We do have composite aircraft around for half a century now, not a single accident so far could be attributed to fatigue.
Nevertheless we have seen cracks developing and growing when the fibre orientation has been poorly selected. Those result from unintended stresses, because otherwise there would be fibres in that direction. The funny thing with composites is, sometimes you need to make it softer, not stronger to prevent cracking. With metal you can not do that, hence many designers are not used to this.
Simulating real in-flight environment in the laboratory is a real challange, but so far no relevant influence could have been identified. We are however still quite conservative with these materials (this is why there is no revolutionary weight saving), it will be interesting to see how far we can push the boundaries without getting hurt.