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The specimen has attached to it a clip that permits us to measure

Â how much the material has elongated during the applied stress.

Â Over to the right are two different types of shapes that are used for

Â this type of test.

Â One is around a cross-sectional specimen, and the other is a flat-plate specimen.

Â So depending upon the particular material that you're using for

Â a specific application, we'll wind up using a different specimen geometry.

Â When we apply the load to the material, we wind up describing

Â a certain portion of this behavior in terms of stress versus strain.

Â And let's go back and look at what we mean by the concept of stress.

Â Stress, much like conductivity that we talked about in earlier modules,

Â is an intensive property.

Â Intensive meaning that we have eliminated the cross-sectional area.

Â So now what we do is we take the force that's applied to cause either compression

Â or tension, divide it by the original cross-sectional area, and

Â that cross-sectional area then will be divided into the force and

Â we have a stress parameter.

Â So on the Y axis we're plotting stress.

Â With respect to the X axis or the strain axis,

Â what we're looking at is the change in length divided by the original length.

Â And when we apply the load, we're, we typically will find ourselves

Â in the early stages, in a region that we refer to as the elastic regime.

Â In this particular case, when we look at load versus strain,

Â what we see is a linear behavior.

Â The slope of that stress-strain curve defines for

Â us the elastic modules or the stiffness of the material.

Â Over to the right what we have,

Â is the geometry of the specimen that we're looking at.

Â This is a cylindrical specimen.

Â It has an initial cross-sectional area, given as a zero.

Â That helps, then, define the stress as we begin to pull the fixtures apart.

Â I want to focus this time with regard to tensile testing on the actual specimen,

Â itself.

Â When we pull a specimen,

Â along the direction of stress axis, either compression or tension.

Â There will be a corresponding change in the material length.

Â When we look at the material from a cross sectional area point of view,

Â we find that if we pull the material in tension,

Â we will see that the cross sectional area will wind up reducing.

Â So we can talk about the strain in the cross sectional area as being a change

Â in the diameter, divided by the original diameter of the specimen, and

Â we can talk about the strain in the direction parallel to the deformation

Â as being the change in length with respect to the original length.

Â What we begin to see is as the material becomes deformed,

Â we see that we ultimately wind up passing through the region that we

Â refer to as the linear region where we have elastic deformation.

Â If we continue beyond the elastic range, we see that the curve begins to deviate

Â from linearity and that region in there is referred to as the plastic regime.

Â If we begin at point B and unload the specimen.

Â What will happen is when we go back down to zero load, or

Â zero stress, we have permanent deformation that's been added to the material.

Â So the material has been permanently deformed.

Â And that deformation is referred to as plastic deformation.

Â When we look at the combination of the stress-strain behavior and

Â we look at the specimen as it has become deformed, what we see is,

Â the first on the left we have the length of gage, and as we begin to pull the gage,

Â we eventually begin to develop something that's referred to as the neck.

Â Sometimes this reason is referred to as the onset of plastic instability.

Â And we begin to see then on the stress-strain curve a bending down, or

Â what might appear as the reduction in the strength of the material.

Â However, what's actually happening is not that the material is getting weaker.

Â What is happening at this point beyond the region where it is necking,

Â is that the cross sectional area of the specimen is significantly decreasing,

Â which means that if we were to compensate for the change in cross sectional area,

Â we would be able to see the actual true stress and

Â strain behavior of the material.

Â What we do then is we come up with another parameter that will describe

Â the tensile behavior, and we'll talk about that in the next slide.

Â But here what we do is, we define the yield strength or the point at which

Â the elastic behavior ends, and we would refer to that then as sigma YS.

Â When we talk about the point of plastic and stability,

Â it occurs on the maximum of the stress-strain curve.

Â And that's referred to as the ultimate tensile strength or sigma UTS.

Â And the corresponding points with respect to strain.

Â Then tells us about the end of the elastic range with respect to strain.

Â The point at which the plastic instability occurs.

Â And then in terms of the final failure or the fracture strain.

Â The point at which the material goes into two parts.

Â Depending upon whether or not you are using the material and

Â the particular application is for a structure.

Â Generally speaking what we do is we consider something

Â we refer to as the engineering stress.

Â When we talk about the engineering stress

Â what we're doing is describing the stress-strain behavior

Â when the stress is calculated on the original cross sectional area.

Â Now, the reason we use this in design is because,

Â generally speaking, we try to avoid having the material change

Â its shape as a result of the load in a particular structure.

Â So, generally,

Â we are down below the yield point when the material is actually used in application.

Â So when we talk about engineering stress,

Â we're talking about the behavior at relatively small amounts of strain.

Â Now if we're using the material ultimately for

Â an application like container products for beverages.

Â We're interested in the onset of that plastic instability for

Â the purpose of making sure that during the deformation process,

Â the material is deforming in a uniform way.

Â Beyond the point of instability, the material begins to deform locally and

Â the cross sectional area is changing.

Â So in order to evaluate a material in terms of the physics of the material.

Â What we often do beyond the yield point,

Â we talk about a parameter that's referred to as the true stress.

Â And in the case of true stress, what we do is to compensate for

Â the change in cross sectional area we constantly update the cross

Â sectional area as we go through the stress-strain curve.

Â So that will take into account those regions in the material where

Â the instability has occurred and the cross sectional area has been reduced.

Â So hence we have a true stress and engineering stress.

Â 8:44

Another parameter that comes directly out of a stress-strain test is

Â the fracture or the strain at failure.

Â And those are given as the Xs on each one of these curves.

Â In the first curve what we have is a material that is behaving

Â in a way that is brittle in nature, that is it's deforming elastically.

Â It reaches a maximum point and then it breaks.

Â This is characteristic oftentimes of ceramic materials that tend to be

Â very brittle and do not allow for any plastic deformation.

Â On the other hand when we look at metallic materials we know that,

Â that not only can they deform elastically but they can deform plastically.

Â And the third curve is one that is characteristic of many polymeric or

Â foam materials.

Â That is what happens is it starts off slow the deformation, the stress and

Â the strain are related to one another.

Â And then there's a region, a flat region called the plateau region

Â where either the material is unraveling or in the case of foams,

Â the spaces that are between the ligaments in the foam begin to collapse.

Â And then eventually, it moves into a location where everything has collapsed,

Â and what we have is the final failure of the material, again, given that at that X.

Â We can begin to talk about the parameter called the material toughness, and

Â that ultimately winds up being related to the area of under the stress-strain curve.

Â So material one would have a low toughness even though it has a high strength,

Â it has a low toughness because the area is small.

Â We look at the metallic material, it's a tough material because it has a good

Â combination of the strength as well as the area under the stress-strain curve.

Â So, that material is tough.

Â When we look at material behavior three, where we have that

Â nice long plateau region, and ultimate failure, when we look at the area

Â under that stress-strain curve, the toughness of the material is high.

Â And generally speaking, what we would like to do is to

Â have a material response like that in specimen three

Â