 In this lecture, we will learn about fracture and creep. Fracture and creep are the two distinct mechanical properties of a material, which define how the material behaves in certain environment. So, like fracture is the fragmentation of material in two or more pieces, whereas creep is the time and temperature dependent deformation of the material. And we will learn about these two aspects of material as we go along. So, to define fracture, but before we define fracture, I would like to say what failure is. So, failure is very much different than fracture, because failure is the loss of functionality. Like if I have a cycle, I am riding a bicycle and if just a little bit there is a deformation of the cycle tire, I will know that I cannot ride the cycle anymore. That is the failure or the failure of the, the tire is no more functional. So, I cannot ride a bicycle anymore. So, that is called loss of engineering functionality. It may not be fracture. Yeah, though this tire, the same tire can fragmented more than two pieces. Still it is a failure, but also it is fragmented of fracture. So, we define fracture as a breakage of engineering component into two or more pieces. And in any engineering process, we do not want fracture to be catastrophic. It means we want fracture to always provide some indication that it is going to fail, because if it fails while fracturing, it can be very catastrophic in nature. So, like say a material is being turned on a lathe machine and if the material fails without any indication, that will be very catastrophic, because it can hit any nearby operating personnel. So, in that case, it might be very, very damaging. But if the component or the material gives an indication that it starts deforming or starts bending itself or starts losing its shape, then we would get an idea that this material is going to fail and we can take precautionary measures. We can stop the instrument or the machine and then we can replace the component. So, that is why it is very important that we learn about fracture, how a material is going to fracture or how it is going to break a particular engineering component. And the indication, the microstructural indication will be very much helpful in altering or altering the microstructure and then basically being able to tap the exact requirements from a particular component. So, in terms of manipulating the component and tailoring it, for a particular engineering need will be very, very helpful, because now we can take care of factor of safety. We can also give the exact weight what is required for taking a particular load. So, designing of engineering component will become very, very helpful in terms of weight saving, economizing the overall component while rendering the exact functionality that is expected out of that particular component. And this fracture can be through mechanical load. So, if I apply a very high stresses or I will be very high load to a component which it is not designed for, then the component can fail or it can fracture. Thermal loading, if I can thermally load a particular component, it can just basically fracture, because at higher temperature, the strength of the material also starts degrading. So, depending on that it can fail. Again, if I take that material and take it to very low temperatures, then even smaller impacts can fragment the material, because the material would have gone undergone that type of brittle transition temperature. It means the component itself becomes highly brittle in nature. So, that can be the thermal aspect of it. Also, it can be related to the creep as I said. At higher temperature greater than 0.4 times the melting point of the material, it can again lead to very lower strength. Yield strength can be very, very low at high temperature. So, it cannot sustain those high loading and it can fragment. Fracture can also occur because of corrosion. The corrosion can start eating away the material. In case, there is a pitting corrosion or very dramatic corrosion, the design strength of the component will not be its exact value, because now the material has been damaged because of corrosion and it will not be able to take as much load as it is being designed for. So, in that case corrosion can also induce much more damage for a catastrophic failure or fracture. Again, some biological entities can also lead to fracture. So, there are certain, say a particular component is being placed where we have very high bacterial activity and that can start doing certain leaching of the material and in turn it will degrade the strength of the material and then obviously the material for which it was designed for is no more serving its purpose. So, it can again fracture. Again, if there is, there are two articulating surfaces. One surface will start operating against the other. So, even wear can cause sudden or dramatic fracture of one of the components or both of the components as well. So, we can see the fracture is very different from failure because failure is a loss of functionality. It may not result to fracture. Fracture is the final component like even after failure, the component can basically fragment that is the next stage of failure or fracture definitely means failure, but failure does not always mean fracture and fracture can be induced by many various input variables such as mechanical shock or thermal shock or corrosion of the material. It can be biological damage to the material. It can again be wearing of material and there can be many other components as well. A combination of these or more can also induce the fracture and just to show a feel of how the ductile and brittle fracture can be induced. So, why ductile and brittle fracture is why because if I am getting some indication, if a material fails very dramatically, catastrophically like if I take a chalk piece and start, I just shear it up, bend it, the material or the chalk piece will fracture in a brittle fashion, but if I take a aluminum wire, I start bending it, the aluminum wire will not break. It will start deforming and I will do the process of bending many a times, so that it finally fractures, but in the process what I have done, the material is undergone much more deformation before it has been fractured and that is very good for us because now we are getting an indication that the material is going to fail and now if the need arises, we can always replace that particular aluminum wire with some more stronger material or a newer material within certain design limits. So, that is the basic need of ductile and brittle fractured components, so we can design them accordingly. In certain cases, we want to work with brittle materials, why because of their very high strength because of even their say optical properties or certain biological properties, we would want to play with brittle materials. So, in that case also we need to somehow impart much more toughening to it, we will see how we can do that as we go along, but in this slide I will just tell about the difference between the ductile and the brittle fracture. So, what happens if I take a small piece of material and I start putting a tensile loading, so I have a ductile material, I can have a moderated ductile material and then I can also have a brittle material. So, let me say the initial cross section of all the three materials are the same, so in a highly ductile material what will happen, the material start necking at certain stage and eventually what will happen it will fracture at a common single point. So, this is the fracture point in case of a very highly ductile material. So, we can see that the material will start deforming at some stage it will start necking just to accommodate the deformation and this neck will start going smaller and smaller. So, finally what will happen will have some area which is very very weak and this point contact will occur in a very highly ductile material. In case of moderately ductile material what will happen that will start creating certain voids in between as soon as the material is being deform the neck is occurring, but not to that large extent it will start creating some voids in between which will try to basically merge together and will get something called a cup and cone type of a fracture. So, this region would have fracture because many micro cracks will not become much bigger cracks and they will coalesce to form this sort of a fracture. So, we will see some sort of a cone and a cup type of a fracture. So, like we have a cone, so cone will appear more like this and cup fracture will be something like this. So, we can see this is kind of a cone and this is a cup. So, we can see this type of fracture in a moderately ductile material because in this case the necking is occurring to a very minor extent and it is occurring because of coalesces of the cracks in between. Just in case of brittle material there is no necking, so material will fracture very flat. So, we will see that the surface is very flat and apparently no deformation is occurred in the material. Apparently what is also you will realize the difference between brittle and ductile fracture is that the fractured surface will be very shiny. Whereas, this surface will be very dull when you see them. So, we can see in ductile fracture it can be a point fracture, it can be cup and cone type of fracture and the surface will appear a pretty dull. Whereas, in case of brittle fracture we will see that the surface is pretty shiny and highly flat in nature. Depending on that the brittle fracture can again be trans granular or inter granular in nature. Trans means it is through the grain, inter granular means in between the grains. So, fracture can also be trans granular or inter granular. So, if you can see a material always have some grains, a polycrystalline material where you will see the multiple number of grains out here and there. So, we can see in both the cases we can have some grainy material. So, we can see that we have certain grains out there. So, in a fracture what will happen the crack has to propagate from one end to the other end. So, in the trans granular what is happening is it is going through the grain. So, it is the through the grains this is in between the grains. So, you can see a crack once it is propagating it can propagate like this from this end to this end and eventually we have a fracture. So, the movement of crack from one end to the other end is through the grains and at room temperature the strength of grain boundary is much more stronger than the grain. So, grain boundary is much more stronger than the grain. So, apparently if we have a nano crystalline material or it means if we have a material with very fine grain size. So, in this case if you have very finer grain size then in turn what will happen the crack has to encounter grain boundaries more number of times and in process we will see a very enhanced strength of the material. So, in this case it was encountering grain boundary at 1 and 2 in a coarse grain material whereas in case of fine grain material or a nano or a nano material the crack is encountering grain boundary at 1, 2, 3, 4, 5 times. So, we can see it is much more it is encountering grain boundary much many more number of times. So, it will provide very high resistance to crack propagation. So, we can see a nano crystalline whereas a coarse grain material will show very easy crack propagation whereas in nano crystalline material we can see much more encountering of the crack path with respect to the grain boundary. So, we can see there will be very high resistance of the crack propagation. In case when we have a nano crystalline material similarly for intergranular fracture also we can see if a crack is propagating in this case of intergranular fracture the crack will initiate from one side and then it will follow. So, let me also draw one for the nano crystalline. So, I will see that in this case we have a very fine grain structure. So, in this case we can see that we have very fine grain structure and then grains will be very very I am drawing little bit more systematic or very self following structure, but it will be very very random in nature. So, in this case of coarse grain material crack will initiate at one point it will follow the grain boundary to finally fracture. So, this is the overall crack path in the case of coarse grain material whereas in case of fine grain material or a nano crystalline material the crack will initiate at one point and it will start following the grain boundary and it will start following the way it can follow may be somewhere it will finally. So, in this case we can see that the crack path is very tortuous and it means that the crack has to change its path very dramatically. So, in a coarse grain material as soon as the crack has initiated along a particular grain boundary it can progress through certain distance without getting affected without changing its direction that is for the coarse grain material whereas in case of fine grain material the grains are so fine that it has to come back to its original point change its direction by say 180 degree it was going down and it has to come up. So, in the process it is getting much more resistance because of the path because if the crack is propagating from left to right it has to go down and then come up it is doing nothing but absorbing certain energy for maintaining its original path. So, in terms we can in turn we can see that the crack path is very very tortuous for a fine grain material. So, we can see there is very high resistance for crack propagation in a fine grain material. So, we can see that whether the fracture is either trans granular or whether it is inter granular a fine grain material will impart much more resistance to the crack propagation or it will make the crack path very very tortuous or in turn the overall strength will be very very high for a fine grain material. In one more turn the toughness also toughness of these fine grain material also will be very very high because now this fine grain material can also realign themselves and they can absorb certain shock. So, overall strain and the stress path can recombine synergistically to enhance the fracture toughness as well. So, generally fine grain material will have very high toughness in comparison to that of coarse grain materials as well. So, that is what we just saw in the micro versus nano crystalline material. So, we can see that in micro in a micro grain material we have much bigger grains whereas in nano crystalline material we have very fine grains. So, that part we already observed that in a case of nano crystalline material the crack has to take a very tortuous path. So, in turn it can provide very high resistance to the crack path. So, in this case the crack path is much easier which in this case it has to go here changes direction come back and may be changes direction and get a very tortuous path. Also the strength of the material also enhances as we go with lower and lower grain size this is given by hall patch relationship. So, we have a coarse grain we have fine grain material. So, what eventually we are seeing that in a coarse grain material the crack path is very very easy it can follow through very easily whereas in fine grain material the resistance offered by the structure itself is very very high and also the strength of the material for deformation also requires very even enhance strength because of it is lower grain size. So, that part is being true for the nano crystalline material that we can enhance the strength of the material via reducing the grain size. But, that is true until only say around 20 nanometer of grain size and below that inverse hall patch relationship also comes into picture. That means that for grain size is lesser than say around 10 or 15 nanometer the strength also starts degrading. So, that is the overall deal with the micro and nano crystalline materials and eventually what happens is that the impact and fracture also is dictated by the grain size of the material like like I said earlier the tortuosity has been increased. So, also the strength of the material has been increased at the same time the nano crystalline grain they can also realign themselves. So, now they can absorb much more shock and then they can impact very high impact energies or they can have very high fracture toughness. The impact energy is nothing but it is defined as a fracture fracture fracturing a standard test piece. So, energy which is being absorbed in while fracturing a standard test piece. So, like we do it tensile test this is much more rapid form of the impact of that particular test that we can achieve fracture very very quickly. So, instead of doing the entire tensile test of loading the material and then seeing the fracture this test can immediately fracture it. So, we can get something called a fracture toughness of the material impact energy it can be identified using iso testing iso notch part testing or charpit charpit testing. In this case what is happening is we take a notch we can we develop a notch on the material and that material is now supported on these two ends and a impact is provided on the other side and then this material entirely fractures. And that is thing is that particular sample is now also been tested using charpit while using this instrumentation that we have load on one side then we have our sample just sitting and then it will again have a notch on this side. So, a notch bar specimen is on this side which is being held on an anvil and for a certain height because this has certain mass this load it has certain mass. So, what happens is this load is allowed to free flow and impact this notch bar. So, with certain height. So, there will be some absorption of this energy because we have certain load and it has certain height once it is allowed to flow or swing from one end to the other end there will be loss of height. So, we had certain height and finally, we can also see some h dash. So, there will be lowering of height because of the absorption of this energy by the notch bar. So, in turn through this particular equation we can always find what is the overall energy which is being absorbed by the sample. So, our sample is a notch bar. So, this is our sample and through that we can also see that what is happening in in terms of the absorption of this energy. So, we have either iso testing or Charpie bar testing. So, this is the bar generated is around 10.8 around 10.6 to 10.8 millimeter square sample and we provide a notch and then it is basically being fractured. The top center schematic shows the for the Charpie impact testing and in this case we have a notch 45 degree v notch which is around 2 millimeter d and it is a root radius of around 0.25 millimeter and the impact direction is shown along with whereas, the right hand schematic shows the way in which we do the impact testing for a for iso testing. So, both of these methods will give us the fractured. So, this is what we can see that the overall impact it basically is to fracture the sample. So, this sample will fracture it wherever we have notch. So, this load will start fracturing will fracture it along the notch and then we will see some fracture surface. So, this impact and fracture toughness can be measured by using iso or Charpie testing and we provide a notch in the sample and a load is swung with a certain height and then that load strikes a sample and there will be reduction of the height because of the absorption of energy by the sample and by changing the height of this load we can calculate what is the impact energy that is being absorbed by the material. It can be either provided either in joules or foot pound or Newton meters. So, Newton meter comes to be joules or it can also be calculated as foot pound and generally energy which is being provided here is around 20 joules or 15 foot pound is basically the minimum requirement for a particular material for certain engineering applications. Now, coming to the fracture toughness. So, apart from impact energy the fracture toughness also is a very very critical component of a material. So, as a material will be very highly tough it will have very high value of fracture toughness and fracture toughness is given by k c that is equal to y that is a constant for a material depending on the geometry sigma c is the critical stress for crack required for crack propagation is the crack length. So, k c is equal to y sigma under root of pi c and generally we can see that the thin specimen when we have a thin specimen the fracture toughness will start depending on the specimen thickness because now the material can also deform along the third direction. So, if you take a very thin material it can start deforming along that side. So, that toughness also will be very very different and if you do not allow the strain to be accumulated along thickness. So, what we can do we can enhance the thickness of the material. So, now in that case it will restrict any deformation along the z axis or the third axis. So, by that we can also induce plane strain conditions and what plane strain condition do it becomes a fundamental property. So, we can see that if you want to have a constant fracture toughness for a material we need to have very high thickness of the material or the crack notch should be much thinner than the thickness of the specimen. So, that there is no deformation occurring in the third direction and again fracture toughness can be defined in terms of plane strain as mode 1, mode 2 or mode 3 and we can see that the mode 1 opening is more like this. So, we can take a sample with certain thickness we can have. So, we can have only the opening mode. So, mode 1 is also called tensile mode or the opening mode. So, we can see that it is just the tensile mode or opening mode it can also be sliding mode. So, we can have this called a sliding mode this second mode is called sliding mode in this the top piece is being taken on the right hand side and this thing is on taking being taken on the left hand side along a notch. So, this is called a sliding mode third mode can be a tear mode. So, we can see that in this case what is happening is. So, in this case we can see that this part is being taken away from each other. So, it is going towards inside this plane and this is going outside the plane. So, in this case it is called a tear mode. So, we can obtain the another plane strain conditions when we have when we limit the deformation along the third axis what we can do we can do this fracture we can evaluate the fracture toughness via tensile mode sliding mode or the tear mode. So, we can call it mode 1 mode 2 or mode 3 toughness or we will call them k 1 c k 2 c or k 3 c for these 3 different conditions. Also the fracture toughness also it is a though it is a fundamental property it basically increases with increasing temperature. Because now with increasing temperature the material is much more it can deform very easily. So, it can absorb much more energy. So, it can provide a higher value of fracture toughness as we increase the temperature. Also it will increase as we lower the strain rate because as we increase the strain rate there is very minimal time for the material to adjust itself or to align or equilibrate with the surroundings. So, in that case as we start increase the increasing the strain rate the fracture toughness of the material decreases dramatically. The third case is the refined microstructure as we talked about once you have a nano grain material what it can do it can provide enhance strength as well it can accommodate much more strain into the material. So, in turn it can provide very high fracture toughness to the material. So, we can see that fracture toughness is a fundamental property it will increase as we increase the temperature or it will increase with decreasing strain rate or it will also increase when we have a very refined microstructure. So, that is the trait of a material. So, once we have a very fine microstructure or a nano structured material it generally shows very high fracture toughness in comparison to that of micro or a conventionally or a conventional material which is a very big grain size. So, fracture toughness is also one of the very important properties of the material. Eventually what can also happen we can also observe a ductile to brittle transition and that occurs the brittle fracture generally occurs because of decreased dislocation velocity. So, now dislocations cannot accommodate the stress because the rate of strain is pretty high or it means once you reduce the temperature the dislocation cannot move that easily. Also the material has increased yield strength. So, in turn it cannot accommodate thus the yielding of the material. So, in turn we can achieve a we will observe very brittle behavior of the material. Generally for low strength or FCC or HCP material they generally show very high higher impact energies and, but they do not show any change of this impact energy with temperature. So, dbt or it is also called ductile to brittle transition temperature ductile to brittle transition temperature. So, we do not see that transition in case of low strength FCC or HCP metals whereas, high strength material also do not show any variation in impact energy with temperature, but they eventually they are highly brittle. So, that is a problem with these high strength materials whereas, BCC materials they show transition from at high temperature they are at high temperature they are very ductile whereas, at certain point they undergo a transition in which suddenly from ductile material they become highly brittle. So, that is the problem with BCC materials and this concept came into existence because of during world war 2 when many naval ships while they were sitting in the sea they broke into two pieces. So, these materials the ferritic steel which had enough strength at room temperature they were left into the sea and because of the temperatures of that zone the ship just broke into two pieces. So, that initiated the this study of what happens at this low temperature why this ships are failing into more than two pieces as it is because of low temperature and essentially we can see that there is no. So, that was the concept of ductile brittle transition temperature and eventually we will see that there is no explicit criteria. So, that when this transition is occurring. So, that is being selected as 20 joules or 50 percent of fibrous fracture or it is also 15 foot pound of energy that can be absorbed. So, we can see when the impact energy is around 15 to 20 15 foot pounds or 20 joules we can call that as ductile brittle transition temperature at what temperature that particular thing is being observed or we can also relatively to 50 percent or 100 percent fibrous fracture also. So, in this case dbtT is given by the 50 percent fibrous fracture, but once it is being initiated we can take it down to say 100 percent fibrous fracture as well. As we see here in FCC and HCP we are not seeing any ductile brittle transition temperature and they generally are low strength materials, but they show very high impact energy and high strength materials also they are insensitive, but they are inherently very brittle. So, coming back to the microstructure of the material when we have a nano crystalline material we are seeing decrease in the grain size and that will allow much more deformation even at much lower temperatures because now grains can realign they also have very high strength and in turn they can have very high toughness or it means they can survive or they can retain this higher impact energy of 20 joules even at much lower temperatures. So, decrease in grain size it also lowers the transition temperature that is very good because now the material can operate at even lower temperatures and that occurs because of both enhancement in the strength as well as toughness due to the lower grain size. So, this is what this is one more functionality of the nano crystalline materials that they can show enhanced toughening in such conditions as well. So, we can see this phenomena of ductile brittle transition temperature how it differs from material to material like in this case of low strength FCC HCP materials it has very high impact energy, low high strength materials they again show non dependence on the temperature of impact energy whereas, BCC materials they undergo a transition and to lower this transition is very much required and that can be achieved via controlling the grain size. So, we can reduce the grain size and then we can achieve enhanced toughening. Now, coming to the another deformation criteria which is called creep, creep is a time dependent permanent deformation of a material, but it is under the influence of constant load of stress which is pretty low much lower than the yield strength, but at pretty high temperatures temperatures are ranging greater than 0.4 times the melting temperature of the material. So, you can see creep is a time dependent permanent deformation of a solid material another influence of load of stress which is much lower than the yield strength at room temperature, but it occurs at very high temperatures which is to the order of greater than 0.4 times the melting temperature. And we can see applied stress is pretty less than yield strength at that temperature and this basically occurs that long term exposure of a material because of high stress and temperature is main reason for the creep. So, if we keep a material at high temperature high enough temperature for long enough duration and that material will undergo some change in the structure it will deform permanently and that is the cause for the deformation of the material and that is not very much desirable because it will change the shape of the component and that might lead to the sacrificing the safety of the component. So, that in that case we can see that the creep also needs to be controlled by enhancing its strength. So, we can utilize again certain design criteria and we can avoid long term exposure of the material to high stress and temperature to avoid the creep. And again the creep rate will depend on the material kind of material we have. So, if we have very high strength material the creep will be delayed the time of exposure. So, if we keep the material for long enough time if we expose it for very long enough time the creep deformation will be pretty much high temperature again if we keep the material at very high temperature the creep rate will be very very dramatic will be very high and the material will deform very rapidly applied stress. So, again it also depends on the kind of loading that is being incurred on the material. So, if we have very high applied stress the material will undergo very high rate of creep. So, we can see the creep is dependent on many parameters such as material its microstructure the time of creep or time of exposure temperature at which the creep is occurring even the applied stress on which this loading is being provided to the material. Though creep induces deformation it may or may not lead to material failure the creep deformation can be very very marginal it can be very very minimal. So, it might deform the material, but may not lead to eventual failure as well that is one more criteria with respect to creep, but sometimes creep is very very useful also because if a material has undergone it has say inculcated much stress because of sudden processing and once we heat it to high temperature for long enough duration it can relieve those stresses because now the yield strength of the material has been reduced. Now, it can release its stresses which might have incur incurred during the processing or even during the even in the functionality or when the material is being utilized during the service. So, that again can reduce the relieve the stresses and that can again avoid the failure of the component in that sense. So, sometimes creep can be little bit useful, but it has to be in a controlled fashion. So, creep accommodates stress with time before eventually the material fails again the concerned areas because once we have a creep it starts accumulating much more strain or it can also starts accommodating stresses. So, the concerned areas which are affected by this creep are. So, steam turbine power plants, nuclear power plants, jet engines, heat exchangers and basically some places where we can have some temperature for prolonged exposures and also some stress that is incurred on the material. So, like we have steam turbine power plants, nuclear power plants, jet engines, heat exchangers. So, here we are talking about certain temperature, certain duration on which that particular component is being operated and also the stress which the component has to resist. So, in those three under those three conditions we can see that it can always induce some deformation in the material because that it is very favorable for very high temperature around greater than 0.4 times the melting temperature. So, there is some stress or loading also there is enough time for the material to correspond to that. So, in that case it creep can become very critical. So, in this case we have to control the creep by designing proper designing proper selection of the material. Also calculating what is the temperature, what is the time and what is the stress level that is acting on the on that particular component. So, in that case we can utilize certain design concepts of controlling the microstructure as well by altering the microstructure we can also control creep in certain sense or by controlling the stress or temperature also we can control the creep. Creep has it is own features we can see that the creep can be divided into three stages it can be stage one stage two and stage three and stage one is called primary or transient creep. So, we can see in first stage what is happening is we have a instantaneous initially as we apply the loading we have some instantaneous deformation that inculcates in the material. So, as soon we apply the load it will have certain strain that instantaneously develops and as soon as the as soon as the time increases what we can see the creep rate is now decreasing creep rate now starts decreasing and in this case what is happening the dislocation climb is occurring which is away from the obstacles and also the strain hardening is occurring in the material that starts reducing the creep rate. So, the creep rate is given by the ratio of a creep strain with respect to time. So, d epsilon by d t that basically starts now reducing in the first stage. So, it is occurring away from the obstacles and we can see the creep rate starts decreasing and there is instantaneous some strain hardening also occurring in the material that provides enhance resistance to the creep. Whereas, in second case what is happening it is called secondary or the steady state creep in this case we can see the creep rate is almost constant it is more like a straight line and in this case what is happening the recovery and the strain hardening they sort of balance each other. In first case we had we had higher rate of strain hardening, but in case of second stage what is happening the recovery and strain hardening they balance each other or the rate of recovery and strain hardening is very similar. So, what we can see here is the rate of dislocation climb equals that of that blocking that occurs by the obstacles and this is nothing but the minimum creep rate and this is the prolonged duration. This is the dominant factor which is basically been incurred in the second stage and that dictates how much is the life time of the material and again d epsilon by d t will depend on the material properties exposure time what is the temperature what is the stress. So, by controlling the microstructure also we can obtain a very high creep resistant material and in this creep basically grain boundaries are very harmful or deleterious. So, that is where the deformation really occurs. So, by incorporating nano crystalline material that will have very high creep rates. So, by increasing the grain size we can have much lower creep rates because now grain is much more stronger than the grain boundary at very high temperatures. In third case what happens the necking starts the stresses also increase the grain boundary separation will occur on all that. So, tertiary creep is generally very rapid and this duration is very very also very very short. So, as soon as the tertiary stage starts the dimensional material also enhances very dramatically and as we can see the creep rate now starts increasing very dramatically and leads to eventual failure or rupture and that occurs by grain boundary separation the formation of internal cavities cracks voids and so on. So, that has damaged the material to a very large extent. So, we can see the creep primary stage we have lowering of the strain lowering of the creep rate because of strain hardening. In second case we have a balance between the strain hardening and the recovery in the third stage we have very rapid enhancement of the creep rate and eventually leads to rupture because of the internal defect generation such as cracks cavities and voids. And the creep rate is basically being given as d epsilon by d t is a function of the sigma that is applied stress with respect to also the temperature. So, as soon as the as temperature is high and stress is high the creep rate also will be very very high it can also be given as k sigma power m e power minus q y k t. So, this can be a constant. So, this is a constant which is a combination of c by d raise to b. So, we can see that c is a constant which depends on the material and the creep mechanics how the creep is really occurring m and b are the exponents. So, we can see m and b are the exponents m is a strain exponent d is the grain size exponent q is the activation energy of the creep rate to the creep mechanism. So, depending on which creep mechanism is active we will have a corresponding q or the activation energy if we relate to that sigma is the applied stress. So, as we are very high stress this exponent will dictate what is the material response to that particular stress applied stress level d is the grain size. So, as we have very low grain size the overall value of this d p will be very very low and eventually the resistance will also be very very low because that is in the denominator. So, higher the value of d lower will be the creep rate. So, we can see that for a nano crystalline material the grain size has to be very very higher or the grain boundary area has to be very very minimum for this particular case and k is the Boltzmann constant is the absolute temperature. So, in that case we can see that nano crystalline grains do not serve as a good resistance for the enhance creep rate. So, to restrain the creep we always need to have a very coarse grain material. So, we can see the effect of temperature and the stress can be given as like this. So, we can define the creep strain along the y axis and time along x axis. So, we can see that when we have lower stress and temperature our second region or the steady state creep region is very very long and also we have a particular instantaneous strain that is also much lower. But, as soon as we increase the temperature and time the region the instantaneous stress also increases also the region in which we have a stationary creep or second stage creep also is now reduced to very very smaller region. So, that what we can see that the region starts decreasing as we increase the stress or the temperature. So, that is the effect of temperature and stress with respect to the creep rate. Also the damage is now to very large extent because now third stage has started very very quickly. So, in this case third stage has not started yet in this case it has started at this particular time whereas, in this case it has started much earlier. So, that will lead to very eventual very rapid failure of the component. So, as we have very high stress level or very high temperature that will lead to a very eventual failure at a much rapid rate. But, now sometimes the extrapolation of data also is very much required because if you do creep we might require E S to complete the test and that becomes impossible. So, there is a Larson miller parameter which can take account of prolonged exposures or enhanced creep rate at enhance at elevated temperatures. So, once we know what is the miller parameter for a particular material we can also calculate what is the stress or the rupture life time of that material at certain temperature. So, the Larson miller parameter can be calculated for certain stress values. So, we can see when the fracture is occurring. So, for a particular stress value say if you want to have a particular stress value of say 100 MPa we can get corresponding Larson miller parameter. So, for a particular strain level or stress level we can keep calculating the Larson miller parameter for a particular temperature. Now, once we know that we have stress of 100 MPa it is giving to such and such Larson miller parameter. Now, we know this term and if you want to calculate what is the rupture life time. So, in this case we had we want to utilize a temperature of 1000 degree centigrade or 1 to 73 Kelvin. So, now once we know what is the Larson miller parameter say it is the value of K C generally 20. So, we can always calculate what is the rupture time. So, we can see Larson miller parameter in this case is K 1 which equals temperature of 1 to 73 Kelvin C is 20 plus log of T R. K 1 is known from this particular point Larson miller parameter it is already known. So, K 1 is known everything else is known what we can find we can identify what is T R at 1000 degree centigrade. So, once we can do test at higher temperature we can always correlate them with the Larson miller parameter and from that we can also identify say what will be the fracture time or the lifetime of this component at say now 300 degree centigrade. And if we actually go about testing this component at 300 degree centigrade we might require at least 4 5 orders of magnitude higher time then the then the material which is filled at 1000 degree centigrade. So, now utilizing this Larson miller parameter now we can back calculate and we can find the rupture time using this Larson miller parameter. So, that is the ideology of using utilizing the Larson miller parameter in calculating the rupture time also the strength of obstacles also come into picture. Once we have the activation energy for overcoming the obstacles the shear what is required for creating the shear for utilize for this creep. So, what we can see the overall obstacle strength it will be very strong from the dispersion. So, once we have nano crystalline materials it and also there is some precipitation at nano scale that can eventually induce very high activation energy. So, it means the creep process can be deterred or it can be slowed down to very dramatic extent when we have nano precipitates. Once we have higher dislocations forest of dislocations or we can have very weak precipitates that will lead to lowering of the activation energy or we require lower stress shear for lower stress for the shearing or the movement of the grain boundaries for this creep creep. And once we have obstacle strength pretty low we require very lower shear strength for causing this creep there will be very lower lattice resistance or it will be very lower of solution hardening. So, in that case we can observe that the spacing between the precipitates or the dispersions is also very critical. So, once we have the spacing very near it can induce very high it can induce very high resistance to the creep of the material. So, we can have obstacle strength which can be strong weak or medium. So, we can see the obstacle strength it can be very strong once we have this order of couple of nanometer also how well they are spread apart. So, if they are very very nearby to each other it means L is very very less. So, this T the force shearing force required for their movement is also very very high and in turn activation energy is also dependent. So, that also will be very high and we can get very high obstacle strength because of those precipitates or dispersions. So, this is very very critical once we have nano phases which are present or nano precipitates or nano obstacles very hard obstacles which are present for reducing the grain boundary movement or even the grain coarsening. So, in that turns we can reduce the creep of the material. So, because we will have some creep we have some pinning agents such as such as very fine dispersants of ceramics which can be there present in a very soft matrix to resist the creep deformation in the material. So, that is how we can enhance the creep resistance of the material by incorporation of very fine ceramic particles to resist the deformation due to creep. And this obstacle strength can vary depending on what sort of obstacle is being is resisting the creep deformation. So, in summary we can see that we have a fracture which can be either ductile or brittle and that depends on the macro structure of the material. If we have very fine micro structure that can induce much more strength and strain that can be accommodated into the material before it fractures. Also we can we also observe the observe that the intergranular and transgranular fracture can also occur in a brittle material. And how nano crystalline grain structure will assist enhanced tortuosity of the crack and enhancing the toughness thereby and impact and fracture toughness again we can see that because of enhanced strength and deformation in the material we can also achieve very high fracture toughness in case of nano crystalline material. Also there can be three different modes it can be opening mode sliding mode or the shearing mode for achieving this fracture toughness in a plain strain condition. And that becomes a minimum value of the fracture toughness and that is independent of the thickness of the material. Because once we have a very thin material fracture toughness can start depending on the thickness to avoid that we can also induce plain strain conditions. And in that we can also see that nano crystalline materials will have much more fracture toughness in comparison to the micro grain structured materials. Coming to creep, creep is a time dependent permanent deformation of the material which occurs at very high temperatures greater than 0.4 times Tm and stress levels much less than the yield strength. And then we have Larson Miller parameter to basically correlate the rupture time at different temperatures. So, if you want to do a test which is kind of impossible or very impractical that can be also evaluated using Larson Miller parameter and that dictates what is the role of temperature and stresses and obstacles in inducing certain creep resistance of the material. So, we can play with the micro structure, we can play with the temperature, we can play with the stress or we can also play with the obstacles which are present in the material and the exposure time to eventually control the creep rate and design a perfect material for its resistance. So, with this I end my lecture. Thank you.