*3.4. Influence of Al2Ca Size and Distribution on Mechanical Properties*

Based on above tensile results, it can be confirmed that multi-pass ECAP is beneficial for improving the mechanical properties of an Al2Ca-containing alloy. Considering the microstructural evolutions, the improved strength of ECAP alloys could be mainly ascribed to three factors, i.e., refined DRX grains, dynamically precipitated Mg17Al12 precipitates, and dispersed Al2Ca particles. To quantitatively describe the contributions of various strengthening factors, Table 1 lists the characteristic parameters of DRX grains and second phase particles.


**Table 1.** Microstructural characteristics of ECAP-ed alloys.

The contribution of fine grain strengthening could be estimated from the Hall-Petch equation:

$$
\sigma\_y = \sigma\_0 + kd^{-0.5},
\tag{1}
$$

where σ<sup>y</sup> is yield strength, σ<sup>0</sup> is material constants, *k* is Hall-Petch slope and *d* is grain size. The value of *k* was employed as 170 MPa·μm1/<sup>2</sup> on the basis of average grains in this work [40]. Accordingly, the contribution of grain refinement strengthening on tensile yield strength could be estimated to be 55 MPa, 97 MPa and 105 MPa for 623 K-4p, 623 K-12p, and 573 K-12p alloys, respectively.

In case of Mg17Al12 nano-particles precipitated at grain internal, they could pin dislocation movement and strengthen the alloy by Orowan strengthening mechanism [41]. The increment of YS associated with Mg17Al12 particles have already been given in an early report [41], and the equation is shown in Equation (2).

$$
\Delta\sigma\_{\text{Orouau}} = \beta \frac{0.4\mu\_m b}{\pi (\text{d}\,\sqrt{\pi/4f\_v} - 1)} \frac{\ln(d/b)}{\sqrt{1 - \upsilon\_m}}.\tag{2}
$$

where β is constant (1.25), μ<sup>m</sup> is shear modulus (16.5 GPa), b is Burgers vector (0.32 nm), *d* is the average size of Mg17Al12, *fv* is the volume fraction of Mg17Al12, and ν<sup>m</sup> is Poisson ratio (0.35). Moreover, is should be noticed from above TEM observations that the nano-sized Mg17Al12 particles were most dynamically precipitated in the un-DRX grains, and they were seldom seen in DRX grains, which has also been reported in other Mg-Al-Ca-Mn alloys [19]. Therefore, we assumed that the Orowan strengthening mechanism caused by Mg17Al12 precipitates is only activated in un-DRX grains, and it could be calculated by the following equation:

$$
\Delta \sigma\_{Mgl17A112} = (1 - f\_{\text{DRX}}) \Delta \sigma\_{\text{Ovvuum}} \tag{3}
$$

where *fDRX* is the volume fraction of DRX grains showed in Figure 6.

As long as the strengthening caused by grain refinement and Mg17Al12 precipitates was estimated, the rest of strengthening effect should be caused by the Al2Ca second phase strengthening, and it is calculated by Equation (4),

$$
\Delta\sigma\_{Al\text{\\$}\text{Ca}} = \sigma\_{\text{YS}} - \sigma\_{\text{Cast}} - \sigma\_{\text{Hall}-\text{Petch}} - \sigma\_{\text{Mg}17\text{All12}} \tag{4}
$$

where σYS is the tested tensile yield strength of ECAP alloys, and σCast is the tested tensile yield strength of cast alloy.

Figure 14a displays the quantitative contributions of grain refinement, dynamic precipitated Mg17Al12 precipitates and dispersed Al2Ca second phase particles, to TYS values of three ECAP alloys. It is apparent that for 623 K-4P and 12p alloys, fine grain strengthening plays a more important role than other two strengthening factors. With the dispersion of Al2Ca phase in 573 K-12p alloy, the strengthening contribution of the Al2Ca phase exceeds the other two factors. To intuitively describe

the strengthening effect of a dispersed Al2Ca second phase, Figure 14b shows the relationship between ΔσAl2Ca and the distance of ribbonlike Al2Ca arm spacing [42]. It is obvious that with the decrease of Al2Ca arm spacing, the contribution of the Al2Ca phase increases remarkably. Therefore, to further improve the mechanical properties of Al2Ca containing Mg-Al-Ca-Mn alloys, additional effort should be focused on the refining and dispersion of Al2Ca second phase particles.

**Figure 14.** (**a**) The contributions of various strengthening factors to tensile yield strength of ECAP alloys. (**b**) The relationship between the ribbonlike Al2Ca arm spacing and the contribution of Al2Ca particles to tensile yield strength of ECAP alloys.
