on a whim, I tossed :“Uncle Sam” into the Google Books Ngram Viewer, and I’m amazed at what popped out.
http://ngrams.googlelabs.com/graph?content=Uncle+Sam&year_start=1800&year_end=2000&corpus=0&smoothing=3
There are very clear peaks coinciding with our major wars. The tallest and most obvious are WWI and WWI, but you can also see peaks for the Spanish-American War circa 1898, the Civil War, and the Mexican American War. Uncle Sam was supposedly created during the War of 1812, but you’d expect a lag. The first book featuring him came out in 1816, which seems to coincide with the first blip.
No big blips after WWII, though. Not for Korea, Vietnam, or the Gulf Wars.