There has been a lot of discussion on this very topic, both on this subreddit and in scholarship. As this question has an endless number of variables (range, angle, specific dimensions of bow and armor, etc.), it's difficult to give an exact answer. However, both historical sources and modern testing indicate that arrows were not capable of penetrating directly through armor such as a breastplate or a helmet. That doesn't mean that archery was useless. Every harness ever made has weak points and vulnerability, because defenses are by necessity a compromise between functionality and protection. Arrows could still cause injuries or kill when they hit joints in the armor or happened to catch a man with his visor up. The goal of mass archery volleys was to disrupt and harass an enemy, not necessarily to produce a huge number of casualties. Archers worked in concert with the other elements of their army, which for English forces generally consisted of dismounted men-at-arms and field fortifications. The archers weren't supposed to win the battle with shooting alone.