Fundamentals of Metal Forming | Mechanical | Praveen Kulkarni

welcome all after a long time have come again and this time it is totally unconventional topic which you have you might not have expected from me so let me tell you I have done my masters in Production Engineering but generally I don't take production classes actually recently on heavy demand from came students that is Kulkarni's Academy students so I took part of production that is metal forming so today I'll take up the topic on production that is metal forming I am planning to take series of lectures on metal forming and let me start with fundamentals of metal forming so after the completion of this water my plan is something like this first I'll take these fundamentals what is true stress what is true strain what is like plastic flow curve during the plastic deformation what is the flow curve and how do we calculate average stress what is the significance of average stress what is strain hardening exponent and how these values are used in calculating various forces and power in like different bulk deformation processes like rolling extrusion all these deformation processes so let's start with fundamentals that is fundamentals of metal forming fundamentals of metal forming champ now let's try to understand things in a very clear manner what is metal forming it is one of the manufacturing processes in which the plastic deformation is used in shaping the component I repeat it is a manufacturing process in which plastic deformation is used in shaping the component stress on the term plastic deformation so the first prerequisite is for plastic deformation you know my dear students try to understand what is a ductile material and what is a brittle material first this is the most important part in today I will discuss fundamentals and in this video we'll be talking about flow curve and with the help of flow curve how we calculate average stress and what is the significance of that Abba distance and with the help of average stress how we calculate various loads may be in extrusion may be in drawing may be in rolling will see all those things you know first I'll talk about ductile and brittle materials then we'll see which material is suitable to be formed they are when you are working it should be conducive or it should help us in forming not all metals can be formed not all materials can be fun let's see now look at now listen carefully that tiny materials are those materials which show large plastic deformation before fracture don't get confused with deformation whenever you want to check whether the material is ductile or between it is not the elastic deformation that matters it is the plastic deformation that is very very important let us take a rubber you stretch it yes it deforms to a significant amount release the load again it comes back so it is elastic deformation and apply load on steel it shows little elastic deformation these terms I will be discussing in strength of materials like what is the significance of elastic modulus all those things but have a look at this when I am stretching the Rabanne and when I am applying a load on steel you see significant deformation in rubber I'm talking about elastic deformation and just by looking at this deformation do not conclude that rubber is ductile it's very wrong whenever you want to check whether the material is ductile or brittle you have to check plastic deformation very good so elastic deformation has nothing for a material to be called as ductile or brittle it may be showing significant elastic deformation but if you learn beyond elastic for rubber with little deformation it fails or fractures that's why rubber is showing very little or negligible plastic deformation once it reaches fracture that's why a material which has a large plastic deformation that is more than five percent plastic deformation before failure or before fracture we call it as a ductile material I repeat if you see our stress-strain curves I'll come to what is engineering stress what is engineering what is conventional stress always I'll be discussing to stress true strain let's have a look at this here I take strain here I take stress very good and you know why we take strain on x-axis because cause effect cause effect strain is the cause of stress that's why we take this strain on this axis deployed bar let's take my dear students one case like this the other case something like this please know done that this part comes under elastic like this part is elastic but please to judge whether the material is wood that time orbital you have to check the plastic deformation have a look at this if you see my dear students it is yielding and when it fractures this is the plastic deformation and if this is less than 5 percent strain what I mean the 5 percent point 0 5 in the strain is less than 5 percent before fracture then such a material is called as brittle you take a rubber you take chalk base it shows negligible or no deformation plastic deformation once it fails now have a look at this this is our elastic zone and this is our plastic zone and have a look at this and this zone let me take different color this zone oh my god it is greater than the but is greater than 5% and this is our ductile material this is our word ductile material so you are deforming so in metal forming plastic deformation enables the material to to be shaped into different components so what is required it should deform plastically so a material which deforms significantly and a plastic zone those materials are suitable to be formed that's why ductile materials are suitable they can be easily found and please note on that the plastic deformation range must be large it should be greater than 5 percent now let's move to our engineering stress engineering strain true stress true strain if you take our strength of materials there all those deformations are within elastic that's why you find the variation in dimensions very small in significant almost negligible or to hunker them what we do is almost negligible elastic deformations but now in metal for male that's why please note on that first let me define what is engineering stress let me designate the Sigma it is the ratio of your load that results in internal resistance to the original area whenever you see let me apply on this okay this is the cross-section let me apply a load now let this area original area be a not due to this tensile load you know the length increases and the cross-section decreases okay so when I use the word conventional stress engineering stress nominal stress we calculate with respect to original area a naught similarly let the original length of the specimen be L naught then conventional strain let me designate with a small a sigma is conventional or nominal stress conventional or nominal or engineering stress please note down that we use original area similarly the engineering strain conventional strain or nominal strain is nothing but change when I am applying this load there will be some deformation that the change in length BD L what is the L the change in length when you calculate with respect to original length we call it as engineering nominal or conventional so please note on that in engineering or conventional it is the original area original length for calculating strains we take original meant for calculating stresses we take original area so it is the original but my dear students it's okay if you take original areas if laws are within elastic limit the changes in dimensions are rather very small whether it is the change in length or change in area if the Lord is within elastic limit they are very small it's okay but if you cross elastic limit and enter plastic zone due to significant plastic deformation dimensional changes are large so if you take actual sorry if you take original it may give wrong information I'll tell you a little later how it gives wrong information that's why there is a need for us to take calculate all this with respect to actual length actually for example let us take a member say subjected to a tensile load maybe compress you also so in metal forming you can subject the material to different loadings maybe ten file may be compressive maybe shear so different loadings because of these loadings the deformation is taking place we sing in different deformation processes okay now let the original length be L knot okay now due to this say now after sometime due to this loading let D length be L okay the process is not over somewhere in the middle I stopped and I started checking still it is going on and say I want to calculate strain from this level from this level from this level look at my dear students if I calculate strain observe carefully let this be a small change in length still the process is going on when I take engineering or conventional stress we will be calculating with respect to this length but actually at this time this is not the length this is not Balan then how will you calculate with respect to this length actually this is the length when you are taking the actual or instantaneous length and calculating the strain that is known as true strain and we represent with epsilon so this small change are the small true strain can be written when I write e it is engineering strain when I write epsilon it is true strength please observe similarly when I read Sigma Sigma it is engineering stress when I read Sigma T it is - stress okay right and some people designate roosters are Sigma and engineering stresses s doesn't matter no issues at all and how does it matter okay chill oh now this small strain is given by changing length to the instant and don't take original it is the true strength that's why at that time length we have to take excellent so when you are calculating with respect to actual length it is also known as actual at that time length or instantaneous length and let us say this is the strain at that instant at that instant now true in fact true because it is giving me the kite picture will I will show you how it is giving correct picture now let us say I am applying this is the final length say this is the final length so you have started from this in the middle you stopped and you checked it is this so you have the other at that time in your creating at that time in your cup reading it is the strain change in dimension to that dimension at that time that will give you true so if you want the total to true strain you integrate whatever we have calculated has become small length and I'm calculating and please note on that this is very important that is the small true strain is given by change in length to the at that time length this is very very important equation is going to greater again so where between what limits you are integrating my length is initial or it can be written as L I or L not or not means original 2l final so epsilon is equal to de what is the a DL by instantaneous length L I by L final so this can be written as true strain is DL by L integral is log n log L F minus log L I log a minus log base block a by B so this is LF by Li this is my true strain this is might restrain so let me take this so true strain is given by Ln L final by an initial excellent my dear students in plastic deformation zone the volume is assumed to be conserved what do mean by concern that is if the material is flowing from one side it has to move to the other side so that the total volume remains constant so therefore and a naught L naught is equal to some instant at some instant look at this the original area original and volume so at that time area at that time length and this is let us say AF l f means some instant this is constant it is the beginning somewhere in the middle I straw branch it and it is the final excellent dancers forum so this can also be written as okay and you know that they come epsilon is equal to Ln what is LF by Li you take this LS by L I is equal to our original arrear i means initial or original both are same I means initial or original no problem LF by L I or L original this can be written as L go also LF by L is equal to LF by L o is equal to a by a f very good so L o can also be written as L initial metal of initial length so therefore final by initial is equal to a naught by K final excellent so observe here the true strain is given by Ln LF by Li but what is LF by Li a not by F so I request everyone to remember this the true strain this is in terms of area this is in terms of length either you write this or this i re Baba L go can also be written as alight this is very very important equation this is the very very important equation now observe here we know that so let me let this be the original length so L naught so I have applied and say this is the final length and obviously what will be this change in length so can we write okay the final length is equal to original length plus changing it absolutely the final length is equal to original cost change in length so therefore now true strain can be written as Ln Ln L F by L o what is LF a lot plus dl by I have just substituted LS as the final length as original length plus change in length yet Ohana this is my final length so final one is equal to L naught plus DL absolutely so final length is L not plus DL by L naught okay so two strain is Ln L naught by L naught is 1 plus DL by L naught observe here what do you strange in length to the original dimension whenever you are computing change in dimension to the original dimension it is engineering stress that is nothing but e so the true strength is given by Ln 1 plus small e so I tell you what are the equations to be remembered the first equation that you need to remember is xicanmei so the first equation that you need to remember is this one this one this one this one this one very very important equation and the second one is this one so just fix it in mind just fix it in mind just fix it in mind so engineering sorry true strain is given by Ln original area to the final area or LM final length to the original or the true strain is given by Ln 1 plus e so let me take to the next slide so no issues at all ok so fierce Emma Dharam so we have this one let me write further so epsilon is equal to Ln pony channel area by final area because these equations will help us a lot in solving questions this can also be written as Ln L final by L original this can also be written as Ln 1 plus e where C all have written take back the Chicana Ln a oh by a F yes Ln L F by L is equal to Ln 1 plus E and these equations will help us solve many numerical so fix it in mind so small e is engineering strain and epsilon is true strain awesome no problem at all just now you saw know you happy decay they observe here now once again so I take this just now aha X second echo a naught L naught is equal to a in area al okay or this can also be written as a naught by a is if or this is a right AF are instant Syria don't worry this can be this can be instantaneous area or final area no problem at all so this can be written as a f LF okay no issues at all so because volume is comes up in plastic during plastic deformation it is one of the important assumptions okay so therefore a not but what is a not L not original volume at some instant volume final volume so volume is same during plastic deformation so therefore volume is Airy until in a not by a is L by L not what is L at that I told you very clearly for example this is L not say this is some L and this is our DL so I can write this as a naught by a is equal to L what is L the curve this is Elna what is L L not plus dl l not plus DL by L not absolutely so a naught by a can be written as L naught by L is one separated DL are L naught by L naught is 1 DL by L naught is change in length to original is original length is true strain now sorry engineering strain okay let me calculate true stress true stress is given by force to the instantaneous area this is our instantaneous area this is our instantaneous area true means instant Innes at that time at that time original means engineering so I can make some manipulations F by a naught into a naught by a I paid so I multiply n divided with a naught I cannot Cooper Sonny Scott Athena you will get the same thing so Sigma T is equal to what is Sigma D true true means instantaneous area what is F by a not slowed by original area is engineering stress this is engineering stress this is engineering into a naught by a what is a naught by a what is a naught by a 1 plus a and this is one of the important relationship between true stress true strain so now finally I request students to remember these things Nicobar true strain is Ln 1 plus Chi 1 plus e okay which is also equal to Ln a original by a final which is also equal to Ln final length to the original length this is very very important equation very good give Organa okay X second final original and similarly the true stress is given by Sigma into 1 plus e now let us see why do we calculate true stress and true strength my dear students in centers materials all our deformations are within elastic limit so variations in dimensions are very small when variations in dimensions are very small the original are actual changes are very very small to key for example so let me apply if it is within elastic limit change or graph so when the area's are changing very in a very small manner the true and actual the actual and engineering the coincide so the variation is very small but once you cross elastic when it enters plastic zone now deformations are significant when deformations are significant how can I take original area there is a large difference between original and actual there is a large plastic deformation that's why we have to take instantaneous that's why in metal forming always remember it is the true stress true strain that we have to take otherwise it will be misleading because there are huge deformations so easily when deformations are large my original area instantaneous area final area there is a big difference that's why it will not give the correct picture so always remember in metal forming as there is a huge plastic deformation and because because of plastic deformation there is a you are getting the shape now required shape that's why always remember in truth in angel in metal forming you have to take to stress true strain because that will give me the correct picture so a equation say hum are gay but they have with this so let us proceed mmm further okay right very good my dear students cello I give out the hair now let's proceed further no cello a big the hair so we have seen up to this now we'll move further and he some basics me here we are in basics only now let us take up hum now we are moving is true stress true strain Sigma T that is true stress true strain actually it is something like this Abbey yoga I saw okay no this is let us say I'm not going into the details of this if you want definitely I can make a video like if you really want because I'll be teaching all this in our strength of metals class like how different curves are obtained all those so let us say this is healed so and this is our maximum this is ultimate ultimate hmm hey come kirtan so I'll remove this and I'll write this as Sigma ultimate Sigma ultimate okay right this is my diagram my students there is one term known as flow mhmm now we are entering our metal forming slowly theory is a hum intro rate there is one term known as flow stress let's see what is the flow stress when you are deforming the material its flowing the instantaneous stress that is required to cause the material to deform or at that instant whatever the stress is required for the material to flow cause the flow or deform that is known as flow stress observe here it is crossing so in metal for me stresses are greater than and there was one beautiful question asked in recent gate do Sul Felicia at forging question ministers couch 300 plus D ahead I don't remember values in stress cush 300 or something even and what a beautiful question some students got proper de with positive negative sign and he gave options has 200 something 200 something plus 2 minus and about a hundred and please again up sir if you do not follow convention and common senses verging method in Hoonah chai a so it has to be greater than yield so obviously both unspoken and bunker capacity which is less than 300 album karaoke so it should be in metal forming my stresses are more than e to e the bit of flow we gonna yield Organa that's why look at observe ear this is actually stresses on increasing they come corroborated you take a rod bend it throb in karo or score further will corrode first big tournament easily you can bend after that when you are bending it becomes very tough so the stress is increasing which we call it as strain hardening or work hardening again if you want I can tell this but that is that comes under middle sense part no issues the molecule of level page of jacket I can get so just remember it is strain hardening mother camera so once you cross this e-liquid röszke the stress required for the flow of material super-handsome no X again so look at either say or slowly the material is flowing so you have a it's enough flow stress I this is the flow stress again and it is further increasing due to strain hardening it is the flow stress again it is increasing means during deformation in the plastic zone the flow stress is not constant that's why I use the word what is process it is the instant stress required the further materially to flow but at this point this is the flow stress at this point at this strain this is the flow stress at this this is the flow stress to flow stress is not constant that's why I use the word instantaneous stress for causing the material to flow but they say actually work hardening a current so the flow stress is increasing it's not constant in the plastic deformation the flow curve is given by Sigma T is equal to K epsilon n I repeat in the plastic zone out above this is the elastic zone and it is very very small and it is negligible that's why though there is some elastic strain elastic strain your become hot ahead we neglect it and actually we start from zero matter plastic deformation zero strains it should look at there this is very very small as this is very very small we start from zero only that's why when we try to calculate average flow stress Abreva Thumba we integrate actually we have to integrate from this to this but actually a Bahat come here this plus here this elastic zone is very small that's why I treat this as almost zero and I proceed so we are the Krenim in metal forming we take the elastic deformation almost negligible that's why we start with zero only okay let this be let this be some Epsilon very good this is known as flow curve this is the true stress true strain and K is known as strength coefficient and n is known as strain hardening coefficient will see what are these two different materials under different temperatures these two values are different strain hardening index our strain hardening exponent this is strength coefficient K strength question let's see what is strength coefficient cancel tsunami tape Epsilon and I repeat this is the flow curve it is known as flow curve during plastic deformation actually from experiments we got this flow curve during plastic deformation to up coke ackerman we are in plastic deformation in metal forming so please learn these hooks safely directly production chain who came an elastically here so in metal forming as there is a plastic deformation use plastic flow curve which is obtained experimentally a big head let us take epsilon is equal to 1 let's take true strain I repeat to strain 1 to agree if only 1 power something is 1 though yoga Sigma T is equal to K so what is strength coefficient it is the value of 2 stress at a true strain of 1 I did strength coefficient it is the value of true it is the value of true stress at a true strain of 1 now we will see what is this it is a strain hardening exponent if there is no strain hardening it is 0 it is you if n value is increasing the effect of strain hardening is high so it varies from 0 to 1 so therefore if the same hardening agar please observe here so if strain hardening effect is murdered the value of n will be high so it is showing strain hardening effect for example look at if I saw her no strain hardening and take ice ahead so definitely any zero income value let us say point four incur value let us say point six so the strain hardening effect is more it is showing that so Java strain hardening effect head the value of n will be high so you have to fit in this curve this is the value so what is the very equation Sigma T is equal to ka equation Sigma T is equal to K epsilon N and this K and n values will be given to us you don't have to worry about that okay now understand carefully observe carefully so we have something like this so this elastic deformation is very negligible up the code here this is the flow stress - yeah here the flow stress is different here the process is different here the force is different here the process is different here the forces is different so it is increasing increasing increasing okay no problem at all let's calculate so you get different marks in different subjects so we calculate average how do you calculate average the total marks with average total mass actual should when you sum up it should be same here also you know when you are deforming the material some what is done so please note down that let us say we have deformed up to this let the maximum strain be say Epsilon now I introduce one word derivative please observe at this point like the true stress Beit Sigma T at this point at this at this point and you know when you are moving along x axis the true stress is changing to my Kokoro I'll take small change in strain which I write it as d epsilon small change in strain small chain let me calculate work and you know if I want work on stress strain diagram calculate the area that will give me work per unit volume how per unit volume the sk unit liquor stress newton per meter square strain know unit you are multiplying both know in it so you get Newton per meter square so multiply and divide with meter so newton meter is Joule Joule per meter cube is meter cube is volume so you get so video integrating this or when you are calculating this total area total area so how to integrate actually plastic difference in here has a this strain to this strain but the elastic is very very small that's why I integrate from 0 to this because yaja Sahara so you are coming from this to this you integrate from 0 to epsilon so no so this area let me calculate as the variation is very small you change become hi between these two points I assume that to stress to be almost same can hear hot come here so the change is very negligible so therefore now small work can be calculated as the strain is the stressing Sigma T into area what is that C length into width is area length is Sigma T and width is de that is the area but this will give me only smaller if you want total you integrate from where 0 to epsilon and again I am telling you what is the Assumption for this elastic deformation is neglected excellent this will give you the work okay let's integrate already you know Sigma T as K epsilon and D Epsilon okay so therefore what is equal to K so what is epsilon and epsilon X power n DX is X power n plus 1 by n plus 1 my limits are of course 0 to epsilon so coyly cut name if you substitute you get woke as K epsilon n plus 1 by n plus 1 this is the equation for work done yay piece of elastic fabric oh this question can also come the work but this will give you work per unit volume because it is not on Lord area it is not unload and length it is on stress strain that's why it is per unit for them now I'll introduce one concept of average flow stress my dear students so a hunk occurring a let's find out one hypothetical stress and please this is the minimum this is the maximum so ache as a average calculate curve between these such that the whatever work you have calculated our area and work this I write it as one second please let me it is this this is our Sigma so each go home average will get Sigma bar but the pan can see they cook from here to here it is changing so is flow stress car and calculating average so for calculating average there has to be some logic what is the logic we actually integrate key you got the word so if I pick average and calculate the work it should be same so let us calculate work with this work with this to e cayuga average program this is average Tokita na hoga so it will be Sigma bar so with average the work is of course per unit volume is gonna be Sigma bond length is Sigma bar into this this width so what is that Sigma minus epsilon is Sigma this will give me what with average flow stress means what so actually this much this is the flow stress required for the deformation so detener on it neva care so whatever is missing here it is covered here it is covered here so no problem at all so therefore this is the work calculated with average and this is with actual let's equate both Sigma bar epsilon and when you're calculating actual maths actual total month's average total marks these total marks with average this total Max with actual should be same so therefore K epsilon n plus 1 by n plus 1 so therefore the average stress this is known as average flow stress mutlar you'll be seeing in our next classes how this term is helping in calculating loads in different deformation the processes so therefore epsilon is some gap K epsilon power n by n plus 1 this is my average flow stress this is my average flow stress k epsilon n by n plus 1 and this will help us in calculating my dear students different different different loads we'll be seeing very clearly hope you have understood excellent so this is a required for flow causing the flow which is due to strain hardening the flow stress is varying varying from this strain to the strength take hypothetical this is actually hypothetical so please remember this equation also excellent now the problem is how do I calculate strain hardening exponent n either the gravity observe here okay let this point be e and you know that it is the ultimate stress it is the ultimate says let this point be can you tell me what is the load here maximum they come the force is or the load is given by Sigma into area okay no problem strain is changing stress is also changing strain is changing stress is also changing look at now you know clearly during plastic deformation the volume is constant during plastic deformation volume is concerned is co differentiate corrupt be a UV principal da into L plus n into da and the differentiation of constant is zero so D a okay one second place small printing mistake Cody curtain I don't worry ba into L plus L in a da into L plus okay a bar I don't worry da into L hoga a into DL excellent UV principle differentiation of this okay wisc about differentiation of this so da by a is equal to B a by s minus DL by L and already I have shown the core already have shown please observe here this is small change in length and this is the instantaneous length and this week I have already told you changing dimension to the original dimension with the small strain and it is the true because you have taken instantaneous and I had integrated this from initial to final so this minus DL by L so dl by l dl by l will give me de so da by a is equal to minus what is DL by L D - D Epsilon excellent this I have already explained in my earlier slides if you want you can see also I'll show you I'll show you I'll show you they come either they come I have already shown you the crater is that echo DL by L is D epsilon Johan integrated here already have shown so again I am doing for your benefit only for your benefit on D AB digna so please note down that so I remove this so that I can use some space yeah yes ba-bye a da by a is this okay now it's Co differential cannot so if this is I'm applying this @e @e what is the load it is maximum and you know this load is varying with strain so it's good differential cannot be f applying this at Point E I am applying this at point a because the load is wearing strain is also very so you differentiate this with respect to strain we have those stress is varying with Sigma is changing Sigma is changing epsilon is our variables so load is varying stress is varying area is changing already so dou Z when you are deforming at different instances area is changing stress is changing the load is also changing its go differential cannot Sigma you are differentiating with respect to D Sigma da by D epsilon plus a into D Sigma by D epsilon and you know you are differentiating this Lord is varying with epsilon but this at Point E at point a this is maximum whenever you want something maximum or minimum you have to differentiate with variable adequately to zero the load is wearing this strain but I want I am applying at E and even the load is maximum so this value will become zero why it is not 0 elsewhere it is a I made jaha Payne making sure ahora you know making starts at this point that is ultimate so I got a pencil lit up like a red tone aching starts at this ultimate ultimate maximum load maximum load maximum load so the Lord is maximum whenever you want something maximum or minimum differentiate variable equated to zero so this value will be zero matter Sigma be a by D epsilon they call my apply Quran is point pain and all points it is not zero when it is maximum or minimum then only it is zero so hung up like error is fine to eat matza ultimate point B so keep it in mind we are applying at the IEP make point where the load is more differentiation of a with respect to two strain is 0 why because load is maximum at the maximum point the differentiation will be equal to zero so ya Macrina I have applied at Point E so at Point D 0 and those who are appearing for Easter or DRDO bar interviews and this derivation is very very important and those who are appearing for simple gate are yes so finally what to remember I'll tell you chello Sigma da plus a D Sigma by D epsilon is equal to 0 or Sigma da by D epsilon is - a D Sigma by D epsilon excellent my dear students so now take off so I'll read this as Sigma into da by a of course - Seiko either leg a I repeat yeah - you either lenient is equal to D Sigma D s 1 DX from gap so therefore this is gone because it is it's same differentiation so therefore Sigma da Aiko is her Lanna is d Sigma so this D epsilon this assumption is gone because we are the differentiating with respect to the same variable so Sigma da I brought a to the side of the curve Sigma into what is minus da by a minus da by D a is D Epsilon so minus da is D Epsilon and that is equal to D Sigma excellent and you know that Sigma is equal to K epsilon N or D Sigma this is the flow curve D Sigma is equal to true stress ha d sigma is equal to harm okay any differential with respect to epsilon so differentiate with respect to Epsilon Sigma by D epsilon K n into epsilon n minus one okay here Sigma is actually represented so I told you initially this can be taken as true stress engineering stress Sigma can be taken as two sometimes I write Sigma T or Sigma no issues at all no issues at all so even if I write for example Sigma if I don't write script T it means it is actually flow curve is for a plastic deformation it is the true stress cello - Iiro gap now I will write this as hmm so k epsilon n so it's quicker looking a k in epsilon n by epsilon okay so D Sigma by D epsilon is equal to what is K epsilon in K epsilon N is Sigma so in into her you have been in here in K epsilon n K epsilon n e Sigma by epsilon so therefore now I write here D Sigma by D epsilon is equal to D Sigma by D epsilon D Sigma by D epsilon is Sigma but what is D Sigma by D epsilon n Sigma by a so this can be written as because D Sigma by D epsilon is n Sigma by a yeah say D Sigma by D epsilon is Sigma D Sigma by D from this it is Sigma but D Sigma medicine is n Sigma n Sigma by epsilon n Sigma by epsilon so Sigma Sigma gap so therefore we have n is equal to n either agha is equal to what epsilon it means it means at the making point at the making point or ultimate stress at the maximum stress or necking point the strain hardening exponent is equal to true strain to come here consume economy is point pay up epsilon calculate gamma is point B maximum stress pay maximum ultimate sisters epsilon calculate Rina that will be my epsilon that will be my water strain hardening exponent so it's very easy to calculate strain hardening exponent so what is strain hardening exponent it is the value of true strain at the I teamate stress are at which the nicking commences excellent materials now let me take up some good questions on this so that you can understand and you'll get everything clearly let me take up some good questions okay now very good so I'd be making point at the ultimate stress the strain hardening exponent n is nothing but true strain at that value okay chiller equation cocaina the flow curve of annealed metal is expressed as Sigma is equal to 200 epsilon over 0.25 very good we're at Sigma this is our two stress strain okay now if we is subjected to a stru strain of 0.3 the work of deformation is a bit over there just now I gave you the equation for work of deformation just now I gave you work of deformation what is the equation for work of deformation k epsilon n plus 1 by n plus 1 K epsilon n plus 1 by n plus 1 so what is given by K epsilon n plus 1 by n plus 1 very good but this will give me what per unit volume unit Sakana as Sigma is in mega Pascal you'll get the answer in mega Joule per meter cube very good per unit volume so as Sigma is in mega Pascal it will be in mega Joule per meter cube so what is equal to K what is K because Sigma is equal to K epsilon M one second please ok so Sigma is equal to na Sigma is equal to observe here no problem at all yeah we'll take up this half Sigma is equal to 200 epsilon power 0.25 compare K is equal to 200 compared and n is equal to n compare karna n is 0.25 okay so put it here K what is K 200 at what strain he is asking up to what straight a strain is asking clearly the point 3 that work chain so means we are deforming like this so up to this is asking you have a strain have point 3 so he's asking this total work so therefore epsilon is point 3 and n is already known 0.25 plus 1 by 1 n is this 1 plus n is 0.25 and if you are calculating I think you should get let me check the value mmm thirty five point three two unit unit mega Joule Y mega Joule because it is already in mega Pascal therefore you get it in mega Joule this is a good question next hmm next question true stress true strain behavior of metal is given by Sigma is equal to is equal to 1750 one second please will change the color evil away again 1750 okay epsilon power 0.37 okay where Sigma is in mega Pascal the true stress at making Mythology Methodius the true stress at nicking at Nikki he is asking true stress Sigma value at nicking and you know that at making everyone knows at Nikki epsilon is equal to n the fiber the cargo konna came and the value of Sigma is K epsilon n K is 1750 okay and M is 0.37 excellent so therefore he is asking the true stress at making madam Sigma available at Nikki Sigma epsilon is equal to what n epsilon is equal to n already n is point three seven point three seven this come at the camp then at making epsilon is n n is point three seven so when it is point three seven at nickel so that will give me the true stress at nicking so kit Onaga Sigma is equal to I repeat copy true stress push are making but at making what is epsilon n so n is already given so at making epsilon is n epsilon is n so when you put epsilon you get the true stress at nicking because at licking epsilon cap value k APPA just aqua kana this is known this is known if epsilon is known you can calculate stress so capacitors which are making pay but making for epsilon k the nagas in hoga the 0.37 so therefore it is epsilon is point three seven power point three seven hello okay and what is the value mm let me check let me check what is he asking to stress at making hannah point three seven power point three seven into one seven five zero it is twelve levin and whatever the unit you have sigma already given in mega Pascal so the answer is 12 and point three five mega Pascal absolutely no issues at all no you should set all okay right let's move to the next i do simple air so camel i making pay conditioner everyone knows it's a straightforward but it is the hot kick of many examiners so at making you know epsilon is equal to and no issues at all next let's take up this question let's take up this question question number is five Julia Deco if the true stress strain curve of a ductile metal is represented by okay a bar deck now what is the value of K Sigma is K epsilon over N K is double one double zero and M is equal to exponent that is point to the teammate stress but he is asking engineering what a good question I don't say tough but it's a good question sue nobody Sigma is this this is the true stress this is the true strength but Leucippus on the IEP made ultimate kimitaka happy ultimate here maximum ultimate is maximum maximum they can making condition but making condition Kelly can have maximum Kelly epsilon is equal to n which is equal to point two two up the coop Sigma is equal to double one doubles ero epsilon power point two okay no problem at all so if you put epsilon is equal to n you will get the ultimate stress because when epsilon is and it is ultimate stress at which nicking is beginning but that when you may in actually it is true but he's not asking true he is asking ultimate in terms of engineering stress field super quorum if I put epsilon is equal to n if I put epsilon is equal to n I'll get the ultimate stress but this ultimate will be true ultimate stress but he is not asking Troy ultimate he's asking engineering the first hump Sigma poke algorithm a double one doubles ero epsilon is point two power point two so it will be double one doubles ero of two kitten arrived X second I will calculate no issues at all let me calculate double x again point to PowerPoint - into 1100 so this is coming out to be seven ninety seven point two five mega Pascal coy decoupling but this is the ultimate look at now understand carefully this is the true stress true intimate to Casa October that the ultimate have whenever you substitute epsilon as n it is ultimate but this is true a true ultimate head lake in what I ultimately puch ahead pooch aha ultimate engineering and you know that Sigma is equal to s into 1 plus e this is engineering stress other yeah ultimate her to give me ultimatums or engineering ultimate is Sigma by 1 plus e again you are in problems what is e it is the engineering stress but engineering stress is not given so you know sink its yeah epsilon is equal to point two but a veto they can epsilon is equal to Ln 1 plus e holiday I gave you epsilon is equal to Ln 1 plus a for epsilon is Ellen van persie so if you want one plus a epower epsilon if you want one plus a it will be e / epsilon but already you know epsilon is point two so therefore 1 plus e is e power point - okay Kyra don't get confused with DC and DC fill up confuse Rachel of my nickel day Tom so X again don't get confused with this is exponent I write the comb very simple the cut name deco about antilog letter 1 plus YZ equal toward exponent exp Kumasi a power a power a power ok ok now please don't get confused with e e is engineering strain exp means what exponent okay or else my is Ikaruga - yaha same Jellico he cut me up don't get confused because simple things are always complicated in life so ok epsilon is how much 0.2 is Ln 1 plus e - yaja say antilog lynge - 1 / Sega so I think you are getting 1 plus e as 1 point 2 - 4 X second metric aruna 1 plus E mmm shift yeah so you will get 1 plus e from this as 1 point 2 - 1 4 so directly Sigma - Otsuka have already Sigma is known how much is that seven ninety seven point two five is equal to s into already 1 + E is known one point two to one fourth so this you will get as into seven ninety seven point two five okay then I write six fifty two point something six fifty two point something where is that where is that C is the right answer a good question a good question okay how you heave-ho Duchessa well hey let's take this very good question actually the ultimate engineering stress is 400 this is engineering ultimate 400 and the elongation engineering engineering is up to 35% but the engineering strain is given by 0.35 okay point 35 35 percent come at the K 35 100 so therefore elongation is 35 percent whenever you say 35 percent it is with respect to two original percentage change is always with respect to origin that's why it is deforming the elongation up to maximum load is 3/8 o maximum here so okay ultimate strength is maximum and that is okay and why are you taking this as small e because it is percentage may be a percentage is always with us for two original original comics of the change in dimension to the original is what engineering strain okay if the material obeys power law what is the relationship it's a good question they commit a look at please look at try to understand things clearly let's calculate Sigma ultimate true-true is equal to s ultimate into 1 plus e ok no problem at all so therefore true ultimate stress calculate current game engineering ultimate stress is 400 into 1 plus e e ek at 0.35 okay so you will get the Sigma ultimate true as 400 into 1.35 hmm 400 into 1 point 3 5 we are i-540 very good let's calculate the engineering true strain what is true strength Ln 1 plus e already I gave this equation already I gave you this equation already I gave this equation so to strain is equal to Ln 1 plus e what is he Oh point 3 5 very good - Ln 1 point 3 5 to get another point 3 so epsilon is point 3 my dear students look at carefully what is e it is the engineering stress at the maximum load maximum load nice job in making sure over at so corresponding to maximum load this is the engineering strain corresponding to engineering strain you have calculated to strain but this point pay up to strain calculate K maximum maximum load Bay but at maximum load this is the strain but at maximum load epsilon is equal to M at the maximum load epsilon is equal to n so at the maximum load the true strain is point 3 but at the maximum load true strain is always giving me strain hardening exponent philosophical yeah bohot meaning a maximum load so at maximum load the engineering strain is given as point effect so I calculated corresponding to strain but this is the true strain corresponding to a debate this is the true strain corresponding to maximum load mother Nikki so but everyone knows true strain corresponding to maximum load is n so therefore all ready to strain is known point three yoga and Sigma is equal to K epsilon K epsilon M okay no problem at all Kansas no look at me dear students now the only problem is to calculate ki very simple any is already known point three okay calculate K how do I calculate look at okay when epsilon is n when epsilon is n this will be ultimate this will be ultimate when epsilon is n when epsilon is then this will be ultimate this will be ultimate but please not dumb it should be true already Sigma true I have calculated already Sigma true the answer so no engineering ultimate is given by he lay up true ultimate KO calculate Quran when you put true ultimate this will occur ultimate means maximum at maximum my epsilon is n so therefore Sigma u is equal to K n power n because at ultimate my at ultimate to stress position pay my epsilon is M so therefore Sigma ultimate is 540 is equal to K n is already known yes point three power point three so X again between point three power point three okay so this Co is are lulling me into 547 seventy five four point nine two seven seventy five so K is 775 for the home and my equation is very simple Sigma is equal to Sigma is equal to epsilon n the Sigma is equal to K what is K what he escaped 775 okay epsilon n what is n point three in his poetry in his poetry so this is my answer this is my answer that is 775 epsilon power point three so I am coming up with many more lectures that is I'll be starting my next class on rolling I'll try my level best to give you all the details of rolling practically Kihara and how to calculate torque how to calculate power and with all derivations I will be discussing in my next class on the metal forming that is my next topic will be rolling thank you for watching me god bless you all thank you

Channel: Unacademy Flux - GATE & ESE - CS & IT, EE, ECE

Views: 15,124

Keywords: metal forming, praveen kulkarni, sheet metal forming, fundamentals of metal forming, fundamentals of forming, forming for gate, forming lecture, what is forming, Unacademy GATE, GATE 2021, GATE Mechanical, gate 2021 mechanical, praveen kulkarni kame, praveen kulkarni unacademy, praveen kulkarni mechanical, praveen kulkarni gate, praveen kulkarni ese, praveen kulkarni metal forming

Id: uae1NFqwV9k

Length: 70min 0sec (4200 seconds)

Published: Sat May 23 2020