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So my unpainted carbon fork should be fine...probably
Lots of naked carbon out there, the nudity doesn't seem to be a primary cause of failure. Interesting anecdote via Leonard Zinn
"Our R & D director...took some of our hockey shafts and fabricated a rooftop carrier for his car. He drove that around San Diego for five years. We took the rack down and performed our standard 3-point bend test...There was no decrease in strength or stiffness after five years on top of the car in Southern California sun and heat"
Since UV degradation is a long-known problem with polymers, a huge amount of R&D effort has gone into making them more stable.
It won't do much at all to the carbon fibres, but it can degrade the resin matrix.
The principle benefit of fibre reinforced composites compared with homogeneous materials is that small chips don't lead to bigger problems (more precisely, the composite structure has mechanisms to resist crack propagation which don't exist in crystalline materials)