What medal might have been given to Northern veterans of the US Civil War?

My great grandfather was a retired Union soldier -US Civil war.  I think an organization that he belonged to might have been called the Grand Army of the Republic.  His picture was in a newspaper, wearing a large round metal.  He served with a Virginia/West Virginia Company.  Is it possible to see a picture of what that metal might have looked like?  Or to know something about the organization?