yield strength is lowest at room temperature. So, the safest case if you want to see the failure mode it should happen at room temperature as far as the failure based on ultimate strength and yield strength is considered. We could also conclude from the two figures that stainless steel has the high strength and is mostly preferred material at cryogenic conditions. So, many applications what you see is having stainless steel as a material. I have just got a small specimen over here you can see a very thin walled tube which has got around 0.15 millimeter thickness and this is welded to a flange what is constituting one tube and if I close from this side if I got some welded structure at this point we have used this tube for pulse tube cooling and we have seen that this particular tube of thickness 0.15 millimeter can stand very high pressures and as high as 25 bar pressure of gas. It shows that such a small thickness of a material also can stand very high pressure and in most of the application therefore what we have used is stainless steel this is SS 304 what we use it stands very high pressure as high as 30 to 35 bar also one has to really calculate the hoop stress in this case and then calculate the dimensions of this, but a thickness of 0.15 to 0.2 millimeter or 0.3 millimeter can stand very high pressure. I just bought this specimen to show you that such a small thin walled tube can stand very high pressure SS 304 is the material which is being used for this particular purpose. Going back from having studied this ultimate strength behavior and yield strength behavior at low temperature let us start to understand why it happens like this ultimate and yield strength of the material largely depend on the movement of dislocations. We have earlier studied the movement of dislocations and its relation with the slip planes and its relation with the lattice structure. The movement of dislocation also depends on the internal energy or the lattice vibrations and at lower temperatures the internal energy of the atoms is very much low. As you know the internal energy is basically a function of temperature and if the temperature is low the internal energy of the atoms also is low. As a result the atoms of the material vibrate less vigorously with less thermal agitation. So at lower and lower temperature the vibrations the lattice vibration is very very minimum and therefore the material vibrate less vigorously with less thermal agitation. When these agitations are low when this agitation are low at low temperature the movement of dislocation is hampered. You can imagine that when the dislocation movement is ultimately it may be a long dislocation movement a very large dislocation movement at room temperature. However at lower and low temperature the motion has come down and this vibration if they are reduced it does not allow the dislocation to move. It will hamper the movement of the dislocation. When the movement of the dislocation is hampered what will you have to do? This dislocation movement now will require a very large stress to tear the dislocation from their equilibrium position. If we want to move this dislocation now when the thermal vibrations are very large or the lattice vibrations are very large we will require very large stress to tear these dislocations from their equilibrium position which means that the material will exhibit high yield and ultimate strength at low temperature. So the behavior of the material at low temperature in terms of increased yield strength and increased ultimate tensile strength at low temperature could be understood by this particular analysis that the lattice vibrations are very very low at low temperatures and this hampers the dislocation movement at low temperature. So till now we studied the yield strength and ultimate tensile strength variations at low temperature. In cryogenics we also have to study fatigue strength. What is fatigue strength? The material exhibit fatigue failure when they are subjected to fluctuating loads. Now this fluctuating loads could be for example I have got a small little sample over here and you can see that this is small bearing through which the piston goes and as you know the piston is going to have an oscillating motion or a fluctuating motion up and down and this is called as flexure bearing and this particular bearing goes up and down and therefore this will be subjected to fatigue failure. If at all it fails it will fail by fatigue. So I have to ensure that while designing this particular flexure bearing the stress achieved by this while in motion are less than a particular value or the particular fatigue strength of this particular material. This is very important that the bearing which is subjected to fluctuating load can stand the stresses generated during this motion. So these failures can happen even if the stress applied is much lower than the ultimate stress value. This is very important that the fatigue strength is actually much less than the ultimate strength of a material. So one has to really compute one has to really understand that the failure of this particular item will because of fatigue. The failure for example of this bearing is going to be because of fatigue and not because of tension or compression. The fatigue strength of a material is the stress at which the specimen fails after a certain number of cycles. This is what a definition of fatigue strength is that it is a stress at which the specimen fails after a certain number of cycle. So fatigue strength is normally defined in terms of cycles 10 to the power 6 cycle 10 to the power 8 cycles etc. Now let us see how the strength variation happens at low temperature. So here again you can see a curve on the y axis what we have plotted is fatigue strength at 10 to the power 6 cycle e to the power 6 cycles over here while on the x axis what we have plotted is temperature and this is my room temperature at 300 Kelvin and this is where you move towards the cryogenic temperature range as you have seen earlier in the yield strength and ultimate strength variation. Then you can see that as the temperature gets lower down the fatigue strength increases. So on all the three cases these are the materials which can stand fatigue strength. Again we have got a stainless steel, beryllium copper over here and carbon steel. In all these three cases what we see is at lower temperature the fatigue strength shows an increase over here. So again the worst case for these materials is at room temperature. So we can conclude again the fatigue strength increases as the temperature decreases. So as the temperature goes down towards cryogenic region the fatigue strength increases. The fatigue strength of a stainless steel is higher as shown over here. So again we can conclude that stainless steel is a preferred material if it is going to be subjected to fatigue loading. Now any fatigue failure begins with a micro crack. Again we will try to understand why does it happen the way it is. We have seen that the fatigue strength increases at lower temperature and any fatigue failure normally begins with a micro crack initiation. And at lower temperature after the initiation of a crack we require a large stress to stretch this crack. Why do we require large strength because the ultimate strength of the material has increased. So at lower temperature ultimate strength increases and therefore the crack stretching or the crack propagation. The crack initiation is okay but the crack propagation or crack stretching the stress required for this is going to be very large because of the increased ultimate strength of a material. And that is why like the ultimate strength the fatigue strength also increases at lower temperature or as the temperature decreases. Now in order to avoid fatigue failure when a specimen is subjected to fluctuating load the working stress is maintained below a certain value called endurance limit. So if I want to worry about a certain failure which I know that it is going to happen due to fatigue what I have to worry about is not the fatigue strength but I should worry about the endurance limit. If I keep the value of the stress generated below the endurance limit that means in principle this material should never fail. And therefore the endurance limit of a material is very important. The property we should know the endurance limit of particular material which is going to be subjected to fatigue loading and I should ensure that the stresses generated are less than this endurance limit. And flexure bearing which I showed to you is made out of beryllium copper alloy. So here you can see a beryllium copper alloy and this is what we call as flexure and this is what is used to manufacture the flexure bearing. The working stress is kept below the endurance limit to avoid fatigue failure. So I should know the endurance limit of the beryllium copper alloy and I should keep the stresses generated below the endurance limit of this particular material which will ensure that this particular material will never fail by fatigue. Now let us come and discuss regarding the impact strength and ductility of the material. These are very important characteristics. We have got various tests which we have studied in metallurgy or in material science that Charpi and Isoate tests are conducted in order to measure the resistance of a material to impact loading. So a certain material we know that it is going to be subjected to impact loading that is sudden loading we conduct these two tests Charpi and Isoate tests from where we understand how much that material is resistant to impact loading. Measure of resistance is basically nothing but the amount of energy absorbed. The energy absorbed when the material is fractured suddenly which means impact loading by a force and this is a measure of the impact strength. How much energy it can absorb after the fracture? If the material is fractured how much energy it can absorb will basically determine the impact strength of a material. More the energy it can absorb it has got more impact strength. In both these Charpi and Isoate tests the difference in the height attained by a hammer basically in these cases what you have is a hammer which comes down from a predetermined height. It hits the material and it fractures the material and this hammer goes beyond the material. So depending on the height which this hammer attains after the fracture is basically determine the impact of a material. So in both these tests the difference in the height attained by the hammer pendulum after the impact that basically it loses potential energy. This determines the impact strength of a material and this is nothing but the amount of energy the material can absorb after the fracture. Now this is a very different curve as compared to what you saw earlier. Here we have got a Charpi impact strength on a y axis and what you see on the x axis is a temperature again. So again we see from room temperature and come down to cryogenic temperature. Now here when we know that a particular material is going to be subjected to impact load we have to check that that the impact strength of a particular material is high enough alright. So you can see different curves here and in general for example you see that this is coming down, this is coming down, this is coming down. Well for this particular material which is stainless steel is almost horizontal that means there is not much variation in the strength value with the temperature. So in general what you can say from this the impact strength of the material decreases with the decrease in temperature or at most it remains constant for a particular material which is SS 304. While for all the material the impact strength has come down. So as the temperature gets reduced the impact strength of a material does get reduced. Now there is a very funny curve in this and this a particular curve I would like to highlight your attention and this material show some very specific characteristic. Few of the materials exhibit ductile to brittle transition or dbt at lower temperature. So you can see from this particular curve that this material can be called as ductile over in this region alright or it has high impact strength in this region while at this temperature around 100 Kelvin it suddenly came down the impact strength came down and came down to very low level and it is we can say that it is no more impact strength has drastically come down that means maybe this material was ductile at in this region during this temperature range and suddenly it has become brittle in this temperature range. It has undergone a dbt or a ductile to brittle transition in this temperature region that is what we call as while this does not happen for stainless steel it is happening for carbon steel ok. So carbon steel basically undergoes ductile to brittle transition at low temperature and the temperature at which this transition happens this dbt happens is called ductile to brittle transition temperature dbt and this dbt for carbon steel around 80 to 100 Kelvin. So carbon steel undergoes dbt at the temperatures around 80 to 100 Kelvin. This causes sudden decrease in the impacts of the material as I just said that this is having high impact strength over here while the impact strength drastically came down at this point. Similarly for 9 percent nickel the impact strength was very high here impact strength suddenly comes down at lower temperature while what you can see from here is the impact strength of stainless steel remains unchanged at lower temperature. This dbt variation the way it looks it is called as sometimes S transformation or S curve. So this decrease is as shown in this S curve many literatures refer this as also S transformation or S curve existence for this particular material. So this S transformation happens at 80 to 100 Kelvin in this particular material. Hence these materials cannot be used for cryogenic application. So for all those material which have got S transformation which have got dbt which has got dbt they cannot be used in cryogenic application because at lower temperatures they do not have any impact strength. Again we can find from the curve that stainless steel is the most preferred material from the impact strength point of view alright this is a very important finding from this curve. The impact strength of a material is largely governed by its lattice structure. At low temperature the material with body centered cubic lattice break easily that means BCC which have got minimum slip planes it breaks easily because the dislocations cannot move in this case. This is due to the reasons mentioned earlier on the slip planes and moment of dislocations. As a result the materials with BCC lattice are not preferred for low temperature application. The material with FCC or hexagonal lattice have more slip planes and these slip planes assist in plastic deformation. As we know that dislocation can easily travel through FCC material through SCP material and hence increase the impact strength of material even at lower temperature. As a result the material with FCC and SCP lattice are preferred for cryogenic application while the BCC material that the carbon steel are not preferred for cryogenic application because they become completely brittle at low temperature or the impact strength is very very low at low temperature. Now, let us see the next property which is ductility which is in a way related to the impact strength what we studied just now. A material which elongates more than 5 percent of the original length before failure is called as ductile material. This is the clear definition of a ductile material which material can be called ductile. When a specimen is subjected to simple tensile test ductility is given as a measure of percentage elongation of the length of the specimen at the failure or the percentage reduction in cross sectional area of the specimen at the failure. So, basically percentage elongation or percentage reduction in cross sectional area will determine whether a particular material is ductile at a given temperature or not. We will call percentage elongation to study the ductility of a particular material. Again this curve shows similar curve as we saw earlier that is the impact strength and this gives percentage elongation before failure versus temperature on the x axis. As you can see as the temperature gets reduced the percentage elongation decreases. So, this is for stainless steel, this is for nickel, this is for carbon steel and this is for aluminum. In all the cases what you see is at the temperature gets lower the percentage elongation gets lower down. So, again you have got a S transformation for carbon steel meaning which that it is it cannot be used at low temperature while the stainless steel, nickel steel and aluminum can definitely be used although the ductility is lower at lower temperature as compared to the room temperature. In general therefore, we can say the ductility of the material decreases with decrease in temperature. The materials which undergo DBT are not preferred due to decrease in ductility that means material like carbon steel cannot be used at lower temperature because they are no more ductile at lower temperature. For stainless steel the percentage elongation is around 30 percent at this point you can see at 0 Kelvin what we have is our 30 percentage elongation at 0 Kelvin meaning that it is fairly ductile for cryogenic applications. In summary what we can see here is a different material the embrittlement at low temperature for different material and under ductile what you see is a FCC and HCP can be used while in brittle material also there is some HCP material and all the BCC material. So, under ductile material we can use most of the FCC material which is copper, nickel, copper, nickel alloys, aluminum and alloys and austenitic stainless steel. The HCP material which we can use as a ductile material is titanium. So, all these materials can definitely be used for cryogenic temperature provided it satisfied other requirement like ultimate strength and yield strength etcetera depending on the failure mode for those particular materials. While these are all material which are brittle which remain brittle at lower temperature and therefore, they cannot be used unless specifically required and specifically evaluated at lower temperature, but mostly these materials will not be used for cryogenic applications. The next property is hardness of material. The hardness is the measure of the depth of standard indentation made on the surface of the specimen by a standard indenter. Most of you have studied this that you got a standard indenter and you see the depth of this indentation. The common hardness tests include brinal test, wicker test and rock weld test. So, you got a brinal test number BHN and VHN etcetera to determine or to measure the hardness number of a particular material. Hardness is directly proportional to the ultimate stress of a material and therefore, we know that the ultimate stress of a material increases at lower temperature meaning which we can conclude that the same trend will be holding good for hardness also that means, the hardness increases as the temperature decreases alright. So, we can conclude from here that the hardness of a material increases at lower temperature. The next property is elastic moduli. The three commonly used elastic moduli are Young's modulus, Shear modulus and bulk modulus. Let us not go into the definition of all these models, but we have studied the Young's modulus for tensile stress as I shown in the earlier curves. With the decrease in temperature, the disturbing vibrations and thermal agitation of the molecules decrease. This is what we studied because they all depend on the temperature of a material. At lower temperature, the vibrations and thermal agitation of the material will be less. This will increase the interatomic forces and verify reducing the strain at low temperature. What we mean to say that at lower temperature the interatomic forces will be higher and therefore, strain induced will be low at lower temperature. So, if I want to understand that thing, if I plot a stress strain diagram for a material, a stress strain curve for a 300 K and at 100 Kelvin and if we see that, if I want to produce the same strain that means, I have got the same strain for these two temperatures, I will say that at lower temperatures, I get higher stress as compared to at higher temperatures. That means, the stress value for the same strain at 300 K is much less as compared to what it is for 100 Kelvin. So, if I want to produce same strain at low temperature, greater stress is required meaning which stress upon strain at 100 K is going to be more than stress upon strain at 300 K. In other words, to produce the same stress at low temperature, less strain is required, I can go in a reverse way now. If I want to have same stress, I will get less strain at 100 Kelvin and more strain at 300 Kelvin. So, my stress upon strain at lower temperature will be different than stress upon strain at higher temperatures. What does it mean? The stress upon strain at lower temperature is more and as a result of which, the Young's modulus will increase at lower temperature because my strain values are less at lower temperature for the strain. So, stress upon strain at lower temperature is going to be more as compared to higher temperature which means that Young's modulus will increase at lower temperature and in the same way, I can conclude that this particular show that the Young's modulus variation at lower temperature with the temperature variation. So, again you can see that there is increase in the Young's modulus at lower temperature. The Young's modulus of various commonly used material is as shown in this adjacent figure. The elastic moduli increases with the decrease in temperature and all the three elastic moduli follow the same strain. So, we will not study all the other moduli, but what we can understand from the Young's modulus is that all this elastic moduli increase at lower temperature. Having studied all these properties for metals, there are non-metals also used as we talked earlier and the non-metal which we want to study here is plastic. So, plastic or polymers, basically plastic are nothing but polymers are made of a long change of molecules that polymers are identified by the existence of long chain of molecules and each molecule has thousands of atoms held together and arranged in a tangled arrays. So, this particular shows the various molecules and they are together with small in arrays basically. Now, the intermolecular forces that unite this polymer molecule are very weak and they are basically van der Waals forces. This particular force keep them united together, all the molecules are kept united because of this particular force. Now, if you want to study the tensile strength behavior of plastics at low temperature, this particular curve shows this behavior. So, if I want to plot ultimate stress of different plastics at low temperature, again what you see is at lower temperature, the ultimate stress of this material increase. So, ultimate strength does show increase and we have got different material like mylar, teflon which is nothing but PTFE, kel F we got nylon, PVC etcetera. In all the cases what we have the ultimate strength increase at lower temperature. The strength of various commonly used plastics is as shown the strength increases with the decrease in temperature, but of all this material the most commonly used material in cryogenics is PTFE. So, of all this plastic PTFE is the only one which can be deformed plastically because it retains its plasticity at low enough temperature at lower temperature of around 4 Kelvin. So, the mostly used plastic in cryogenics is nothing but teflon or PTFE. So, as we saw earlier that mostly used material metal is stainless steel similarly, we can say that PTFE is the mostly used plastic in cryogenic application because it retains it has got good strength at lower temperature at the same time it retains it plasticity at lower temperature. The effect of stress on plastic or elastomer is very less as compared to metals all right. The metals show different behavior high stresses while the plastic do not show that because they yield partly by uncoiling the long chain of molecules and sliding over one another. The effect of stress actually does not show so much in case of plastics. This motion is also facilitated by the thermal energy possessed by this molecules and at low temperature material deformation is more difficult due to decrease in thermal energy all right. So, as you know that at low temperature the deformation is not possible because of the decrease in thermal energy. So, we talked in brief about plastic and we talked at length about the mechanical properties of different metals. If I were to summarize the whole lecture we will summarize as follows. We found that stainless steel is the best material or the most preferred material for the cryogenic applications. Carbon steel cannot be used at low temperatures as it undergoes a ductile to brittle transition existence or DBT or DBTT ductile to brittle transition temperature. We also saw that the ultimate and yield strength fatigue strength of any material increase at low temperature while the impact strength and ductility decrease at low temperature. They could still be acceptable for example, we saw that for stainless steel the impact strength and ductility is still acceptable at low temperature. PTFE or Teflon can be deformed plastically at 4 Kelvin as compared to other material and also therefore PTFE is the most preferred plastic at lower temperature. Again we have got a self assessment exercise is given after this slide. Kindly assess yourself for this lecture. So, we got around 12 questions for you. Please do self assessment for yourself honestly and we have given the answers also for those questions at the end. Thank you very much.