  Flows of hard granular materials depend strongly on the interparticle
friction coefficient $\mu_p$ and on the inertial number ${\cal I}$, which
characterizes proximity to the jamming transition where flow stops. Guided by
numerical simulations, we derive the phase diagram of dense inertial flow of
spherical particles, finding three regimes for $10^{-4} \lesssim {\cal I}
\lesssim 10^{-1}$: \textit{ frictionless, frictional sliding, } and {\it
rolling}. These are distinguished by the dominant means of energy dissipation,
changing from collisional to sliding friction, and back to collisional, as
$\mu_p$ increases from zero at constant ${\cal I}$. The three regimes differ in
their kinetics and rheology; in particular, the velocity fluctuations and the
stress ratio both display non-monotonic behavior with $\mu_p$, corresponding to
transitions between the three regimes of flow. We rationalize { the phase
boundaries between these regimes}, show that energy balance yields scaling
relations { between microscopic properties} in each of them, and { derive the
strain scale at which particles lose memory of their velocity. For the
frictional sliding regime most relevant experimentally, we find for ${\cal
I}\geq 10^{-2.5}$ that the growth of the macroscopic friction $\mu({\cal I})$
with ${\cal I}$ is induced by an increase of collisional dissipation. This
implies in that range that $\mu({\cal I})-\mu(0)\sim {\cal I}^{1-2b}$, where
$b\approx 0.2$ is an exponent that characterizes both the dimensionless
velocity fluctuations ${\cal L}\sim {\cal I}^{-b}$ and the density of sliding
contacts $\chi\sim {\cal I}^b$.
