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The effects of T4, T5, and T6 treatment on the microstructure and mechanical properties of the extruded Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr (wt.%) alloy with a relatively low RE content (7.5 wt.%) were investigated. T4 treatment at 450–500 °C induces a gradual grain growth of α-Mg but an obvious transition of texture component from ⊥ED to ∥ED. Interdendritic LPSO phases are highly stable against annealing while intragranular ones experience dissolution and re-precipitation. After peak-ageing at 200 °C, the elongation of as-extruded and T4 samples is just slightly reduced or even increased due to the weak ageing hardening response. T5 sample exhibits an attractive combination of strength and ductility, with a tensile yield strength (TYS) of 303 MPa and elongation of 20.0%. The Hall–Petch relation for the alloys with or without ageing treatment has been estimated. Grain boundary strengthening rather than precipitation strengthening has the dominant contribution to TYS, and a modified equation is developed to predict grain boundary strengthening values for Mg-Gd-Y-Zn-Zr alloys which contain different Schmid factors for basal slip.

Hall–Petch slope (k), an important parameter in Hall–Petch relation, describes the efficiency of strengthening effect by grain boundaries. Previously, a highly texture dependent k for Mg alloys is frequently reported, but, in the present study, we report a weak texture dependence of k in a rare-earth containing Mg-2Zn-1Gd plate with two peaks of (0002) poles inclining approximately ± 30° away from the ND toward the TD. Although there is a strong mechanical anisotropy between tension along the TD and RD, the k for TD-tension (280 MPa μm1/2) is quite similar to that for RD-tension (276 MPa μm1/2). Here, RD, TD and ND refer to the rolling direction, transverse direction and normal direction of the plate, respectively. The weak texture dependence of k is well predicted by the compound use of the activation stress difference between neighboring grains (ΔStress) and the geometric compatibility factor ( m ′ ). By analyzing how the texture affects the values for ΔStress and m ′ , the mechanism for this texture independence of k is ascribed to the activation of a high fraction of additional deformation mode, besides the predominant one for both RD-tension and TD-tension, namely, prismatic slip accompanied by a high fraction of basal slip for RD-tension and basal slip accompanied by a high fraction of prismatic slip for TD-tension. This will lead to multiple deformation transfer modes and, consequently, the effect of texture on the ease of deformation transfer across grain boundaries is weakened. As a result, there is a similar k for TD-tension and RD-tension.

To have an insight into the occurrence of inverse Hall-Petch relationship in ultrafine-grained (UFG) aluminum alloys produced by severe plastic deformation (SPD), ultra-SPD (i.e. inducing several ten thousand shear strains via high-pressure torsion, HPT) followed by aging is applied to an Al-La-Ce alloy. Average nanograin sizes of 40 and 80 nm are successfully achieved together with strain-induced Lomer-Cottrell dislocation lock formation and aging-induced semi-coherent Al11(La,Ce)3 precipitation. Analysis of hardening mechanisms in this alloy compared to SPD-processed pure aluminum with micrometer grain sizes, SPD-processed Al-based alloys with submicrometer grain sizes and ultra-SPD-processed Al-Ca alloy with nanograin sizes reveals the presence of two breaks in the Hall-Petch relationship. First, a positive up-break appears when the grain sizes decrease from micrometer to submicrometer which is due to extra hardening by solute-dislocation interactions. Second, a negative down-break and softening occur by decreasing the grain sizes from submicrometer to nanometer which is caused by weakening the dislocation hardening mechanism with minor contribution of the inverse Hall-Petch mechanism. Detailed analyses confirm that nanograin formation is not necessarily a solution for extra hardening of Al-based alloys and other accompanying strategies such as grain-boundary segregation and precipitation are required to overcome such a down-break and softening.

The mechanical properties and the localized plasticity characteristics of polycrystalline aluminum are compared to explain the nature of the Hall–Petch relation for the deformation of a polycrystalline metal in two grain size ranges. The Hall–Petch relation for the flow stress is shown to be related to an elastoplastic deformation invariant, which unites the characteristics of elastic deformation and localized plastic flow.

A model is developed to calculate the Hall–Petch relation parameters for the submicrocrystalline (SMC) metals fabricated by severe plastic deformation (SPD) methods. The model is based on the assumption that the flow stress in SMC metals includes both conventional contributions (caused by lattice dislocations, impurity atoms, etc.) and a contribution related to the long-range internal stress fields created by the SPD-induced defects distributed over grain boundaries. Equations are derived to calculate the Hall–Petch relation parameters as functions of the strain and the strain rate. The results calculated by the derived equations agree well with the experimental data. The low resistance of grain boundaries to the motion of grain boundaries in SMC materials (see part I of this work) is found to be related to a violation of the Hall–Petch relation in SMC metals.