I've heard many times that one of the factors that causes wear and tear to the fuselage of airliners is the pressurization and depressurization from each flight.
From what I recall these were referring to aluminum fuselages.
Does this also apply to a carbon fiber fuselage? Is a carbon fiber fuselage affected in the same way aluminum is on each pressurization/depressurization cycle?
Yes, it does.
CFRP's fatigue manifests through multiple mechanisms. It usually begins with matrix cracks, causing a loss of bonding, and grows through delamination, i.e. loss of adhesion between the layers of fiber fabric or tape.
Initially it was believed that CFRP has a fatigue limit, similar to carbon steel. "Fatigue limit" means that, if loaded lightly enough, carbon steel will not suffer fatigue at all. That limit is quite high (just over 50%), and at design load for less-weight-sensitive applications (e.g. for ships it's 40%) it's usually within its fatigue limit. Steel in a ship can realistically experience a billion load cycles.
In comparison, any load on aluminum leads to a small amount of fatigue. High-strength, high-alloy steel used in aviation, e.g. maraging steel, also doesn't have a fatigue limit, but remains extremely fatigue-resistant.
Gigacycle tests, done in 2003-2005, have changed that opinion. Their results show that CFRP fatigue does continue past the previously-thought fatigue limit, even at loads as small as 30% of the static limit. So there's no known loading small enough that it won't eventually lead to failure.
When the term "fatigue limit" is used for CFRP today, it should be taken to refer to the engineering custom of using strength at 10^7 cycles, rather than a true limit. Note that gigacycle tests also question if it exists even for metals; rather, 10^7-10^9 just might be a flatter region.
You can find an analysis of factors that impact CFRP's fatigue life, as well as a review of the mechanisms. To get the full papers with all the graphs, one needs academic or other science paper access, though.
A notable finding is that the fatigue failure behavior of CFRP is highly non-linear. Its loss of strength is rapid for early intralaminar failure (within a layer), then slows down as the interlaminar cracks are expanding.
The mechanisms and the curve also differ a lot depending on how the composite is built up and what the loading is.
It's not so much that CFRP is unique in its fatigue resistance, as that aluminum is an outlier in being particularly vulnerable to and having its service life dominated by fatigue-related failure modes. Aside from regular fatigue, it can fail to stress corrosion. Steel, titanium, nickel, copper, and other structural metals are also subject to fatigue, but it's less dominant in their failure behavior.
To be specific, the minimum weight of a CFRP fuselage is mostly determined by impact and primary static loads. It has excellent tensile strength to resist internal pressure, but no plastic region at all, so where metals can bend to distribute the energy of impacts or concentrated stresses, carbon stands firm till it breaks. For most aluminum fuselages, it's low fatigue strength that sets their minimum weight.
TL;DR version: Yes, but carbon fiber has bigger problems than fatigue, while aluminum doesn't. That's why it's economical to use a lower pressure altitude for CFRP fuselages.
