Typically we do not do metal structure type fatigue analysis (crack imitation and growth) for aircraft composites. Carbon fiber composites for aircraft are certified to "no-growth" of damages under fatigue loads. The "no-growth" stress or strain levels are validated by test data, not by analysis. See FAA AC20-107B. See also Composite Materials Handbook, CMH-17, Volume 3 Chapter 12 (Durability and Damage Tolerance) - currently Rev G is published; Rev H will be published in a year or so, and will have a lot more info.