My PS3 Blue-Ray Drive cannot read any disks anymore
Is there a possibility to replace the drive with a normal standard spare parts?
I believe if you crack open the box you void any warranty or agreement with Sony, so I would advise against it if at all possible.
Having said that I have taken a PS3 apart and fiddled around with the inner workings a few times for various side projects and while its not particularly easy you can replace the blu-ray drive in a PS3 by yourself. Assuming you have a secondary drive from Sony that is compatible with the PS3.
But if you are going through all the trouble of taking it apart just to replace a stock piece I would first suggest contacting Sony and seeing if they can replace the entire PS3 and save yourself the time, and you may end up with a completely new console.
I recently had a similar problem with my PS3 and replaced, not the whole drive, but just the laser and the "deck", which is the little track that moves the laser back and forth. Search ebay for "PS3 laser" - mine cost about £23 (UK pounds, equivalent to about $40 USD).
The decks are specific to different hardware revisions of the PS3, so be sure to check your model number (on the bottom of the PS3) and get exactly the right part.
It's a reasonably straightforward repair if you're comfortable taking electronic stuff to bits. You do need a special screwdriver (T8 security torx), and I recommend using a YouTube video to guide you through the procedure, if you possibly can. Took me about an hour and my PS3 is now working perfectly again.