@Aaron You have to look at the Characteristic Tripping Curve for the breaker. You'll want to look at the Thermal Tripping Characteristics. This documentation should be available online from the manufacturer, if it's not supplied with the breaker.
For example: Schneider Electric QO molded case miniature 20 ampere circuit breakers will trip after ~8 - 35 seconds with twice the rated current.
The higher the current, the faster they should trip. If the current is high enough, the magnetic protection will kick in, and the breaker will trip in less than a cycle (1/60th of a second [0.01667 seconds]).