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

how much the material has elongated during the applied stress.

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

this type of test.

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

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

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

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

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

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

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

is an intensive property.

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

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

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

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

we have a stress parameter.

So on the Y axis we're plotting stress.

With respect to the X axis or the strain axis,

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

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

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

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

what we see is a linear behavior.

The slope of that stress-strain curve defines for

us the elastic modules or the stiffness of the material.

Over to the right what we have,

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

This is a cylindrical specimen.

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

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

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

itself.

When we pull a specimen,

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

There will be a corresponding change in the material length.

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

we find that if we pull the material in tension,

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

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

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

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

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

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

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

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

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

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

If we begin at point B and unload the specimen.

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

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

So the material has been permanently deformed.

And that deformation is referred to as plastic deformation.

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

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

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

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

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

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

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

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

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

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

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

we would be able to see the actual true stress and

strain behavior of the material.

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

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

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

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

When we talk about the point of plastic and stability,

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

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

And the corresponding points with respect to strain.

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

The point at which the plastic instability occurs.

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

The point at which the material goes into two parts.

Depending upon whether or not you are using the material and

the particular application is for a structure.

Generally speaking what we do is we consider something

we refer to as the engineering stress.

When we talk about the engineering stress

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

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

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

generally speaking, we try to avoid having the material change

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

So, generally,

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

So when we talk about engineering stress,

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

Now if we're using the material ultimately for

an application like container products for beverages.

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

the purpose of making sure that during the deformation process,

the material is deforming in a uniform way.

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

the cross sectional area is changing.

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

What we often do beyond the yield point,

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

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

the change in cross sectional area we constantly update the cross

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

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

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

So hence we have a true stress and engineering stress.

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

the fracture or the strain at failure.

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

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

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

It reaches a maximum point and then it breaks.

This is characteristic oftentimes of ceramic materials that tend to be

very brittle and do not allow for any plastic deformation.

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

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

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

foam materials.

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

the strain are related to one another.

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

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

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

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

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

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

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

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

it has a low toughness because the area is small.

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

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

So, that material is tough.

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

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

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

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

have a material response like that in specimen three