# Proving Ingliss right: Griffith uses the power of plastic deformation

No I haven’t started an incredibly nerdy superhero webcomic, starring two of the scientists I discussed last time. Instead, the title refers to a rather elegant experiment, which I think is a good illustration of how science works.

To understand this experiment we first need to talk about the different ways in which materials can deform. Whenever you exert a force on an object, it will deform. In daily life you generally don’t notice it; the deformations will be very small, perhaps even smaller than the width of a human hair. Nevertheless, these deformations exist, and if we make the forces large enough, or our measurements sensitive enough, we can observe them. Deformation comes in two main types: elastic and plastic. Elastic deformation is a deformation that is reversed when the force is removed. The most well-known example is an elastic band: apply a force to the band and it will stretch. Release the force, and the band will return to its original shape. If the change in shape is permanent (like if you bend a paperclip far enough), we call this plastic deformation.

All materials deform elastically, but only some deform plastically. Materials that only deform elastically are called brittle, and examples include glass and other ceramics. Materials that also deform plastically are called ductile, and include metals and certain types of plastic. I should point out that whether a material is brittle or ductile can depend on its temperature. Think of glass-blowing, where hot glass is deformed plastically, or forging, where heat is used to make metals more ductile then they would otherwise be.

You might have noticed that I said that ductile materials are materials that also deform plastically. That’s because you can’t have plastic deformation without elastic deformation*. You can see this quite easily by returning to the example of a paper clip. If you try to bend it carefully, applying only a small amount of force, the paper clip will snap back to its original shape when you let go. However if you apply more force before letting go, the paperclip will still spring back a little bit, but the rest of the deformation will remain. Obviously there is some kind of threshold that you need to cross before you get plastic deformation. It turns out that once again what is important is not the amount of force, but the amount of stress (force per unit area). If you increase the stress in a ductile material above its ‘yield stress’, you will start to get plastic deformation. Although you can use a variety of techniques to modify it**, the yield stress is in principle a material property. A certain material will always start to yield (i.e. plastically deform) at the same stress. It is this feature that brings us back to Griffith.

When Griffith started his research on failure of cracked specimens he was faced with an enigma. It was known that scratches and holes could concentrate stress. Prof. Ingliss had even mathematically derived a way of calculating how much the stress would be concentrated. Yet specimens were breaking, even though according to the calculations the stress in the material should be well below the ultimate stress. There were two possibilities: either the stress calculations were wrong, or the concept of ultimate stress did not work for materials containing cracks. What Griffith needed was a way of testing whether the stress values predicted by Ingliss’ theory were correct. Something that is not trivial to do, as you can’t directly measure stress. This problem was compounded by the fact that Griffith wanted to measure the stress at a very particular spot in his specimens: at the tip of a crack, where the stress is much higher than in the rest of the specimen.

In his paper, ‘The Phenomena of Rupture and Flow in Solids‘ Griffith explains the solution he came up with:

“A specimen of soft iron wire, about 0.028-inch diameter and 100 inches long, which has a remarkably definite elastic limit [i.e. yield stress], was selected. This was scratched spirally (i.e. the scratches made an angle of about 45 degrees with the axis) with carborundum cloth and oil. (Griffith, 1921)

Because the scratches are spiral, when you pull along the axis of the wire the stress will be concentrated along the scratches. This will impart a twist to the wire (even though you are pulling straight along the wire). Griffith noticed that if a sufficiently large force was applied to the wire the twist would remain, even after the force was removed. Since the deformation was permanent, the material’s yield stress must have been exceeded near the tips of the scratches, where the stress is concentrated. As the yield stress of the material is constant, Griffith knew exactly what stress had been reached at the crack tip. Ingliss’ theories predict the ratio between the stress you apply to an object as a whole, far away from any scratches, and the stress at the tip of a scratch. By comparing the stress applied to the wire as a whole to the yield stress of the material, Griffith was able to check Ingliss’ formulae and show they were in fact correct; thus it must be the idea of ultimate stress that needed to be re-examined.

If you read about science, especially about physics, you may have read about the importance some scientists attach to the ‘elegance’ of a theory or experiment. For me, this experiment really is a great example of elegance. The idea and set-up of the experiment are simple, yet the implications are profound. Although stresses can’t be measured directly, this experiment allowed the predictions made by Ingliss’ theories to be tested; the ultimate scientific proof of the pudding.

Although the concept of plastic deformation formed the basis for Griffith’s further investigations into crack growth, it is also one of the reasons that Griffith’s work was a starting point, rather than a final answer. But that is a story for next time.