[MUSIC] Dear students in today's lecture we will discuss the solid solution strengthening of metals. So, in metals we have interstitial and substitution of solid solutions. And here we will see the situation for interstitial solid solutions first. So here we have a typical stress strain response of an interstitial solid solution and you can consider this as iron Carbon or is simply just a steels. So, in this iron carbon interstitial alloy carbon atoms will occupied interstitial sites in an iron lattice. And then you will have a very interesting stress string response like this. Where after you have loaded your sample, beyond your elastic regime, it will go through plus deformation and then your stress will drop first. And then there will be a kind of a zigzag, discontinuous deformation regime, after which you will continue to have this relatively smooth typical stress strain response. So, this is actually very unique for interstitial alloys. And, consistent with the stress strain response, you have these non uniform deformation bands which form is 45 degrees relative to your loading axis. And they are called looters band because this phenomenon is discovered by a German scientist B Looters. And then your sample will have this quite now uniform deformation feature. So, why is that okay. So I will explain what happens exactly. So, initially, once you go beyond your elastic regime, you are actually entering into the plastic deformation regime. And then the situation is that in your interstitial alloys, the interstitial items turn to segregate into the dislocation course. For example, this is your iron lattice and here you have a lot of Carbon atoms segregating at the dislocation core. And then once your resolve the shear stress on that slip plane, on that dislocation is sufficient high enough and then your carbon atoms will be moved away from your dislocation core. So, and this process of removing these carbon items away from your dislocation core will actually make the dislocation movement easier. So that you have in an immediate low job or stress job corresponding to the removal of these carbon items. And then upon your further deformation, you will have a continuous generation of this kinetic process and it continues removal of carbon atoms in a lot of dislocation course. And that's the reason why you have these zigzag shaped, deformation feature. And afterwards, once all of your carbon items are moved away from your dislocation core, then your resume your normal, smooth stress strain response like other metals. So that's essentially what happens phenomenological. So in that case you can define two yield points. The first one is the so called upper yield point which is the higher yield point of your stress strain response. And there will be also a so called lower yield point which corresponds to the low job after the initiation of carbon removal from this location course. Okay. So and then you're please continue step formation regime from B to C. So, this is the exact formation regime is called a yield extension regime. And in this regime you have the propagation of these localized looters, their formation bands. And once these losers banned propagate across the entire cross section of your sample, your continuous smooth stare formation is resolved. So that's the complete scenario of this yield phenomenon. So this is called a yield phenomenon. So essentially, the this continuous deformation feature of your interstitial alloys is caused by the interaction between your interstitial solute items with dislocation course. And this theory is called. So this theory we just explained is quite qualitative and it is proposed by a scientist called Cottrell, and the carbon items and a dislocation coil is actually called a cottrel atmosphere, okay. And then, you can actually more accurately quantify this phenomena by a more quantitative theory using our knowledge on dislocations. And in particular in the chapter on defects on dislocations you have this equation right. So, your plastic strain rate is equal to your mobile dislocation density times your velocity of dislocations and burgers vector magnitude. So, in your tensile test usually you will have a constant strain rate, right. The strain rate keeps as a constant. So, this means your mobile dislocation density times your velocity of dislocations will be a constant because your progress back dramatic magnitude is a constant. And then because initially suppose this is your dislocation core. Initially, you'll have a lot of interstitial items such as carbon solid items in your dislocation core. So initially this dislocation is immobile. So initially you have a low mobile dislocation density. And then upon further deformation of your sample, these carbon items or interstitial items are removed from the dislocation core. And then you will have a relatively larger mobile dislocation density, because the product of your mobile dislocation density and your velocity of dislocation remains the same because this constant string rate requirement. So initially, you'll have a high dislocation velocity with low mobile dislocation density. And afterwards, you will have a low dislocation velocity with a high mobile dislocation density. And then you know that from your knowledge on defects, you know that the dislocation velocity is proportional to your resolve the shear stress. So, at the beginning of your information again, you have a low mobile dislocation. There's the high dislocation velocity. And this means you have a high resolved shear stress. And afterwards, when your carbon items are removed away from your dislocation core, you will have a high mobile dislocation density. Low dislocation velocity and then you will have a low resolve the shear stress. And that is the reason why you have an upper and lower yield point. Okay, so this is what I have just explained in texts. So I'll skip this and then because the formation of Luder band and the discontinuous deformation is usually not a good thing. So practically people want to reduce such discontinuous deformation interstitial alloys. So you have quite a few methods to do it. The first is intuition by intuition to reduce the impurity counted, right. And in cases where you cannot reduce the impurity content because you want to have a certain impurity content to make stronger the alloy. Alternatively you can add so called stabilizers such as different types of solute items into the alloys as well to stabilize your interstitial solutes. And finally, you may pre deform the material beyond the yield extension regime so that when you deform it again, it will just directly go through the smooth deformation regime. And here we have this interstitial alloys situation where the strengthening is caused by this cultural atmosphere which can also be explained by the strain rate. Dependence of mobile dislocation density and dislocation velocity. So the situation for the substitution of alloys is simpler, where essentially you have a substitution of solute item either bigger than your matrix items are smaller than your matrix items. And these bigger or smaller solute will usually cause a lattice distortion. And this lattice distortion will cause strain energy, so strain energy of your around your solute items. And this will make your dislocation movement more difficult. And this is to In improve your strength and hardness, but usually decrease your ductility and toughness. So in general if we will combine both interstitial and substitutional strengthening mechanisms. You will see that usually was the solute concentration Increasing you will have a stronger material so the strengthening effect is more significant. And in the case of substitution of solid solutions, if you have a larger lattice mismatch between the solute and solvent items. You will have a larger string stress filled around the solute and you're strengthening effect will also increase. And then finally, if you have a larger difference between the valence states of your host and solute items, the strengthening effect will also be increased. So in today's lecture, we have talked about the solid solution strengthening in metals. Thank you very much. [MUSIC]
