The ALMA Frontier Fields Survey. VI. Lensing-corrected 1.1mm number
  counts in Abell 2744, MACSJ0416.1-2403, MACSJ1149.5+2223, Abell 370 and Abell
  S1063
  [abridged] Probing the faint end of the number counts at mm wavelengths is
important to identify the origin of the extragalactic background light in this
regime. Aided by strong gravitational lensing, ALMA observations towards
massive galaxy clusters have opened a window to disentangle this origin,
allowing to resolve sub-mJy dusty star-forming galaxies. We aim to derive
number counts at 1.1 mm down to flux densities fainter than 0.1 mJy, based on
ALMA observations towards five Hubble Frontier Fields (FF) galaxy clusters,
following a statistical approach to correct for lensing effects. We created a
source catalog that includes 29 ALMA 1.1 mm continuum detections down to a
4.5sigma significance. We derived source intrinsic flux densities using public
lensing models. We folded the uncertainties in both magnifications and source
redshifts into the number counts through Monte Carlo simulations. We derive
cumulative number counts over two orders of magnitude down to 0.01 mJy after
correction for lensing effects. Cosmic variance estimates are all exceeded by
uncertainties in our median combined cumulative counts that come from both our
Monte Carlo simulations and Poisson statistics. Our number counts are
consistent to 1sigma with most of recent ALMA estimates and galaxy evolution
models. However, below 0.1 mJy, they are lower by 0.4 dex compared to all deep
ALMA studies but ASPECS-LP. Importantly, the flattening found for our
cumulative counts extends further to 0.01 mJy. Our results bring further
support in line of the flattening of the number counts reported previously by
us and ASPECS-LP, which has been interpreted by a recent galaxy evolution model
as a measurement of the "knee" of the infrared luminosity function at high
redshift. Our estimates of the contribution to the EBL in the FFs suggest that
we may be resolving most of the EBL at 1.1mm down to 0.01 mJy.
