August Wohler's Study on Fatigue

August Wohler: historic engineer
with an appropriately impressive beard. 

So in the last post I covered the period of initial discovery of fatigue between about 1840-1870. This period was mostly characterized by the realization that "Hey...these things are breaking when it doesn't seem like they should and bad things are happening as a result. We should probably get on that." Although fatigue was not well understood at the time, work done by August Wohler and William Fairbairn between 1860 and 1870 provided a good baseline for most of what we know about fatigue. While a more in depth explanation of the testing practices of Wohler can be found here in an except from "History of Strength of Materials," I will do my best to briefly summarize the work and findings of Wohler, Fairbairn, and some of the engineers that came after.

Wohler was a German railroad engineer and as such, had a vested interested in understanding the mechanics of fatigue that caused dangerous and costly axle failures. Wohler used a device mounted on the axle of a working railroad car to measure the stresses applied to to the axle during operation. He then used these measurements to replicate those stresses in a testing apparatus (now known as the Rotating-Bending fatigue test) that would reapply those bending stresses to axles used for testing. The nature of fatigue ("small" cyclic loads applied many, many times over time) dictated that this testing took quite some time but Wohler's research was very important in providing an in depth understanding of fatigue. Wohler's work led to the development of the S-N curve (or Wohler Curve) seen below.

A basic S-N curve comparing aluminum and steel.

The y-axis shows the stress (S) applied to the material, while the x-axis shows a log scale of the number of cycles (N) that the material is subjected to. These curves reveal a great deal about how materials respond to the cyclic loads that result in fatigue failure. Steel, shown in blue, exhibits what we now call an endurance limit. As I mentioned previously, an endurance limit is a stress that can be cycled nearly indefinitely without inducing failure (although some more recent research has shown that materials can sometimes experience fatigue failure below it's endurance limit after 10^9 or 10^10 cycles). Wohler also was among the first to note the importance of fillets in railroad axles. It was common practice at this time for railroad axles to look like two smaller diameter cylinders on the edges of the axle with a larger diameter cylinder in the middle to increase the strength of the axle and resist bending. What Wohler showed was that fatigue failures invariably occurred at the sharp edges where the smaller and larger cylinders met. This is known as a critical point, or area of critical stress.

Sharp edges (left) made the part more vulnerable to fatigue failure than fillets (right). 

By using fillets instead of sharp edges, the stress concentrations at those points were lessened; this resulted in better resistance against fatigue. Finally, Wohler was a big early proponent of standardization and testing. One reason for this is because fatigue is a stochastic process, meaning that it is that it is impossible to predict exactly when a part will fail because there are so many factors that affect that outcome. That said, fatigue design estimates are made more reliable if the materials that are used in construction have standard strength, grain size, etc. In short, August Wohler's was an important figure in engineering due to his important research into fatigue and foresight into the importance of material standardization. And with that, I must finish up and entertain my visiting family :)