The metal will stress, and over time micro cracks will form inside until one time it wont hold and will blow apart.
I could understand making an overcharged load by accident, but feeding it a a steady diet of above max loads ? Why would you even think of doing something like that unless you have a death wish.
"Maximum" is a variable that is different for every rifle, rather than being based upon any realistic set point. Action sizes and materials vary, the quality of the fit of the parts varies, and the particulars of reality vs. specifications of the steel used, and it's inherent flaws, varies.
Reading and following the reloading manual is a safe way to go, but it is very possible that the "maximum" loads listed there are neutered down to be used in some really questionable pieces of hardware too. Load manuals are filtered through liability lawyers.
End of day, each rifle is it's own individual case, and must be adjudged accordingly.
Depending upon what exact form of "maximum" loads are used, the net result might be nothing at all, might be a gradual and predictable destruction of a firearm, or it might work just fine until one day it decides to disassemble itself at speed.
From the theoretical aspect, it comes down to engineering student homework, using Hoop stress, and other stress analysis on the various parts, using values decided upon as representative of what the materials are supposed to have. Lots of higher maths and (preferably) computer programming.
Lots of blown up gun pictures around. Not that hard to form an opinion of how they are most like to come apart even for a layman. But I would not be betting my grocery money on any one failure mode to be likely. If at all. Too many uncontrolled variable to deal with.
Cheers
Trev