How much of an effect do structural overloads have on an airframe's safe fatigue life?

Question

Most aircraft¹ are built primarily out of various aluminium alloys. Aluminium and its alloys have multiple physical and chemical properties that make them terrible choices as structural materials, except in situations (such as the primary structure of aircraft) requiring the excellent strength-to-weight ratio of many aluminium alloys. One of these unpleasant properties is that they have no fatigue limit,² so that any change in stress magnitude or direction, no matter how small, will produce cumulative damage to the material. When used as part of an aircraft's primary structure, this means that the airframe has a hard limit on how many times it can be stress-cycled³ before the cumulative effects of fatigue damage render the aircraft unsafe to fly unless repaired.

Occasionally, aircraft encounter circumstances that place greater-than-usual stresses on their primary structure, such as hard landings, encounters with extreme turbulence, or overly-aggressive maneuvering. These aggravate fatigue damage in two ways:

• The abnormally-large amplitude of the stress cycle during which the structural overload occurred causes the additional fatigue damage accrued during said stress cycle to be greater than that accrued during a more-normal stress cycle.
• Large overloads can directly produce small-scale cracking and buckling within the aircraft structure, which (as they produce stress concentrations in whatever structural element they occur in) can serve as initiation points for progressive fatigue cracking.

How much of an effect does a structural-overload event have on an airframe's remaining safe fatigue life? Are there any rules of thumb that say that (for instance) a hard landing takes off X number of takeoff/landing cycles from the remaining fatigue life of the hard-landed aircraft? Are there qualitative effects on the airframe's fatigue life that I hadn't thought of?

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¹: Despite the best efforts of both Boeing and Airbus in this regard.

²: A minimum level of applied cyclic stress below which the material in question does not experience fatigue damage even if stress-cycled indefinitely.

³: Stress-cycling takes different forms for different portions of the airframe; for instance, the wings care about takeoffs and landings, when they have to suddenly start or stop carrying the weight of the rest of the aircraft, while the pressure cabin cares about every time you climb or descend to, from, or between altitudes requiring that it be pressurized, which causes it to start, stop, or change the degree to which it's holding in a lot of air that would really like to get out.

Answer 1

Airplane structures are designed to take a certain number of extreme conditions during their life which are defined based on statistical analyses of past flights.

For example a manufacturer can design the structure expecting (just random numbers) 10 minutes of flight in extremely severe gusts, 80 minutes in severe gusts, 5 very bad landings, 20 bad landings and so on. This kind of statistics are obviously confidential and possibly different among manufacturers.

If an unusual circumstance happens, the manufacturer is informed and appropriate measure are taken. Most of time it's something that can be easily corrected using standard procedures otherwise specific analysis are performed.

FAA has a very nice section about past accidents happened due to fatigue problems

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As a side note, structural aeronautical aluminium has the same strength-to-weight ratio of structural aeronautical steel. It has been chosen over steel because it is easy to work, doesn't rust (more or less) and everybody can learn to correctly rivet in a couple of minutes. There's obviously much more than that, but that would be another question.

Answer 2

Even a single overstressing accident can have a disastrous effect on fatigue life. For example, the 747 that crashed in Japan some years ago, claiming over 500 lives, had been subject to a runway tailstrike due to over-rotation a few years before that which significantly overstressed its rear pressure bulkhead. Field repairs were carried out to strengthen it, but were improperly executed- and the bulkhead's weakened state persisted until the microcracks in its structure grew far enough to cause the bulkhead to explosively fail.

ONE tailstrike!

Answer 3

A single overload that doesn't exceed the yield limit on the structure has no effect. It's a spring; as long as you didn't permanently bend it, it's good.

This is why when hard landings, or turbulence encounters occur, the resolution is an inspection to see if any part of the structure has yielded, torn or cracked. If not, it's good to go and there isn't any service life penalty.

I know of an RJ in service in Scandinavia that had a bird strike that took out some fan blades and vibrated the back end of the airplane so violently the flight attendant strapped in back was injured from having her arms and legs flung all over the place.

They inspected the plane, nothing was permanently bent, and it was returned to service.

I know of another RJ that was overstressed in a pre-delivery production test incident. It was inspected, nothing was bent, and it was delivered to the customer.