  Previous work on protoplanetary dust growth shows halt at centimeter sizes
owing to the occurrence of bouncing at velocities of $\geq$ 0.1 $ms^{-1}$ and
fragmentation at velocities $\geq$ 1 $ms^{-1}$. To overcome these barriers,
spatial concentration of cm-sized dust pebbles and subsequent gravitational
collapse have been proposed. However, numerical investigations have shown that
dust aggregates may undergo fragmentation during the gravitational collapse
phase. This fragmentation in turn changes the size distribution of the solids
and thus must be taken into account in order to understand the properties of
the planetesimals that form. To explore the fate of dust pebbles undergoing
fragmenting collisions, we conducted laboratory experiments on dust-aggregate
collisions with a focus on establishing a collision model for this stage of
planetesimal formation. In our experiments, we analysed collisions of dust
aggregates with masses between 1.4 g and 180 g, mass ratios between target and
projectile from 125 to 1 at a fixed porosity of 65%, within the velocity range
of 1.5 $-$ 8.7 $ms^{-1}$ , at low atmospheric pressure of $\sim 10^{-3}$ mbar
and in free-fall conditions. We derived the mass of the largest fragment, the
fragment size/mass distribution, and the efficiency of mass transfer as a
function of collision velocity and projectile/target aggregate size. Moreover,
we give recipes for an easy-to-use fragmentation and mass-transfer model for
further use in modeling work. In a companion paper, we utilize the experimental
findings and the derived dust-aggregate collision model to investigate the fate
of dust pebbles during gravitational collapse.
