Mechanical properties of steel 3: Plastic deformation
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Formal Metadata
Title 
Mechanical properties of steel 3: Plastic deformation

Title of Series  
Part Number 
3

Number of Parts 
24

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
University of Cambridge

Release Date 
2013

Language 
English

Content Metadata
Subject Area  
Abstract 
The third in a series of lectures given by Professor Bruno de Cooman of the Graduate Institute of Ferrous Technology, POSTECH, South Korea. This particular lecture introduces what happens beyond the elastic limit, i.e., plastic deformation.

Keywords 
The Graduate Institute of Ferrous Technology (GIFT)

00:00
Hot working
Paper
Finger protocol
Game
Buckelschweißen
Turning
Computer animation
Basket
Spare part
Mode of transport
Steel
Hose coupling
Material
06:28
Weapon
Ramjet
Computer animation
Tin can
Piston ring
Remotely operated underwater vehicle
Book design
Singlecylinder engine
Steel
Model building
Material
08:58
Matrix (printing)
Hot working
Scouting
Sewing
Steel
Engine
Material
Ship breaking
Cylinder head
Ramjet
Mechanic
Ford Transit
Train
Doorbell
Sizing
Belt (mechanical)
Computer animation
Screw
Cartridge (firearms)
Train
Photographic processing
Engine
Remotely operated underwater vehicle
Book design
Steel
Flatcar
Sheet metal
Shock absorber
22:16
Computer animation
Stagecoach
Work hardening
Scouting
Spare part
Engine
Mode of transport
Material
Scouting
29:29
Computer animation
Remotely operated underwater vehicle
Steel
Engine
30:30
Schlicker
Typesetting
Mechanic
Scouting
Sewing
Scouting
Ship
Computer animation
Photographic processing
Plane (tool)
Spare part
Mintmade errors
Negation
Gas turbine
Remotely operated underwater vehicle
Engine
Material
Steel
Material
Kümpeln
Drill bit
Last
36:34
Playground slide
Computer animation
Mechanic
Work hardening
Spring (device)
Remotely operated underwater vehicle
Gas turbine
Engine
Material
Material
Scouting
39:24
Computer animation
Screw
Work hardening
Stagecoach
Gas turbine
Hose coupling
Steel
Ship of the line
41:16
Cut (gems)
Bomb
Stem (ship)
Engineering fit
Fulling
Computer animation
Cartridge (firearms)
Work hardening
Spare part
Remotely operated underwater vehicle
Steel
Mintmade errors
Engine
Steel
Ship of the line
Hose coupling
Material
50:11
Semifinished casting products
Nut (hardware)
Hot working
Computer animation
Cartridge (firearms)
Ship class
Worm drive
Spare part
Remotely operated underwater vehicle
Train
Ship of the line
55:19
Watch
Computer animation
Cartridge (firearms)
Gas turbine
Train
Material
Printing
1:00:49
Ford Focus
Computer animation
Cartridge (firearms)
Remotely operated underwater vehicle
Steel
Engine
Mode of transport
1:02:52
Typesetting
Train
Sizing
Computer animation
Cartridge (firearms)
Ship class
Alcohol proof
Spare part
Remotely operated underwater vehicle
Steering
Steel
Shipwreck
Material
Steel
Material
Model building
1:10:01
Computer animation
00:01
To further serve before we start we're going to be talking a lot about major past carols In the course of the lecturers and so it's kind of nice to have an idea physically hard onwards made a pass at all what's the modalities stresses like so when Europe piece of paper to ever thought about final how strong his status in terms like a part of actually takes a lot to the river paper is work but I would be able to do a lot of papers trying to say colonel in the area of maker pass cults that's the kind of strength looking at which would steals it's a lot stronger deaths of tens of synapses couple of pieces of steel here and either 1 of them I can't pull them apart but they're very different in In strength properties and in particular on so you can't really test intention by yourself you know even if it's only a matter of Pascal no piece of paper you would have largely hard time ripping it apart in tensions but but you can always know and we know that you can have an idea of the strength latest everything there is easy to write steals lost lost harder to read it's it's related to and and you know when you bend it's more related to would we call elastic collapsed the gives you an idea of new strength is the kind of forensic so I have here by 2 pieces of steel and iron at the same thickness actually knows and I'm going to ask the lady to come forward but has only once a year will come forth and you're going to test this for us in Bandung didn't take this in your favorite the band and see if you can rent them so yeah go ahead so that an easy ride now no problem to do this would be steel got like the strength of Order of few hundred denied and tried to the same thing with this bar and it's a lot here you can bend it but it's just elastically so that in looking at something at 1500 about 10 make 10 times the difference is that you can really feel the difference even know you're out the United would be impossible To put of test of this way with kind of gives you could feel it still going the nobody can have a loss for themselves just bending between your fingers because no of obviously if somebody very strong I don't doubt I so just just went offenders and just have a feeling of how easy 1 to then the 1 and only I think it was a very strong men don't break the make her such a site to use next year perhaps so so that gives you can have an idea of what began you're not testing the tensile strength right because you bending the material you basically their collapsing but it gives you an idea of of you know that you know if you were to do test would know which your own muscle power went what if you were to make a Pascal's are but when the material is with a few hundred that make a basket you can bet that you can still than this would you most of the thousands over a thousand 1500 effects becomes really hard to do it good so so when and we were robbed uh I would close the last lecture by saying well and it in turn it is so interesting things to say about the elastic properties that in in some a subtle way the populated also plastics and and we said that found in particular the ratio of bulk to shear modulus was was there or the personal the original I could tell you something about the abuses predictor for plasticity that people in the sense of what images on the brittle or ductile but because the the the bulk modulus is related to the destruction of the resistance to fracture notes and the shear modulus is related to how easy it is to share crystal and so if the material has enticed high resistant to fracture idea high bulk modulus desk and a lower value of the shear modulus II it's easy to deform the materials by by cheering then up the materials are much more likely to behave in ductile matter and when we've seen this would we apply this the argument to we find that the you alFaruq variety most of our steals apart from Riddick where do we find that it's you just barely above the brittle like this so I obviously and we know when we can see from this example bending this piece of steel that steals our our former notes or that they can be readily would discuss talk about this in certain conditions but in general the ductile and up and so the foreign and very ductile and the reason is that I and the reason why doesn't come out of this analysis is because obviously we're looking only at the elastic properties and then we should be looking at the properties of the things that cost plastic deformation those the dislocations already said so but before we got its we go into this so and I told you trusting equations which
06:30
allowed you to 2 calculates your model is as a function of temperature as a function of compositions were you to neatly stacked values for for research in general so we can assume there's an approximation that you can use the isotropic took so long to both described assisting in steals arm which averaged values of the modulus plastic models and the sheer monitors and possible racial groups so I don't know if we had to think we we hadn't seen this yet but this is an example where it were you use this uh well known hoax low in Europe and
07:30
South I will be talking a lot about the tensile curves and this discourse and the reason why as is is Lucy maybe not this lecture the next lecture is that the tensile test it is very important test I think when you doing still design and because it will see that when you take a tensile test you also have the tensile also gives you the equivalent stress as a function of the equivalent strain yes and the equivalents of the stress and strain played a central role in materials plasticity that's that's been when you taking it in making a tensile test you automatically get you automatically get the equivalent stress equivalents strength that but that's not what we just basically looking at the at the elasticity the properties of the materials so severe have stressstrain curve here it's from the steel and job well you can already see the FAA 1st problem here is that I and I will need to do to to get the modulus in it to plug into my books law here and here what's more ham and I
08:59
welcome to do this right I need to find out where my yield points this etc. so and and there is no clear yield .period and there is no clear transition from elastic behavior to plastic behavior but that's sister that's and often encountered problems in you and practice you know when you're dealing with steals there's no shock yield .period and the reason the and and 2nd the modulus can be very variable in view of a few have experienced this already perhaps we did you look at the steel the the elastic modulus can vary anywhere from 220 to 190 the capacity of the reason s of of course is because you're not measuring a single pressed on their lots of defects In the this the structure in particular there are dislocations already in the in the structure and you have grain boundaries you have a point defects such as vacancies in all these have an impact on your monitor we know that you are actually measure and as a consequence when you're measuring and very very low strains yes and no stresses yes I these defects are already in Florence by these very low so the stress levels that you were applied and in particular will see but it doesn't take much stressed to have dislocations so even at very low stresses very low strain you get phenomena that have called microplastics there is not merely a currency of plastic gift macroscopic sees that who missed his cue to make sure that but I it's uh it already of course and that's the reason why we have this summer many steals we have this continuing change from Leicester City to but from elasticity to pass this week because of the microprocessor so what we do is we take aim at the year of the tension and to our stressstrain curve yes to define B the modulus and the other thing we do is if we want to decide where isn't where the yield strength as we just did it take by definition has just agreed that a strain of . 2 per cent is the . 2 per cent is the is the elastic strap and soak .period . 2 per cent or 0 . 0 0 2 the strength to for so and that allows me for instance in this case you can see the modulus is dead what is this the value I find year divided by this distance here so gives me 188 the capacity of its kind alone about and then I can quite understand here in this equation assuming that have also measured the Wessel ratio by looking at the With strain here and I'm inside his plugging this into my head the matrix in all of the year the for the year books locked and members of his allows me to calculate the the strain in the the tensile direction and then also the strain the last experience in the 2 perpendicular directions so there is elastic strain in 1 direction as positive and and contractions in the 2 other perpendicular directions so there is volume change in and elasticity and there is no volume Change in contrast there is no volume change in Europe plastic deformation and although that's not 100 per cent correct because when you deforming material plastic late you are introducing dislocations and point defects and so there is a volume change but it's extremely small and you don't really need to worry about it unless you are very special situations but added that there is a volume changing this this but so you what we are going to say now we're going to go through with relatively quickly and that only highlights what is important to remember so if you know that if you if you take a stressstrain curve you can define what's called an engineering stressstrain curve and they have a true stressed Rinker with In in them in practice for instance if you look in catalogs again of US steel producers you will find engineering stress catering trained persons mostly report because the standards for the the steel grades define the materials properties based on the engineering stressstrain but the 4 materials development and when you really want to describe the materials property you should use the true stressed training Kirk and of reasons why there is a difference between an engineering true stressstrain
15:32
curve that is that because that's we are as we see it as a restraining materials cast the the status is round section this as we strain materials indeed the stresses the this is the forest and this is an area in the beginning area His mother forests these values change in in particular the section changes in the case of an engineering stressstrain curve you assume that there is no change in the crosssection there which is not true however that's the way we define most of our engineering properties mechanical problems so and then so obviously this also implies that whatever you've chosen as a specimen will have an impact on would you report as values and it's it's important also that the 4 in standards the related to mechanical properties that the the specimen yes dimensions are very well defined because the properties are related to the specimen the initial specimen dimensions so then so when you report engineering properties he always have to say you know what specimens you use yes because the values the report the maid differ yes depending on whether you use the European standard specimen for instance for flat steel yes the North American sample sizes or just the sample sizes and he's a very common the values 4 the specimen sizes so a stress drainage Kirvin engineering stress train curve that is just given just like this it's actually meaning less yes and others so you should should always give you know if you read if you yourself are reporting you should always sigh the conditions in which they were measured and so they could be the samples used then 1 1 of the interesting things to illustrate that no specimens are important is because depending on how you measure the stressstrain curve you may get very different stressed that in particular for instance on but if you if you get your stressstrain curve not from 80 stressing but the union actual tension tension tests but for instance from the bulged you can also get stressed from about that or you can get stressed thinkers from torsion tests the also you get very different results not so much in the data because you can recalculate instance the test results from a bold steps 2 but true stressed or equivalent stress curve versus true strain or equivalents and and and then what you find is that the tensile test results and the bulge test results they should be fall each other however the bulge test as if very interesting peculiarity is that you don't get natural there's no way for the material to net so instead of having a tense which you in the 10 cell the case stops at about in this case about 10 15 per cent of the information because your samplejust snacks and breaks indicates that the belts that you can explore a much larger storing range than in the case of the Union actual test the same holds what portion portions of the torsion and Inc both steps you don't get Medicaid so you get a different stressed rendered in particular you get a much wider strain on him but also for you and for those who are not familiar with the the bells test would the start this is what the samples look like you basically have to be that you love you have your material is still in kept in position by drawing guy and by a blindfolded hands as a as a film as at work and then you have a hunch that prices oil against the EU sheets surface and union becomes a sphere spherical and it eventually but you know it does fracture of the and and then but it is the strain at which the the strains at which the fracture begins and ends this is a much much larger than in the case of the union actual tensile test but in an
22:19
instant and so what I mean is this diffuse snack that we discussed in the past as is diffused neck does not occur now the occurrence of the
22:30
diffuse neck is important let's let's talk about it for a moment so when we have a we do with the Union actual test when we start when a section of a crosssectional area and as with the the material the plastic late in the 1st stage we have we have which called home which he strain and then to the material becomes longer your sample becomes larger and so because we have the constant volume there reason is that no change in volume if if you becomes longer you cross section must be reduced To that end what happens is a new sample you've got to competing things happening 1 is the material hardens as you and becomes you need more forces to the former Mets 1 aspect of the union forced beef the other thing is that the yeah this section becomes smaller and smaller than you have these 2 competing effects yes so and at 1 point no there's will be a situation where because of the reduction in section the effect of this section reductions will the larger than destroyed the facts of the strain hardening and you material well start to localized the locally deformed only so you'll get paid what what we call this enacting this Snack will will form which to will talk about this the chemically in a moment and and will say why it happens locally but it went when this happens uh things change dramatically because whereas you have uniforms straining the material is the 4th elastically everywhere at once you have the the localization of the strain of the deformation the other parts of the specimens stopped the forming plastic this no plastic deformation anymore in In these sections that the outside the neck area all the plastic strain is fully localized here are so we can express relatively simply the relation between a stresses and strains In the engineering approach and stresses and strains in the in the actual approach as long as we have home watching you strength so let's let's go through these equations because the very important and all will be using them in a moment so what you basically expressed is very simply that there is a need the volume of new material doesn't check so the the original section the original length is the instantaneous section times to instantaneously and so I can rewrite this equation by as saying that length people fell 0 instantaneous length of the length is equal to the initial crosssection divided by the instantaneous process now the engineering stress which is defined as the force divided by the original section and the engineering strange is the the elongate showing that I measure divided by the original and I can rewrite this as instantaneously divided by 12 0 minus1 but in other words this B plus 1 it is this racial here In contrast the the true stressed there's the the ratio of the force divided by the instantaneous the the value of the section of and the that the strain is not defined St Delta held over serial serial but as the integral all the increment in length divided by the instantaneous and integrate that's so that is very simple that's the natural log of the ratio of the instantaneously over the initial length and if I use this equation here I find that the true strain is equal to the natural log 1 plus the engineering who have so that's very nice because if I have data engineering strain data I think very simply we calculated that the the true strength and I can also calculate the true stress because when I can I can calculate the instantaneous section were very simply by use this last equation when I rewrite it as 1 plus is Bisbee exponent of the true strain In 1 must be you can see from here 1 Leslie was gave me the ratio of the initial section divided by the current section but this gives me this exponential relations between the initial section and the true strength of this maybe this section so I can I and very simply go out here
29:31
it's very easily calculated for have engineering strain engineering stressed I can recalculate discover this engineering stressstrain curve too this true strength Strasbourg and you know something interesting happens is that whereas the engineering stressstrain curve had a maximum yes the the true stressstrain curve is now the continuous curve and the the position wherever this point of instability was is now not very visible on this it somewhere somewhere here it's it's not this maximum here that that maximum is related to to fracture and so will seize the moment I
30:36
think so this is for Europe
30:51
and in information just to connect the little bit with what will say what see in the future when when you actually there would look at the small crystals in your steel yes they don't strain like a little box yes like putty or but you pull in 1 direction and then gets the narrow its with which he sees that the material the grains slept there is sharing of Kurds in that there is a shear deformation that causes the the strength to job if if you look at the rain on at the grain level here you you scene you can visually see there's that the grains part of the grains slipped over 1 another in and as a consequence of this select group can see if you slip the top part with respect to the bottom part of a certain distance the Crystal has become longer yeah Crystal has become a lot and it's this select think they know the slipping mechanism that actually gives me plastic deformation but the Butler will continue for a few lectures they wanted to let you Nora this this crystal bits of the the plastic deformation of the students and now let's let's have a look at this this this maximum indicated In the engineering stressstrain curves because it's an important 1 it's an important .period from from a technological point of view In terms of materials development so unique factual test me so we have the following equation is this I always correct that means that the derivative of the truest stressed to strain is equal to the derivative of the forest over the section to section all devoted to with respect to the distract so if I if I calculated derivative this is what you get and and we can rewrite this I write this thing here this equation is a function of the by picking up the at the at the at the epsilon is equal to this these Tudor a time this segment at long last half overrated VAT and so have the derivative the change of the applied force with the strain as a function of the the answer is related to 4 2 phenomena which already scribe this to competing phenomenon there the 1st factor is that the material will harden what can hard for this this segment the absence and kids mean it's nothing else and saying Well this is positive the material hardens if it's negative it's the material softens with stress that this is basically tells me what is the materials in response to the force and the 2nd for the factor is a reduction in error area the the aid the absence on the change of the section where the deformation and in the tensile test it's and it's a negative the value me because as I make things longer they necessarily have to reduce in crosssection due to the because we have constant volume and so when these 2 factors are equal the at the moment 0 hour at reach this the maximum in distressed To reach a maximum values that put this equal to 0 and I find that so this equation and if I now use the relation between the instantaneous cross section and the strain which we just the right from the instantaneous section is the initial section times exponent of minus 2 estranged I find it very simple relations for the many changes the section with strained it's my mistake anything like this and I find that when asked his maximum the derivatives to the stressstrain curves at that point it equal to distress at that point now that this equation which is called the goal Sedaris equation yes it is very and very fundamental equation because the the only thing that I didn't say anything about the way the materials trying hard and or anything I think it's a pretty
36:37
just based on you know what is this segment the Epsilon yes but am in my material and and just doing this mathematical derivation and then by using a fact this equation here which is basically based on no change in volume during plastic deformation so and this is what you get it it tells you that material will become a classically unstable when the strain hardening is equal to the stress "quotation mark you may be familiar with another equation uh which which is very popular in the introductory materials mechanics courses where but they say that you reach the maximum in the stressstrain curves against the new engineers have when the but the strain they should be in here but what if you're writing intelligently Neil corrected when they were opposed to this slide the engineering strain is equal to that and where it's usually the rise in undergraduate courses is divided by saying well we knew we know what stressstrain but the equation is for stressstrain relations they needed stress is constant times straining to certain power and an end being this all a factor that we call strain hardening and this equation can be normalized and have this formerly know this 1 of joke it's not a good way to look at facts this this approach that because you did and it's absolutely not universal also in the sense that I am you but still the hardening law and this this their relationship doesn't assume anything about the material properties have doesn't say what whether the material hardens or softens or whatever it is OK end of so the I'm I'm
39:16
not saying that this is kind of interesting to use as a handwaving arguments against something spring
39:25
hardens the end values higher you will get more uniform along and that's the only you can say but if you actually wanting to seriously look at strain hardening and the it's the moment of instability you should you should actually use this call suggest criteria which is illustrated here for a number of steals highstrength I steals a couple of trips deals and twitch steel here at this stage not so important and what what these grades are and this is the stressstrain could be continuous lines and adopts body derivative to discontinue 1 and you see that the as I increased the the distressed the strain hardening his me the uniform along geisha increases this because that's that is this course criteria you can also see then the strain hardening This is the segment the Epsilon it is not a constant yes it depends on the strength the when you assume but the the next was intial hardening that like the 1 that here the strain hardening is a constant yes
41:07
it's basically a constant it's not the function of the stress right so this is the equation you want to use to to get the
41:21
so but let's have a look now act why it is that this exponential strain hardening laws and the the use of this and the value which will talk about that in a moment in more detail why it's such a a concept that remains very strong in engineering but it turns out that In many cases the in particular for fairer Dickstein when you take your data from the stressstrain thank you plot the stress and strain yes data and now you popped and not in a linear way but you plot to in a Loblaw plot against the Pokemon lower than which you very often see Is that for instance here lowcarbon steel you find a straight line also very close to the end this is a frantic stainless steel a straight line yes so it basically means that your this idea of having the exponential hardening this you may not be very Korac from a fundamental point of view but in practice it's actually a pretty solid concept to follow because of its simplicity and so as a consequence if if you're longblocked lots are pretty much straight and that means that your and value In the end value you get from is basically the slope of the stressstrain curve and European value is it's actually pretty constant as a function of strength but just to illustrate that that's not always correct you have now here Tuesday other steals and 18 chrome 8 % nickel 17 Kroll 7 % McGowan are to Austin and there if you know what I'm saying that is the the stressstrain curves In a lot lot lot you find not the linear behavior the trees cut of Kirby this 1 curves up this 1 also curves up here a lot of strange and if we the determined the the slope to these lines you we do find that the end value is not constant with and there is in fact with this 17 per cent growth 7 Mickelson it even has a big bump in so obviously has found something is happening in these materials and which makes the use of 8 simple single parameter 2 look at the strain hardening a nonworking concept in this case OK so bright so so
44:57
it's very important that we we should use the course their criteria to describe plastic instability and is considered a criterion is very important because it tells you that this strain hardening yes has a big impact on indeed plastic instabilities of the higher readers yes the higher my plastic instability the highest strains my plastic instability will occur again but it also means that if you can increase the strain hardening against you also increased the strength of the material right the strain hardening allows you to the engineering the strain hardening allows you to increase the uniform the full amount of uniformed information can give but also increase the strength of the material it's a very powerful thing to control if you can't control them trade but never what where do these where do this idea come from that we all strain hardening strain hardening which is basically the segment the that's a lot the bomb which is like the correct scientific and wait to 2 look at strain hardening found in engineering has this pretty much engineering practice that it's pretty much been replaced by an invalid in which which again as I said in you look at manufacturing data catalog of steals etc. that's basically what you'll get pulsated in value areas .period all we guarantee you a value of 2 . 22 and our steel is better because we have .period 23 and value open on so that is what it did to the wrote of this is what we call the conventional stressstrain relationships so and these ways there were using to represent the stressstrain curve we have stressstrain data the intended to things you can get this to your customer here this is nothing or you can just say that well use the stressstrain curve to 2 derive some key parameters of the material so 1 these are it's an empirical approach there's no science involved right so you can do whatever you want if you and if you have an interesting equation yes go ahead of have Europe and there are a couple of directly many more than the ones I'm going to show you but in in in in engineering the most important 1 spot and you probably know than the ones that already mentions the Holleman power alone so you basically fit your data know however well you can follow this curve segment is 8 times Epsilon to the to the end and then there's the and an or 2 cost but it did not strain dependent and you basically fitness to your unity of the obviously aren't you already know probably feel that knowing that you stressstrain curve has like an elastic part and then and then in the curved part here but it's going to be a lessthanperfect to fit the below low strain that 2nd and that's true with great deviations are always between defined between the equation and measure data is for low strain of you know where it doesn't really do the job nicely affecting the elastic part and antiArab becomes negligible at lodges all of these conventional stretching you can for comparison reasons you can bet you can normalized feeding you divide distressed by by Sigma 0 and epsilon by epsilon fuel will save you more things about this animal but obviously
50:16
this and clever people who said well you know but we don't like this behavior very much but we like to have another equation which describes the plastic parts felt life of stressstrain curve into 1 of them in 1 of these equations is the new tricks powerless and segment is the yield strength class and then it's basically looks like the the Holleman equation it doesn't really look like it it's because in this case your the strain is not the total strain but the plastic surgery so you have to remove the elastic strain from your data if you think so so if you have a stressstrain curve it's a data was financed take a new look at any point here there so so did this train here is the total strength is its a total for so if if you were to unload this it would go like this it would you would you would have elastic the number reduction in the In the length due to elastic part of the stress so this would be the plastic strain and this would be the last years and then the elastic strain so you know that segment is the NYTimes epsilon elastic and many here so the elastic strain is the line it's not the real strength in all of that this this is the last 3 changes With the amount of strain you get right because there is a lot of stress so that you can get you can calculate that if you know the modulus and you know the stress levels so you can you can affect your data to the bulk this equation what is important is that the end value In this that yet in the end value to you and you would obtained by fitting the previous Holloman equation is not the same value right dozens don't it's not fitting procedure involved in the case of the equation situation remember year for instance and this was ah modulus and then we had a year old .period 2 strain has sold this was yield stress so what would you do With the Goodwick equation you take this state and then you transform it in the plastic string and then the equation starts with yield stress tests OK and that's what you feel 2 this equation but whereas in the Holloman cases you take all the data and you just right To invaluable not necessarily the site to somebody gives you any value and doesn't tell you well equation he stated 2 yes you don't really know what it means right OK I now but a good 1 that's used for wild and that's as good as the swift equation to works so well that like be the debates equipment is different this time set so here you you don't define I didn't thing Ludwick you already defined with the yield strength right here you can't keep it open it's scary times lost again the plastic strain of the but this would
55:20
make I only have 2 parameters they and In this
55:27
case yeah I have brothers K 8 and which I confess I was a little bit more flexible but again we haven't any value which may not mean necessarily the same as in parliament's case and in the case of but the nice thing
55:56
about these switches function words that you think you can get very clear approximations for calculated approximation for you know things like uniforms dress uniforms training who wanted to basically if look at the equator to you find relatively simple formulas that once you have determined what and value as you can determine the the strain hardening coefficient but the problem with these 3 approaches Hallerman swathed in the thing is that this end value which may be different in all cases there is a constant once you figured it it's it's got a value and that's it doesn't it's not strain dependence and so 1 and and for the obvious reasons that you on some very simple materials will do not have as a constant value both ends the news media previous equations implicitly assumed that the strain Hanukkah has a single value and we you avoid this but the assumption by using this watching exponential but and this is the general view but such services and with the equation looks like him the general for there's an immediacy you have promised a and B and and that's it there is no hardening law in this yeah at the end you can derive a hardening of the relation from this just by doing the derivative of distress to the plastic strain that will give you a variable the stress but it is it looks like a little bit of trivial but if is this equation is you look like equation need to do the derivative you will find that certified by derivatives of derivatives of this equation it'll be fairly flat flatline yes the Holleman Italy however with budget equation in which this really may look rather similar right up your end value well will vary yes and that's that's not much closer to the actual material behavior that some people favor this approach technically it's not being used appliances not going to find materials descriptions and produces catalog would that in any industry which which actually I use this approach however had been scientifically it's it's actually the preferred empirical equation because you don't assume that's the case and again using this this long you can you have formalist simple formulas based on the fitting parameters that allow you to determine the uniformly along the nation and the uniform stressed that the uniforms along with Kent and hearing you can you basically compared with 4 . 4 different values and values so In the case of and values are constant disappointed because not this and that and then what's what the watches empirical equation gives you is that this exponential share to the risk as it were an asymptotic stress value but no during the day and found not cost concurred so
1:00:53
I let's have a look this is an are still misses the engineering stressing that this is the true stressstrain curve but this is just data from yeah so what can we do
1:01:08
well we just do curve fitting procedure and we use Ludvig swift and watch it but you just do the least square factor right and this is the parameters you find and cede some reason it to drop down here but anyway let's focus on the thing and swift equations and and as I told you for instance you look at the end value beauty and values .period 55 beauty and value this point 24 so again any time somebody gives you and value yes without telling you you know where it comes from Swift would all along meaningless right on the ones that there is actually a most users this equation from the technical engineering point of view that's the 1 people use so although they don't usually left to guess here is so when people tell you that typically a variety in the strain hardening coefficient and the Saints .period 22 4 . 1 5 in this case for instance that's within weeks the 2 areas where the values
1:02:56
right and and then I can so
1:03:00
if I if I have K and ii what's the uniform along nation here I don't know rights the you but you can using these associated formulas determined the yield strength proved strength of the yield strength proves to the . 2 cent and the the yield strength at the point of the set the ultimate tensile strength and a uniformly longer each year and of course in this case that because you have it's it comes as no surprise that uniform along it should be cost and think is the world is equal to standard value posters
1:03:42
and value this this is an approximation .period 24 right so but that's Sayuri you you're like like yourself you're young researcher you you know you you'd like to have some equations on gas would you know I have some real equations we'll data that you could play with these empirical formulas don't help you at all in you if you don't have data you knowing can't really you anything much with them but the foot in terms of design purposes but of course there are many steel companies and research have been using on these swift equations for years you know they have a huge databases yes and I have determined these 3 parameters 8 K and what thousands of steel so after a while you were able to set up equations yes there are again empirical equations which tells you what the value of k the value and this set of steels that was analyzed over the years and as a function of and this week comes interesting as a function of the composition the silicon manganese phosphorus brain size whatever parameters they've put any of that taking into account the wondered if the statistical analysis tour the value too so this allows you to no residents think about a steel mill with certain composition with a certain grain diameter end if you look at the previous equation there is a parameter for the amount of carbon and solid solution you can take that into account if the Steelers well and we'll that amount is very low and you can assume Europe and then you can basically get your switched equation plugging the parameter yet the stressstrain curve & and here I have added myself by hand and elastic Part 2 even so and the recent move the results of reasonable and you can say Well you know what happens if change a carbon content of phosphorus content of and you get a you can get trends which again are based on entirely empirical there's no theory behind it is empirical at an empirical approach and lots of data analysis so I have to go minutes before I close the door but the stressstrain curves as I said that in practice they depend on the sample dimensions they depend on other aspects of the test and the 2 aspects of extremely important 1 as the temperature and many other aspects is this train wreck notes and the strain rate this is usually from a technical point of view it's once you you want temperature data it becomes more difficult to get this type of data but the strain rate data is sometimes you or very often available in and In order to take the the strain rate into account we again have conventional equations and that are extended to take the strain rate into account and the extension of the whole among equation you probably know is by adding might multiplying your Holleman equated with this Epsilon adopt the strain rate kind to the powers that be in this and is called the the strain rate sensitivity and this parameter again the way suggested by the whole among the extended Holleman equations suggested it's a constant but it's it's not at all a concert it's it's it's very dependent on the strain rate itself this is plot here of the strain range the string great sensitivity as a function of the strain right now and you can see very long very large variations are usually for steals are strain rate sensitivity this and value as it appears in this equation here is 0 . 0 5 2 small but you can see that as we reduce the strain rate on this value can go very high they can cross it can be hired and . 5 but this is taken by the way at 800 degrees C and this means that you're material can behave supra plastic but I've come to the end of my class and lecture today that you will have to wait till Thursday to hear more
1:10:01
about thank you for your attention