A Stunt is a better way to model that.
If you want it to be mechanically important that your character constantly, obsessively, sharpens their knives, above and beyond the call of duty, it's easiest to model that as some sort of stunt, a per-character benefit that breaks the usual rules of skills and the skill pyramid. Maybe one of these:
Pockets Full Of Sharp, Sharp Knives. If it is at all possible, you can draw and wield a Weapon:2 knife any time you want.
The Whetstone's Song. +1 to Overcome or Create an Advantage when a handy, sharp blade might make the difference, such as bursting through a tent wall or cutting a restraining rope.
Don't Underestimate Me. The knife is usually a humble, even desperate, weapon. Not in your hands. +2 to Attack anyone unaware of how sharp your knives are. (Usually this is just the initial exchange in a conflict.)
So why do you model it this way as opposed to stapling a dozen "Very Sharp Knife" aspects onto your character with one free invoke each?
What An Aspect Is
An aspect is something important about the story that you need to know. Let's take Athens, for example, a character with a standard number of aspects:
High Concept: Former Imperial Intelligence
Trouble: I Have Enough Regrets
Add'l: A Subtle Hand in the Shadows
Weapons And Equipment Are Procure-On-Site
It Always Pays To Keep In Practice
If she were showing up in a major motion picture you could cram all of those into a single intro scene at a space bar if you had a mind. She's drinking and laughing with some outlandish alien and then sudden swoosh cut into backstory. She walks into a spaceport clutching a folder of important space documents. Explosions erupt on the planet's surface behind her and she bites her lip. Reverse cut to a bunch of spaceport guards charging for the doors. Cut back and she isn't there anymore and the guards run past, but she emerges from a shadow on the wall to yank the last one in. Nobody notices. She races for the shuttle and types on the guard's space PDA and the shuttle controls at the same time and the shuttle takes off, its screen full of notices about docking protocols and such. Cut back to the bar and she claps the alien on the shoulder and walks out the door. She flourishes an outlandish set of space car keys and gets in a nearby runabout as the alien frantically starts searching its space pockets through the bar windows.
Total elapsed time... maybe a minute? Depending on how frantic the editor was in getting the movie down to time. At some point in the movie all of those things are probably going to be important.
Okay, cool. So now imagine what twelve aspects named "Very Sharp Knife" mean. The next guy at the space bar has a bandolier of knives, and the camera spends two and a half minutes slow-panning over the whole assembly, with flashback shots framed around each knife getting sharpened down against various backgrounds and lighting. Somebody's doing it somewhere but we don't get any kind of definite indication. It's just two and a half minutes of knives getting sharp.
After a while you just start laughing, right? This can't be serious. It's something you might do in a comedy movie after you introduce a bunch of characters with cliche backstory cuts - put one with a bunch of weapons at the end and their "backstory" is just weapon, weapon, weapon, weapon. How can each of these weapons possibly matter that much?
Right, so taken all at once a giant pile of Aspects doesn't make a lot of sense. How about taken individually, a bit at a time? How would you get those free invokes, anyway?
How You'd Get Those Free Invokes, Anyway
Free invokes will happen as a result of an action roll. Usually a roll to Create an Advantage, though some stunts can have them sprout up as a result of other rolls, often on aspects more important than the less-plot-defined Boosts.
And the important thing you have to know to make and adjudicate rolls is that every roll happens in a scene, and every roll is dramatic. Fate is a game of dramatic action. Every roll must represent something that's happening in some time at some place for some reason, perhaps with some audience. Every roll can fail, and it's on the GM to decide exactly what that failure means - which is easier given a time and place - and how success plays into the story going forward - which is easier given a reason and an audience. You never roll for the same thing twice, success or failure.
So, you want to show up to a fight having put twelve "Very Sharp Knife" aspects on your character? Great! Just convince your GM to set you twelve separate flashback scenes, only you and no one else, where you roll to put the perfect touches on each of your particular knives. Just how are you different from everyone else, to deserve all this time and attention?
I mean, maybe the GM quick-clicks through a montage of the things everybody's doing to prepare for the rumble in the abandoned refinery, and somebody's trying to buy some thugs off and somebody's scouting the place out and somebody's flipping through records at the City-County building with a worried look on their face and then quick-cut to you in the workshop on the second-floor loft, bent over a workbench, sharpening knife after knife after knife. That's justification for showing up with Obsessively Sharpened Knives with two free invokes on, certainly! But everyone else is also showing up with their own personal spice, so it's fairer, and that was the only thing you had time to do before the rumble in the abandoned refinery, making it appropriately dramatic.
For Everything Else, There's Stuntstercard
Yes, you're going to have extras per your favorite Fate flavor, but stunts are part of the core trifecta and in a lot of ways they bridge the gap between aspects and skills. (Sometimes literally in certain flavors, where every stunt ties into one of your character aspects.)
Aspects are personal, broadly defined, and dramatic to use. Skills are impersonal, narrowly defined, and dramatic to use. Stunts are personal and narrowly defined, but not necessarily as dramatic to use. Especially the ones which just stick a bonus onto regular ol' skill use and call it a day. They're ways in which your character is meaningfully distinct from others, but the precise story events that power them are just kind of assumed to be ticking over in the background somewhere. They're not usually dramatic enough to scene around, though see above about the last thing you can do before the rumble at the abandoned refinery.
"When I'm not onscreen, I'm often somewhere obtaining and/or sharpening knives" is a definite enough, but not dramatic enough, character detail, that it's worth modeling somehow in a stunt. Exactly how is going to depend on the specifics of your character and the campaign and maybe even associated extras, but it's certainly stunt material.
But How Long Should Free Invokes Last?
Practically speaking, free invokes don't survive a play session. The index cards are wiped clean, all the Fate Points go back in the bag, and you head off to spend a week frantically pumping two levers with giant comedy knobs reading "MY" and "LIFE". When you sit down to play again, what even happened last session? Why are there two paperclips on Mimbledrone Manor? Eh, probably not important.
We've talked about what makes free invokes; they arise in a dramatic scene for a dramatic purpose. Regardless of what happens in relation to Mimbledrone Manor, the session ended and that drama is over. There are three cases where you might possibly have them stick around.
You're playing short games. If you only have an hour to sit down and play at a time, each sit-down is something less than a single session, for refresh purposes. You can very easily set up more drama than you can pay off, in which case you have to take notes when you put things away so you remember that Twilliam drank a lot of drinks with a lot of maids and butlers and styled out the hidden aspect The Secret Vaults Of Lord Mimbledrone with two free invokes on it.
You're playing the long game. Fate can use its fractal nature to frame "the game behind the game", such that the GM's statted up the Horizon Empire and the Stellar Loyalists as organizations trying to take each other out, with PCs playing important roles in one or the other. An entire session might represent and influence a handful of rolls in this game, and as a result organization-scale free invokes and even boosts can stick around from session to session. There's probably space on each organization's character sheet to keep track of that.
You remember the time when. After a significant (story-concluding) milestone in Atomic Robo, for instance, characters write down the arc name and can burn it like a free invoke whenever it would be appropriate - if you learned a thing or two about crystals battling the Savage Sword of Dr. Dinosaur, say, or remember the basics of world communication standards you learned confronting the Ghost of Station X. This is a special game mechanic designed to evoke the little yellow boxes in comic books that say "see issue #5", but the idea's surely popped up elsewhere.