It wouldn't work as well as the OP requires. A copper nail would swell all the way from the 'dead end' to the head. What is needed is a rivet that can be set and grip the components it is fastening together at the same time.
Bifurcate rivets can be partially set by using a wedge, or blunt chisel shaped punch, so that the components are compressed together and then the rivet can be formed by another, flatter punch and then have the ends curled into the washer by a third concave punch.
Also, steel would be a better metal to use.
Dave