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Let's continue on with our discussions of various strengthening mechanisms.

Â And the second one we're going to look at is dislocation strengthening.

Â In the case of dislocation strengthening, we can look at the diagram

Â that we have illustrated in the slide that is on the board.

Â What we see is that when we look at a material like a whisker,

Â that we just described previously in an earlier lesson,

Â where that dislocation, where that structure contains a single dislocation.

Â What we find is that the flow stress that we measure in a material like a whisker is

Â going to be very, very high, extraordinarily high,

Â close to the theoretical strength of the material.

Â Now, as more dislocations are added to the material,

Â what we find is, the strength of the material winds up reducing.

Â And the reason that this is occurring is,

Â that when we have dislocations present, and

Â energetically we're always going to have a certain number of dislocations present.

Â What we find is, if we just have the right number of dislocations,

Â what we find is they will help the slip process.

Â Eventually, as the concentration of

Â dislocation's winds up changing and increasing.

Â What we find is that the material now begins to increase in strengths,

Â so that whole region between the minimum point and

Â as we go to higher dislocation contents,

Â what we're seeing is an increase of the strength of the material.

Â And that increase in strength material is

Â due to the interaction of the dislocations with one another.

Â So the more dislocations we have in the system,

Â then what we find is the higher the strength of the material,

Â because that dislocation, dislocation interaction winds up reducing the mobility

Â of the individual dislocations and hence, the deformation process.

Â It requires more force in order to have the dislocations move

Â through this high density of dislocation arrangements.

Â We can examine the behavior that we've been describing with respect to

Â increasing the dislocation content by examining what happens

Â during a stress strain curve where we test the material.

Â Remember that when we look at the result of the stress strain curve,

Â we have a region where we first begin to load the material.

Â And in the region, we go up to position A, that's at the red circle,

Â and what happens at this particular point is we deviate beyond A over to B.

Â We deviate from the elastic portion and

Â now we're into the plastic regime, and what you can see is as you go from A to B,

Â there is a corresponding increase in the stress of the material.

Â And now if we would unload it and take it back to our original position,

Â of course what we would find is, we would see that the material has undergone some

Â permanent plastic damage, and as a result of unloading from B down to C,

Â what we will wind up with is a recoverable elastic deformation.

Â Now if we were to reload the specimen from C back up to B.

Â Effectively, rather than talking about the strength being at position A,

Â it's now at position B.

Â Position B is now our new yield strength of the material.

Â If we were to continue on beyond B up to larger and larger amounts of deformation,

Â what we are in effect doing is increasing the amount of deformation we put in.

Â And that deformation is manifested in an increase in the dislocation density.

Â So that dislocation density now is

Â causing a reduction in the mobility of individual dislocations.

Â And hence, when we reduce the mobility of dislocations,

Â we wind up decreasing or increasing the strength of the material.

Â So one of the mechanisms by which we can strengthen a material is

Â to go through a deformation process like a rolling process.

Â So for example when we look at material that undergoes rolling,

Â what can be done is you can go through a series of steps during rolling,

Â increasing the dislocation content and thereby increasing the strength

Â of that sheet that is, that has undergone the rolling process.

Â Now there's only a limited amount of increase in strength that you

Â can achieve by doing this because at some point and time,

Â the more deformation you put in you'll ultimately wind up reaching the point

Â where the material can no longer withstand all the deformation and it fails.

Â But this is a mechanism by which we can in fact increase the strength of a alloy.

Â 5:29

Now, the way we consider this is there's a relationship that says that

Â the flow stress of the material is going to be related to some

Â value which is inherent of the particular structure that we're working with, and

Â will add the contribution to that parameter, tau zero.

Â And that is going to be related.

Â The additional strength is going to be related to the dislocation content.

Â So what I have here is sum constant k which is characteristic of

Â the particular material.

Â On to the square root of rho,

Â which represents the density or the dislocation density.

Â So as the dislocation density goes up,

Â then what we find is an increase in the strength of the material.

Â And people have done experimental observations

Â looking at the electron through the electron microscope.

Â And you can see increases in the dislocation density

Â that correspond to this increase in strength.

Â And here are some examples that show you these large arrays of dislocation networks

Â that are associated with the increase in deformation that goes into the material.

Â In addition to showing those networks of dislocations, I've also indicated

Â the presence of dislocations that happened to be around particles or second phase.

Â We'll see more of this coming up.

Â But all around those particles,

Â we have a number of dislocations that are interacting with those particles.

Â Over here, we see another clumping or

Â distribution of those particles of the second phase.

Â So, when we begin to look at the microscope images, we see that

Â they're really quite complex when we're dealing with large dislocation contents.

Â But, certainly what we're seeing is, with this increase in dislocation density,

Â we're seeing this corresponding increase in strength so this now represents

Â the third mechanism by which we can improve the strength of an alloy.

Â Consequently, as a result of adding these dislocations

Â during the deformation process we have in fact

Â shown the second mechanism by which we can strengthen material, and

Â that is by increasing the dislocation density through the deformation process.

Â Thank you.

Â