  We study a phenomenological class of models where dark matter converts to
dark radiation in the low redshift epoch. This class of models, dubbed DMDR,
characterizes the evolution of comoving dark matter density with two extra
parameters, and may be able to help alleviate the observed discrepancies
between early- and late-time probes of the universe. We investigate how the
conversion affects key cosmological observables such as the CMB temperature and
matter power spectra. Combining 3x2pt data from Year 1 of the Dark Energy
Survey, {\it Planck}-2018 CMB temperature and polarization data, supernovae
(SN) Type Ia data from Pantheon, and baryon acoustic oscillation (BAO) data
from BOSS DR12, MGS and 6dFGS, we place new constraints on the amount of dark
matter that has converted to dark radiation and the rate of this conversion.
The fraction of the dark matter that has converted since the beginning of the
universe in units of the current amount of dark matter, $\zeta$, is constrained
at 68\% confidence level to be $<0.32$ for DES-Y1 3x2pt data, $<0.030$ for
CMB+SN+BAO data, and $<0.037$ for the combined dataset. The probability that
the DES and CMB+SN+BAO datasets are concordant increases from 4\% for the
$\Lambda$CDM model to 8\% (less tension) for DMDR. The tension in $S_8 =
\sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ between DES-Y1 3x2pt and CMB+SN+BAO is
slightly reduced from $2.3\sigma$ to $1.9\sigma$. We find no reduction in the
Hubble tension when the combined data is compared to distance-ladder
measurements in the DMDR model. The maximum-posterior goodness-of-fit
statistics of DMDR and $\Lambda$CDM model are comparable, indicating no
preference for the DMDR cosmology over $\Lambda$CDM.
