A primer on the strength of materials - Metals

The cases we've looked at so far have been clear cut cases of a structural element being overloaded. Before I go on to other cases we need to understand what is happening when a structural element is overloaded. What is happening when something is overloaded? Logically if something is overloaded we need a bigger beam or something, but we also need to consider what the beam is made out of and how strong that is.

The strength of any structural element is related to:

1. Its geometry/shape
2. The material it is made out of.
3. External factors such as bracing.

1 and 3 we will go over another time, the geometry of structural beams is a complex subject in of itself. In virtually all structures today the primary structural elements are steel, wood, masonry and concrete or some combination thereof. This post will look at steel and metals in general.





The strength of materials - Metals

This is going to get fairly theoretical here, so hopefully I won't make this too boring. Anyhow, lets consider the supply chain that results in a steel beam ending up on a construction site.

Composition
After the ores bearing our metals are mined, they are then all smelted to produce an actual metal. At this point the thing that concerns us is the composition of the metal. When a metal is in its pure form it has a crystalline structure. It's a little odd to think of a metal as a crystal since it doesn't look like a piece of quartz, but a crystal is really anything that has a regular and orderly lattice structure.

When our metal is melted down all the atoms of metal have their bonds shaken apart by heat and it becomes a liquid. When it cools down and solidifies the metal atoms begin to bond with each other, and they do so by forming a a lattice system. Normally crystal formation like in quartz or salt forms around some nucleation point and all the subsequent atoms/molecules bond to the easiest available surface which results in a very orderly growth which is why you can get quite large pieces of quartz or salt that are very close to perfect. For metals, this also occurs, but within the metal the crystals form pretty much everywhere at the same time so a piece of metal is not a single monolithic crystal, but rather a huge collection of small ones.

Metals could thus by considered polycrystalline if we look at this image.

Something most people know is that pure iron is a fairly weak metal and it is pretty much always alloyed with carbon as well as other metals in one way or another to give it a great deal of strength. In fact most alloys are stronger than pure metals. To explain this I need to explain a little more about the metallic crystal structure.

Virtually all structurally useful metals and allows have either a face-centered cubic (fcc, on the left) or body-centered cubic (bcc, on the right) structure. In these diagrams the dots represent the atoms of metal and the lines represent the bond between those atoms. Ferrous (iron) alloys are generally fcc while aluminium and other metals tend to be bcc, this has an effect of their mechanical properties, for now this isn't too important to us though.

The main advantage to either the fcc or bcc lattice structure is that the atoms are packed in much closer together than in other arrangements. Having the atoms packed in closer together means the bonds between the atoms are stronger because when everything is packed in as close as possible its harder to move any single element without affecting the structure as a whole. Imagine a bowl of marbles that has been carefully packed by hand so that each marble is touching as many other marbles as possible and compare it to another bowl of marbles where the marbles have just been dumped in. Which is harder to push your hand into?

Alloys can further improve strength by allowing the atoms to pack in even closer together. Imagine our bowl of marbles, except now there are two different sized marbles. The smaller ones pack into the spaces between the larger ones and now there is even less space for the marbles to move.

Dislocations

This is all very well for a single crystal of metal, but the metal is made up of many tiny crystals. The first thing here is that this isn't like a bunch of marbles, all the little crystals are bonded together. The boundary between where one crystal meets another is usually called a dislocation. As our crystals form within the metal they grow and link up with the other crystals near them, except that they aren't all in the same alignment. They still bond together, but since they aren't in exact alignment they're all jumbled up. Depending on the heat treatment the metal is given these resulting grains can be bigger or smaller, under certain conditions they can even make the entire piece of metal a single crystal, which is something they typically do for turbine blades in jet engines. Contrary to what you might think the giant single crystal is generally not as strong as the jumbled mess, although it has its own properties that make it useful in niche applications.

So why make the grains bigger or smaller? How does this affect the properties of the resulting metal?

As a general rule, larger grains results in a metal that is softer but more ductile, while smaller grains result in a metal that is harder but more brittle. This is a massive generalization but it generally works. Metallurgy is a complex subject which I'm frankly not an expert in. Lets not get too bogged down in it and try to stick to the basics. There are essentially two main processes that either induce dislocations or reduce them and hence make larger or smaller grains. Work hardening and Annealing.

Annealing and Work hardening

After our metal is smelted and cast into solid billets of steel it will be then formed into an appropriate shape. They either re-heat it, or more usually shape it while the metal is still hot. It should make sense why they do this while the metal is still hot - the metallic bonds & crystal grains are still forming in the hot metal so the metal is relatively weak which makes it easier to form into shape. While the steel is red hot the billets are run through rollers which form it into an I-beam or some other shape.

There are effectively two separate processes here that are being used together, but lets look at them individually.

Annealing is simply heating up the metal, which weakens the metallic bonds enough in the metal that crystal grains will re-form. The purpose of annealing is to get rid of dislocations and residual stresses within the metal. The metal grains are allowed to grow and the metal becomes more ductile.

Work hardening is putting the metal under stress, which has the effect of creating more dislocations. This makes metals harder and stronger, but more brittle. The way it works is that the metal grains get all smashed up, which means any further stress is placed on the metal has to deal with those dislocations trying to move past each other. Imagine it is like a bucket full of sharp angular gravel versus a bucket full of smooth round gravel. The sharp edges of the angular gravel lock into each other while the rounded gravel has less resistance to sliding past each other. A practical example of work hardening in action is the method most people use to break a paper clip. You bend it back and forth and you'll notice that the point where it bends becomes stiffer and stiffer until the metal becomes brittle enough that it snaps. This same principle is used to "work" a metal until it becomes significantly stronger.

So our metal comes through the rollers while its still hot and the grains are still forming. The grains are actually flattened out by this process and essentially make the beam stronger in one direction. Pretty neat.

Theory over

So how does all that stuff relate to things like this?

Or this?

Firstly the dam. This was the Sayano–Shushenskaya Dam in Russia. The turbine where the bolts failed was known to have excessive vibration for many years before failure. When high tensile strength bolts are fabricated they are work-hardened. A lot. High tensile strength bolts start as a cylindrical feedstock of metal that has no head. Massive forges hammer it into shape without heating them up at all. This is known as cold-working. The effect is to produce a bolt that has very high strength, but is relatively brittle and sensitive to high temperatures (because that would anneal them and ruin the work hardening). These bolts are not especially susceptible to metal fatigue, however when they fail they tend to shear quickly in a brittle manner.

Metal fatigue occurs when a metal is repeatedly loaded and unloaded. Even though the load is well under the strength limit for the metal there is enough load to open tiny microscopic cracks just a tiny little bit every time it is loaded. Harder, more brittle metals are more at risk because they are more likely to fail in a brittle manner (ie, suddenly and without warning). The solution is regular maintenance and replacement of fatigued parts. The bolts holding down the turbine cover failed one-by-one and finally the last few bolts couldn't hold the cover down anymore. The cover blew off and the water washed everything away. It's hard to say whether the whole disaster could have been prevented by replacing the bolts. The bolt failure was the most visible failure, but the whole turbine system was reaching the end of its life and had excessive vibration for decades. If the bolts didn't fail there was a good chance something else would have.

As for the ship. The ship shown broken in half was a Liberty ship built in WW2. These ships were rush built extremely quickly and with unskilled labor. The earlier ships tended to crack in half because of metal fatigue as the Russian dam bolts did. Unlike the Russian turbine cover, they were not designed properly to begin with. It's hard to fault the original designers, because they had to crank these ships out so fast and they were actually in uncharted territory as far as the naval architecture of the time went. Tried and true ship design of the time used rivets to hold everything together, but the new Liberty ships were all welded. Unlike riveted plates a crack can propagate through a weld - a crack that propagates through a riveted plate will stop when it reaches the end of the plate, but a welded connection will allow the crack to continue to the next plate.

Other issues with the Liberty ships was poor understanding of stress concentrations which occur at sharp corners. Maybe you've noticed it yourself, but whenever you see a crack forming it's almost always at a corner. This is why ships have rounded portholes and rounded doors. Believe it or not, a crack propagating from the corner of a door or window has the potential to crack an entire ship in half. Lastly many of the ships that broke in half in the open sea were doing lend-lease runs to Russia. The frigid northern waters cooled down the steel of the hulls enough that the mechanical properties of the steel actually changed and it became much more brittle than usual. A similar behavior can be observed in certain plastics. When they are warm they are ductile and just bend instead of snapping. Now put it in the freezer and it snaps in half instead of bending.

Frankly I didn't even scratch the surface of material behavior but I've gotta stop somewhere. If you want more of this sort of thing let me know!