Lecture 08 : Basics of Materials Science-X (Part 02)

[Music] welcome back to second part of this lecture 8 so as you have seen we have been discussing about the tensile testing and the various strength and ductility parameters we talked about strength ill strength UTS fa stress and then indu we talk about percent elongations and percentage reduction in the area so let's now see actual values of the stress and strength typical mechanical properties are measure at room temperature it can measure high temperature low temperature also but typically you measure at room temperature and these are the values it shows so let's take aluminium aluminium Alloys has very low strength something like you know ill Str is 35 to 55 and UTS is something about say 900 so that means that's aluminium and an aluminum all right that's why it is shown like that then your elongation can be something like 45 to 50 and uh some zeros have got deleted because of the size of table and you know I didn't talk about poison ratio that's also important parameter poon ratio is talk about the ratio of radial versus aial deformation if you deform any material in tensile strength what will happen that there will be two kind of strain one is the increase of length other is the reduction of the area right and it is not always true that both the things will be same so depending on the type of materials there'll be variations so poison ratio for metals and mostly almost close to 1/3 or 3 to. 34 copper all are much stronger and as you can clearly see that uh the strength of copper allies are much higher it can go up to 1100 mpm ill strength UTS even much higher then many Steels are more important you should use these values and T State and Sal is zero elongation but very high strength you can clearly see then I given you some properties of other nonmetal IM Mater like diamonds even rubber thop plastic therates you look at it at your own space I don't want to dis spend a lot of time on this table look at your own space because you should know this values some idea of the values because you're going to design materials discover new materials so you should have fair amount of idea of these values I'm not saying that you should remember mag up no but get an idea of what the range is in which the values of strength dity can vary for each set of materials well we talked about mostly parameters tensile stress parameters related to the original area and original length right but as you know that's not the case always because as you are the forming the material the area also changing as well as the length only thing which is remaining constant is the volume of the material right as we have we already talked about it that a0 l0 is equal to a into L right origin area original length equal to length area and length at any time during deformation so that means what the stress and strength which you're measuring using the original area original length will not be correct when the material is getting deformed so what you do you take care of that part using the actual or intous area or instaneous length so two new parameters comes in picture Str stress and two strength true stress is what this equal to force divid by the instaneous area or actual area at any point of the test during the testing St Str is basically nothing but change in length divided by the actual length or instaneous length DL by L remember the the engineering strain was changing L by the original length here we are changing the definition what is that changing or changing is basically Delta L by L so total strain is nothing but integation l0 to l d l by L that's equal to log of L by L am I clear so this is the difference between two stress and two stren Vis engineering stress and Engineering stren please keep in mind these definitions are very important because two stairs two St can be used when you process materials using deformation processing engine stress enging strength are used for design of any component if you want to use any material in actual application what kind of parameters you'll be using using ill stress that's why you ous there you are going to use or you know original uh length and original area one can actually you know convert or one can get relationship very easily from two stress to engineering stress and two strength to engineering strength these are there in the book of George you can easily find out more accurate measurement should be what this way like spce SP inter area or here you can see even if you can consider diameter also so what do you see is this two strs = to 2 log of d 0 by D or d0 is the original diameter and D is the instaneous diameter well I've given you the relationships you can clearly see here for the two stress and two Str with two stress the enging stren and therefore two stress is equal to engineering stress plus into multip 1 Plus Engineering strain and two strain is nothing but log of 1 plus in Str this is very easy you can also do that so no problem so how does this two St two s c will look like well two St two stin c will never go down as the engineering St St curve does you can see State strength curve is behaving like this but two St two St curve is going up and up that's because you have taken care of the change of area or the length that's why otherwise this should have been behaving same way this gives you much better perspectives in terms of the how the material is behaving so there is nothing like a going down like a Yang C please remember these aspects well this is in a Nal showing you everything two St two St versus Eng stest 10 curve and at this two St at the 10 UTS or the peak of this engine stest Cur your stress strain is equal to the strain hardening coefficient we'll talk about a little bit later so you know this this portion of the curve in t curve the linear non linear person Cur can be fitted with a with equation and that equation is basically this which is known as a flow C which is nothing but Sigma T = to K multiplied by Epsilon to the^ n where K is a strength coefficient and N is the strength hardening exponent because it is in the power that's why it's called exponent so this curve is defined by this equation this equation is very fundamental because it talks about two important material parameters one the strength coefficient K other one one is the n or strain hardening coefficient why it is called strain Harding coefficient very easy to understand as you can see as the curve goes up the slope of the curve is changing slope of the Cur actually gradually decreasing that means what material is becoming harder and harder as you deform as you deform material become much harder that's why if you take a piece of metal a steel actually hammer it hammer it hammer it hammer it after that if you measure strength it much stronger by hammering you're introducing lot of defects and the defects will increase the strength of the material that's that is what is called as a strain hardening and N determines that behavior n tells you the strain hardening coefficient how it is going to change as the material is deforming so these two parameters are fundamental or other material properties you should know it very carefully if you want to design new Mater the constit equation is exactly like this Sigma is equal to Kon to^ n you can put T also doesn't matter but that's a true stress actually by the way this is true stress that's why it is called Sigma T better to put Sigma T otherwi you'll not forget and Epson is two Str and you know if I take log on the both side what do you get you get this curve so if I plot log of let's say if I plot log of what log of a Epsilon so L of Sigma T versus log of Epsilon what do you get you get a St line very easily you get a St line right the St line is what St line is this equation this equation and this St line slope of the St line will give you the value of n slope of the straight line will give you the value of N and this intercept will give you value of K this is EV evident from this equation itself so one can measure these parameters from this and I'm giving a list where the values of both K and N are given n is always less than one you can see here in this chart maximum value of p is 49 that's for the brass 7030 brass copper zinc alloy most of the cases values are even close to 0.1 less than 0.1 and K can vary depending on type of material so that's what is to be also taken to be consideration when you want to design materials K and N values well there are different types of Po behaviors for a material like if a material is ideally plastic they'll start deforming at the from the zero stress or as you not zero stress as you increase the stress from zero it's ideally Elastic Plastic then initially it will up elastically then it will become plastic and the third one is called peie wise linear where this part is linear and this part is nonlinear but one can actually make that as a PR wise or pricewise linear but that is an approximations mathematically that's a curve well there are many other parameters which you also need to consider energy absorbing by material is information is very important because that's what tells you how much energy it can absorb before it fractures so there are two parameters for that one is called resilence that is the ability of material to absorb energy and deform elastically and it will return back or return to it original shape and size when you unload that's called modul of villance this is what is used in the golf bat the material which is used to make golf bad must have very high resence because it is going to impart the energy from the bat to the ball but material will never deform plastically so therefore during hitting of the bat to the ball when the bat hits the ball it lot of energy is absorbed by the material it must have the ability to absorb the energy otherwise it will break that's why resilience is very important when you want to design a new material for the golf bat okay there are many other instruments which will require High resence I'm just giving you only one example you can see the how the golf golf bats are used by the different players in the TV or in the internet and you can understand how important is this the sports goods are very any genetic ones where which requires design of new materials so how do you measure the zence it's measured by measured by the modulus of villance that is the S energy absorb per unit volume and this is nothing but area under the curve so you could have seen that if I draw the ST stand curve it looks like this s plus Z the curve looks like this so this part of the curve is your elastic portion right so area under this curve is what is known as the resilience and that's nothing but half into ill stress this the ill stress this the height of that triangle into strength that's what it is and you can convert this using hooks law so this will become ESS Square by 2 into elastic modulus y because e0 is equal to Sigma y / e that's why so hence this is what is called modulus of resilience very important parameter if you want to design new material so for golf bat you would like to increase ill strength decrease e right as you decrease C Ur will increase as we increase stand Ur also will increase and effect is more but by effect is more more subtle or more pronounced when you use high value of ill stress very very subtle because it say a square ter and therefore the design or when you discover new materials you need to discover one which has very high ill stress that's to be specific metallic glass is used in the GOL flat because metallic glass has a very high strength it can be having strength of 3 to 4 GPA you probably may not have heard it very high strength is possible in those materials okay but it has very low ductility doesn't matter because here material is not going to deform plastically for the gall pad another important parameter is called toughness ability of a material to absorb energy in the plastic range remember this curve which I talked about it this Cur this is the plastic range right this particular portion of the Cur the right side that's called the plastic range this one this is a plastic range and area under this curve is what is known as this toughness because that is the area that is the this area indicates amount of energy absorbed by the material when plastically deformed and this is very important why because real application many the many of the materials plastically gets deformed and when the plastically get deformed they have to withstand this occasional stresses of the stress without any facture and this is desirable in many components you can think of cycle pedals you apply a lot of force but it never breaks because it is a huge toughness so stuff is very fundamental parameter and I'm showing you the you know how two different category of Steels high carbon sping Steels which is used in the in the trains as well as in the in the cars to absorb the vibrations or absorb the impact loading high carbon spring steel has much higher resilience compared to the Stockell Steels you can see the area of the curve right very easily so that's why almost all the uh the Springs are made up high carbon Steels which contains a lot of silicon so whether it's in trains or in the in the cars or in the trucks this is what is used as a important material to design this kind of or use the to make this kind of components well the some of the values of these provided here model of resilience you can see the high carbon spring still has a very high residence almost you know 10 times higher than the medium carbon St steel similarly rber has also very high resiliance you can see 2,140 but metallic glass has a surprisingly water of magnitud higher resence 30,000 kPa that's why for the golf bats metallic glass is used even all these projectors you see electronic projectors right in the projector there are many mirrors are there which is used to project in the uh using computers right so there these glasses are used for making these mirrors because they also have very high resilience well that's for the resence now what happens in facture so factures can be two types B and dutile dtile factures have necking and this kind of things happen you see there's a neck and Then followed by pores are bubbles and then this bubbles basically these are basically small pores they join and then form a uh you know crack and then it breaks down you looking at the crack surface you can clearly see whether it's a darkle fracture or a brittle pcture brle pcture will have flat surfaces dle pctures will have a capc type of surfaces you can see this is a cup it's a cone right so that's by looking at that you can determine that this indicates the behavior material remember facture will be able to change depending the temperature some material may be ductile at room temperature but B at temperature liquid n temperatures many application requires you to materials which will be used at low temperatures like cryogenic engines for the space applications well so how does it happens for the uh dtile factures as I told you the neing happens in the materials and then there's a small Sports forms the sports then join and form a crack and this cracks actually then separate these two pieces on the other hand for the d b factures you will not have much significant plastic deformation that's why they look like a flat and many cases you can have also CR bands by 45° angle with respect to the Loading axis of this axis that's very common in case of fure so uh this strength of material or direct material depends on temperature also I already talked about it temperature has a strong effect on that so as you see if we increase temperature both will strength and ductility it Str and TS and decreases this is very important if you want to use some material high temperature like in case of turbine engines we have talked about it on the other dity will increase as a function of temperature as increase temperature is to increase there are exceptions of that also but in general this is what is this trend is followed so strength and ductility we have in opposite way as a function of temperature this is the real experimental curves Steels actually mild steel at 400° room temperature and minus 196° temperature that is at liquid n temperature so as you what you see at 400° is very dtile the strength is low compared to room temperature as well as low temperature and low temperature strength is very high but ductility is poor so therefore you have balance of strength and ductility as a function of temperature that you must remember when you want to design material for application at different temperatures this is also shown here different kinds of metals like nickel iron mly Tain tantalum remember nickel is FCC or the tungen tantela m and RN BCC so that's why nickel for nickel You Don't See Much change of ELD strength little change as function of temperature but for iron Tung stain mly tantalum massive change of ill strength very massive change you can see stren drops as we increase temperatures to 600 500 3 cus temperature that's very evident well what happened to dity as you can see Nel the activity doesn't change much it remains 80 to 100% as you increase temperature but fire and mly tungsten tantalum all of them dity goes down to zero at low temperatures these are actually Body Center cubic structure Metals nickel is per Center cubic so it's very clear structure determines the property for the pent cubic Metals there'll be no brittleness at low temperatures for the BCC structures material will become brittle that's why we Define a dtile to transition in of Body Center cubic or hexagon close pack structure materials but for the per Center cubic structure there is no such thing possible so I think stop here because we have been discussed a lot of things in the last about 15 minutes or so so please keep in mind that these are very vital things to understand when you want to design something new because if you want to design using machine learning you will be using a lot of features or a lot of parameters and this features will be this aspects like resilience ductility strength UTS fracture these will be all used as a feature or parameters but now without knowing these aspects you cannot design a new material right that is what you should have a fair idea what these parameters are how they are measured and what is their behavior in terms of different materials as a function of different temperatures as well as as a function of different stress a different type of loading and strain rate some of this we'll discuss in the next lecture also but this fundamental knowledge is very very vital for you to take forward otherwise you will be using all these parameters for design of any new materials using machine learning without knowing them and that will give you wrong results or that will give you non-interpretable results which you yourself will not be able to interpret it and that's not that's basically useless if you want to produce something which is not interpretable then it's not useful to Mankind and that's why fundamental understanding of these kind of parameters are very important and that is the reason I'm spending so many lectures on the structure property correlations in this uh part of this course before I take off different machine learning algorithms and give you different kinds of examples so I request you to go through this slides and lecture as soon as this book if possible in a detail manner so that things are very clearly understood to you so let's stop here thank you we'll see you in the next lecture [Music] [Music] [Music]