  We study numerically the failure of an interface joining two elastic
materials under load using a fiber bundle model connected to an elastic half
space. We find that the breakdown process follows the equal load sharing fiber
bundle model without any detectable spatial correlations between the positions
of the failing fibers until localization sets in. The onset of localization is
an instability, not a phase transition. Depending on the elastic constant
describing the elastic half space, localization sets in before or after the
critical load causing the interface to fail completely, is reached. There is a
crossover between failure due to localization or failure without spatial
correlations when tuning the elastic constant, not a phase transition. Contrary
to earlier claims based on models different from ours, we find that a finite
fraction of fibers must fail before the critical load is attained, even in the
extreme localization regime, i.e.\ for very small elastic constant. We
furthermore find that the critical load remains finite for all values of the
elastic constant in the limit of an infinitely large system.
