Airport security X-rays will not damage the DVDs.
There's no logical reason why they should object to carrying DVDs, but you never know. Some ignorant security people just might blindly follow orders not to allow any computer related item, especially as hand baggage. Some post office staff refuse to accept even CDs to be sent by mail.
It will be best if you put the DVDs in your suitcase. They tend to be more wary of electrical and electronic products in hand baggage. Can't really blame them.
Personally, I have carried lots of electronic stuff, including parts, wires, instruments, motherboards, etc packed inside my booked luggage or in separate cartons. When they show up on the scanning screen, sometimes they ask me to open my luggage and explain what they are, sometimes they don't.