  We present a study of a sample of 254 clusters from the SDSS-DR7 Yang Catalog
and an auxiliary sample of field galaxies to perform a detailed investigation
on how galaxy quenching depends on both environment and galaxy stellar mass.
Our samples are restricted to 0.03$\leq$z$\leq$0.1 and we only consider
clusters with $\rm log(M_{halo}/M_{\odot}) \geq 14$. Comparing properties of
field and cluster galaxies in the Blue Cloud, Green Valley and Red Sequence, we
find evidence that field galaxies in the red sequence hosted star formation
events $\rm 2.1 \pm 0.7$ Gyr ago, on average, more recently than galaxies in
cluster environments. Dissecting the star formation rate vs stellar mass
diagram we show how morphology rapidly changes after reaching the green valley
region, while the star formation rate keeps decreasing. In addition, we use the
relation between location in the projected phase space and infall time to
explore the time delay between morphological and specific Star Formation Rate
variations. We estimate that the transition from late to early-type morphology
happens in $\rm \Delta t_{inf} \sim$1 Gyr, whereas the quenching of star
formation takes $\sim$3 Gyr. The time-scale we estimate for morphological
transitions is similar to the expected for the delayed-then-rapid quenching
model. Therefore, we suggest that the delay phase is characterized mostly by
morphological transition, which then contributes morphological quenching as an
additional ingredient in galaxy evolution.
