CF, as all composites are subject to fatigue/stress cracking, energy is dissipated by cracks advancing along the fibers within the material. Crack propagation being a function of cycles and stress levels.
All of this is well and good, which leads us to Malcolms point, that their are measures which can be taken to alleviate the situation, to reduce the stress levels, thus either reducing or eliminating the issue.
In some instances it is worth recognising the viable (often quoted materials properties) have limited range when compared to metallics materials. Becoming brittle at not particularly low temperatures, and in some instances entering the plastic range at temperatures we humans see as normal.
Finishing the discussion on polymers, they are far more restricted on loading rates than metallics quoted properties.
Lecture over.