Try this:
1/ F1 2011 Crashes In China/Black Screen
People are having this problem on high-end machine where they like to play in highest settings.
Turning off the Vsync can solve the problem.
2/ To fix this, go to the replay file usually found in
C:\ProgramData\Codemasters\F1 2011\DataCache\Administrator\replay\replay.pbf.
If you can’t find it, just search for replay.pbf in Windows 7.
Once you found it, right-click the file, go to Properties, and set permissions to ‘Read only.’
You should notice better framerates afterwards.
3/ An alternative workaround is change the default Rapture setting under Audio options to “Software”.
This reduces usage of the replay file and will increase performance.
Another option is to tweak the settings in the hardware_settings_config xml file,
which can be found in your save game directory. Turn down the shadow mask quality to 0.
Just in case you’re an Xbox 360 user, the solution is to delete the game from your HDD,
and ‘Run the game from Disk’.