  RX J0440.9+4431, a Be/X-ray binary, had its brightest outburst in 2022 since
its discovery, with a peak X-ray flux of 2.25 Crab (as recorded by Swift/BAT,
15-50 keV). We analyze the timing properties of this giant outburst using data
from Insight-HXMT and NICER, focusing on the evolution of the pulse profile and
pulse fraction. We observe that when the luminosity reached around ~ 3*10^{37}
er s^{-1}, a transition from double-peaked to single-peaked pulse profiles
occurred across the energy range, with the peak of the low-energy profile
aligning gradually with the peak of the high-energy profile. This change
indicates a transition from subcritical to supercritical accretion.
Additionally, we found a concave in the pulse fraction as a function of energy
around 20-30 keV throughout the entire outburst period. Compared to the low
luminosity, the concave becomes weaker in high luminosities, and overall, the
pulse fraction is higher. We propose that this concave could be caused by the
scattering of high-energy photons by the atmosphere of a neutron star, leading
to a dilution of the pulse fraction. As the accretion reaches the supercritical
state, the accretion column height increases, resulting in a larger direct
component of strongly beamed X-ray flux, and an elevated pulse fraction.
