  The wear-free sliding of layers or flakes of graphene-like 2D materials,
important in many experimental systems, may occur either smoothly or through
stick-slip, depending on driving conditions, corrugation, twist angles, as well
as edges and defects. No single parameter has been so far identified to
discriminate a priori between the two sliding regimes. Such a parameter,
$\eta$, does exist in the ideal (Prandtl-Tomlinson) problem of a point particle
sliding across a 1D periodic lattice potential. In that case $\eta >1$ implies
mechanical instability, generally leading to stick-slip, with $\eta =
\frac{2\pi^2 U_0}{K_\mathrm{p} a^2}$, where $U_0$ is the potential magnitude,
$a$ the lattice spacing, and $K_\mathrm{p}$ the pulling spring constant. Here
we show, supported by a repertoire of graphene flake/graphene sliding
simulations, that a similar stick-slip predictor $\eta_\mathrm{eff}$ can be
defined with the same form but suitably defined $U_\mathrm{eff}$,
$a_\mathrm{eff}$ and $K_\mathrm{eff}$. Remarkably, simulations show that
$a_\mathrm{eff} = a$ of the substrate remains an excellent approximation, while
$K_\mathrm{eff}$ is an effective stiffness parameter, combining equipment and
internal elasticity. Only the effective energy barrier $U_\mathrm{eff}$ needs
to be estimated in order to predict whether stick-slip sliding of a 2D island
or extended layer is expected or not. In a misaligned defect-free circular
graphene sliding island of contact area $A$, we show that $U_\mathrm{eff}$,
whose magnitude for a micrometer size diameter is of order 1 eV, scales as
$A^{1/4}$, thus increasing very gently with size. The PT-like parameter
$\eta_\mathrm{eff}$ is therefore proposed as a valuable tool in 2D layer
sliding.
