The way fatigue cracks propagate through metal is very different from the way damage accumulates in composites. In particular, fatigue cracks in metal form and progress at very small stress loads - 10% or less of the maximum yield load**. The cracks start at some tiny mismatch in grain structures and, because the crack is into metal crystals, the size of the front edge of the crack is as little as a single atom in size, causing a huge stress concentration.
I think composites tend to fail from separation of the fibers from the matrix (usually epoxy for carbon fiber.) The usual final failure is by rupture of the fibers from the matrix which is usually rather explosive as the fibers can store a lot of energy from the combination of strength and elasticity, but the composite can accumulate damage with even the smallest loads, a characteristic shared with aluminum.
For much more about composite fatigue failure than is suitable to type here see
Principal Features of Fatigue and Residual Strength of Composite Materials Subjected to Constant Amplitude (CA) Loading, section 2.5. The Hierarchy of Damage. It's an NIH report and mostly technical, but the 2.5 section gives a good overview.
**I have seen metal parts that failed in use where more than 90% of the original material had succumbed to the fatigue crack and only 10% or less remained to be twisted loose; a load that was very small compared to the strength capacity of the undamaged part.