Say a player wants to break down a door and has a weapon that they think could help (a hammer, a small explosive, or something like that), how do you add that to the roll? Just say "sure, you get +2 to the roll"? And should that be a "create an advantage" roll or just a simple passive opposition roll?
There is no such thing as a weapon (or anything else noteworthy in a Fate game) without an aspect, so invoke away! But see the bottom of my answer for a challenge to the idea you need a numerical bonus (or an action!) at all.
Aspects are explicit statements about implicit narrative truths. This means that everything which is true about your story has an assumed aspect associated with it; we just write down the ones we know/hope are important.
When something that's obviously true about the story becomes important to the story, we can simply write down its aspect. No roll is needed, but no free invoke is gained.
The "create advantage" action is about changing the story so that a new truth is made, or an existing truth is bent to our advantage. This is why it can be used to add free invokes to existing aspects, as well as change them, remove them, or create new ones.
- So you can always spend a fate point to invoke a narrative truth, because there's an implicit aspect in play already: "I have a Fireaxe, so I spend a fate point to get +2 to break down the door with it because that's what it's made to do."
- If you want to get free invokes, you can create an advantage targeting that aspect: "I'm going to limber up with a few practice swings, rolling Physique to place a free invoke on my Fireaxe."
- If you play in a game where weapons automatically have ratings or stunts attached to them, then your weapon already has a bonus (a rating of 2, or a +2 to attack, or whatever your game defaults to): "I have a fireaxe, and that means I get +1 to attack, +3 if I'm attacking a door."
- If you play in a game where weapons don't have those kinds of qualities automatically, you can spend a fate point to temporarily gain a stunt to that effect anyway. "I spend a fate point to get +1 to attack with my fireaxe, +3 when attacking doors."
- And if your weapon is particularly suited to the task, the GM may grant you that stunt for free or determine that the opposition is reduced commensurately. "Normally I'd say this door is a +4 difficulty, but you're perfectly equipped for the task with a fireaxe so the difficulty is just +2."
As for the kind of roll it is to break open a door--often that'd be Overcome but it depends entirely on the fiction. In particular, usually breaking down a door isn't something to spend a lot of time on. Giving a door a stress track and a defensive skill is almost always overkill, and using Create Advantage is probably only applicable if there's a particular way the player is trying to open the door which will be important later.
Looking at it from that perspective ("What drama does this action create/solve, are both success and failure interesting, how important is this door anyway?"), I'd be inclined to say the appropriate action is none at all. If you've got the right tool for the job and failure would be boring: as a GM I'd say "Great, the door's open and you rush in."
Personal anecdote: I once gave an immortal ninja a flimsy (target +0) motel door to kick down. I wanted the ninja to have a moment of awesome kicking in the door to the wizard's motel room before the wizard's wards kicked back (I thought I was handing him a free invoke for a success with style). Instead, he failed so utterly that he gave up and went for the window.
I would simply change the difficulty. You want to kick open that door? Sounds like a you need a great (+4) effort. But with the right tools the difficulty might drop to fair (+2).
But opening a door does not sound like something your want your players to roll on - remember: Only let them roll if both results (success and failure) are interesting.