We present a new set of index-based measurements of [$alpha$/Fe] for a sample of 2093 galaxies in the SAMI Galaxy Survey. Following earlier work, we fit a global relation between [$alpha$/Fe] and the galaxy velocity dispersion $sigma$ for red sequence galaxies, [$alpha$/Fe]=(0.378$pm$0.009)log($sigma$/100)+(0.155$pm$0.003). We observe a correlation between the residuals and the local environmental surface density, whereas no such relation exists for blue cloud galaxies. In the full sample, we find that elliptical galaxies in high-density environments are $alpha$-enhanced by up to 0.057$pm$0.014 dex at velocity dispersions $sigma$<100 km/s, compared with those in low-density environments. This $alpha$-enhancement is morphology-dependent, with the offset decreasing along the Hubble sequence towards spirals, which have an offset of 0.019$pm$0.014 dex. At low velocity dispersion and controlling for morphology, we estimate that star formation in high-density environments is truncated $sim1$ Gyr earlier than in low-density environments. For elliptical galaxies only, we find support for a parabolic relationship between [$alpha$/Fe] and $sigma$, with an environmental $alpha$-enhancement of at least 0.03 dex. This suggests strong contributions from both environment and mass-based quenching mechanisms. However, there is no evidence for this behaviour in later morphological types.
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