When materials get tired...
Fatigue is one of the ways in which a material can fail, and it has only been studied closely relatively recently. As with many areas, the study of fatigue is often related to the occurrence of large scale disasters. It was first observed by a German mining engineer, Wilhelm Albert, in 1837. He observed that the chains used to lift elevators were failing when carrying weights that they should have been able to support. He determined that materials subjected to a repeated load, lower than the load at which they would normally break, become weaker over time.
Research into fatigue was driven further in the mid 19th Century due to several railway accidents, particularly the Versailles crash, in which at least 55 people were killed. These accidents were attributed to fatigue failure of axles. Several theories for the processes behind fatigue failures were proposed at the time, but the one that we now know to be correct, developed by the Scottish civil engineer William Rankine and others, was not accepted for many years. He showed that fatigue failures are due to the growth of a crack through the material, usually originating from a stress concentration. These are geometric features such as corners or notches, which increase the stresses experienced by the material in that region.
Research into fatigue continued at a steady pace from this point until the 1950s. In 1952 the deHavilland Comet, the world’s first jet airliner, entered service. This was hugely popular with passengers early on due to its speed, quietness, and openness. One of the features contributing to this was large, square windows, which allowed a lot of light in, however these turned out to be a huge design mistake, as the corners acted as stress concentrations. In 1954, two Comets were lost, killing 56 people. Both of these accidents were attributed to fatigue failures, with the cracks initiating from the corners of the windows.
Mechanism of Fatigue Crack Propagation
Fatigue crack growth is a cycle dependent phenomenon. This means it does not depend on the time in service, rather the number of load cycles experienced. In a jet engine, for example, there are two cycles of importance. The first is the main cycle of the engine, in the simplest form from rest, through take-off, cruise and landing and back to rest. The amount of crack growth is related to the load range experienced, which in this case will be from zero load at rest, up to a peak load and back down to zero. Every time this cycle repeats, the crack would grow a certain amount.
The other cycle that needs to be considered is caused by vibration. Certain components in an engine are subjected to almost continual vibration. The load range imposed by this vibration is very small, however the frequency is extremely high, and as the propagation is dependent on the number of cycles, this can be very damaging.
Dealing with Fatigue
Fortunately, the crack propagation is also dependent on the existing length of the crack, so the longer the crack is, the further it grows with each cycle. Also, for a given load range, there is a crack length below which cracks will not propagate. This is known as the propagation threshold, and is good news when considering vibration, because the low load range means that cracks have to be relatively long to propagate.
The rate of propagation for any given load range and crack length can be determined on small samples in the laboratory, and related to full scale components using empirical relationships. From this, the number of cycles it would take for a crack to grow from a certain size to a defined end point can be calculated.
So ideally we would like to know how large a crack could be present in a component when it enters service. There are a variety of non-destructive techniques available to examine the material with, however there is a limit to how small a crack can be detected. The safest approach, and for jet engines in particular we want to be as safe as possible, is to assume that there is a crack present that is essentially the same size as the smallest crack the examination technique could see. It is extremely unlikely that a crack would be present, but there is no way to determine that there isn’t one there. So we work from this starting crack size.
Now, how do we determine how large a crack would be safe in the component? This is where we go back to the principle that crack growth is dependent on the number of cycles experienced. In one flight, components will be subjected to thousands of vibration cycles, but as mentioned before, the load range of these cycles is very small, so a small crack will be below the threshold for propagation under this cycle, and will only grow due to the main engine cycle. However, as it grows under this main cycle, it will start to approach the threshold for propagation for the vibration cycle. As soon as it hits this threshold, it will start to grow extremely quickly, potentially failing within a few flights, so the maximum length a crack can be allowed to safely grow to is set below this point, with a factor of safety included.
The number of main engine cycles it would take this crack to grow from its initial size to this end point can then be determined, and thus the number of flights the engine is allowed between service intervals. At service, all the components are re-examined, and if no damage is found, then the cycle is repeated.