Sorry if this is the wrong subreddit for this. I know the rules are strict here but I figured it's worth a shot.
Honestly I think you are right for asking this question on this sub.
It was either made from stainless steel or aluminum. It would be more than likely steel.
If you want to wear the tags, I'd use a copy of the tags, meaning that you have the tags duplicated and you would wear the new tags, and you can keep the originals in a safe place where it won't be exposed to acids, oils, and etc. to further it's corrosion. There are some artisans who can make tags look vintage.
http://agilewriter.com/History/DogTags.htm
Quote from the pages:
"During WWII, tags were stamped by a machine and were rectangular shaped with round ends and a notch at one end. It was rumored that the notch was put in the tag so that the tag could be placed in a dead soldier’s mouth and would hold it open so that the gasses would escape and the body wouldn’t become bloated. Fortunately, the truth was a little less gruesome. The stamping machine required a notch to hold the blank in place as it was being stamped. The tags were first made of brass and later a corrosion-resistant alloy of nickel and copper. By the end of the war, all tags were made from stainless steel. They were suspended from the neck by a rope, a beaded chain or a stainless steel wire with a plastic cover."
Edit: Another link for you OP, as it would seem that within the different branches of the US military there where different patterns used. (assuming your Granddad served in the US military)
http://usmcwwiidogtags.com/about.html
"Initially, dog tags of the for all branches of the armed services were fabricated from a trademarked alloy called "Monel." Monel was produced by the Special Metals Corporation and was composed of up to 67-percent nickel, with the remainder consisting of copper, iron, and manganese. Due to the rapid mobilization of personnel into the armed forces and the increased production in war materiel that followed the attack on Pearl Harbor, shortages of metals soon developed. As a result of these shortages, the supplier simply could not keep up with the demand for dog tag blanks fabricated of Monel. The armed forces solved this problem by utilizing either brass or stainless steel in the fabrication of dog tags—a practice that continued throughout the remainder of the war."