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In previous papers of this series, we developed a new algorithm for modelingthe formation of star clusters in galaxy formation simulations. Here weinvestigate how dissolution of bound star clusters affects the shape of thecluster mass function and the metallicity distribution of surviving clusters.Cluster evolution includes the loss of stars that become unbound due to tidaldisruption as well as mass-loss due to stellar evolution. We calculate thetidal tensor along cluster trajectories and use it to estimate theinstantaneous mass-loss rate. The typical tidal tensor exhibits largevariations on a time-scale of $\sim100$~Myr, with maximum eigenvalue of$10^7$~Gyr$^{-2}$, and median value of $10^4$~Gyr$^{-2}$ for the first Gyrafter cluster formation. As a result of dynamical disruption, at the finalavailable output of our simulations at redshift $z\approx1.5$, the cluster massfunction has an approximately log-normal shape peaked at $\sim10^{4.3}M_\odot$.Extrapolation of the disruption to $z=0$ results in too many low-mass clusterscompared to the observed Galactic globular clusters (GCs). Over 70\% of GCcandidates are completely disrupted before the present; only 10\% of the totalGC candidate mass remains in surviving clusters. The total mass of survivingclusters at $z=0$ varies from run to run in the range $(2-6)\times10^7M_\odot$,consistent with the observed mass of GC systems in Milky Way-sized galaxies.The metallicity distributions of all massive star clusters and of the survivingGCs have similar shapes but different normalization because of clusterdisruption. The model produces a larger fraction of very metal-poor clustersthan observed. A robust prediction of the model is the age-metallicityrelation, in which metal-rich clusters are systematically younger thanmetal-poor clusters by up to 3~Gyr.

Star cluster formation in cosmological simulations. III. Dynamical and chemical evolution