The moon is pretty reflective... If the rings were oriented just right it might actually mirror lots of light that would have missed earth and bounce it down to ground. Possible it would heat the earth.
My suggestion is not to blow up the moon, but to launch payloads from earth via nuclear pulse propulsion containing extremely low albedo material, like coal dust, and create an artificial ring that way.
-Future historians were baffled by the extinction of 99% of life on earth after the planet inexplicably became surrounded by a cloud of radioactive soot. Monuments were discovered exclaiming "at least we're not speaking German"
