Hard spherical particles may exhibit a variation in impact damage on a
softer target depending on the particle diameter and particle velocit
y. In this paper quantitative equations will be derived for these tran
sitions in material behaviour. These equations have been presented in
an erosion map of particle size against impact velocity. The equations
used for the erasion map presented here resembles the mathematical re
lationships presented by others. The difference with earlier reports i
s that in this paper not only proportionalities are given but also the
prefactors are determined. The theoretically derived erosion map has
been validated for spherical particle impacts on borosilicate glass. T
he results show that the theoretical derived erosion map is generally
correct. Most remarkable is the existence of cone cracks in the plasti
c regime. (C) 1998 Elsevier Science S.A.