What I can see of the bike looks a bit neglected in general…
True; however I can't think of / see any consequences of neglect that should have caused the crank to have failed in such a way. That's either been massively over-loaded, or more likely seen a high degree of cyclic loading - as one might expect given its application.
From P31
here Brompton recommend that ally components are replaced every 5k miles. If one assumes a mean cadence of 90 rev/min and a mean speed of 12mph over this distance, this suggests a total number of crank rotations of 2.25 million; which appears to be the right ballpark for fatigue to be an issue; loading dependent of course.
This raises an interesting question; since no. cycles and load both play a part in defining fatigue loading, I wonder if, for a given power output there's an optimum speed / load condition for best component life..?
Looking at the graph below for the fatigue characteristics for 2014-T6 ally (
sauce) suggests a curvilinear, exponential relationship between stress and no. cycles. It appears that the material will endure around 10^4 cycles at a stress of around 330MPa, or at the other end of the graph 10^7 cycles at a stress of around 160MPa.
So, by halving the stress / loading the cycling failure point is raised by a factor of 1000.. or, if we're looking purely at power transmission pedalling twice as fast at half the load should increase component life in terms of miles travelled / absolute service time by a factor of around 500.
It seems that load is the dominant factor here, so it seems highly likely that this failed crank arm is the result of a very heavy / powerful rider with a panchent for low cadence. Makes me feel not-so-good about grinding up the hill on the way to work...