  Most of planet formation models that incorporate planetesimal fragmentation
consider a catastrophic impact energy threshold for basalts at a constant
velocity of 3 km/s during all the process of the formation of the planets.
However, as planets grow the relative velocities of the surrounding
planetesimals increase from velocities of the order of m/s to a few km/s. In
addition, beyond the ice line where giant planets are formed, planetesimals are
expected to be composed roughly by 50 percentage of ices. We aim to study the
role of planetesimal fragmentation on giant planet formation considering
planetesimal catastrophic impact energy threshold as a function of the
planetesimal relative velocities and compositions. We improve our model of
planetesimal fragmentation incorporating a functional form of the catastrophic
impact energy threshold with the planetesimal relative velocities and
compositions. We also improve in our model the accretion of small fragments
produced by the fragmentation of planetesimals during the collisional cascade
considering specific pebble accretion rates. We find that a more accurate and
realistic model for the calculation of the catastrophic impact energy threshold
tends to slow down the formation of massive cores. Only for reduced grain
opacity values at the envelope of the planet, the cross-over mass is achieved
before the disk time-scale dissipation. While planetesimal fragmentation favors
the quick formation of massive cores of 5-10 Earth masses the cross-over mass
could be inhibited by planetesimal fragmentation. However, grain opacity
reduction or pollution by the accreted planetesimals together with planetesimal
fragmentation could explain the formation of giant planets with low-mass cores.
