  Fatigue can cause materials that undergo cyclic loading to experience brittle
failure at much lower stresses than under monotonic loading. We propose that
the lithospheres of icy satellites could become fatigued and thus weakened by
cyclical tidal stresses. To test this hypothesis, we performed a series of
laboratory experiments to measure the fatigue of water ice at temperatures of
$198$ K and $233$ K and at a loading frequency of $1$ Hz. We find that ice is
\textit{not} susceptible to fatigue at our experimental conditions and that the
brittle failure stress does not decrease with increasing number of loading
cycles. Even though fatigue was not observed at our experimental conditions,
colder temperatures, lower loading frequencies, and impurities in the ice
shells of icy satellites may increase the likelihood of fatigue crack growth.
We also explore other mechanisms that may explain the weak behavior of the
lithospheres of some icy satellites.
