  We investigate the high-order harmonic generations (HHGs) of graphene
irradiated by linearly polarized lasers with intensities in a wide range from
$10^{8}$ W/cm$^2$ to $10^{13}$ W/cm$^2$. We find a striking knee structure in
the laser intensity dependence of HHGs, which consists of a linear growth
regime, followed by a plateau of the saturated HHGs, and then a transition to a
nonlinear growth. The knee structure is rather universal for the varied
harmonic orders and has been certificated by the calculations of two-band
density-matrix equations as well as the \textit{ab initio} calculations of
time-dependent density functional theory. Based on the two-band model, we
reveal the underlying mechanisms: The behavior of linear growth can be depicted
analytically by the perturbative theory of optical conductivity; While, the
plateau of saturated HHGs and the transition to a nonlinear growth are caused
by the quantum destructive interference and constructive interference of
harmonics generated by the electrons corresponding to the lattice momentums
around Dirac points and M points in Brillouin zone, respectively. In
particular, we find that tuning Fermi energy can effectively alter the knee
structure while the profile of the knee structure is not sensitive to the
temperature. Our calculations of the third-order harmonic vs. tuning Fermi
energy are compared with recent experiment showing a good agreement. Our
predicted knee structure and its associated properties are observable with the
current experimental techniques.
