One of the benefits (apart from re-usability) of circuit breakers is that they have two mechanisms for dealing with over currents.
Circuit breakers have a slower thermal sensor for normal over currents, this would be the typically the breakers rated current , i.e. 40A.
This slower trip follows a curve so the higher the over amp, the shorter time is will trip, also dependent on outside temperature.
They also have a fast magnetic trip for short circuits, typically rated 2.5kA or 6kA for domestic breakers. Though this short circuit refers to an short between conductors.