  We present a semi-analytic model for the growth, drift, desorption, and
fragmentation of millimeter- to meter-sized particles in protoplanetary disks.
Fragmentation occurs where particle collision velocities exceed critical
fragmentation velocities. Using this criterion, we produce fragmentation
regions in disk orbital radius-particle size phase space for particles with a
range of material properties, structures, and compositions (including SiO$_2$,
Mg$_2$SiO$_4$, H$_2$O, CO$_2$, and CO). For reasonable disk conditions, compact
aggregate H$_2$O, CO$_2$, and CO ice particles do not reach destructive
relative velocities and are thus not likely to undergo collisional
fragmentation. Uncoated silicate particles are more susceptible to collisional
destruction and are expected to fragment in the inner disk, consistent with
previous work. We then calculate the growth, drift, and sublimation of small
particles, initially located in the outer disk. We find that ice-coated
particles can avoid fragmentation as they grow and drift inward under a
substantial range of disk conditions as long as the particles are aggregates
composed of 0.1 $\mu$m-sized monomers. Such particles may undergo runaway
growth in disk regions abundant in H$_2$O or CO$_2$ ice depending on the
assumed disk temperature structure. These results indicate that icy collisional
growth to planetesimally-relevant sizes may happen efficiently throughout a
disk's lifetime, and is particularly robust at early times when the disk's
dust-to-gas ratio is comparable to that of the interstellar medium.
