  The effect of geometrical shape of eroding absolutely rigid particles on the
threshold rate of failure has been studied. The Shtaerman-Kilchevsky theory of
quasi-static blunt impact, which generalizes Hertz's classical impact theory,
is used for modeling the frictionless contact interaction of an
axially-symmetric particle with an elastic half-space. The incubation time
fracture criterion is applied for predicting surface fracture. It is shown that
there exist a critical value of the particle shape parameter such that for all
its lower values the fracture energy possesses a nonzero minimal value.
