I've got a pretty basic question about lumber.
As I'm sure you know, when you reduce a board down to the desired thickness (in my case, often 3/8" or 1/2") and don't use it immediately, you may find when you do pick it up again that it has developed a bit of bow or cup or wind.
For box making, can you use pieces that are not PERFECTLY flat?
Also, I understand the things that need to be done to account for the inevitable movement of the wood in its width and length. But given that a thicknessed board can change as described above...isn't that same tendency to cup or bow wind still going to be in the individual boards in a finished piece? In this case, are we relying on the strength of the joinery to stop it from happening?
If wood is stickered so the drying (or gaining moisture) occurs on both sides of the stock equally, the bowing is less likely to occur. It is also less likely if you are using wood under the same conditions of atmospheric humidity under which it has been stored for a significant period of time.
Also, you ask about the wood after it is assembled into a box. The inside of a box and the outside of a box also offer faces to different levels of atmospheric humidity, which too, can cause complications due to expansion and contraction of wood. Normally, the humidity difference between the inside of the box and the outside of the box will not be enough to cause such severe warping as will happen in the top board of a stack. A humidor is a classic example of high humidity inside the box, while the outside conditions may be much less humid. Using mechanical fasteners, including nails, dowels, miter keys, splines, finger joints and the like, are ways to attempt to control the behavior of wood under adverse circumstances.
You can test this by leaving a board laying on the ground out of doors, or on a concrete floor. You will notice that the wood will generally cup upwards on the edges due to expansion of the downward side from absorption of humidity from the ground.
So how do you fix this? If you've resawn wood for box sides, don't leave them in an unstickered stack if you are planning to walk away and come back next week to cut and assemble a box. Also, store your woods for a period of time in the same place and under the same humidity conditions under which you will make the box. Making the box the same day you resawed your stock is also an option.
Even leaving a piece of wood unstickered on top of your table saw overnight can be a cause for grief when you come back the next morning to make a box. It is far better to leave your box stock leaning up against the work bench where it gets adequate air circulation on all sides.
Your most difficult question has to do with whether or not you can use a piece of wood for box making that's not perfectly flat. The only reasonable answer to that is, "it depends." How perfect do you want the box to be? I've made some boxes that turned out OK despite minor cupping. But hopefully, careful handling of your stock will enable you to avoid that.
In any case, I hope this helps.
The image above is my new bookazine published by Taunton Press, including 5 chapters by me and 4 another Taunton author, Strother Purdy.