Hi 2old,
The answer is not simple. Continuous loads in Canada require derating of 20% so 15 really equals 12 amps. I would imagine that US code is quite similar.
"Manufacturing tolerances result in a curve that is a band bound by minimum and maximum values of total clearing time. Total clearing time is the sum of the circuit breaker’s sensing time, unlatching time, mechanical operating time and arcing time. For currents in excess of 125% of the circuit breaker rating at an ambient of 40°C, the circuit breaker will automatically open the circuit within limits specified by the band"
My "reading" of the above suggest that the breaker will do a magnetic trip after a few seconds if the load is 18.75 amps or higher, on a breaker rated for 15 amps.
http://static.schneider-electric.us/docs/Circuit%20Protection/Molded%20Case%20Circuit%20Breakers/0100-400%20A%20Frame%20FA-LA/FA-FC-FH/0600DB0105.pdf