You are here: Material Science/Chapter 1/Failure

Time to talk about material failure. We’ve only talked really about yield so far, which you now know about. Failure is what happens when you continuing stressing the material past the yield point, and eventually the atomic bonds in the material can’t handle the stress anymore – they rip apart, and the material fractures, tears, separates.  What are some examples of failure?  Anytime the material is separated into two or more pieces. Imagine a car crash – if it’s a big one, the material in the body and frame, and suspension will rip apart. Similar with a bridge crashing to the ground. While engineers generally like to avoid yield in any component, failure is almost always unacceptable. Failure means that the component is essentially useless and won’t be able to carry any load, potentially resulting in catastrophe, and, depending on the application, potential loss of human life.

 

What kind of stress will cause failure?  Any that we’ve discussed. It could be a tensile force, a compressive force, or maybe torsional or shear forces.  What we’re really interested in as engineers is the mode of failure, and there are two for metals: ductile or brittle failure. You probably have an idea of the difference just based on the names alone. Whether a material fails in a ductile or brittle manner depends on the material, and how much it will elongate. Let’s take a simple example. Imagine throwing a baseball at a window: will the glass elongate much before it fractures?  No, not really. It will just shatter. You could probably pick up all those pieces and fit them back together. There wouldn’t really be any elongation. That’s brittle failure. Compare what would happen with ductile failure. As an extreme example, imagine slowly pulling apart silly putty, or clay. The material is really going to stretch out before it finally breaks into two materials. In the case of silly putty, I wouldn’t be surprised if it reaches 2,3,4 even 5 times or maybe even 10 times it’s original length before it snaps.

 

Whether it’s classified as brittle or ductile usually depends on the amount of elongation before failure. If it’s greater than 5%, then it’s usually classified as ductile. This is a rule of thumb.  You might already have an idea that the material itself isn’t the only factor in determining whether the failure will be ductile or brittle. Silly putty is an amazing example, and you should definitely purchase some if you don’t have any lying around. If you roll silly putty into a cylinder-like shape, grip both ends, and pull it slowly in tension, it will elongate like crazy. You’ll end up with a cylinder that is very thin – there has been a very large reduction in cross sectional area. Now, recreate the same shaped cylinder, grip both ends, and pull it as fast as you can. It will snap, with almost no stretching. Fitting the two pieces back together, it looks exactly like it did before it failed. Which goes to show, that the rate of loading – or the “strain rate” – has a huge impact on whether the failure is ductile or brittle.

 

It’s not hard to appreciate why this happens. If the material is loaded slowly, the dislocations have a chance to flow and move around – i.e there is extensive plastic deformation before the failure. If it is quickly loaded, there is no time – the stress is applied so abruptly that the dislocations do not have time to move in a nice matter and the atomic bonds just rip apart.

 

We can describe the difference a little better. So failure occurs when the material separates into two or begins to tear. This typically happens in two stages – first, a crack develops somewhere in the material. Then the crack begins to grow until it propagates through the entire material. Imagine a piece of paper and you pull it from opposite ends with all your strength. If you can apply a high enough stress, then it will rip apart eventually into two pieces. But this would have happened by the method I described above. A crack would have appeared, and then the crack would have grown until it severed the whole sheet. Why does it happen this way?  That’s because this is the mechanism that requires the lowest stress. When a crack develops, it can easily grow since it creates a stress concentration, and the bonds at the edge of the crack can be easily ruptured. The other way would be all the bonds across the sheet being severed at once – which would require a much higher stress. This is exactly why they put little notches on the top of soy sauce packets. The stress gathers here and it’s easy to propagate this crack. Imagine trying to open the packet by pulling the pack into two by rupturing all the bonds simultaneously – never gonna happen.

 

With ductile fracture, there is a lot of plastic deformation in front of the advancing crack – there is high stress here, and the ductile material will plastically deform. What’s nice about this is that we know plastic deformation increases the strength of a material, so it becomes more difficult for the crack to continue growing. This means the crack is stable. Stable, in the sense that it won’t continue to grow unless the applied stress is increased. The crack is content to remain as it is. Brittle fracture however, the cracks spread extremely quickly – like a pane of glass shattering. There is usually very little or no plastic deformation in front of the advancing crack, meaning that the crack is unstable – it will continue to grow without an increase in applied stress. Once it starts, it pretty much won’t stop until the material has completely fracture. It is a violent and aggressive form of failure.

 

Which mechanisms do engineers generally prefer, ductile or brittle?  Ductile of course. Ductile offers some warning about what is happening. Imagine the silly putty that you’re stretching out slowly – anyone watching can see that if the stress is continually applied, it will eventually break. It’s kind of like a bridge that’s sagging under weight and slowly deforming. That warning might provide enough time for everyone to move safely away from the bridge. On the other hand, brittle provides nearly no warning. You quickly pull apart the silly putty and it breaks. Or the bridge all of a sudden snaps. This is termed a catastrophic failure – a very bad thing in the engineering world.  Apart from providing warning, ductile failure requires more strain energy as ductile materials are generally tougher – they can absorb more strain energy before failure.

 

Let’s get into ductile fracture a little bit more, on both the microscopic and macroscopic level. Ductile failure is accompanied by what is called ‘necking’. Imagine a tensile specimen that you are stretching in tension. After yielding has occurred, the specimen will begin stretching and narrowing in the middle – the cross section area will begin reducing. For an extremely ductile material, such as silly putty begin very slowly stretched or a soft plastic, the reduction in area will be nearly 100% – the specimen will narrow down to a point in the middle and then separate into two pieces. Conversely, a brittle material will show almost no erudition after fracture, you could take the two pieces and fit them back together to have pretty much exactly the same shape.

 

After a ductile material begins necking, the first thing that happens is small cavities begin to form. What is that?  Locally, the bonds in the parent material can no longer survive the applied stress, and they begin to rupture to form small holes – or ‘cavities’ – in the center of the material.

 

The technical term for these little holes is ‘microvoids.’  As the stress continues to be applied, the deformation continues. These micro voids grow in size, and eventually they all come together to form one shallow hole – a crack – in the centre of the material. The crack forms such that it’s long edge is located across the specimen – perpendicular to the applied stress. Fracture eventually occurs when this crack quickly grows at a 45 degree angle to the surface of the material, which as you’ll remember, is the angle at which shear stress is a maximum, and it’s easiest at this angle for atomic planes to slide past one another, ultimately resulting in failure of the material. Looking at test specimens which have been stretched in tension to failure shows exactly these failure characteristics.  On the surface that has separated, small dimples appear, which are just the halves of the microvoids that first formed.

 

Brittle fracture as you know happens with almost no deformation. The crack forms and grows extremely quickly. The crack will grow roughly perpendicular to the direction of applied stress. That is intuitive. If you take a piece of paper with a small cut in the side, and pull it in tension, it should rip roughly in half, leaving you two squarish pieces of paper.  Crack propagation in brittle materials is due to the breaking of atomic bonds along favourably oriented atomic planes – jargon for, whichever planes require the lowest stress to break and rip apart. This process is called cleavage. The crack actually rips through grains, and is called transgranular for this very reason. As it travels through the grains, it may shift direction slightly based on how the atomic planes are aligned. The resulting surface then will have a grainy texture, as the crack changes direction as it moves through. If the crack propagation happens strictly along grain boundaries, as it does in some alloys, and never runs into grains? Then it is intergranular fracture instead.

 

So we have two types of failure: ductile and brittle. Whether it is ductile or brittle depends on a few things: the material is very important, along with temperature and the rate at which the stress is applied. If it’s ductile fracture, elongation occurs of usually greater than 5%. Microvoids will form, eventually resulting in a crack, which will propagate at the shear direction until the material splits. The crack is stable – it won’t just propagate quickly without warning. You’ll need to keep applying stress. This is partly because because it is a ductile material, there will be extensive plastic deformation in front of the crack, making the material stronger and more difficult for the crack to move. Brittle, on the other hand, is highly erratic and unstable. The crack will propagate quickly and without warning, even if no more stress is applied. Which makes it slightly terrifying, and dangerous, so engineers generally prefer ductile failure.

 

Now to introduce the topic of fracture mechanics. Basically, this is the topic of how a material fails, considering the material properties but also the stress, potential flaws in the material, cracks, and how cracks grow. Understanding how all these work together can give the engineer a decent idea of how and if the part will fail.

 

Stress concentrations are a big part of this. We haven’t explicit discussed stress concentrations yet, and they are relatively easy to understand. You know that, at the lowest level, stress is carried through a component by all the atomic bonds.  You can almost imagine stress as something that flows through the part when it is loaded. If there is a sudden change in geometry in the part, then the stress field has to abruptly change direction, and it will bunch up against this feature, like shown below in a simplified illustration. Well, a crack is a perfect example of a stress concentrator. The stress has to ‘flow’ around the crack, and it increasing dramatically at the edge of the crack. This is exactly what the little notch is for in a pack of soy sauce, or in the side of any packet you tear open. A pack of ketchup with all those little jagged peaks at the edges is another prime example. When you try to tear the pack open, that little ‘crack’ elevates the stress to be very high at the edge of the crack, and the material fails allowing you to access what is inside.

 

Fracture strengths for many brittle materials is a lot lower than material scientists predicted based on the strength of atomic bonds. Why?  It’s explained by the presence of very small cracks within the material that exists at both the surface and in the interior of the material. These cracks act as stress concentrations – take a look at the example below. The presence of this small crack at the surface means that the applied stress of say 100 MPa, which isn’t enough to break the material (theoretically based on atomic bonds) turns into a local stress of maybe greater than 200 MPa, enough to break the bonds at the edge of the crack, allowing the crack to propagate and rip through the material. A note: as you move away from the crack, the stress lines can straighten out to be more normal and the stress goes down.  These flaws, or cracks, are usually called stress raisers.

 

How much the crack increases the stress really depends on the geometry of the crack. If the crack is aligned with the direction of the applied force, then the stress doesn’t have to change direction as much to flow around the crack and the stress doesn’t rise as high. So the crack length makes a big difference. As well, how sharp the crack is – the technical term is the radius of curvature. If the crack is really sharp, then the stress lines really bunch up and the stress at the crack edge increases like crazy. If you know the crack length and the radius of curvature, then you can calculate how high the maximum stress at the crack will be compared to the applied stress.

 

It’s not just flaws in the material that can result in a stress concentration. Any dramatic change in shape in the design will essentially do the same. Remember that the stress has to ‘flow’ through the component. If the component changes direction dramatically, then the stress will have to as well, and it will bunch up and result in stress significantly higher than you might have expected. This is why you want shape changes in any design to be as gradual as possible – no sharp corners!  This is precisely the problem with a plane that was designed in the 50s. The fuselage had square windows – and a square is a sharp corner. When the fuselage was loaded, the stress bunch up at the corners of the window, resulting in much higher stress than the engineers predicted – enough for the material to eventually fail, bringing down the plane. This is a classic example in material science, and a sober reminder to engineers of the dangers of not fully understanding the behaviour of materials.

 

Wait a second here. Are we still talking about brittle materials, or do these concepts apply to ductile materials as well?  Of course – the concept of stress concentrations/raisers is to do with geometry and the flow of stress – not the material. Any design with a crack or that has a sharp change in geometry will result in high localized stress. But the consequences of this high stress is a bit different, depending on whether the material is brittle or ductile.  If the material is ductile, the stress concentration will result in yielding around the crack (if the stress is high enough). This yielding will change the shape of the crack so that the stress is more evenly distributed and the stress will go down. Brittle materials do not behave this way.  There is no plastic deformation; the stress does not decrease – it will be the theoretical value calculated at the crack tip. Another reason why ductile is more stable and safer. The ability to plastically deform is actually a good feature – a great big warning sign to everyone that the stress is too high and failure may soon be following, so, you know, scram.

 

All brittle materials, for whatever reason, have these microscopic flaws. These flaws take on many different shapes, sizes, and can be oriented in any number of different ways. There will always be some crack that has the sharpest tip, or the longest, or best orientation, or some combination of all three of these factors that means the stress at that crack is highest. It is here that the crack propagation will start and the material will fail. Scientists, of course, have produced brittle materials in carefully controlled environments with fancy processes that are near flaw-free, and their strengths approach their theoretically calculated values.

 

Let’s talk about another fracture mechanic concept called fracture toughness.  Fracture toughness: is just the ability of a material to resist fracturing when a crack is present. A material that has a low fracture toughness will fracture easily if a crack is present. Obviously, as the fracture toughness increases, it becomes less likely that the material will fail even when a crack is present. And of course, that’s a very good thing. We would like components in service such as airplane fuselages and bicycle frames to resist failing even when there is a crack present – and it is likely that there are cracks present (although probably pretty small ones) in both of those applications. This fracture toughness depends on the stress required for a crack to propagate. But it also depends on the geometry of the part and the size of the crack. The size of the crack is always important.

 

We already know that brittle materials fail catastrophically. Because, there is no plastic deformation ahead of the crack, and the material doesn’t get any stronger to resist the crack, so it just goes – fails – violently. Fracture toughness is higher for ductile materials and the cracks are stable. Fracture toughness depends of a couple more things: temperature, strain rate, and microstructure being the most important ones. It makes sense intuitively that if the temperature is lowered, cracks can propagate easily. You’ve seen it in movies – something made of metal is sprayed with something extremely cold, such as liquid nitrogen. Once frozen, all that it takes is a tap from a hammer for the metal to shatter. But an aside here – why is that exactly?  On an atomic level, what is the mechanism here?

 

Strain rate affects fracture toughness too.  If you apply the load very quickly, the fracture toughness is lowered – the crack is more likely to propagate. An excellent example that we already discussed is the silly putty. A great way to prove to yourself how strain rate effects the failure of, well, silly putty. But the principles still apply to other materials. It’s just that you can tear apart steel with your bare hands, so as a physical example it’s quite poor.

 

What is kind of a bummer is that if we increase the yield strength of a metal say by solid solution strengthening, or by adding small impurity atoms, or by cold working it, the fracture toughness decreases. The good news though is that fracture toughness will increase with decreasing grain size. Decreasing grain size is always good to us.

 

You might think it’s obvious how cracks grow, but is like to cover the three modes right here, since they have proper names. Mode I is the opening if a crack in a tensile matter. This is probably most familiar to you. Basically, there is a crack, and you pull in opposite directions to open up the crack. Mode II is the sliding mode. This one I’ll draw for you instead of explaining. Basically, the two pieces slide past one another. Mode III. This is tearing, like tearing a piece of paper. When you tear a piece of paper next, remember that that is Mode III: tearing.

 

To get a sense of fracture toughness for different materials, the fracture toughness of a mild steel is anywhere from 10-500x greater than that of a ceramic such as concrete.

 

Here’s an important practical question. How the heck do we know when there is a crack in the material?  They can be pretty small. As well, it can be more difficult to check for cracks in parts that are already in service – cracks can develop over time, which we’ll discuss when we go over fatigue. How would you go about inspecting an entire aircraft?  Or a bridge?  Often, visualize checks are done by an engineer or technician – literally someone or a team combing over the part/machine, looking for cracks that can be seen with the naked eye. Although useful, this won’t always be enough. The part may not be easily viewed or maybe it’s too big or maybe the cracks of concern won’t be able to be seen without special equipment. Tests called NDTs are performed. These are Non-destructive tests, which is where the acronym comes from.  Non-destructive in that the part will not be negatively affected in anyway. It will remain ‘untouched’.

You are here: Material Science/Chapter 1/Failure
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