  Grain growth and fragmentation are important processes in building up large
dust aggregates in protoplanetary discs. Using a 3D two-phase (gas-dust) SPH
code, we investigate the combined effects of growth and fragmentation of a
multi-phase dust with different fragmentation thresholds in a time-evolving
disc. We find that our fiducial disc, initially in a fragmentation regime,
moves toward a pure-growth regime in a few thousands years. Timescales change
as a function of the disc and dust properties. When fragmentation is efficient,
it produces, in different zones of the disc, Fe/Si and rock/ice ratios
different from those predicted when only pure growth is considered. Chemical
fractionation and the depletion/enrichment in iron observed in some chondrites
can be linked to the size-density sorting and fragmentation properties of
precursor dusty grains . We suggest that aggregation of chondritic components
could have occurred where/when fragmentation was not efficient if their
aerodynamical sorting has to be preserved. Chondritic components would allow
aerodynamical sorting in a fragmentation regime only if they have similar
fragmentation properties. We find that, in the inner disc, and for the same
interval of time, fragmenting dust can grow larger when compared to the size of
grains predicted by pure growth. This counter-intuitive behaviour is due to the
large amount of dust which piles up in a fragmenting zone followed by the rapid
growth that occurs when this zone transitions to a pure growth regime. As an
important consequence, dust can overcome the radial-drift barrier within a few
thousands years.
