Strengthening

On this page, we will learn about the four main mechanisms to strengthen crystalline materials that have dislocations. Start with an exploration of one in Exercise 12.6.1 and then learn about other mechanisms below.

Exercise 12.6.1: Dislocation Motion
Not Currently Assigned

Use NetLogo model 12.6.1 to answer the following questions.

  1. On the right-hand side of the simulation, activate all "links" (these are bonds): diagonal-right-links, diagonal-left-links, diagonal-horizonatl-links.

    Then press go. Try to "catch" the configuration in which a dislocation exists by pressing go a second time to pause the simulation. (In a second we'll talk about why it might not be stable). Describe the strain fields ((yellow is tensile and red is compressive) that around the dislocation. Generally, where the the compressive and tensile strain fields?

  2. Click the edit-atoms button. You can then click on atoms to select them and increase or decrease their size using the buttons.

    See if you can create a situation in which the dislocation is pinned and does not migrate out of the system without an external force by changing the size of any one atom. There's a few ways to do this! Consider the strain fields associated with such an impurity atom.

    Upload a screen shot of your solution and explain what you did. Why do you think your actions pinned the dislocation?

  3. Can you move the dislocation to the surface using your newly discovered structure? Try to do so using the force-applied control and report how much force is necessary to move the dislocation. After the dislocation is moved out of the system, is this amount of force enough to cause further plastic deformation?

    (I'm not sure the best arrangement to pin the dislocation - let's see who has the largest required force!)

1. Solid-Solution Strengthening (Impurities)

Many materials are quite weak in their pure form due to dislocations. One method for strengthening materials is by adding impurities which impede dislocation motion. This is known as solid-solution strengthening and it is what we explored in Exercise 12.6.1. A solid solution, as discussed in Section 10.3.2, is a solid of one type with atoms of another type "dissolved" in it, i.e., it is a solid with impurity atoms. In NetLogo model 12.6.1 we edited the sizes of atoms to model substitutional impurity atoms. A solid solution can also be made a of a host lattice with interstitial atoms and these can also hamper dislocation movement. Both options are illustrated in Figure 12.6.1.

Both substitutional impurities (left) and interstitial impurities (right) can cause bonds to be stretched and compressed in the lattice. These can counteract the compressive and tensile strain from a dislocation, making it harder for the dislocation to move.

Figure 12.6.1 Both substitutional impurities (left) and interstitial impurities (right) can cause bonds to be stretched and compressed in the lattice. These can counteract the compressive and tensile strain from a dislocation, making it harder for the dislocation to move.

High purity metals are typically softer than their alloys for this reason. There are many common examples of metals that are strengthened by adding impurities. For example:

  • The most basic type of steel is iron with carbon interstitial impurities added.
  • Pure gold is extremely soft. So, gold used for jewelery is alloyed with some combination of silver, copper, nickel, and zinc.

It is important to realize, that a solid solution can strengthen a material even when you add atoms from a weaker material! This is shown in Figure 12.6.2. Copper and nickel form a complete solid solution (Figure 10.6.1). Even though pure copper is weaker than pure nickel, an alloy of the two is still stronger than pure nickel because the copper impurities block dislocations.

Tensile strength of Copper-Nickel alloy as a function of weight percent Nickel. Even though pure nickel is stronger than pure copper, adding copper to nickel still strengthens it, because the impurities block dislocations.

Figure 12.6.2 Tensile strength of Copper-Nickel alloy as a function of weight percent Nickel. Even though pure nickel is stronger than pure copper, adding copper to nickel still strengthens it, because the impurities block dislocations.

2. Precipitate Hardening

As discussed in Chapter 10, it is possible to have two different solid phases coexisting in a single solid. When one of the phases comprises most of the volume, we call the small volume phase a "precipitate." This is different from solid-solution hardening discussed above in which there is only one phase with some impurities present. In precipitate hardening, there are at least two phases present in the solid creating a microstructure. The precipitates act as blockades for dislocation motion, hardening the material.

Many types of aluminum used in the automotive and aerospace industries use precipitate hardened aluminum. Figure 12.6.3 shows a microscope image of a precipitate hardened aluminum in which precipitates are visible as black dots.

[6061 aluminum alloy](https://en.wikipedia.org/wiki/6061_aluminium_alloy) is aluminum containing magnesium and silicon as major alloying components (as well as small amounts of other elements). $\ce{Mg2Si}$ precipitates, visible as black dots in this image ([image source](https://commons.wikimedia.org/wiki/File:6061_Aluminum_Grain_Boundaries.png)).

Figure 12.6.3 6061 aluminum alloy is aluminum containing magnesium and silicon as major alloying components (as well as small amounts of other elements). $\ce{Mg2Si}$ precipitates, visible as black dots in this image (image source).

3. Grain Size Reduction

In the vast majority of macroscopic crystalline materials, the material is not a single crystal. Instead it is made up of many "grains" (also called "crystallites"). All the grains have the same crystal structure, but they are rotated so they don't line up. Figure 12.6.4 shows a schematic of grains at the atomic level on the left and a micrograph of grain boundaries in a real alloy on the right.

**Left**: a schematic of grain boundaries at the atomic level. All the grains have a simple cubic lattice, but they are rotated relative to one another. At the grain boundaries, the lattice gets distorted. **Right**: A micrograph of grains in a metal alloy ([file source](https://commons.wikimedia.org/wiki/File:CrystalGrain.jpg)). With proper preparation, called "etching", grain boundaries can be seen under a microscope.

Figure 12.6.4 Left: a schematic of grain boundaries at the atomic level. All the grains have a simple cubic lattice, but they are rotated relative to one another. At the grain boundaries, the lattice gets distorted. Right: A micrograph of grains in a metal alloy (file source). With proper preparation, called "etching", grain boundaries can be seen under a microscope.

Grain boundaries disrupt dislocation motion because they cause a discontinuity in the slip plane. For the dislocation to traverse from the slip plane in one grain to that in another requires extra energy/force.

When the angle between the grains is large, dislocations my fail to traverse from one grain to the other and they can "pile up" at the grain boundaries. These introduce stress in the lattice which can cause brittleness and can also generate new dislocations in neighboring grains.

Finally, we can explain why decreasing grain size strengthens materials: if the grains in a material are smaller, there are more grain boundaries. More grain boundaries means more barriers for dislocations.

A grain boundary causes a discontinuity in slip planes, hindering dislocation motion.

Figure 12.6.5 A grain boundary causes a discontinuity in slip planes, hindering dislocation motion.

4. Strain Hardening

The last main mechanism for strengthening metals is seemingly paradoxical: adding more dislocations! If you plastically deform a piece of metal, it will become harder, and this is because the deformation introduces new dislocations. This might seem strange at first, because dislocations are the reason that metals are much weaker than perfect crystals! So, it turns out that a low density of dislocations makes a material weaker compared to zero dislocations, but after a certain density is reached, adding more dislocations strengthens the materials again. Why is this?

The reason is that dislocations interact with each other. Two dislocations or opposite sign (which can be quantified with the Burger's vector), will cause opposite strains on the lattice. This will cause them to attract one another an annihilate. A simulation of this is shown in Video 12.6.1. On the other hand, two dislocations of the same sign will repel each other. It turns out, that when you have a lot of dislocations, the average interaction is repulsive, making it harder for dislocations to move.

Strain hardening is also frequently called cold working or work hardening.

The main way to introduce more dislocations into a material is through strain hardening (also known as cold working). In this process, a material is stretched or bent into the plastic regime (permanent deformation) which creates more dislocations. These usually make the material stronger, but also more brittle. The dislocations do not change the nature of the bonding in the material, so work hardening has little effect on the elastic modulus.

Exercise 12.6.2: That Which Impedes Dislocations Makes Metals Stronger
Not Currently Assigned

  1. We have various methods to strengthen materials. What, generally, is are we trying to do when we strengthen a material?

  2. In class, we showed the atomic trampoline (video here). Explain how you think this works - that is, why does the structure of the amorphous metal allow the ball bearing to bounce up and down without losing energy, while the crystalline metal does not?