**3. Results and Discussion**

## *3.1. True Stress–Strain Curves*

Before the stress–strain curves are presented, the initial microstructures are shown in Figure 1. It is shown that all three alloys demonstrated large grains with casting dendrites inside. The grain size is very close for the alloy with a Zn/Mg ratio of 6.3 (as shown in Figure 1a) and a Zn/Mg ratio of 8.3 (as shown in Figure 1b). The grain size for the alloy with a Zn/Mg ratio of 6.3 is relatively more prominent than the other two alloys. The measured average grain sizes are 200 ± 35 μm, 156 ± 28 μm, 175 ± 40 μm, respectively. However, this is not conclusive as the as-cast microstructure varies from place to place. It is also noticed that some eutectic phases can be observed. This could be due to the high alloying content for the studied alloys.

**Figure 1.** The initial microstructure of the studied alloy with (**a**) Zn/Mg ratio of 6.3, (**b**) Zn/Mg ratio of 8.3, and (**c**) Zn/Mg ratio of 10.8.

There are five different temperature conditions, four different strain rates, and three different alloys. In total, 60 curves need to be present. For the readers' convenience, the true stress–strain curves for the alloy with Zn/Mg = 6.3 were chosen to demonstrate the data process routine, while the results of other alloys are calculated using the same methodology.

Figure 2 shows the true stress–strain curves during the hot-compression testing of alloy AA7003 with a Zn/Mg ratio of 6.3 under the strain rate condition of (a) 0.01 s−1, (b) 0.1 s<sup>−</sup>1, (c) 1 s−1, and (d) 10 s−<sup>1</sup> for different temperatures. The true stress–strain curves need to be corrected as the friction could either leading to inhomogeneous deformation or temperature rising. As a result, the deformed samples start to form a barrel shape. The

detailed friction correction method and temperature correction method can be found from Ebrahimi [9] and Z-P Wan et al. [20]. The authors here use the Ebrahimi method to correct the stress–strain curves; the basic equations are:

$$\frac{P\_{\rm avc}}{\sigma} = 8b \frac{R}{H} \left\{ \left[ \frac{1}{12} + \left( \frac{H}{R} \right)^2 \frac{1}{b^2} \right]^{3/2} - \left( \frac{H}{R} \right)^3 \frac{1}{b^3} - \frac{m}{24\sqrt{3}} \frac{\exp\left(-b/2\right)}{\exp\left(-b/2\right) - 1} \right\} \tag{1}$$

$$b = \frac{4m/\sqrt{3}}{(R/H) + \left(2m/3\sqrt{3}\right)}\tag{2}$$

$$m = \frac{(R/H)b}{\left(4/\sqrt{3}\right) - \left(2b/3\sqrt{3}\right)}\tag{3}$$

where *m* is the constant friction factor in the compression test, *σ* is the corrected true stress, Pave is the uncorrected external pressure applied to specimens in compression (the measured stress), *b* is the barrel parameter, and *R* and *H* are the radius and height of samples during compression. Temperature correction was also carried out so the raw data and corrected data are shown in Figure 2. It is shown in Figure 2a that, for a given temperature condition, the true stress values initially increase rapidly with increasing true strain values. It reaches its maximum values after a small number of strain values and remains constant for the rest of the strain values before it descends to tremendous strain values. Comparing stress values at different temperatures demonstrates that the alloy is more resistant to deformation at lower temperatures. This trend is generally observed in other strain rate conditions, as shown in Figure 2b–d. When comparing different strain rate conditions for a given temperature, the true stress increases with increasing strain rate conditions (as shown in the same color in different figures). It is also interesting to find out that the true stress is relatively stable at low-strain-rate conditions (as shown in Figure 2a,b). The strain–stress curves become more fluctuated at relatively high-strain-rate conditions (as shown in Figure 2c,d). Moreover, the stress curves exhibit a significant drop at high-strain-rate conditions. This could be an indication of the instability of the studied alloys.

**Figure 2.** *Cont*.

**Figure 2.** Raw and corrected (friction and temperature) stress vs. true strain curves of alloy AA7003 with Zn/Mg ratio of 6.3 during hot-compression testing at different strain rates for different temperatures. (**a**) strain rate of 0.01 s<sup>−</sup>1, (**b**) strain rate of 0.1 s<sup>−</sup>1, (**c**) strain rate of 1 s−<sup>1</sup> and (**d**) strain rate of 10 s<sup>−</sup>1.

Table 2 summarizes the detailed flow stress values (in MPa) of alloy with a Zn/Mg ratio of 6.3 at different temperatures and strain rates for various strains.


**Table 2.** Flow stress values (in MPa) of alloy with Zn/Mg ratio of 6.3 at different temperatures and strain rates for various strains.
