Depending on the size of the barrel the contact time will be longer. The smaller the barrel the larger the surface contact to volume ratio there is, and the shorter the mead/wine/beer/sake/brandy/etc. should be exposed lest the oak overrun the flavor of the beverage. You'll need a good glass wine thief that will pull between 25-50 ml of fluid and begin tasting after a week or so for a barrel/cask that is less than 20 gallons in size, a month or so up to 30 gallons and about three months at 60 gallon or greater. That's my general model. There are modifications based on new oak, used oak and neutral oak.
New oak will require that you check a bit earlier on volumes up to 30 gallons (say two weeks), and on up to 60 gallons (about a month or six weeks). This is also dependent on what you are putting in the barrel. For traditional mead I'd stick with the formula above, for higher gravity melomels, metheglins, pyments, braggots, etc. a bit later. Generally you want to get the influence but not over the top depending on what you like when it comes to influence and character. You should have a good idea if you've used cubes, staves, dominos etc. If you've used chips, you'll need to re-train your palate a bit as chips give a mono-dimensional and disjointed impression of oak which takes a long time to mellow and integrate.
Used oak (3-5 usages) you can factor another month or two on the larger volumes and another week or so on smaller volumes. Use barrels are good for traditionals. Barrels that have contained other beverages (wine, port, sherry, etc.) can lend some very favorable characters from the beverage that was aged within. Remember that whiskey, bourbon, rye and other spirits are aged in barrels that are sawn rather than split and have a rougher finish and charred toast level so you'll have to adjudicate what the influence you are trying to impart will be. Bourbon, Whiskey, Rye, Rum and Brandy barrels all impart some very nice flavors into your meads depending again on what it is you're putting in the barrel.
Neutral oak (generally more than 5-8 useages) does not need to be checked as frequently as the two preceeding levels of usage. The character, flavor and oakiness will be minimal in contribution unless another type of beverage was stored in it (wine, whiskey, etc) in which case the flavor of the beverage will be more prevalent than the actual oak itself. There are hybrid barrels that are made of different types of oak that can have some very favorable effects on your mead as well. It's a matter of characteristics of each of the oak type used in the barrel, as well as what your palate prefers. Some folks like French Oak, others prefer American, others like Hungarian/Eastern European.
I personally preferred the barrels from the oak forests in Croatia, which have pretty much become far and very few between. I generally prefer a light influence from American Oak in Metheglins, Red Pyments, Braggots and some varietal traditionals. I like French or Hungarian in cyser, traditional, white pyments, hippocras and some fruit melomels. In big berry melomels I like either American or French, and sometimes a layered influence from both. Starting with American and then into French Cooperage.
That's my view. I'm sure there are others out there as well.