Airbus Girl
Go ahead and try calling in "fatigued", and see how long it takes your employer to discipline and/or fire you.
Fatigue is a clinical condition, and most airlines will simply say that you are fatigued as a result of your not planning adequate rest between duty periods. As you are (I assume) working to an approved FTL scheme, and therefore your rest periods are deemed adequate by law, most companies will simply deny any responsibility and point to your use of your "rest period".
Of course this is stupid, I remember how when our first baby arrived, I didn't sleep much for three months, and was a zombie at work. Same goes for trying to sleep in noisy hotels, thoughtfully located next to motorways. And if you are under some form of life stress, it gets even worse.
Airlines choose (generally) to ignore all this, which tells you a lot about how seriously they
really take safety...
But go ahead, try it, and tell us how you get on...