Metals and dust content across the galaxies M 101 and NGC 628

We present a spatially resolved study of the relation between dust and metallicity in the nearby spiral galaxies M 101 (NGC 5457) and NGC 628 (M 74). We explore the relation between the chemical abundances of their gas and stars with their dust content and their chemical evolution. The empirical spatially resolved oxygen effective yield and the gas-to-dust mass ratio (GDR) across both disc galaxies are derived, sampling 1 dex in oxygen abundance. We find that the metal budget of the NGC 628 disc and most of the M 101 disc appears consistent with the predictions of the simple model of chemical evolution for an oxygen yield between half and one solar, whereas the outermost region (R ≥ 0.8 R_{25}) of M 101 presents deviations suggesting the presence of gas flows. The GDR-metallicity relation shows a two slopes behaviour, with a break at 12 + log(O/H) ≈ 8.4, a critical metallicity predicted by theoretical dust models when stardust production equals grain growth. A relation between GDR and the fraction of molecular to total gas, Σ _{H<SUB>2</SUB>}/Σ _{gas} is also found. We suggest an empirical relationship between GDR and the combination of 12 + log(O/H), for metallicity, and Σ _{H<SUB>2</SUB>}/Σ _{gas}, a proxy for the molecular clouds fraction. The GDR is closely related with metallicity at low abundance and with Σ _{H<SUB>2</SUB>}/Σ _{gas} for higher metallicities suggesting interstellar medium dust growth. The ratio Σ _{dust}/Σ _{star} correlates well with 12 + log(O/H) and strongly with log(N/O) in both galaxies. For abundances below the critical one, the `stardust' production gives us a constant value suggesting a stellar dust yield similar to the oxygen yield.