A multi-mechanism constitutive model is proposed in this paper to better describe the effect of the local hardening behavior of the interface layer on the mechanical heterogeneity of dual-phase (DP) steel. The constitutive equations considering the geometrically necessary dislocations (GNDs) and back stress at grain level and sample level were established. Based on the finite element simulation results, the influences of local hardening and microstructure characteristics on the strain–stress evolution, statistical storage dislocations, GNDs, and back stress of DP steel were studied and discussed. Due to the local hardening effect, the ferrite phase was treated as an inhomogeneous matrix reinforced by some small islands of martensite in the simulation. The simulation results show that the thickness of the interface layer has a significant effect on the macroscopic hardening property of DP steel, while the number of interface layers has little effect. Meanwhile, the GNDs and back stress at the grain level also have little effect on the strengthening of DP steel. The contribution of GNDs at the sample level to the flow stress is about 47%.

Carbon nanotube-reinforced aluminium normally considered to be composed of Carbon nanotube (CNT) free grain interior (GI) and CNT containing grain boundary affected zone (GBAZ). Research works showed that the property of GI varies with the distance from the boundary. To better understand the influence of this mechanical heterogeneity, we introduced a transition zone (TZ) to emphasise the mechanical heterogeneity of the GI. A dislocation-based plastic strain constitutive model was used to analyse the mechanical response, and the simulation results fit well with the experimental result. Moreover, the TZ thickness with a large simulation influence was found, and its strengthening mechanism, the influence of TZ thickness on the macroscopic mechanical response, geometrically necessary dislocation distribution were discussed in this study.