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Railroad Fatigue

August 16, 2016 By: Michael Bak

I recently travelled to New York City for a business meeting from my office in Connecticut, and since I don’t like sitting in my car in traffic jams, I decided to take the train. I always get a sense of nostalgia riding the train, since it represents a transportation method that goes back to the mid-1800’s. You may not be aware that during that time, spurred on by early railway accidents caused by axle failure, the science of fatigue of metals was born1.

Most historians point to the deadly Paris-Versailles train accident in May of 1842 being the event that began the study of fatigue, since it was caused by an axle failure and there were many fatalities, between 50 and 200. The train was crowded and pulled by two locomotives. The axle of the first locomotive broke, causing it to suddenly stop, and the second locomotive was driven on top of the first. The contents of the fire-boxes were thrown over the debris, starting a fire. Three carriages with passengers crashed into the locomotives, with deaths occurring from the initial impact and the subsequent fire. The exact number of dead could never be determined due to the severity of the wreckage.  Since no photographs are available, a drawing depicting the carnage is shown in Figure 1 (above).

As the number of accidents from axle failure increased to an almost daily occurrence, researchers started looking into possible reasons. By reviewing unbroken and failed axles, it became apparent that the appearance of the metal at the point of eventual fracture indicated a gradual deterioration of the material. Researchers reported seeing a crystalline appearance of the failure surfaces, which is evidence of brittle fracture (although this knowledge was unavailable to the practicing engineers of the time). This observation led to the understanding that failure was due to the growth of cracks that occur under repeated loading.

Some additional important consequences came from observing axle failures:

1. Discovery of an engineering solution of the axle failure problem. Researchers realized that many of the axle failures started at sharp corners in the transition regions or keyway locations of the axles and recommended the use of gradual thickness transitions. Thus, the importance of stress concentrations on fatigue life was discovered. Figure 2 shows a drawing of the location of fatigue failure of the axle from the Versailles accident.

2. Researchers recommended limiting the service life of the axles on passenger carriages to 60,000 kilometers. Thus, the concept of endurance limit was introduced.

3. Researchers also found that the safe mileage limit, or endurance limit, decreased with speed. This led to the realization that the fatigue life decreases as the load amplitude increases.

Figure 2: Drawing of a Fatigue Failure in an Axle, 1843

It is amazing that all of these concepts were discovered before the year 1850!  

It wasn’t until August Wöhler, a German railway engineer, performed a systematic fatigue test program that the study of fatigue began in earnest. Wöhler developed the first S-N curves, which are sometimes called Wöhler curves, to characterize the fatigue behavior of metals, which he presented in 1867. But the groundwork was laid years before by early researchers trying to understand and solve the failure of railroad axles.

And just in case you think that fatigue is no longer a problem in the railroad industry, a recent publication2 reported on causes of major train derailment and their effect on accident rates.The paper reports that from the interval 2001 to 2010, there were 11,215 Class I freight railroad accidents.The majority and the most serious accidents were due to derailment caused mostly by broken rails or welds, as indicated by Figure 3 which is repeated from the publication. Although fatigue failure is not the explanation for all of these failures, it certainly plays a role.

Figure 3: Frequency and Severity of Class I Freight Train Derailments, 2001-2010

Fatigue failure is still a leading cause of failures in many engineering structures, even today with the availability of sophisticated numerical simulation techniques and fatigue codes. Application of fatigue life prediction methods will lead to the reduction of these kinds of failures. The tools are out there, but is everyone using them? Do you incorporate fatigue life prediction in your analyses? Something to think about, next time you ride the rails.

Feel free to add your comments below.

[1] Nicholas, T., High Cycle Fatigue: A Mechanics of Materials Perspective. (2006). Elsevier. ISBN 978-0-08-044691-2.  

[2] Liu, X. et al, Analysis of Causes of Major Train Derailment and Their Effect on Accident Rates. Transportation Research Record: Journal of the Transportation Research Board, Dec. 2012, Vol. 2289, pp. 154-163.