You are here: Material Science/Chapter 1/Dislocation Movement

Introduction

We’ve talked about elastic and plastic deformation, and yield strength, fracture, ultimate strength, all of these. But on an atomic scale – what is actually occurring here?  What happens to the crystal structure of a material when it yields, for instance?  That’s what this section will focus on – the inner workings of everything discussed in the last chapter.  Specifically, we’ll talk about the movement of dislocations within a solid – a discovery that was huge in the field of material science in the twentieth century.

Plastic deformation, we know, is when the material doesn’t return to it’s original shape after being stressed. Elastic deformation, nothing permanent happens. The atomic bonds holding the material together basically act as springs at low stresses – they stretch out, then rebound when the load is removed, so nothing changes at an atomic level. As soon as a material plastically deforms, there is movement of many, many atoms. Many atomic bonds are ruptured and then reformed (because the material is still together, it’s just changed shape).  The energy required to yield can be predicted by looking at force vs. interatomic separation, which we reviewed early. It details the force that two atoms exert on each other as they move closer to one another, and how there is an equilibrium point where the net force is zero. The actual process of yield is probably not exactly what you think though. It took material scientists a long time to figure out what was happening when a material began to yield.  You may think that the atomic bonding in the crystal structure begin to rupture – just as scientist initially did – but, well, that’s not exactly it.  It’s actually due to the movement of dislocations through the crystal structure. Dislocations (such as edge and screw dislocations), if you recall, are crystalline defects that we discussed earlier (material defects), and are common throughout a material.

Dislocation Movement

Let’s say we apply a shear stress to a nice little block of atoms with a perfect crystal structure. For the atoms to move, you’d have to shear all of those bonds so that we could shift over one unit, or by a Bergers vector.  That would be pretty difficult to do. All of those bonds holding the material together are pretty strong. What if we only have to shear (rupture) one bond, however?   With that dislocation in there, when we apply the shear stress, it pushes on the adjacent plane of atoms. If the stress is high enough, the original bonds on the third plane are broken, and they snap back and rejoin with the second plane. The dislocation is still there; it’s just shifted over.  With continued stress, this dislocation will continue to move, breaking and reforming bonds, until it pops out the other end, forming an edge, or something stops it from moving, such as a grain boundary.  It’s difficult for dislocations to move through grain boundaries because the crystal structure changes across grain boundaries, so the dislocation basically has to change direction.

This was discovered first by scientists in the 1930s.  Initially, materials were yielding far below their theoretical strength and they knew that there was some concept that they were missing.  Eventually, the movement of dislocations (not entire planes of atoms) was discovered. They realized that to yield a material, you didn’t need to break the atomic bonds on an entire plane of atoms so that they could slip past one another – that would require all the bonds to break simultaneously, a tremendous effort.  Instead, the bonds could be broken one at a time as a dislocation moves through the crystal structure. While a dislocation is moving through the structure, the crystal structure is disturbed, but it returns to it’s original shape once the dislocation has moved on.  An analogy that is frequently used is an inchworm moving along the ground.

Remember that there’s a lot of dislocations in a given solid, and when a large number of them start to move when the stress exceeds the yield strength, the result is the shape of the component being permanently altered.  It might not be intuitive at first – you probably thought that the ‘main’ atoms in the crystal structure would be the ones to start moving when the yield strength was exceeded, just as early material scientists did.

Slip

This whole process, plastic deformation caused by movement of dislocations, is called slip (the plane of atoms is ‘slipping’). The plane along which the atoms move is called the slip plane: pretty straightforward naming.  What’s an important point here is that plastic deformation generally occurs due to shear stresses: the dislocations move as the atomic planes shear. You’ll notice in the illustrations that they aren’t tearing apart lengthwise. This is an important distinction.  So how come materials still plastically deform when say, a tensile stress is applied?  If you think about it, there is still a shear component to this tensile stress because of the crystal structure and randomly oriented grains. When a material fails by fracture or tearing, this is when the atomic bonds rip apart.

You may recall that two main types of linear crystallographic defects were talked about: edge and screw dislocations. I don’t want to focus too much on the individual types, but here’s a little picture of what happens during an applied stress acts on both types. With the edge dislocation, the movement is in the same direction (parallel) as the stress. With the screw, the direction of movement by the dislocation is actually perpendicular. Turns out, that doesn’t matter. Although the dislocations move in different directions, the end result is the same; the extra half plane of atoms both pop out on the same side.

Origins of Dislocations

Where did these dislocations even come from?  Many of them form naturally during the solidification process when the metal is formed. It’s difficult for all the atoms to bond together perfectly. As well, more dislocations are introduced into the structure during any plastic deformation. How many are we talking here?  We can talk in dislocation densities or the number of dislocations in some area of the material; for example, dislocations per square millimetre. We can select some random area and look at the dislocations. If the metal is allowed to cool slowly and solidify properly, then around 1000 dislocations per square millimetre is about right. If the metal has been heavily deformed and plastic deformation has introduced many dislocations (talked about below) then there might be as many as 10 billion in every square millimetre. For ceramics, it’s generally around 100-1000.  For very pure materials, such as single crystals of silicon used in electronics, there can be as little as 0.1 dislocations per square millimetre, on average. So one dislocation every 10 square millimetres!

Crystal Structure Distortion

If you look at the force required to shift a dislocation by one position, it’s very low. In fact, looking at this alone, it would seem that these metals should yield far below where they actually do. That’s because we’re missing an important piece of the puzzle here: the distortion created in the crystal structure surrounding the dislocation. The presence of an extra plane of atoms causes a bit of a disruption in the crystal structure. See the picture below: in the top half where the extra plane is located, the atoms are all squished together, like having too many people in an elevator. This region is in a state of compression – the atoms are pushing on each other, compressing the bonds because there isn’t enough room.  Below the dislocation, the opposite happens – the atoms are a bit stretched out due to the crystal structure above. This puts these atoms in a state of tension – all the atoms are pulling on each other, like being a room with a few people holding hands but all trying to move in their own direction.  Now as the dislocation moves through the crystal structure, it essentially has to drag these states of compression and tension around with it. When it moves over by a position, it puts different atoms on the top in compression and different ones below in tension. So the dislocation has to fight it’s way through this ‘friction’ created by the regions of tension and compression.

Preferred Slip Planes

You know that in the case of metals there are three types of main crystal structures –  FCC, BCC, and HCP. How do the dislocations actually now through these different crystal structures?  What ‘route’ do they take?  Clearly, to begin moving, they’ll take the path of least resistance. What am saying is, we know that dislocations move along certain planes. Some crystallographic directions will be very difficult for the dislocation to move, and some will be easy.  The preferred plane for this slip to occur is called the slip plane, along with a direction along that slip plane called the slip direction. The slip plane and the slip direction is the slip system; it is in this system that the dislocations move along.  Atoms move wherever it is easiest for them to do so. This involves minimizing the distortion that occurs by the moving dislocation. Slip planes are along the most densely pack planes, and slip directions are in the direction of highest linear density. Seem counterintuitive?  It seems like if the atoms are moving along atomically dense planes and atomically dense directions, more atoms would have to be moved. The reason that they move along the densest planes is that the distance between these dense planes is larger – so the bonds between the planes are looser. And along the atomically dense directions, the distance between each atom is shorter – so the moving atom doesn’t have to move as far to rupture it’s bond with the original atom and bond with the new atom.  So it has (relatively) weak bonds holding it in place and can easily move along to bond with an adjacent atom. For a FCC metal, which includes copper, aluminum, nickel, gold and silver, there are 12 slip systems. Generally there are 12 slip systems for BCC as well, which includes steels. Some BCC metals have 24 slip systems.   The more slip systems there are, the easier it is for dislocations to have a potential direction to move in. This means that extensive plastic deformation is possible – this is part of the reason these materials are ductile.  HCP generally has 3-6 slip systems, meaning that dislocations have fewer options. As a result, they tend to be more brittle. This includes a whole bunch of metals such as titanium, manganese, and zinc.

Temperature has a pretty big effect on the ability for dislocation movement to occur.  This is the reason why steel can become dangerously brittle when it’s very cold.

Critical Resolved Shear Stress

To get the complete picture of yielding, we need to talk about the stresses required for this slip to occur.  Slip occurs when the stress required to initiate slip is exceeded. This stress is referred to as the critical resolved shear stress. Why critical?  Critical because after this stress, slip begins on the most favourably oriented slip system. The concept that may be difficult to grasp is that it is shear stress, not tensile stress that causes yielding to initiate.  It’s shear stress that is needed because the dislocations move such that the plane of atoms is essentially sliding past each other. And that’s pretty much the definition of shear – stuff sliding past other stuff. For example, let’s examine what happens when a specimen of metal is pulled in tension, and that the specimen of metal is a single crystal – it has a perfect crystal structure throughout, with no grain boundaries. Lets assume that there are still dislocations present even though it is a single crystal. Let’s look at three differently oriented planes within the specimen – three extremes. One plane is located aligned. with the direction of the tensile force. Another plane is at 45 degrees. The third plane is located perpendicular to the tensile stress. If we look at plane of atoms that are oriented perpendicular, we can see that the shear stress is zero. The stress is pure tension. We know that these atoms aren’t going to tear apart – the crystal structure itself isn’t altered. So this plane of atoms won’t do anything. No dislocations can move, no planes of atoms will slid relative to each other.

How about the plane oriented so that it is aligned with the tensile force?  This seems like it would cause some yielding to occur. But if you really examine it, the shear stress again is zero. The specimen is being gripped and pulled equally from both ends – so how can these planes of atoms slide past each other?  Here again, there is no shear stress on this plane.

The plane that is of interest is the one oriented at 45 degrees. With some trigonometry, it can be shown that there is a shear stress acting on these planes. Since it’s located at 45 degrees (I picked this number for a reason) the shear is half of the tensile stress that is being applied. These planes are being pulled in opposite directions – they are being sheared – and so they can slip past one another. This is why it’s called the resolved shear stress – it is ‘resolved’ from the tensile stress being applied. The tensile stress acting normally on the plane is irrelevant. Yielding is all about two planes sliding relative, and we need shear stress for that.  In fact, you can take the original tensile stress, and with a few calculations (using high school trig) you can resolve the shear stress for any plane in the crystal. Once the resolved stress reaches the critical amount in one of the slip systems – one of the systems where dislocations can move – yielding will begin to occur.  Again, yielding will begin on the plane that is most favourably oriented. If the stress continues to increase, the resolved shear stress will reach the critical value in some of the other slip systems – remember that for example there are 12 such systems in the BCC crystal structure.  The shear stress is maximum at 45 degrees – it’s halfway between planes that are perpendicular and aligned with the tensile force, where the shear stresses are both zero. As you swing from 0 degrees to 45 degrees to 90 degrees, the resolved shear stress goes from zero, to the maximum of half of the tensile stress, back to zero. Our single crystal specimen will have numerous ‘steps’ on the surface after it has yielded, which are known as slip lines, as seen in the picture below.

The Importance of Grain Size

Now we know the mechanism for yielding and how it occurs and at what stresses.  It is very useful information, because now we can start adjusting the crystal structure to get the strength that we need.  What do we need to alter in order to increase the yield strength of a particular metal?  We know that yielding begins when the critical resolved shear stress reaches a certain value, and dislocations begin to move.  Clearly, we need to make it more difficult for those dislocations to begin moving.  If we can prevent them from moving, then we can increase the yield strength.  Although you may think of it as a flaw, it actually helps if the metal is polycrystalline – made up of many randomly oriented crystals in distinct regions called grains.  Some of these crystals may be aligned in such a way that their slip systems that are more favourably oriented than others.  Jumping back for a second, it is important to note that during yielding, the grain boundaries don’t rip open or come apart.  They stay together.  This means that to a certain extent, the plastic deformation across all the grains has to remain somewhat consistent.  Say if one grain plastically deformed and elongated, and the neighbouring one didn’t, then there would probably be a tendency for those two grains to pull apart.  But since the bonds between atoms of adjacent grains are stronger than that, this doesn’t happen during yield.  This means that plastic deformation in one grain is sort of limited by the neighbouring grains – they have to deform together.  The result is this: although there may be certain grains that are extremely favourably oriented and the resolved shear stress is high enough to cause slip, it cannot do so until the neighbouring grains (which may be less favourably oriented) are capable of slip as well.  The final consequence is that a higher stress is needed to initiate plastic deformation.  You can draw the conclusion that grains are very important to yield strength, and the size of the grains also has a great influence.

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