Could a faulty stove burner trip the circuit breaker?
The resistive plates are the main wearing element on an electric stove.  That is why they are made to be not expensive and easily replaced.  

If one is tripping your 40-50A stove breaker, stop using it. Repeatedly tripping a breaker to see what happens will tend to destroy things which are not yet broken -- since you are, after all, surging well north of 100,000 watts of power through equipment rated for 1/10 that.  Why are people so unafraid of electricity?