They may or may not be required for all living spaces where you live when upgrading the panel. Call your local inspector to find out. In my area they are not required on an upgrade but I always install them in bedrooms, closets, living rooms, den, sun room, breakfast room, dining room, libraries, any place people gather may require them. AFCIs will not be required in bathrooms, kitchens, laundry rooms, unfinished basements, garages, attics or outdoors. I personally install them when I upgrade a service panel. They are a great safety device that will protect the people living in that home. I also recommend and install GFCI outlets where needed if the homeowner agrees.
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Short circuit fault.
If the main breaker has ground fault detection, and the fault is a ground fault, then only the main may trip. Also if the fault is a direct short, the fault current may be several thousand amps, much greater than the trip point of both breakers. Breakers have an I^2T curve (current squared-time), which is an indication of how fast the breaker will trip at a given overload. When both breakers are overloaded, the breaker with the faster I^2T rating at that current level will trip first. This would be an indication that the breakers are improperly specified or adjusted.
You don't specify whether you mean low-voltage circuit breakers, such as MCBs (miniature circuit breakers) or high-voltage circuit breakers. In either case, repeated tripping under fault conditions causes arcing which damages the main contacts of the circuit breakers. For this reason, high-voltage circuit breakers are taken out of service after a specified number of tripping operations, so that the contacts can be maintained or, if necessary, replaced. MCB contacts are inaccessible, and the MCB may eventually require replacing.
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There is a heated bimetallic strip that provides a time delay small overload protection. When its contact makes, it energizes a coil to trip the breaker. Some breakers are mechanical, though. There is a coil that trips the breaker instantly on large overload.