What is the temperature of brake disks at maximum altitude of a jumbo like a 747 and airbus A380 for say a 10 hour flight. Does the temperature drop below zero and what is the effect on the metal material used on the disk from the sudden change in temperature from one extreme, below zero degrees celcius to over 700 degrees celcius when braking?
The temperature changes from altitude to ground are not (usually) rapid. Therefore the possible sub-zero to red-hot case is not as severe as may be thought. If carbon discs are the example, they require temps that are almost beyond steel discs braking capability.
Having worked in a wheel and brake shop for years and being an ATP Airline pilot for most of my career I can tell you that brakes won't freeze up unless there is moisture present. Even taking off on snow and flying long hours at high altitude will not cause a problem.
Brakes are a machine. They turn kinetic energy into heat. Here is the problem. It is not the rapid change of temp but the temp limit at which they can continue to function and dissipate the heat at the same time. This is why manufacturers print brake energy charts. Once the limit has been reached, they must be cooled for the period stated or they can no longer stop the aircraft. The factors that matter are OAT, aircraft weight, runway length and prior immediate applications. Not all are considered in the calculations as some are not as critical. The manufacturer doesn't usually tell you the runway required, they just block off that part of the chart where braking effectiveness becomes nil.