I have been shooting for nearly 50 years. Wood, fiberglass, aluminum, carbon. From target arrows to heavy compressed cedar and everything in between. I do a fair amount of stump shooting which can be punishing on arrows.
In all that time, I have had one arrow explode and that was a carbon I had already killed another deer with. I had cleaned and checked it thoroughly and everything seemed OK, but when it was shot the next time it went out in pieces.
When I was a teenager and had no money to speak of, I used to salvage wood stump shooting arrows that split diagonally on the grain on a very hard stump hit and glue them back together with Elmers wood glue...then shoot them some more. Never even had one of those explode. Generally shot around 50 lb bows back then.
Net is, it can happen, but I think it's extremely rare. If I were to make a bet, I would say aluminum would have the least chance...carbon the most.