My friends and I have a long standing disagreement...
Let's assume we're in a $500 - $1000 live tournament with the opponent types etc. that go with that.
Semi early - Shall we say avg stack = 70BB (bubble is long way off)

What's the maximum amount we should be willing to get allin preflop with AK?
Obviously we're thrilled to put in 10 or 20BB allin preflop, but what's the upper cap?
My position is that it's at least 40BB but many of my crew believe is should be less than that.

What does 2+2 say?

That depends entirely on the action and on the tendencies of the players involved. If you've been 4-bet by someone capable of 4-betting light, a 5-bet jam would be reasonable perhaps upwards of 80bb. If you've been 5-bet by someone capable of 5-betting light, a 6-bet jam of up to 160bb could be reasonable (assuming it went something like 3bb -> 10bb -> 25bb -> 60bb).

Or perhaps you meant as a 3-bet all-in? 40bb would be very large if so.

Its situational for me. If I am the original raiser and there are one or more calls and then somebody goes all in for like <25 blinds I will often Jam if my 4-bet would be >33% of my stack (or effective stacks remaining) to get the others to fold and get it HU.

It may also matter to me if we are able to rebuy. Especially if I am below starting stack.

For a 3-bet my limit is usually 25bb HU. In general I will 3-bet to 3x original raise (or 4x if I am SB or BB) plus 1x for every caller. If that puts me over 33% effective stack I would jam (so if original raise is 3x and there are 2 callers and I am in SB that would put me at 54bb's all in limit or so). Unless the opening bet is greater than 3x. Then I am fairly certain I am up against JJ and would rather not shove there. The main thing for me is position as well. If UTG or UTG+1 is original raiser I won't be jamming much. In position I usually prefer to call unless original raiser can be somewhat wide.

Agree there is a massive difference between being the original raiser vs being the 3better.

40BB as the Original Raiser
Pretty much a slam dunk shove against a new school 3bettor.
Could consider just flatting vs an old school 3% 3-bet type.

40BB as the 3-bettor
This is where things get sticky. 100% Agree that 25BB or more is too big for a 3bet shove.
Against an old school "I only 4 bet AA, KK" I could see 3betting to 2.7x and potentially making a tight fold to a 4-bet

Against somebody decent, we need to be willing to commit preflop
I like to 3 bet to 20 - 25% of my stack and:
Call it off vs a 4bet shove.
Shove any flop if they flat preflop.

I had a number immediately in mind, and before reading everyone else's replies, and that number, in a vacuum, is 26BBs.

In a $500-$1000 live tournament against most of the population, I'm at least considering folding AKo to a 4-bet 35-40BB jam. You're just not going to see hands you dominate very often. You're almost always going to be up against JJ+ and AK and you're not doing great against that range. There will be players I will slam dunk call off against, but those are the players I know that can have AQ/AJ/TT at least and that's a far smaller percentage of the pool than you might think. In a tournament with more pros and good regs this calculus obviously changes, and then you're probably calling off 60BB+ 5-bet shoves with AK a decent amount.

AKs off 40BB is closer, probably always calling there just because that extra 3% equity is usually the difference between a slightly winning and slightly losing call.

You will be shocked at how many players in the $500-$1K pool will 3-bet cold call stuff like AQ and TT off 35BB rather than stuff it.

Against a reasonable 3-bet jam size, like, say 25-30BB, I'm probably always calling off AK against all but the tightest players, because even the somewhat nitty players in a $500 or $1K will be capable of finding the AQ/AJ 3-bet shove.

General rule of thumb: if you're in a 40BB spot with AK, the best thing to ask is whether you believe your opponent ever has AQ there. If they do, you're probably good to just get it in. If not, then I'd tread very carefully.

That would be consistent with my buddies thinking. IDK... Seems very Sklansky circa 1992 to me?!?!!
In today's games (even live), I gotta think AK is +EV for 40BB vs an average to decent opponent.

Against people that are stuck in a time warp, AK is obviously garbage for that amount.

Also, what people say and what people do can be completely different things.
One of my friends in the "40 is too much camp" once shoved for 65BB with AK vs my 8BB 3bet (I had KK).
Funny thing is, at the time, he didn't even realize the irony.