Current pulses at high repetition rates and extremely high current density (> 107A/cm2) were applied to small geometry, thin-film aluminum-copper alloy conductors. The conductor lifetimes were measured as a function of current density and duty cycle. While the observed open-circuit failures are evidently related in some way to the temperature excursions produced by Joule heating, the exact mechanism(s) causing failure is not so clear, and probably varies depending on test conditions. A previously described [8] ohmic nonlinearity measurement was used to characterize the conductor's ability to dissipate heat. A strong inverse correlation was found between the ohmic nonlinearity and time to failure.