This is a post inspired in an article about bone plasticity and fracture toughness published in the most recent issue of Physics Today. No, I will not teach you how to break someone's arm or leg (although if I knew how to it would probably be cool to teach, wouldn't it?). What I want to talk about is the concept of fracture toughness and the mechanisms that increase it in materials.
For a crack to be created you need energy. Everyone is familiar with mechanical energy, you can push, bend or throw a cup and it will break. You could also use thermal energy, heat (or cool) certain objects and they will crack. But it is not at the slightest push that an object will break, there is a minimum of energy that you need to create a crack.
A crack is nothing more than breaking chemical bonds and creating more surfaces (think about it, if you break a plate now you have at least 2!! =P). There is an energy associated with keeping a bond and there is an energy associated with an exposed surface. When it is energetically favorable (that is, breaking the bond has less energy than keeping the bond) the object will crack.
So, that's what a crack is and although learning about how cracks originate is an interesting topic, it is not the most interesting part of fracture theory for me. What I find really cool is how a material deals with a crack once this one is formed. Materials possess a quantity called fracture thoughness, which is a measurement of how hard (or easy) it is for a crack to propagate through. The most critical part of a crack is the tip because here is where the higher stresses (or forces if you prefer) concentrate. Just as you need energy to create a crack, you need energy to grow it. However, just as some materials have mechanisms to prevent cracking (for example, a clothes hanger bends significantly before you can break it) some materials have mechanisms to prevent the cracks from growing (in other words, they increase the fracture toughness). Some of these mechanisms can even be artificially engineered, isn't that cool?
Ok, so what are these mechanisms that increase fracture toughness? One of them is crack deflection. The idea here is to change the direction of crack propagation to eliminate (or at least minimize) the force applied at the crack tip. Crack deflection occurs very often in porous materials and at the interfaces in composite materials. Bone being a porous matrix does exhibit crack deflection.
Another way of increasing fracture toughness is by creating microcracks around the crack tip. In this case the effect is double, first when a force is applied to a material containing both a crack and microcracks, the force is distributed among all of them and therefore can reduce the stress concentrated at the main crack tip and inhibit crack growth. The other way in which microcracks help is by expanding the region around the crack and "closing" its size. Radiographs of damaged bone can show multiple microcracks, although in some cases the microcracks are way too small to be seen by eye.
Lastly, crack bridging can also hinder crack growth. Bridging is, by design, the main fracture toughness mechanism in most fiber-reinforced materials but in monolithic ceramics (i.e. alumina) exhibit grain-bridging. In fiber reinforced materials, the idea is that the matrix cracks easier than the fibers, and thus when force is applied the crack will form but the fiber across the crack will remain intact and support the load. Grain-bridging is a much more subtle idea and it consists of grains in the crack rubbing against each other and carrying the applied force instead of the crack.
Any fracture toughness mechanism will show up in what engineers call an R-curve. If this curve rises with crack extension then you can be certain the material possesses some kind of fracture toughness mechanism. Determining which one, on the other hand, is not always that easy. Now to come back to the Physics Today article, it turns out bone has all three of them:deflection, microcracks and bridging. I am not surprised that bone is really hard to break now.
Burton Richter Dies at 87
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