On the significance to use dislocation-density-related constitutive equations to correlate strain hardening with microstructure of metallic alloys: the case of conventional and austempered ductile irons

In order to highlight the importance of selecting the proper constitutive equation of plastic flow in metallic alloys, the strain hardening behaviours of conventional (DI) and austempered ductile irons (ADI) with similar hardness were investigated as study-case. The empirical Hollomon equation and the dislocation-density-related Voce equation were compared. Hollomon equation showed strong limitations in describing the different strain hardening behaviours of DIs and ADIs. Conversely, Voce equation approximated properly all the flow curves, and Voce parameters could describe successfully the different strain hardening behaviours of the two groups of alloys. Voce parameters, rationalised by the Kocks-Mecking-Estrin physical concepts, could also give an insight to the micro-mechanisms that underlie strain hardening, like dislocation density multiplication, dynamic recovery and microstructure features that affect these micro-mechanisms during straining. Through the analysis of Voce parameters it could be highlighted that the DIs strain hardening behaviour was mainly caused by the fine pearlitic structure, consisting of ferritic lamellae with sub-micrometric widths. The improvement of austempered alloys in strength and ductility was related to a significantly lower propensity of ADIs to recover dynamically, which was mainly attributed to the dual phase structure of these alloys. Furthermore, the strain hardening analysis through Voce formalism could identify in ADIs a critical condition of strain hardening rate to be investigated to improve further their ductility, which could not be found with Hollomon equation. The dislocation-density-related Voce equation describes properly the strain hardening behaviour of metallic alloys and give certain correlations between strain hardening behaviour and microstructure.