The MCB contains two distinct types of circuit to monitor the current - Magentic, which responds to instantaneous overloads, and Thermal, which detects overload over a period of time depending on which curve the breaker is designed to. Both these circuits will work on DC. However - and this is where the major difference lies between AC and DC breakers - DC breakers have an extinguishing magnet (permanent) to pull the arc away from the contacts as they open, AC breakers rely more on the fact that the current will fall to zero as the voltage crosses from positive to negative so extinguishing the arc. For this reason if you use an AC breaker on DC you will find that manufacturers de-rate the voltage that they can be used at, for example a breaker rated for 240VAC may only be suitable for use at 24VDC. The trip rating is reduced though, i.e. the MCB will trip at a lower current when operated at DC. This is because the trip current is based on the RMS current at AC, but with DC the RMS and peak current should be the same (barring any transients). So the DC tripping current will be 0.707 * the AC rating.