Fatigue fracture through the rivet hole, where the stress is the highest:
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But where's the control?
That's not fatigue fracture in the true sense of the word. That crack started in the hole of the side plate at a tiny little nick where the hole wasn't perfectly round. The rivet is countersunk with force and puts a radial force on the hole (sideplate) that propagates. Fatigue happens through cyclic stresses close to the elastic limit.
In your case the crack was vertical, I have chains in my collection with cracks in just about every direction, it just depends where the imperfection was.
Electro-plated chains crack more often than non-plated ones because the process causes hydrogen embrittlement.
This didn't happen in the days before flush-peened chains. Modern chains require very high tolerances in manufacturing and hence cost a bomb.
If it's cheap, it probably ain't good.