the diaphragm spring is the bit which is inside what most people call the ‘clutch’ or ‘clutch cover’ and is the bit which bolts to the flywheel. the spring presses the friction surface of the clutch against the flywheel and clamps the friction disk (which is the bit with the friction material on it) inbetween.
so the spring itself is not part of the friction material but it is in an assembly (the clutch cover) which has friction surface(the pressure plate) ie the friction material slides against it as you launch the vehicle
http://ww2.justanswer.com/uploads/xsvectOR/2010-06-26_165511_1.gif
you release the clutch by pressing the fingers of the spring which the release bearing