I imagine cycles with regard to crop dusters should be measured in some other metric other than take offs/landings.
I’ll preface this with I don’t know that much about fatigue analysis, but you’re right that’s an oversimplification of a cycle. There are lots of types of cycles, including aerodynamic loads, gust loads from turbulence, landing loads, ground handling loads, vibrations (like what limits helicopter blades to a certain number of hours before they get thrown in the trash) or even sonic fatigue due to noise.
They’re split up into high cycle or low cycle like this:
You can make a fatigue spectrum by superimposing the high cycle stuff on the low cycle stuff as shown to try and approximate the different types of cycles an airplane will see each flight.
There’s a specific fatigue spectrum picture I remember from school called the Ground Air Ground (GAG) cycle, and that’s what I was referring to before with takeoffs and landings, but really it should include the low cycle and high cycle fatigue stuff superimposed and try and predict a whole flight:
(Source, looks like a good read:
https://smartutsa.files.wordpress.com/2014/07/load-and-stress-spectrum-generation_ld.pdf)
Unlike steel there’s no fatigue limit for aluminum and as you continue to add cycles it just keeps degrading until it forms a fatigue crack. Extensive materials testing has been done on every type of aluminum to generate S-n curves (stress vs. number of cycles) and you can see the difference between steel and aluminum in this one - as cycles (n) increase the allowable stress (S) continues to go down, where as it bottoms out for steel and theoretically continues to infinity.
I want to read up more on the C-130 accident you talked about due to the 3 bladed props being out of sync, but I think that’s an example of unplanned for high cycle fatigue (due to vibration from the out of sync props?) eating away at the number of cycles the engineers had anticipated and prematurely weakening the metal in the wing carrythrough box until it cracked.
As for the ag plane example, I would think types of cycles would include takeoffs, landings, each drop itself and yanking and banking around at low level (all low cycle fatigue events) along with the high cycle events like gusts etc. Fortunately ag planes are built like brick •-houses so I imagine this stuff takes a long time to manifest, but with enough maintenance neglect (specifically inspecting for cracks and arresting crack growth with repairs) and the perfect storm of fatigue and corrosion that is ag flying I guess it can inevitably happen like what happened in Brazil.