Zardnaar
Legend
Absolutely. My point is that bows were better at penetration than crossbows. Armor was effective for many reasons, but no armor in history reliably stopped a direct good hit from a contemporary ranged weapon. If they did, armor would have been even more widespread and/or those weapons would have fallen out of use, obviously.
The armor could stop an arrow but it assumes the right angle. Much like tank armor it was sloped and curved. Angle changes slighlt or the armor hits 45 degrees into the side where its 1mm thick vs 3mm and you're in trouble. Modern comparison was the IS-3 tank pike nose. Front on very thick, angle changes its thinner. Height difference (attacker is up higher eg a hill) and you are in big trouble.
Most armies didn't have powerful bows though. English longbow is famous for a reason. In antiquity the bows were comparatively weak. Hence why heavy infantry dominated in Europe for 1000 odd years.