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 :)

The Beginnings of Fatigue

Considering my last post, I thought I would blog a bit more about the start of the history of fatigue. As an engineer I find the study of how to safely design and construct things very interesting; but I find the history of science and engineering that led to that understanding perhaps more interesting still. As is the case in all areas of scientific study (chemistry, biology, physics, etc.) the study of engineering follows the story of the successes and failures of those attempting to understand the rules and principles of the natural world. Fatigue is just one of a near infinite supply of examples.

Fatigue was first conceptualized in 1829 by a German mining administrator named Wilhelm Albert who noticed that the iron chains used to hoist carts from the mine would break from small, repeated loads even if they were not accidentally overloaded. Although Wilhelm's training was in law, he built a machine that would repeatedly cycle a load on a chain and found that the failure of the chain was due to the number of loads the chain experienced rather than the load itself. He published a paper on this concept in 1837 and the idea of mechanical fatigue was born.

While the idea of fatigue was now out there, Wilhelm's paper changed very little about the way humanity operated on a day to day basis. Some research was done but as is the general rule regarding our species, we did not see the need to understand something until after a horrific tragedy resulting from neglecting it. On Sunday May 8, 1842 there was a catastrophic failure of the front axle of the primary steam locomotive pulling 16-18 carriages in an event that became known as the Versailles Rail Accident. This caused the locomotive to derail and set off a chain of events that led to the fire box flipping over and a total pile-up of the passenger carriages. Needless to say, the practice of locking passengers in their carriages while the train was in motion did little to help matters as somewhere between 50 and 200 people (sometimes whole families traveling together) died in the aftermath.

Artist Depiction of the Accident (Source - http://en.wikipedia.org/wiki/Versailles_rail_accident)

This sparked an uproar in France. Newspapers were sent letters with criticisms and suggestions. Some religious groups suggested that God was punishing the wicked for traveling on the Sabbath (some things never change). Meanwhile, French engineers got to work attempting to understand the unique failure that led to the tragedy. The French government started a commission to investigate the cause of the failure; this commission recommended a procedure of monitoring and testing axles to determine their service life. The basis of these practices are also applied today to the frames of airplanes (who also undergo cyclic loading via the pressurized cabin of the plane). Legendary scientist and thermodynamics co-founder William Rankine (who I just learned was actually Scottish, not French) helped the movement to find a solution for safe management of railway axles. Although many scientists worked to research the idea of fatigue, German engineer August Wöhler and Scottish engineer William Fairbairn launched perhaps the most comprehensive investigation of fatigue between 1860-1870. Though I could spend a whole blog posting on their findings alone, the basic summary is that they found that the range of cyclic loading is more important that the peak stress that occurs from the load. They also introduced the extremely important idea of an Endurance Limit: the idea that for some materials, there is an amount of stress under which failure will "never" occur regardless of the amount of cycles of loading. Above that? Haha, well things get complicated but more on that in the next post.

So it's been a while...

Well that didn't last long haha. As I mentioned in the introductory post, I'm new to this whole blogging thing and didn't really have a good plan for how to keep up with the routine of blogging. As a result, this blog kind of fell by the wayside when time demands from a family house renovation, the holidays, and the job search took over. But the New Year has come and gone so I've decided to make blogging more of a priority this time around. My goal is to post at least once (but hopefully more) per week.

In my first post back, I'd like to talk a little bit about an idea that I came across while reading "To Engineer is Human" by Henry Petroski. The overall goal of the book is to talk about human nature and the role of failure in engineering and life. He argues that we often learn the most from failure because until the point of failure, we assume that we understand the stresses and forces involved in designing an object or structure. One example of this idea is the concept of fatigue. Once engineers had a pretty good idea of how to design things to combat stress, they thought that these structures would last forever as long as the load on the structure was less than the yield strength of the material.

In this case, they were mistaken: the primary example of this being railroad components and structures. These components are exactly the kinds of components we now know to be most vulnerable to fatigue: components that undergo high stress cyclic loading. Mechanical fatigue is very similar to the idea of fatigue in people: it is the idea that a repeatedly applied (cycled) load or strain can cause damage over time and eventually lead to fracture. None of these loads by themselves cause the structure to break (as it would with a sudden impact), but over time microfractures that are difficult to see develop and weaken the constitution of the material. Eventually, these microfractures can cause the complete collapse of the structure.

Though the idea of fatigue was first proposed in 1837, engineers did not begin to really understand the idea of fatigue until much later after the failure of parts that were supposed to be sound and the death of passengers resulting from collapses that weren't supposed to happen. The point Petroski makes is that we should not to try to forget or endlessly criticize these failures, but instead to accept them as an unfortunate and necessary part of being human. Only through failure can we grow and progress, not only as engineers, but also as people.