You are here: Material Science/Chapter 1/Material Strengthening

We’ll discuss for a while different methods of increasing the yield strength of materials. Keep in mind that there is essentially one goal: limit the movement of dislocations. One the best ways to do that is reducing the grain size, since as we discussed above, dislocations have a difficult time crossing grain boundaries and so grain boundaries are great at limiting (but not completely stopping) their motion. This is a reason why perfect crystals with no grain boundaries are quite weak. Initially, there is nothing stopping those dislocations from moving around freely.

 

There’s a bit more to how grain size affects strength, which will be discussed now. You know that when yielding begins, dislocations begin moving. When dislocations begin moving, they are impeded by grain boundaries, because the crystallographic orientation between the two grains is not the same. The dislocation has to cross this boundary and change direction as well, to match a slip system in the grain that it is trying to reach. So it makes sense that if there are more grain boundaries, there are more boundaries to cross – dislocations have a harder time moving around, the material is stronger. Check.

 

There is another reason that smaller grains strengthen a material.  If you recall, with high angle grain boundaries, there is a high angle of mismatch between the two grains and the dislocation probably won’t be able to change direction and continue moving in the next grain, so it stops. One way that dislocations are able to ‘move’ across boundaries if many dislocations begin to pile up at the boundaries and push on each other, causing a concentration of stress at the edge of the grain boundary. In larger grains, there are more dislocations contained within each grain. That means that more dislocations can pile up at a grain boundary, and the stress of all them piled up can either create or initiate a dislocation to begin moving in the adjacent boundary. Conversely, if the grain is small, then there won’t be as many dislocations available to bunch up at the edge of a grain boundary. There won’t be as much force on the dislocation at the boundary and the stress concentration isn’t as high on the adjacent grain.  In this case, the applied stress would have to increase to initiate yielding in the other grain. This makes the material stronger.  Key take away here: materials with smaller grains are stronger as the stress required to initiate yielding is higher.

 

How small can we make these grains?  There is a theory that details the size of grains called the Hall Petch equation. Theoretically, the material would be infinitely strong if the grains were infinitely small – which of course is impossible. Let’s think of something more reasonable. What if the grains were the size of a unit cell?  All the unit cells would have to be oriented differently from the ones surrounding it. Kind of like haphazardly throwing a bunch of square moving boxes into the back of the moving van so that none of them for together.  Aha, but what is wrong with this?  If this were to be true, then there wouldn’t actually be any crystal structure – there would be no order in the structure of the material, meaning it would be amorphous.  Dislocations wouldn’t be possible – which makes sense. If every grain was a perfect unit cell, where would the dislocations be located?  It actually turns out too that if the grains are too small, then another mechanism takes over called grain boundary sliding.  This is when the grains are so small that they move around, slipping and sliding past one another.  If you want to know more about this, see the box below.

 

The Hall-Petch equation predicts that decreasing grain size results in increasing yield strength of the material. This works up to a point. We saw that infinitely small grains is not possible. And grain boundary sliding of extremely small grains can actually decrease the yield strength. Is there a ‘critical’ grain size?  Turns out that it is around 10 nm. That’s 10 nanometers. It’s difficult to explain how small that exactly is. It’s roughly 1/1000 the width of a human hair.  To give you a sense of how grain size and yield strength are related, there is a chart below for ___ material.

 

The main method of increasing or decreasing the grain size is to control the rate of cooling (solidification). If we allow the metal to solidify very slowly, then fewer sites will begin to nucleate initially and the grains will be allowed to grow much larger before bumping into one another. As the cooling rate from molten to solid becomes faster, the grains have less chance to grow before bumping into neighbouring dendrites which are also growing, resulting in smaller grain sizes.

 

Apart from reducing the grain size, there are other options for increasing the strength of a material. Always remember that our goal here is to inhibit the movement of dislocations. We need them to stay where they are!  We can achieve this through solid-solution strengthening.  The basis of this method is to introduce impurity atoms in the crystal structure, either replacing a parent atom in the unit cell (substitutional), or fitting it into an interstitial site (refer to chapter 3).  Why does this make the metal stronger?  The impurity atom introduces strains in the surrounding lattice, because it isn’t the same size as the other atoms. Dislocations trying to move around will interact with these regions of strain within the crystal structure and they will have more difficulty moving. Why?  If we look at an edge dislocation again, we can see the region of tension and compression surrounding the dislocation because the extra plane of half atoms doesn’t quite fit. There is a certain strain energy associated with this dislocation. What would happen if we replace that entire half plane of atoms with very small atoms?  It would relieve the field of the compression. Those atoms would no longer be squeezed and crammed in there.  It seems like they wouldn’t be as easily moved by shear stress because they have a greater distance to move. The strain energy would be lower, and as a result, the dislocation would be more content with where it is and less likely to move. It has been trapped. Intuitively, this seems to make sense too. The crystal structure is now more stable in that region.  Well, solid solution strengthening is a kind of like this, except the entire plane of atoms isn’t replace with small atoms, usually just a couple of atoms around a dislocation. But the smaller impurity atoms do tend to move to locations such that the strain energy is reduced, as shown in the picture below. Remember that this would occur during formation of the metal. It would naturally take this high energy spot because everything wants to be at equilibrium.  Similarly, larger impurity atoms would take the spot below the dislocation where the field is in tension. Putting a larger atom in there would also decrease the strain energy of the dislocation, meaning that it is harder to move.

 

Are there any rules for what atoms will work as solid solution strengthening?  Yes. The atom has to be similar to the host material. It has to have a similar atomic size, generally it shouldn’t be more than 15% larger or smaller. It should form into a similar crystal structure. It should have a similar electronegativity so that the bonding is similar. And it should have a similar valence.

Many times, solid solution strengthening isn’t the best way to increase strength. The solubility of the impurity atoms isn’t usually high enough to get a significant number of impurity atoms into those sites, and so while they do create obstacles for dislocations, usually it is not enough for appreciable strengthening.  There is a very notable exception here, which is steel. Don’t worry – steel will get it’s own dedicated chapter where all of this will be explained.

 

Another major strengthening mechanism is strain hardening. Here’s the basis: if a ductile metal such as steel begins yielding (plastic strains), it becomes stronger. Yes, it may seem odd, but the yield strength will increase. We’ll get to the details in a second. This is called work hardening sometimes. You’re ‘working’ on the metal and it’s hardening. Another name is cold working. This is because this happens at room temperature, which is considered cold compared to the melting temperature of the metal.

 

If we look at a generic ductile metal stress strain curve, we can see the linear elastic region where the metal acts like an elastic band. Pull on it, deform it, it will spring back. You can do this to stresses up to the yield point – then: dislocation movement. But it turns out that dislocations are actually created during plastic deformation. They multiply and new ones are created. When two dislocations are close to each other, they are on average aligned in such a way that they repel each other. Imagine that two compressive fields meet: they both have the same ‘sign’: compression. They will want to repel each other, and this makes it difficult for them to continue moving in whatever direction they need to move, depending on the direction of stress. Notice I said on average, because it is possible that the dislocations meet in such a way that the compressive field of one dislocation is aligned with the tensile field of another.  They attract, and the two half planes eventually meet up – voilà!  A full plane of atoms results and the dislocation is annihilated. Gone.  So once the metal begins yielding, more dislocations are created, which inhibits the movement of other dislocations, and the yield stress goes up. If we unload the material, then it will actually follow the same linear path back down to zero yield stress. That is, the modulus of elasticity hasn’t changed at all. But you can also see that there is some residual strain left in the material even when all the force has been removed. Makes sense – if you’ve plastically deformed it, then the shape will have a changed a little bit, and the remaining plastic deformation represents that.  If we reload the component, the stress strain will again be linear. But this time to yield it, we need to go back to the same stress that we left off at before.  So you can see how the material gets stronger.

 

Side note: this permanent strain is sometimes called permanent set, and is usually unwelcome in engineering. For example, if I am designing a door hinge for a car, then there is a certain load case called ‘open overload’. Basically, the door is fully open, and someone keeps pushing on it more. If the hinge begins to yield at all, it will change shape – maybe only slightly. But the problem is that even a small change in the shape of the hinge will be magnified by the length of the door. If we measure the permanent set at the door where it shuts (called the latch point), it could be high enough to cause the door latch to not function properly anymore – you wouldn’t be able to close your door, or it would stick out from the rest of the car body noticeably.  This all relates back to how yielding is usually unacceptable, because it changes the shape if the design in some way, and usually designs are shaped a way for a reason!  We also don’t want yielding because that means the stress is getting dangerously high. So while work hardening does indeed improve the strength of the material, we usually want to have performed this strengthening operation before the material is put into service.  Sometimes, it is inherent in the forming of the component. For example, many automobile suspension components are made from stamped sheet metal and then bent into the final shape. When you take a piece of flat metal and bend it into a different shape, that is plastic deformation right there. When designing parts, this localized increase in strength is usually accounted for with software that calculates the plastic strains in the formed part. This increase in yield strength is then included in analysis to determine if the part is strong enough to survive the loads the engineers expect it to see while in service.  Engineers can also remove this plastic strain if they want, with heat treatments.

 

If we do want to remove the permanent plastic strains introduced to the crystal structure, we can do so with recovery and recrystallization.  This basically has to do with removing the extra dislocations that were introduced when the material was yielding.  Other properties that we haven’t discussed such as electrical conductivity are affected by plastic deformation too, and doing these heat treatments will ‘reset’ these properties to how they were before the plastic deformation.

 

So recovery: recovery is basically heating the metal to some temperature below it’s melting point.  This means that all the atoms have more thermal energy, and as such are able to move around more easily with the crystal structure: this is called ‘enhanced atomic diffusion’. If you recall, dislocations with opposite signs that meet will ‘annihilate’ each other, leaving behind a perfect crystal structure. In other words, two half planes of atoms meet and form a full plane. The increased temperature allows dislocations to move around until they find an annihilation partner. Of course, not every dislocation will be removed – many will still be left over.  These remaining dislocations tend to oriented themselves in such a way that they create tilt boundaries – and what exactly is that?  First off, it is a low energy grain boundary. Everything wants to be low energy, so when dislocations are given a chance to move around at the recovery temperature, they will try to orient themselves to be low energy.  Kinda like how water wants to flow downhill, from a high potential energy to a lower one.

 

Remember that recovery does not mean melting the material, just heating it up so that the dislocations can move around more easily.  During recovery, grain structure itself doesn’t change – just the dislocations within those grains.  What temperature does recovery take place at?  Roughly above 0.3 to 0.5 of the melting temperature. If the melting temperature is 1000 degrees, then recovery could begin around 300-500 degrees.

 

Recovery isn’t the whole story. Recovery doesn’t affect the grains themselves, and we know that grain size contributes hugely to material properties. What can we do to recover grain size if we desire?  This happens with recrystallization. The name – self explanatory. The crystal structure is essentially redone. Let’s say that we have a crystal structure that has been altered due to plastic deformation and the grains have been stretched out in a certain way. In that form, they are in a high energy state – kind of like stretching an elastic band. It wants to go back to an equilibrium position, but it cannot. If we recrystallize, then it can. Recrystallization happens at some temperature. This temperature is specific: it is defined as the temperature needed to completely recrystallize the material in exactly one hour. Obviously this will vary from material to material, and other factors such as the amount of cold working that was performed (i.e. level of plastic deformation), but a rule of thumb is that the temperature is generally between 33% and 50% of the melting temperature of the metal.  What you might not expect is that increasing amount that you cold work a metal actually decreases the recrystallization temperature. If you plastically deform the metal more, it will recrystallize  in one hour at a lower temperature.

 

Why is that?  Well, the driving mechanism behind recrystallization is the difference in energy between the strained parts of the material and the untrained parts. Essentially, new grains begin as small nuclei with the material and grow, eventually consuming everything. The high temperature means that all these atoms have more energy, and they can break their bonds more easily. This means they can move around and be consumed by the newly growing grain. This is essentially short range diffusion.  Mechanical properties generally return to ore worked conditions – softer, weaker and more ductile. Say you had a component that has been cold forged – basically hitting a metal with tremendous force to turn it into a specific shape – it would have been cold worked. But if you wanted to retain the ductility of the parent material, then you could heat treat it and recrystallization would occur, allowing you to keep the material properties but maintain that certain shape.

 

Pure metals vs alloys. Which one will recyrstalize more easily – at a lower temperature?  Pure metals do. With alloys, it is believed that impurity atoms sometimes hang around at the newly formed grain boundary as it is trying to spread and grow through the rest of the cold worked material. Basically, the impurity atoms slow these advancing boundaries down. They get in the way. They’re a nuisance. The result is that for certain alloys, you may to raise the temperature to as high as 70% of the melting temperature for recrystallization to occur within the hour.

 

Here’s an idea: what if we desire a certain shape but don’t want to introduce any plastic deformation – we don’t want to have to recrystallize at all. If we raise the temperature of the metal enough, and then bang it into whatever shape we want, there won’t be any plastic deformation. The atoms themselves move around easily – dislocation motion not required. The material remains soft and ductile.  This is called hot working, and will be discussed later.

 

One more thing to talk about in this section. Recrystallization is all about the formation of a new set of grains – ones that are strain free and have approximately equal dimensions to all directions, like a circle – as opposed to cold worked grains, ones that have high strain energies and generally have an elongated shape.  What would happen if we left that material at a high temperature for longer than an hour?  The grains would actually continue to grow after recrystallization is complete. If you remember, there is a certain energy associated with grain boundaries. If the grain is larger, it will have a larger boundary and overall, less total energy. Which may seem counter intuitive, but if there are many many small grains then the total boundary length is large. If there was just one big grain, like a single crystal, there would be a big boundary but the overall length would be less, and the energy would be less. So grains want to do this, but can’t at room temperature. Give the atoms a little free will by the form of thermal energy, and grain growth occurs. This will happen in any polycrystalline material – basically any metal. It didn’t need to be cold worked first. It didn’t need to go through recovery or recrystallization. It just needs grains, so that they can grow. Grain growth occurs when atoms are allowed to diffuse across the grain boundary and fit nicely into the grain on the opposite side. Which way will they go?  That depends of which way it is easier for them to travel. So while one grain is growing, the adjacent grain is shrinking in size.

You are here: Material Science/Chapter 1/Material Strengthening
<— Dislocation Movement/Failure —>