Yes, what time period are you going for? Kettle hats were in use from the 13th century, though you'd probably get away with using one for the third crusade (I wouldn't go any earlier though).

Have you seen this site? It's quite useful for reference pictures of people in armour. You can search by date, or by tag, ie. chapel de fer

EDIT: I've just found that one of the twelfth-century Lewis chessmen has a helmet with a brim, so it may very well be appropriate for the entire crusades.