the response stops being elastic the point where this happens is actually not the point and this requires a little bit of discussion we're testing metals you probably remember from your source in material science that at the atomic scale were the material consists of atoms metal atoms that are organized together in Blackie's in structures that are regular crystal type lattice structures forming grains and then each grain has its own crystal structure but the material itself consists of a number of grains that are aggregated together and then at the point where grains come together you have boundaries
and in those boundaries the atoms are not exactly organized perfectly what furthermore metals are very kind very specific kind of material that allows atoms to stick together while moving past each other slipping past each other so the atomic level the mechanism of slip in metals is the basis for what we call plastic deformation yield so as you load the material in the fly higher and higher stress the atoms are forced to split the part to go farther apart from each other and then when you remove the load they come back to where they were as
the level of stress increases the atoms in the grain boundary region are going to undergo slip they're going to move to a position because of loading and not come back when you're moved along this is a progressive process that starts at some point and becomes more prevalent more generalized as the stress level is increased so in fact yield does not physically start at one particular stress level these yield is and slip at the atomic slip and as a result structural yield is the process that is progressive however however there needs to be some way to
for us to determine when permanent information really starts two parts to it first of all as you start increasing the stress level in the region that is where the response is elastic and nonlinear you are going to observe that you don't come back exactly on the loading line you load in this line and you come back and there's a little bit of plastic deformation if you perform a very precise experiment and you're very careful with your measurements you're going to discover that there's a little bit of permanent information that starts occurring the question is this
test enough can I determine that since I'm able to measure a very small amount of permanent deformation I have yield well the practical problem would be the following different experimenters different labs would have capabilities of determining the smallest amount of slip at different levels the the smallest amount of permanent information at different levels there needs to be for practical purposes for reporting and understanding there needs to be a common definition of when does permanent information set when does it start and here's the company agreed upon definition when for the permanent information is equal to 2,000
micro strain which is 0.2% we can declare that yield has occurred so yield or the onset revealed plastic deformation is decided to have occurred when upon removal of the load the permanent strain is 0.2% or 2000 micro strain or not at this level at which the permanent deformation abort unloading ends up being 2000 micro strain this stress level is what we call yield stress so yield stress is the stress level causing epsilon permanent 2000 micro strain now you see what is happening here this is an implicit definition as opposed to being an explicit definition so
we tell the yield stress rights property but this by itself doesn't give you immediately a way of finding yield stress we'll talk about that a little later now if one continuous below the material past this stress level there were response and that ends up leveling off and this range here is typically that firm defined as perfectly plastic response or yield the stress remains substantially constant and then does the strain its increasing up to a point where the stress starts picking up again and it peaks at some level the stress level corresponding to that peak we
called Sigma ultimate so the ultimate stress is the largest value of stress that dispersed specimen experiences and then something interesting happens beyond that beyond that to the right if we continue to load the spacer to stretch the specimen the stress required to continue to stretch the specimen apparently goes down such that at the very last moment when the specimen breaks into we're going to have the Sigma F Sigma F is failure stress whereas Sigma ultimate see my you is ultimate stress that's the largest stress that the Megillah is corresponding to the fracture we're going to
have the value of strain at the moment of fracture which is extra Epsilon fracture however at the moment the fracture the specimen breaks into the two pieces are still under stress and the two pieces upon failure upon separation are going to shrink back because the load goes down to zero so the two the length of the two pieces as the stress reduces the strain is going to come back and the change in length it measured upon the broken specimen is called elongation so elongation is the final length of the specimen minus the initial length of
the specimen this change in length you take the specimen after failure the two pieces and you put them head together you know together and you measure the length subtract the initial length before you started applying the information applying load that is the elongation and it corresponds to this strain here not this strain but this train here all right nothing these are the important elements of the response the slope of this curve is Young's modulus so from the slope one can determine Young's modulus from the point by determining the point or the response stops being following
a straight line one can determine the proportionality stress from the response from the point where the permanent deformation is mm microstrain one can determine the illustris from the highest peak of the response one can determine the ultimate stress and from the stress at the moment of failure one can determine fracture stress now all this is nice but built into this explanation there is a book how do you actually determine the yield stress because I gave you the property that the permanent deformation is two thousand micro strain but you don't know as you love the specimen
at no time when the specimen is under load do you actually know how much permanent deformation there's gonna be how much permanent strain there's gonna be if you remove the load so one way to try to determine this would be to lo the specimen and then unload measure easily did I get there is there enough permanent strain is no reload then go a little bit higher unload come back and measure permanent strain am i in two thousand micro strain yet or not if not you go and load and unload and load and unload this is
not practical so that's not the way to do but the important thing to observe is the following the slope of the unloading wall in here is always one and he paralleled the unloading line has the property of being parallel to the loading line so then why don't you do this we take a specimen we perform a test we measure the stress versus strain response and we pull on the specimen all the way to fail that's the curve that we mention the first thing that we do easily determine the slope in this initial initial region out
of which we determine Young's modules then we determine the point where the response no longer follows this straight line and this is going to give us Sigma proportionality from here from zero to Sigma P the response is linear elastic linear elastic were linearly elastic Hookes law applies everything is nice everything disease
