*Article* **First-Principle Investigation into Mechanical Properties of Al6Mg1Zr1 under Uniaxial Tension Strain on the Basis of Density Functional Theory**

**Lihua Zhang 1,†, Jijun Li 2,\*,†, Jing Zhang 2, Yanjie Liu 2,\* and Lin Lin 3,\***


**Abstract:** The influences of uniaxial tension strain in the *x* direction (*ε*x) on the mechanical stability, stress–strain relations, elastic properties, hardness, ductility, and elastic anisotropy of Al6Mg1Zr1 compound were studied by performing first-principle calculations on the basis of density functional theory. It was found that Al6Mg1Zr1 compound is mechanically stable in the range of strain *ε*<sup>x</sup> from 0 to 6%. As the strain *ε*x increased from 0 to 6%, the stress in the *x* direction (*σ*x) first grew linearly and then followed a nonlinear trend, while the stresses in the *y* and *z* directions (*σ*y and *σ*z) showed a linearly, increasing trend all the way. The bulk modulus *B*, shear modulus *G*, and Young's modulus *E* all dropped as the strain *ε*<sup>x</sup> increased from 0 to 6%. The Poisson ratio *μ* of Al6Mg1Zr1 compound was nearly unchanged when the strain *ε*<sup>x</sup> was less than 3%, but then it grew quickly. Vickers hardness *H*<sup>V</sup> of Al6Mg1Zr1 compound dropped gradually as the strain *ε*<sup>x</sup> increased from 0 to 6%. The Al6Mg1Zr1 compound was brittle when the *ε*x was less than 4%, but it presented ductility when the strain *ε*x was more than 4%. As the strain *ε*x increased from 0 to 6%, the compression anisotropy percentage (*A*B) grew and its slope became larger when the strain *ε*<sup>x</sup> was more than 4%, while both the shear anisotropy percentage (*A*G) and the universal anisotropy index (*A*U) first dropped slowly and then grew quickly. These results demonstrate that imposing appropriate uniaxial tension strain can affect and regulate the mechanical properties of Al6Mg1Zr1 compound.

**Keywords:** Al6Mg1Zr1; mechanical properties; uniaxial tension strain; first principles

#### **1. Introduction**

From an industrial point of view, the aluminum–magnesium (Al-Mg) based alloys and intermetallic compounds are considered as very promising engineering materials, and have been widely used in aviation, aerospace, shipbuilding, rail transportation, and automotive industries owing to their high strength-to-weight ratio, good formability, excellent corrosion resistance, and good weldability [1–4]. However, Al-Mg based materials only have a low to medium strength, which severely restricts their application in industry [5–7]. With the rapid development of industrial technology, a further improvement of the comprehensive performance of Al-Mg based materials is required. An effective approach to improve the performance of the Al-Mg based materials is by adding the appropriate elements [8–12]. The rare-earth metal scandium (Sc) has proved to be the most effective element to improve the performance of the Al-Mg based materials [13–16]. However, the application of Sc is greatly limited in industry due to its high cost. Therefore, it is of great significance to search for another lower-cost additional element to replace Sc. The transition metal zirconium (Zr) is of much lower cost (its price is only about 1/100 of that of Sc), and can serve a similar strengthening function to Sc in Al-Mg based materials [17–21].

**Citation:** Zhang, L.; Li, J.; Zhang, J.; Liu, Y.; Lin, L. First-Principle Investigation into Mechanical Properties of Al6Mg1Zr1 under Uniaxial Tension Strain on the Basis of Density Functional Theory. *Metals* **2023**, *13*, 1569. https://doi.org/ 10.3390/met13091569

Academic Editors: Alain Pasturel and Varvara Romanova

Received: 5 July 2023 Revised: 14 August 2023 Accepted: 29 August 2023 Published: 7 September 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In recent years, it was reported that the functional properties of materials were regulated by imposing strain [22–25]. Fu, et al. quantitatively analyzed the effects of heterogeneous plastic strain on hydrogen-induced cracking of twinning-induced plasticity (TWIP) steel by electron backscattered diffraction (EBSD) technology. According to a quantitative calculation of EBSD crystallographic data, the larger the geometrically necessary dislocation density (ρGND), the greater is the heterogeneous strain. It was evident from the overall statistical analyses that hydrogen-induced crack initiation depends on interactions between heterogeneous strain and hydrogen atoms generated by local grain orientation deviation (deviation from ideal) and gradient (misorientation). The larger the ρGND, the easier it is to cause local enrichment of hydrogen atoms, which in turn leads to hydrogen-induced cracking in TWIP steel [26]. Liang et al. investigated the strain-induced strengthening in superconducting β-Mo2C through high pressure and high temperature. It was found that strain-induced high-density dislocations and low-angle grain boundaries were introduced and enabled the synthesized β-Mo2C ceramics to exhibit surprising mechanical properties [27]. Du, et al. studied the Poisson ratio of in-plane pristine armchair and zigzag graphene under uniaxial tensile loading by molecular dynamics simulations, which indicated that the Poisson ratio strongly depends on the tensile strain. At the critical strain, the Poisson ratio will transform from positive to negative, and the critical strain of the zigzag is far less than that of armchair [28]. Rasidul Islam, et al. investigated the strain-induced mechanical properties of inorganic halide perovskite CsGeBr3 through first-principles based on density functional theory. It was found that the bulk modulus, shear modulus, and Young's modulus all increased with increasing compressive strain but decreased with increasing tensile strain. The brittleness of CsGeBr3 increased with compressive strain, whereas CsGeBr3 offered significant ductility with more than 2% tensile strain [29]. Tan et al. investigated the mechanical behavior of AlSi2Sc2 under uniaxial tensile strain by performing first-principle calculations based on density functional theory. It was found that the estimated elastic moduli of AlSi2Sc2 decreased with increasing uniaxial tensile strain, but the brittleness of AlSi2Sc2 did not change when strain was applied [30]. However, there has been little investigation into the effect of strain on the mechanical properties of Al-Mg-Zr compounds based on the density functional theory.

In the present study, the first principle calculations based on density functional theory were used to investigate the elastic properties, hardness, ductility, and elastic anisotropy of Al6Mg1Zr1 compound at different uniaxial tensile strains. The current research will contribute to a better understanding of the modulation of strain on the mechanical properties of Al-Mg based alloys and compounds.

#### **2. Computational Methods**

In this study, the structural model of Al6Mg1Zr1 supercell viewed along the c axis is shown in Figure 1. Grey, orange, and green spheres represent Al, Mg, and Zr atoms, respectively. The *x*, *y*, and *z* direction are parallel to the a, b, and c axis, respectively. Our calculations of Al6Mg1Zr1 were carried out by the Cambridge Serial Total Energy Package (CASTEP) code, using the plane-wave pseudopotential method based on density functional theory (DFT) [31–33]. For the exchange and correlation terms in the electron–electron interaction, the generalized gradient approximation (GGA) in the scheme of Perdew–Burke– Ernzerhof (PBE) was used [34]. The valence wave functions were expanded in a plane-wave basis set up to an energy cutoff of 600 eV. For the *k* point sampling, a 3 × 6 × 6 Monkhorst– Pack mesh in the Brillouin zone was used. The other parameters used default settings of ultra-fine accuracy.

**Figure 1.** Structural model of Al6Mg1Zr1 supercell.

#### **3. Results and Discussion**

#### *3.1. Mechanical Stability*

Elastic stiffness constants *C*ij are very important physical quantities used to express the elasticity of a solid material in engineering applications. In this work, the elastic stiffness constants were calculated using the stress–strain approach based on Hook's law by imposing uniaxial tension strain in the *x* direction (*ε*x). The elastic stiffness constants *C*ij of Al6Mg1Zr1 compound at different *ε*<sup>x</sup> are presented in Table 1. It can be found that there are nine independent effective constants (*C*11, *C*12, *C*13, *C*22, *C*23, *C*33, *C*44, *C*55, and *C*66) in the elastic stiffness matrix for Al6Mg1Zr1. Therefore, Al6Mg1Zr1 is determined to be of orthorhombic structure [35].

**Table 1.** Calculated values of the elastic stiffness constants *C*ij (in GPa) of Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).


Based on Born–Huang's dynamical theory of crystal lattices, the mechanical stability standards for orthorhombic crystals must meet the following requirements [36]:

$$\begin{cases} \mathsf{C}\_{ii} > 0\\ \mathsf{C}\_{11} + \mathsf{C}\_{22} - 2\mathsf{C}\_{12} > 0\\ \mathsf{C}\_{11} + \mathsf{C}\_{33} - 2\mathsf{C}\_{13} > 0\\ \mathsf{C}\_{22} + \mathsf{C}\_{33} - 2\mathsf{C}\_{23} > 0\\ \mathsf{C}\_{11} + \mathsf{C}\_{22} + \mathsf{C}\_{33} + 2(\mathsf{C}\_{12} + \mathsf{C}\_{13} + \mathsf{C}\_{23}) > 0 \end{cases} \tag{1}$$

It was noted that the elastic constants *C*ij of the Al6Mg1Zr1 fulfilled well the mechanical stability standards in the range of strain *ε*<sup>x</sup> from 0 to 6%, while they could not meet the standards when the *ε*<sup>x</sup> was more than 6%. Therefore, the orthorhombic of Al6Mg1Zr1 is mechanically stable in the range of strain *ε*<sup>x</sup> from 0 to 6%. In this study, we are only concerned with the mechanical properties of Al6Mg1Zr1 in the range of strain *ε*<sup>x</sup> from 0 to 6%.

#### *3.2. Stress–Strain Relations*

The stresses in the principal axis direction (*σ*x, *σ*y, and *σ*z) of Al6Mg1Zr1 at different uniaxial tension strains in the *x* direction (*ε*x) were calculated based on Hook's law, and the calculated values are presented in Table 2 and Figure 2.

**Table 2.** Calculated values of stresses in principal axis directions (*σ*x, *σ*y, and *σ*z) of Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).


**Figure 2.** Stress–strain relations of Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).

It can be seen that, as the strain *ε*<sup>x</sup> increased from 0 to 6%, the stress in the *x* direction (i.e., *σ*x) gradually grew to 7.7129 GPa. The *σ*x-*ε*<sup>x</sup> curve of Al6Mg1Zr1 had a linear formation in the range of strain *ε*<sup>x</sup> from 0 to 3%, and then followed a nonlinear trend in the range of strain *ε*<sup>x</sup> from 3% to 6%. It is indicated that the deformation of Al6Mg1Zr1 was elastic in the range of *ε*<sup>x</sup> from 0 to 3%, after which plastic deformation occurred. The stresses in the *y* and *z* directions (*σ*<sup>y</sup> and *σ*z) were almost equal and had good linear relation with the uniaxial tension strain in the range of *ε*<sup>x</sup> from 0 to 6%. On the whole, the stress *σ*<sup>x</sup> was much higher than *σ*<sup>y</sup> and *σ*<sup>z</sup> due to the uniaxial tension loading being in the *x* direction.

#### *3.3. Elastic Properties of Polycrystalline Materials*

In many cases, polycrystalline materials have advantages in practical applications compared to single crystal materials [37]. Therefore, it is more meaningful to examine the elastic properties of polycrystalline materials. The elastic properties of polycrystalline materials can be characterized by the bulk modulus *B*, shear modulus *G*, Young's modulus *E,* and Poisson ratio *μ*.

There are two approximation methods to obtain polycrystalline elastic moduli, namely, the Voigt method and the Reuss method. The Voigt method provides the upper bound to the polycrystalline elastic moduli, and the Reuss method provides the lower bound to the polycrystalline elastic moduli. For different crystalline systems, the bulk modulus B and shear modulus G according to Voigt and Reuss approximations are given by the following equations [38]:

$$B\_V = \frac{\mathcal{C}\_{11} + \mathcal{C}\_{22} + \mathcal{C}\_{33} + 2(\mathcal{C}\_{12} + \mathcal{C}\_{13} + \mathcal{C}\_{23})}{9} \tag{2}$$

$$\mathbf{G}\_{\rm V} = \frac{\mathbf{C}\_{11} + \mathbf{C}\_{22} + \mathbf{C}\_{33} - \mathbf{C}\_{12} - \mathbf{C}\_{13} - \mathbf{C}\_{23}}{15} + \frac{\mathbf{C}\_{44} + \mathbf{C}\_{55} + \mathbf{C}\_{66}}{5} \tag{3}$$

$$B\_{\rm R} = \frac{1}{S\_{11} + S\_{22} + S\_{33} + 2(S\_{12} + S\_{13} + S\_{23})} \tag{4}$$

$$G\_{\rm R} = \frac{15}{4(S\_{11} + S\_{22} + S\_{33}) + 3(S\_{44} + S\_{55} + S\_{66}) - 4(S\_{12} + S\_{13} + S\_{23})} \tag{5}$$

where the subscripts V and R denote the Voigt and Reuss averages, *C*ij are the elastic stiffness constants, and *S*ij are the elastic compliance coefficients.

The arithmetic average of the Voigt and the Reuss bounds is referred to as the Voigt– Reuss Hill (VRH) average, and it is considered as the best estimate of the theoretical polycrystalline elastic moduli. The VRH averages of B and G are given as follows [38]:

$$B = \frac{B\_{\rm V} + B\_{\rm R}}{2} \tag{6}$$

$$G = \frac{G\_{\rm V} + G\_{\rm R}}{2} \tag{7}$$

The Young's modulus *E* and Poisson ratio *μ* of the polycrystalline material can be obtained from the bulk modulus *B* and shear modulus *G*, while the corresponding calculation formulas are as follows [38]:

$$E = \frac{9BG}{3B + G} \tag{8}$$

$$
\mu = \frac{3B - 2G}{6B + 2G} \tag{9}
$$

The Bulk modulus *B*, shear modulus *G*, Young's modulus *E* and Poisson ratio *μ* of polycrystalline Al6Mg1Zr1 at different uniaxial tension strains in the *x* direction (*ε*x) were calculated using the above formulas, and the calculated values are presented in Table 3 and Figure 3.

**Table 3.** Calculated values of the elastic moduli (*B*, *G*, and *E*) and Poisson ratios *μ* of polycrystalline Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).


**Figure 3.** Elastic moduli (*B*, *G*, and *E*) and Poisson ratio *μ* of Al6Mg1Zr1 at different uniaxial tension strains (*ε*x): (**a**) Bulk modulus *B* vs. strain *ε*x; (**b**) Shear modulus *G* vs. strain *ε*x; (**c**) Young's modulus *E* vs. strain *ε*x; (**d**) Poisson ratio *μ* vs. strain *ε*x.

The bulk modulus *B* is a measure of the resistance of a solid material to a volume change. Figure 3a presents the calculated bulk modulus *B* of Al6Mg1Zr1 at different strains *ε*x. It can be seen that, as the strain ε<sup>x</sup> increased from 0 to 6%, the bulk modulus *B* dropped from 82.93 GPa to 60.63 GPa. The bulk modulus *B* reduced by 26.9%, which showed its negative relation with the uniaxial tension strain for Al6Mg1Zr1. The Al6Mg1Zr1 alloy has the largest incompressibility at the unstrained state due to the largest *B* value, while it has the largest compressibility at the strain *ε*<sup>x</sup> of 6% due to the smallest *B* value.

The shear modulus *G* is defined as the ratio of shear stress to the shear strain, which characterizes the ability of a solid material to resist deformation under shear stress. The greater G corresponds to the stronger shear resistance of the solid material. Figure 3b presents the calculated values of shear modulus *G* of Al6Mg1Zr1 at different strains *ε*x. It can be seen that as the strain ε<sup>x</sup> increased from 0 to 6%, the shear modulus *G* dropped from 53.77 GPa to 22.88 GPa. The shear modulus G was reduced by 57.5%, which indicated that shear resistance is greatly influenced by the uniaxial tension strain. Al6Mg1Zr1 alloy has the smallest shear resistance at the strain *ε*<sup>x</sup> of 6% due to the smallest *G* value.

Young's modulus *E* is defined as the ratio of tensile stress and axial strain and serves as a measure of the stiffness of solid materials. Figure 3c presents the calculated values of Young's modulus *E* of Al6Mg1Zr1 at different strains *ε*x. It can be found that Young's modulus *E* dropped with increasing strain *ε*x. When the Al6Mg1Zr1 was unstrained, the Young's modulus *E* was 132.63 GPa. When the strain ε<sup>x</sup> reached 6%, Young's modulus *E* dropped to 60.96 GPa. Young's modulus *E* was reduced by 54.0%, showing its negative relation with uniaxial tension strain. The unstrained Al6Mg1Zr1 has the largest stiffness due to the largest *E* value, while Al6Mg1Zr1 alloy has the smallest stiffness at the strain *ε*<sup>x</sup> of 6% due to the smallest *E* value.

Figure 3d presents the calculated values of Poisson ratio *μ* of Al6Mg1Zr1 at different strains *ε*x. It can be found that when the strain *ε*<sup>x</sup> was less than 3%, the Poisson ratio *μ* remained nearly unchanged. When *ε*<sup>x</sup> was more than 3%, the Poisson ratio *μ* grew quickly with increasing strain *ε*x, showing its positive relation with uniaxial tension strain. Generally, when the Poisson ratio *μ* is between −1 and 0.5, the solid is relatively stable under shear deformation. From Figure 3d, it can be seen that the Poisson ratio *μ* of Al6Mg1Zr1 ranged from 0.23 to 0.33, which is between −1 and 0.5, indicating that Al6Mg1Zr1 is a stable linear elastic solid. Al6Mg1Zr1 has the maximum *μ* value at the strain *ε*<sup>x</sup> of 6%, indicating that Al6Mg1Zr1 has the highest toughness at the strain *ε*<sup>x</sup> of 6%.

By comparing Figures 3a–c and 3d, it can be found that with the strain ε<sup>x</sup> increasing from 0 to 6%, the elastic moduli (*B*, *G,* and *E*) monotonically decreased with the increasing strain εx, while the Poisson ratio *μ* was first nearly unchanged and then grew quickly. The variation trends of elastic moduli (*B*, *G,* and *E*) and Poisson ratio *μ* of Al6Mg1Zr1 alloy with the uniaxial tensile strain ε<sup>x</sup> are similar to that of AlSi2Sc2 [30].

#### *3.4. Hardness and Ductility*

Hardness is a measure of the resistance to localized deformation induced by either mechanical indentation or abrasion. In general, hardness is linked with the elastic and plastic properties of a material, and the shear modulus *G* is the more important parameter governing hardness than the bulk modulus *B*. There have been some semi-empirical models developed to predict the hardness of materials. Chen et al. [39] proposed a model to predict the Vickers hardness *H*<sup>V</sup> of polycrystalline materials and bulk metallic glasses based on the shear modulus *G* and the Pugh's modulus ratio *k* (*k* = *G*/*B*) as follows [39]:

$$H\_V = 1.887k^{1.171}G^{0.591} \tag{10}$$

The above formula has been successfully used to predict the hardness of many compounds.

The ductility or brittleness of a solid material can be estimated by the ratio of the bulk modulus *B* to the elastic shear modulus *G* (i.e., *B*/*G*). If the modulus ratio *B/G* is more than 1.75, the solid is classified as ductile material; otherwise, it is brittle [40,41].

Table 4 and Figure 4 present the calculated values of Vickers hardness *H*<sup>v</sup> and the modulus ratio *B*/*G* of Al6Mg1Zr1 at different uniaxial tension strains εx.


**Table 4.** Calculated values of the Vickers hardness *H*<sup>V</sup> and the modulus ratio *B*/*G* of Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).

From Figure 4a, as the strain *ε*<sup>x</sup> increased from 0 to 6%, the Vickers hardness *H*<sup>V</sup> of Al6Mg1Zr1 dropped gradually from 11.97 GPa to 3.83 Gpa. The Vickers hardness *H*<sup>V</sup> of Al6Mg1Zr1 dropped by 71.746%, showing its negative relation with the uniaxial tension strain.

**Figure 4.** Vickers hardness *H*<sup>v</sup> and the modulus ratio *B*/*G* of Al6Mg1Zr1 at different uniaxial tension strain (*ε*x): (**a**) Vickers hardness *H*v vs. strain *ε*x; (**b**) the ratio *D* (*D=B*/*G*) vs. strain *ε*x.

From Figure 4b, when the strain *ε*<sup>x</sup> was less than 3%, the modulus ratio *B/G* remained nearly unchanged. When the *ε*<sup>x</sup> was more than 3%, the modulus ratio *B/G* grew quickly from 1.55 to 2.65 with the increasing strain *ε*x. When the strain *ε*<sup>x</sup> was less than 4%, the modulus ratio *B*/*G* < 1.75 and the Al6Mg1Zr1 was brittle. When the *ε*<sup>x</sup> was more than 4%, the modulus ratio *B*/*G* > 1.75 and the Al6Mg1Zr1 was taken as ductile. Al6Mg1Zr1 would become most ductile at the strain of 6% due to the largest modulus ratio *B/G* value of 2.65.

#### *3.5. Elastic Anisotropy*

Elastic anisotropy of a solid material is very important in diverse applications such as phase transformations and dislocation dynamics, and it can be characterized by the elastic anisotropy indexes. The elastic anisotropy indexes include compression anisotropy percentage *A*B, shear anisotropy percentage *A*G, and the universal anisotropy index *A*U, and can be calculated using the following expressions [42]:

$$\begin{cases} \begin{aligned} A\_{\rm B} &= \frac{B\_{\rm V} - B\_{\rm R}}{B\_{\rm V} + B\_{\rm R}} \\ A\_{\rm G} &= \frac{G\_{\rm V} - G\_{\rm R}}{G\_{\rm V} + G\_{\rm R}} \\ A\_{\rm U} &= 5 \frac{G\_{\rm V}}{G\_{\rm R}} + \frac{B\_{\rm V}}{B\_{\rm R}} - 6 \end{aligned} \end{cases} \tag{11}$$

If *A*<sup>U</sup> = *A*<sup>B</sup> = *A*<sup>G</sup> = 0, the material shows characteristics of elastic isotropy. Otherwise, it has elastic anisotropy, and the larger the deviation of elastic anisotropy index values from 0 (the corresponding elastic isotropy value), the greater its degree in elastic anisotropy.

Table 5 and Figure 5 show the calculated values of elastic anisotropy indexes (*A*B, *A*G, and *A*U) of Al6Mg1Zr1 at different uniaxial tension strains *ε*x.

**Table 5.** Calculated values of elastic anisotropy indexes (*A*B, *A*G, and *A*U) of Al6Mg1Zr1 at different uniaxial tension strains in *x* direction (*ε*x).


**Figure 5.** Elastic anisotropy indexes of Al6Mg1Zr1 (*A*B, *A*G, and *A*U) at different uniaxial tension strains (*ε*x): (**a**) *A*<sup>B</sup> vs. strain *ε*x; (**b**) *A*<sup>G</sup> vs. strain *ε*x; (**c**) *A*<sup>U</sup> vs. strain *ε*x.

From Figure 5a, the compression anisotropy percentage *A*<sup>B</sup> of Al6Mg1Zr1 grew slowly as the strain *ε*<sup>x</sup> increased from 0 to 4%, and then it grew quickly as the strain *ε*<sup>x</sup> increased from 4% to 6%. *A*<sup>B</sup> reached its maximum of 4.58% at the strain *ε*<sup>x</sup> of 6%. From Figure 5b, when the strain *ε*<sup>x</sup> was less than 3%, the shear anisotropy percentage *A*<sup>G</sup> dropped slowly with the strain *ε*x. *A*<sup>G</sup> reached its minimum of 0.32% at the strain *ε*<sup>x</sup> of 3%. When the strain *ε*<sup>x</sup> was more than 3%, *A*<sup>G</sup> grew quickly with the strain *ε*x, and reached its maximum of 7.37% at the strain *ε*<sup>x</sup> of 6%. The universal anisotropy index *A*<sup>U</sup> can reflect the anisotropy more accurately because both bulk modulus *B* and shear modulus *G* are deliberated in its expression. As shown in Figure 5c, the change trend of *A*<sup>U</sup> with the strain *ε*<sup>x</sup> is similar to that of *A*G. The variation trends of elastic anisotropy indexes of Al6Mg1Zr1 with uniaxial tensile strain are similar to that of hexagonal C40 MoSi2 [43]. Moreover, the values of the elastic anisotropy indexes (*A*B, *A*G, and *A*U) are small and the degree in elastic anisotropy of Al6Mg1Zr1 is relatively weak in the range of strain *ε*<sup>x</sup> from 0 to 6%.

#### **4. Conclusions**

To sum up, in this work the mechanical stability, stress–strain relations, elastic properties, hardness, ductility, and elastic anisotropy of Al6Mg1Zr1 at different uniaxial tension strains in the *x* direction (*ε*x) were examined by first principle calculations based on density functional theory. The influences of strain *ε*<sup>x</sup> on the mechanical properties of the Al6Mg1Zr1 were studied. It was found that Al6Mg1Zr1 was mechanically stable in the range of strain *ε*<sup>x</sup> from 0 to 6%, while it was unstable when the strain *ε*<sup>x</sup> was more than 6%. As the strain *ε*<sup>x</sup> increased from 0 to 6%, the stress in the *x* direction (*σ*x) first increased linearly and then followed a nonlinear trend, but the stresses in the *y* and *z* directions (*σ*<sup>y</sup> and *σ*z), which were almost equal, showed a linear, increasing trend all the way. Due to the uniaxial tension loading in the *x* direction, the stress *σ*<sup>x</sup> was much higher than *σ*<sup>y</sup> and *σ*z. The bulk modulus *B*, shear modulus *G* and Young's modulus *E* of Al6Mg1Zr1 all dropped with

increasing strain *ε*<sup>x</sup> from 0 to 6%, showing their negative relations with uniaxial tension strain. Therefore, the incompressibility, shear resistance, and stiffness of the Al6Mg1Zr1 all dropped with increasing uniaxial tension strain. When the strain *ε*<sup>x</sup> was less than 3%, The Poisson ratio *μ* of Al6Mg1Zr1 was nearly unchanged. However, it grew quickly when the *ε*<sup>x</sup> was more than 3%, showing its positive relation with uniaxial tension strain. The Poisson ratio *μ* ranged from 0.23 to 0.33, which is between −1 and 0.5, indicating that Al6Mg1Zr1 is stable linear elastic solid in the range of *ε*<sup>x</sup> from 0 to 6%. Al6Mg1Zr1 has the highest toughness at the strain *ε*<sup>x</sup> of 6% due to the maximum *μ* value. The Vickers hardness *H*<sup>V</sup> of Al6Mg1Zr1 dropped gradually with the increasing strain *ε*<sup>x</sup> from 0 to 6%, showing its negative relation with uniaxial tension strain. When the strain *ε*<sup>x</sup> was less than 3%, the modulus ratio *B/G* of Al6Mg1Zr1 remained nearly unchanged but it grew quickly when the *ε*<sup>x</sup> was more than 3%, showing its positive relation with uniaxial tension strain. Al6Mg1Zr1 was brittle when the *ε*<sup>x</sup> was less than 4%, while it exhibited ductility when the strain *ε*<sup>x</sup> was more than 4%. The best ductility was achieved for Al6Mg1Zr1 alloy at the strain *ε*<sup>x</sup> of 6% due to the maximum *B*/*G* value. The compression anisotropy percentage *A*<sup>B</sup> of Al6Mg1Zr1 grew slowly as the strain *ε*<sup>x</sup> increased from 0 to 4%, while it grew quickly as the strain *ε*<sup>x</sup> increased from 4% to 6%. Both the shear anisotropy percentage (*A*G) and universal anisotropy index (*A*U) dropped slowly with increasing strain *ε*<sup>x</sup> from 0 to 3%, and then grew quickly with increasing strain *ε*<sup>x</sup> from 3 to 6%. In addition, the values of the elastic anisotropy indexes (*A*B, *A*G, and *A*U) are small and the degree in elastic anisotropy of Al6Mg1Zr1 is relatively weak in the range of *ε*<sup>x</sup> from 0 to 6%. These results show that applying uniaxial tension strain is an effective and promising strategy to improve the mechanical properties of Al6Mg1Zr1.

**Author Contributions:** Conceptualization, J.L. and L.L.; methodology, L.Z. and Y.L.; software, L.Z. and J.Z.; validation, L.Z. and Y.L.; formal analysis, L.Z. and J.L.; investigation, L.Z. and J.L.; resources, J.L. and L.L.; data curation, L.Z. and J.Z.; writing—original draft preparation, L.Z. and J.L.; writing—review and editing, J.Z. and L.L.; visualization, L.Z. and J.Z.; supervision, J.L. and Y.L.; project administration, J.L. and Y.L.; funding acquisition, J.L. and L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant Nos. 2022MS01009 and 2018MS01013), the National Natural Science Foundation of China (Grant Nos. 11972221 and 11562016), the College Science Research Project of Inner Mongolia Autonomous Region (Grant No. NJZY22383), and the Key Research Project of Inner Mongolia University of Technology (Grant No. ZZ202016).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are contained within the article and can be requested from the corresponding author.

**Acknowledgments:** The authors acknowledge Mechanics Department of Inner Mongolia University of Technology and the Mathematics Department of Shanghai Maritime University for providing technical support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

## *Article* **Investigation of the Quenching Sensitivity of the Mechanical and Corrosion Properties of 7475 Aluminum Alloy**

**Puli Cao 1, Guilan Xie 1, Chengbo Li 1,2,\*, Daibo Zhu 1,\*, Di Feng 3, Bo Xiao <sup>1</sup> and Cai Zhao <sup>1</sup>**


**Abstract:** Based on end-quenching experiments combined with conductivity, hardness testing, and microstructural characterization, the quenching sensitivity of the mechanical and corrosion properties of 7475 aluminum alloy was investigated. The study revealed that as the quenching rate decreased, both the mechanical properties and exfoliation corrosion resistance exhibited increased quenching sensitivity. With the quenching rate decreasing from 31.9 ◦C/s to 2.5 ◦C/s, the conductivity increased by 4.1%IACS, the hardness decreased by 31%, the exfoliation corrosion grade transitioned from EC to ED, and the maximum exfoliation corrosion depth increased from 237 μm to 508 μm. As the quenching rate decreased, the η phase sequentially precipitated at recrystallized grain boundaries (RGBs), E phase particles, and subgrain boundaries (SGBs), while the T phase primarily precipitated on E phase particles. Furthermore, the significant precipitation of η and T phases led to a notable reduction in the quantity of age-precipitated phases, an increase in their size, and poor coherency with the matrix, resulting in decreased mechanical properties and a higher quenching sensitivity of the mechanical performance. Meanwhile, with the reduction in quenching rate, the size and spacing of grain boundary precipitated phases increased, the Zn and Mg contents of grain boundary precipitated phases increased, and the Precipitation Free Zone (PFZ) widened, leading to decreased exfoliation corrosion resistance and higher quenching sensitivity of the exfoliation corrosion performance.

**Citation:** Cao, P.; Xie, G.; Li, C.; Zhu, D.; Feng, D.; Xiao, B.; Zhao, C. Investigation of the Quenching Sensitivity of the Mechanical and Corrosion Properties of 7475 Aluminum Alloy. *Metals* **2023**, *13*, 1656. https://doi.org/10.3390/ met13101656

Academic Editor: Frank Czerwinski

Received: 12 August 2023 Revised: 16 September 2023 Accepted: 25 September 2023 Published: 27 September 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Keywords:** high-strength aluminum alloy; mechanical; corrosion properties; quenching sensitivity; microstructure

#### **1. Introduction**

Al-Zn-Mg-Cu aluminum alloys, due to their high strength resulting from solid solution, quenching, and aging processes, are widely utilized as structural materials, being particularly extensively employed in the aerospace industry [1,2]. Quenching is a crucial step in the preparation of high-strength aluminum alloy materials. Rapid quenching leads to a high degree of supersaturated solid solution in the alloy, and subsequent aging results in the precipitation of numerous strengthening phases, thus achieving high strength. However, excessively high quenching rates often lead to elevated residual stresses [3]. Reducing the quenching rate can mitigate the residual stresses in the alloy, but this may result in decreased alloy performance. This phenomenon, where the alloy's performance diminishes after aging as the quenching rate decreases, is referred to as quenching sensitivity [4].

In general, for high-strength aluminum alloys, as the quenching rate decreases, the quantity and size of quenching-precipitated phases increase. This leads to a reduction in the solute atom concentration and vacancy concentration in the alloy after quenching. Subsequently, the number of precipitations strengthening phases decreases upon aging, resulting in a decline in mechanical properties and an increase in the quenching sensitivity of the mechanical performance [5–8]. Liu Shengdan et al. [9] found that in 7055 aluminum

alloy, the quenching sensitivity of mechanical performance increases as the quenching rate decreases. Li Peiyue et al. [10] studied the quenching sensitivity of 7050 aluminum alloy using spray end-quenching and discovered that, as the quenching rate decreases, mechanical properties decrease, and quenching sensitivity increases. Liu et al. [11] found that the quenching sensitivity of the mechanical performance of 7085 alloy increases as the quenching rate decreases. Zheng Pengcheng [12] and Ma Zhimin et al. [13] found that the quenching sensitivity of the mechanical performance of 7136 aluminum alloy increases as the quenching rate decreases.

Variations in the quenching rate also impact the size, composition, spacing of grain boundary precipitated phases, and width of the Precipitation Free Zone (PFZ), thereby exerting complex effects on the alloy's corrosion resistance. However, there is still some controversy regarding its influence on the quenching sensitivity of localized corrosion performance. Many studies have indicated that as the quenching rate decreases, the exfoliation corrosion resistance of the alloy diminishes and the quenching sensitivity of the exfoliation corrosion performance increases. Marlaud et al. [14] found that the exfoliation corrosion resistance of 7449-T7651 alloy decreases with the decreasing quenching rate. Song et al. [15] observed an increase in the exfoliation corrosion sensitivity of the AA7050 alloy with a decreasing quenching rate. Li Dongfeng et al. [16] discovered that as the quenching rate decreased from 2160 ◦C/min to 100 ◦C/min, the exfoliation corrosion grade of Al-5Zn-3Mg-1Cu alloy sheets gradually shifted from P grade to ED grade. Liu et al. [17] revealed that the maximum exfoliation corrosion depth of AA7055 alloy gradually increases as the quenching rate decreases, indicating an ascending trend in exfoliation corrosion sensitivity. Ma et al. [13] also found an increase in the exfoliation corrosion sensitivity of 7136 aluminum alloy with a decreasing quenching rate.

In summary, it is evident that high-strength aluminum alloys exhibit not only quenching sensitivity in terms of mechanical performance, but also significant quenching sensitivity in their corrosion properties. Therefore, this study utilizes end-quenching experiments in conjunction with Transmission Electron Microscopy (TEM), High-Resolution Transmission Electron Microscopy (HRTEM), and Scanning Transmission Electron Microscopy (STEM) to systematically investigate the types, nucleation sites, sizes, and morphologies of precipitated phases under different quenching rates. The study also discusses the precipitation behavior of these quenching-induced phases and their influence on the quenching sensitivity of mechanical and exfoliation corrosion performance. This research aims to provide a better understanding of the quenching precipitation behavior and the mechanisms behind quenching sensitivity in high-strength aluminum alloys.

#### **2. Experiment**

The experimental material used was a hot-rolled thick plate provided by a certain company. The casting temperature was 700 ◦C, followed by a 24 h homogenization heat treatment at 465 ◦C. The hot rolling temperature was 390 ◦C, with a deformation amount of 90%. The chemical composition (wt%) of the plate is shown in Table 1. Cross-sectional samples with dimensions of 25 mm × 25 mm were cut from the surface of the hot-rolled plate with a length of 125 mm for subsequent solution heat treatment and end-quenching. The samples were heated to 470 ◦C and held in an air furnace (TPS, New Columbia, PA, USA) for 2 h. They were then transferred to an end-quenching device [18] and rapidly water-cooled by spraying water onto the groove end until reaching room temperature. The quenching water temperature was approximately 20 ◦C. The quenched samples were subsequently subjected to artificial aging in an oil bath at 120 ◦C for 24 h. After aging, half of the samples were polished using sandpaper and subjected to hardness testing. The test was conducted using three parallel samples. Hardness measurements were taken along the rolling direction at 5-mm intervals, starting from the water-cooled end. The hardness tests were conducted using an HV-10B Vickers hardness tester (Suzhou Nanguang Electronic Technology, Suzhou, China) with a load of 3 kg. For exfoliation corrosion testing, slices (2 mm thick) were cut from the aged samples. The test was conducted using three

parallel samples. The testing was performed following the GB/T 22639-2008 standard [19]. The area-to-volume ratio of the solution was 25 cm2/L, and the testing temperature was maintained at (25 ± 2) ◦C. After 48 h of corrosion, the samples were evaluated according to the standard using an EXCO solution (4 mol/L NaCl + 0.5 mol/L KNO3 + 0.1 mol/L HNO3). Metallographic samples were prepared from different locations and observed for corrosion using an XJP-6A metallographic microscope (Suzhou Hongtai Instrument, Suzhou, China). After coarse grinding, fine grinding, and polishing, the metallographic samples were observed, and the corrosion depth was measured under the microscope. Additionally, samples of the same size were taken, and thermocouples were embedded at different distances (3, 13, 23, 53, 78, and 98 mm) from the water-cooled end. Cooling curves were recorded during the end-quenching process at these positions, and the average cooling rates were calculated in the temperature range of 185 to 415 ◦C [20]. The calculated average cooling rates for the respective positions were 31.9, 17.5, 8.4, 3.3, 2.9, and 2.5 ◦C/s, as shown in Figure 1. Thin slices (2 mm thick) were taken and subjected to water quenching at room temperature after solution treatment, resulting in a corresponding quenching rate of 960 ◦C/s.

**Table 1.** Chemical compositions of the alloy (wt%).

**Figure 1.** Schematic diagram of end quenching and quenching rate curve.

After aging, samples were extracted from the end-quenched specimens for microstructural analysis. The samples were first thinned by grinding to a thickness of approximately 60–80 μm. Circular discs with a diameter of 3 mm were then punched out. Thinning was further performed using dual-jet polishing in a solution containing 80% methanol and 20% nitric acid. The electrolyte temperature was controlled at around −25 ◦C using liquid nitrogen. Subsequently, the precipitated phases from the quenched samples were observed using a Tecnai G2 F20 (FEI, Eindhoven, The Netherlands) TEM and a Titan G2 60–300 (FEI, Eindhoven, The Netherlands) STEM. JMatPro 8.0 (Sente Software, London, UK) software was employed to calculate Time-Temperature-Transformation (TTT) curves and Continuous Cooling Transformation (CCT) curves.

#### **3. Results**

#### *3.1. Electrical Conductivity and Hardness Tests*

Figure 2 shows the conductivity curve. From the graph, it is evident that the alloy's conductivity increases with an increase in the distance from the water-cooled end. When the distance from the end is less than 60 mm, the conductivity rapidly increases with the distance, followed by a smaller increment in conductivity as the distance further increases. As the distance from 3 mm to 98 mm increases, the conductivity rises from 28.9 %IACS to

33 %IACS, resulting in a conductivity difference of 4.1 %IACS between the two ends. The conductivity in the quenched state serves as a reliable indicator of the quenching-induced precipitation behavior.

**Figure 2.** Conductivity curve.

Figure 3 represents the hardenability curve. From Figure 3a, it is evident that as the distance from the water-cooled end increases, the hardness gradually decreases. Within the region where the distance is less than 63 mm, the hardness value rapidly decreases with an increase in the distance, while beyond 63 mm, the change in hardness value with distance is relatively small. To further study the variations in hardness, based on the hardenability curve shown in Figure 3a, the retained hardness values were calculated, leading to the retained hardness curve depicted in Figure 3b. The trend of this curve is consistent with that of Figure 3a. Beyond a distance of 63 mm, the retained hardness value stabilizes around 70%, indicating a reduction in hardness of approximately 30%. At a distance of 98 mm, the hardness decreases by 31%.

**Figure 3.** Hardenability curve (**a**) and hardness retention curve (**b**).

#### *3.2. Exfoliation Corrosion*

Figure 4 presents macroscopic images of the end-quenched samples immersed in EXCO solution for different durations. The regions farther from the water-cooled end exhibit a higher quantity of bubbles and more intense reactions. After a 2-h immersion, the sample surfaces show no significant corrosion. After 6 h of immersion, slight pitting corrosion is observed on the sample surface (Figure 4). In the areas beyond 23 mm from the water-cooled end, the corrosion grade is classified as PB. As the immersion time increases, the corrosion severity intensifies. After 12 h of immersion, significant corrosion is evident on the sample surface. Noticeable exfoliation is observed in the regions far from the watercooled end, resulting in an EB corrosion grade. Extensive corrosion products are generated (Figure 4b). With prolonged immersion, severe delamination and exfoliation occur on the surface. After 24 h of immersion, exfoliation corrosion products become prominent, particularly in the regions far from the water-cooled end (Figure 4c). In areas with distances less than 23 mm, the corrosion grade is categorized as EA, while in regions beyond 23 mm, the grade is classified as EC. Following 48-h immersion, severe exfoliation corrosion is evident, with more corrosion products in positions farther from the water-cooled end. A substantial amount of corrosion products detaches, and the corrosion extends into the deeper metal interior. In regions beyond 23 mm, the corrosion grade is classified as ED (Figure 4d).

**Figure 4.** Corrosion morphology of end-quenched sample after soaking in EXCO solution for different times (spray end is on the left): (**a**) 6 h; (**b**) 12 h; (**c**) 24 h; (**d**) 48 h.

According to the GB/T 22639-2008 standard, the exfoliation corrosion degree of the samples was rated. It is evident from the graph that corrosion becomes increasingly severe with prolonged immersion. Exfoliation corrosion is more pronounced in regions with lower quenching rates than in those with higher quenching rates. Beyond 23 mm from the water-cooled end, the severity of exfoliation corrosion is notably high, with minimal difference in corrosion grades. After 48 h of immersion, samples with quenching rates above 8.4 ◦C/s are rated as EC. Samples with quenching rates below 8.4 ◦C/s are rated as ED.

Figure 5 displays cross-sectional metallographic images of the end-quenched samples after exfoliation corrosion at different quenching positions. It is evident from the images that the corrosion depth of the samples increases with a decrease in the quenching rate. Lower quenching rates lead to more pronounced exfoliation corrosion. When the quenching rate is 8.4 ◦C/s, the sample surfaces exhibit typical layered exfoliation corrosion morphology. The expansion of exfoliation corrosion products creates stress that lifts the metal layers one by one, resulting in severe exfoliation. The maximum and average exfoliation corrosion depths are shown in Figure 6b. From the graph, it can be observed that as the quenching rate decreases, both the maximum and average exfoliation corrosion depths increase. Moreover, lower quenching rates correspond to a greater increase in corrosion depth. At a quenching rate of 31.9 ◦C/s, the maximum and average exfoliation corrosion depths are 237 μm and 203 μm, respectively. At a quenching rate of 2.5 ◦C/s, the maximum and average exfoliation corrosion depths are 508 μm and 418 μm, respectively.

**Figure 5.** Metallographic photos of cross-section after spalling corrosion of samples at different quenching positions: (**a**) 31.9 ◦C/s, (**b**) 8.4 ◦C/s, (**c**) 3.3 ◦C/s, (**d**) 2.5 ◦C/s.

**Figure 6.** Spalling corrosion degree rating (**a**) and corrosion depth (**b**) of end-quenched sample.

#### *3.3. Microstructure*

Figure 7 presents TEM images of samples quenched at a rate of 960 ◦C/s. As observed in Figure 7a, a significant number of dispersed particles are present within the aluminum matrix. These particles exhibit irregular shapes and non-uniform sizes, ranging from circular and triangular to elongated forms, with dimensions ranging from 50 to 150 nm. Notably, these particles are non-coherent with the matrix [8]. Energy-dispersive X-ray spectroscopy (EDS) analysis results (Figure 7b) indicate that these particles consist of 81.5% Al, 2.4% Zn, 10.8% Mg, 1.8% Cu, and 3.5% Cr (atomic fractions). It is likely that the Cr-containing dispersed particles are associated with the E phase (Al18Cr2Mg3).

**Figure 7.** TEM photos at a quenching rate of 960 ◦C/s: (**a**) Bright field phase, (**b**) EDS.

Figure 8 displays TEM images of samples quenched at a rate of 31.9 ◦C/s. In Figure 8a, it can be observed that quenching precipitation occurs at recrystallized grain boundaries (RGBs), while no quenching precipitation is observed at subgrains (SGs) and their boundaries. Figure 8b reveals that the intragranular η phase nucleates and precipitates on E phase particles, with η phase sizes ranging from 100 to 150 nm. Simultaneously, age-related precipitates can be observed within the grain. Figure 8c demonstrates the fine and uniform dispersion of age-related precipitates within the grain's matrix. These precipitates exhibit spherical and rod-like morphologies. For a more detailed examination of the age-related precipitates, high-resolution TEM was employed to observe from the <011> direction. The HRTEM images (Figure 8d,e) reveal that the size of the age-related η' phases is 5–10 nm, indicating a relatively good coherence with the matrix. At this stage, the age-strengthening effect is notable, resulting in higher hardness.

**Figure 8.** TEM photo of a quenching rate of 31.9 ◦C/s: (**a**) grain boundary, (**b**) intragranular, (**c**) aging precipitate, (**d**) <011>Al HRTEM, (**e**) Inverse Fast Fourier Transformation (IFFT), (**f**) Fast Fourier Transformation (FFT).

Figure 9 displays HAADF-STEM images of samples quenched at a rate of 8.4 ◦C/s. In Figure 9a, it is evident that prominent quenching precipitates are present at RGBs, while SGs and their boundaries also exhibit quenching precipitates. Within the matrix, a substantial amount of quenching precipitates, identified as the η phase, can be observed. These precipitates exhibit plate-like shapes of uneven sizes, with some reaching lengths of up to 400 nm. Additionally, hexagonal T-phase precipitates with dimensions ranging from 100 to 200 nm are present within the matrix. Furthermore, numerous smaller quenching precipitates are distributed within the matrix, as shown in Figure 9b. Based on EDS analysis, it is revealed that the η phase primarily contains 75.7% Al, 11.5% Zn, 9.6% Mg, and 3.2% Cu (at%). The T phase mainly comprises 86.1% Al, 5.8% Zn, 6.3% Mg, and 1.8% Cu (at%).

**Figure 9.** HAADF-STEM photos with a quenching rate of 8.4 °C/s: (**a**) low power, (**b**) high power.

Figure 10 presents TEM images of samples quenched at a rate of 3.3 ◦C/s. In Figure 10a, a significant amount of quenching precipitates, identified as the η phase, can be observed within the grains. These precipitates exhibit plate-like shapes of considerable size, with some reaching lengths of up to 500 nm. Additionally, hexagonal T phase precipitates are also present. In Figure 10b, it can be observed that a substantial quantity of η phase quenching precipitates exists within SGs and at their boundaries. The sizes of these quenching precipitates vary, with some being larger and others being much smaller.

**Figure 10.** TEM photos at a quenching rate of 3.3 °C/s. (**a**) intracrystalline, (**b**) grain boundary.

Figure 11 depicts TEM images of samples quenched at a rate of 2.5 ◦C/s. In Figure 11a, an abundance of η and T phases are observed within the grains. Simultaneously, numerous η phase precipitates are observed within SGs and at their boundaries, displaying uneven sizes and being distributed along the deformation direction, as shown in Figure 11b. Observations at higher magnification in Figure 11c reveal age-related precipitates. It is evident that a noticeable Precipitation-Free Zone (PFZ) forms around a wider area of the quenching precipitates, where age-related precipitates are absent. Age-related precipitates near the quenching precipitates and grain boundaries are relatively larger and less abundant. HRTEM observations from the <011> direction (Figure 11d) indicate that the size of the age-related η' phase is 10–20 nm, indicating relatively poor coherence with the matrix. At this stage, the age-strengthening effect is relatively weak, resulting in lower hardness and a significant hardness drop of 31% in this region.

**Figure 11.** TEM photo of quenching rate of 2.5 ◦C/s: (**a**) intragranular, (**b**) grain boundary, (**c**) aging precipitate, (**d**) <011>Al HRTEM.

Figure 12 illustrates the HAADF-STEM images of samples quenched at a rate of 2.5 ◦C/s. In Figure 12a, large-sized quenched precipitates are observed at RGBs, with sizes around 500 nm. Some of these quenched precipitates have been corroded, leaving behind dark features, indicating that the precipitates at grain boundaries are susceptible to corrosion. Precipitates are also observed at subgrain boundaries (SGBs), with sizes around 250 nm. Within the grains, in addition to the larger-sized quenched precipitates, a multitude of smaller-sized quenched precipitates are observed. From the higher magnification image in Figure 12b, it is evident that quenched precipitates of η phase are precipitating on Ephase particles, resulting in larger and less abundant age-related precipitates around them. A distinct Precipitation-Free Zone (PFZ) is observed surrounding the η phase, leading to a significant reduction in mechanical performance.

**Figure 12.** HAADF-STEM photos with a quenching rate of 2.5 ◦C/s: (**a**) grain boundary, (**b**) intragrain.

Figure 13 depicts the composition of grain boundary precipitates at different quenching rates. As shown in the figure, with decreasing quenching rates, the content of Zn, Mg, and Cu in grain boundary precipitates increases. Zn content exhibits the most rapid increase, followed by Mg, while the increase in Cu content is comparatively slower. At a quenching rate of 31.9 ◦C/s, the grain boundary precipitates contain lower levels of Zn, Mg, and Cu. In contrast, at a quenching rate of 2.5 ◦C/s, both Zn and Mg content show significant increments, and there is also a notable increase in Cu content.

**Figure 13.** Components of grain boundary precipitated phase at different quenching rates.

#### *3.4. TTT and CCT Curves*

Figure 14 illustrates the TTT and CCT curves. In Figure 14a, the curve for the η phase is on the left side, while the curve for the T phase is on the right side. The nose temperatures for the η phase and T phase are 332.1 and 301.2 ◦C, respectively, corresponding to transformation times of 20.6 and 47.1 s, respectively. From the CCT curve in Figure 14b, it can be observed that during the decomposition of the supersaturated solid solution, the η phase precipitates first, followed by the T phase.

**Figure 14.** (**a**) TTT, (**b**) CCT curve.

#### **4. Discussion**

The quenched precipitates and their nucleation sites at different quenching rates are summarized in Table 2. It is evident from the table that as the quenching rate decreases, both the types of quenched precipitates and their nucleation sites increase. The quenched precipitates include the η phase and the T phase. The η phase preferentially precipitates at RGBs s, while it also precipitates on the E phase particles as well as at SGBs. Combined with Figure 14, it can be inferred that the η phase precipitates first during the quenching process, followed by the T phase.

**Table 2.** Quenching precipitates and nucleation positions at different quenching rates.


The sizes of the η phase precipitates at different quenching rates are presented in Table 3. As indicated in the table, the size of the η phase precipitates gradually increases with the decreasing quenching rate. The largest η phase precipitates are observed at RGBs, followed by those on the E phase particles, while the η phase precipitates at SGBs are smaller in size.

**Table 3.** Size of the η phase at different quenching rates.


During the quenching cooling process, the quenched precipitation phase at the grain boundaries is primarily the η phase, which mainly contains Zn, Mg, and Cu elements. The diffusion rates of Zn, Mg, and Cu in the Al solid solution are in the order Zn > Mg > Cu [21,22]. Generally, the nucleation activation energy of the η phase is not very high. At room temperature, the diffusion rate of Zn in the Al matrix is 1.64 × <sup>10</sup>−<sup>12</sup> cm2/s, while that of Mg is 7.33 × <sup>10</sup>−<sup>15</sup> cm2/s. The activation energy for aluminum self-diffusion is 142.8 kJ/mol, for Mg in aluminum it is 135.1 kJ/mol, and for Zn in aluminum it is 106.1 kJ/mol. Therefore, it can be inferred that with increasing temperature, the diffusion of Zn atoms in the system becomes relatively easier. The η phase preferentially nucleates at the RGBs with high interfacial energy. Since the grain boundaries serve as fast diffusion paths for solute atoms such as Zn and Mg, the η phase preferentially nucleates and grows

at the grain boundaries [23,24]. Subsequently, nucleation occurs on E-phase particles, and finally at the SGBs. During the alloy quenching process, a significant amount of η phase preferentially precipitates, consuming a substantial number of Zn atoms. This leads to a low local concentration of Zn atoms. Meanwhile, the high interfacial energy of the E phase particles provides a favorable site for the nucleation of the T phase, resulting in the precipitation of the T phase (Figure 9).

During quenching, precipitation occurs due to desaturation, leading to a reduction in the supersaturation of the solid solution and a weakening of the lattice distortion, thereby causing an increase in conductivity. Locations closer to the water-cooled end experience a higher quenching cooling rate, resulting in the formation of a highly supersaturated solid solution and significant lattice distortion, which leads to lower conductivity. In contrast, positions farther from the water-cooled end experience a lower quenching cooling rate, causing a significant amount of equilibrium phase to desaturate, resulting in a lower supersaturation of the solid solution and reduced lattice distortion, hence leading to higher conductivity.

As the quenching rate decreases, quenching-induced phases precipitate at both grain boundaries and within the grains, with their sizes gradually increasing. The precipitation of η and T phases consumes the Zn and Mg solute atoms in the matrix, resulting in a reduction in solute atom concentration and vacancy concentration in the alloy after quenching. Subsequently, during aging, the precipitation-strengthening phases exhibit reduced quantities and increased sizes. These phases exhibit relatively poor lattice compatibility with the matrix (Figure 11c,d), leading to weaker aging strengthening effects. Furthermore, the quenched precipitation phases at the grain boundaries and within the grains can continue to grow by absorbing surrounding solute atoms during the aging process, forming broader PFZs (Figure 12b). The broadened PFZs further contribute to a reduction in mechanical properties. Consequently, the quenching sensitivity of the mechanical properties increases as the quenching rate decreases.

As the quenching rate decreases, the alloy's resistance to exfoliation corrosion diminishes. Considering the observed microstructural features (Figures 8a, 9, 12a and 13), this phenomenon is mainly attributed to the increased size and spacing of grain boundary precipitates, elevated Zn and Mg content in the grain boundary precipitates, and broadening of the PFZs with decreasing quenching rates. Prior investigations have indicated that the potential of the grain boundary η phase is −1.05 V, PFZ is −0.85 V, and the potential of the matrix within grains is −0.75 V [25]. In corrosive environments, the differing corrosion potentials of various phases in the grain boundary regions of the matrix solid solution can lead to galvanic corrosion, resulting in along-grain boundary corrosion in high-strength aluminum alloys. The formation of corrosion microcells between grain boundary precipitates (η phase), PFZs, and phases within the grain can establish anodic dissolution sites. The grain boundary η phase acts as the anodic phase and is preferentially dissolved, and PFZs often function as anodic sites that are susceptible to corrosion, thereby creating pathways for along-grain boundary anodic dissolution channels [26–28]. As the quenching rate decreases, coarser η phase precipitates form at grain boundaries, exhibiting increased and non-uniform sizes, along with elevated Zn and Mg content in the precipitates. Simultaneously, PFZs broaden, further promoting grain boundary dissolution. This corrosion process generates substantial corrosion products during corrosion, leading to exfoliation corrosion and ultimately reducing the alloy's resistance to exfoliation corrosion.

#### **5. Conclusions**

(1) As the quenching rate decreases, the electrical conductivity increases, and the quenching sensitivity of both the mechanical properties and exfoliation corrosion increases. With a decrease in the quenching rate from 31.9 ◦C/s to 2.5◦C/s, the electrical conductivity increases by 4.1 %IACS, hardness decreases by 31%, and the exfoliation corrosion grade transitions from EC to ED, with the maximum exfoliation corrosion depth increasing from 237 μm to 508 μm.

(2) With a reduction in the quenching rate, the variety, nucleation sites, size, and quantity of quenching-induced precipitates increase. During quenching, η phase precipitates first, followed by the precipitation of T phase. η phase predominantly nucleates at RGBs, on E phase particles, and at SGBs, while T phase primarily forms on E phase particles.

(3) Decreasing quenching rates lead to abundant precipitation of η and T phases within the matrix and along grain boundaries. This results in a significant reduction in the quantity and an increase in the size of precipitates during aging. These precipitates also exhibit poorer coherency with the matrix, and a PFZ forms, contributing to reduced mechanical properties and heightened sensitivity to quenching-induced variations. Moreover, lower quenching rates lead to larger precipitate sizes and spacings at grain boundaries, increased Zn and Mg content in grain boundary precipitates, and broadened PFZs, all contributing to diminished resistance against exfoliation corrosion and heightened sensitivity to exfoliation corrosion performance.

**Author Contributions:** Investigation and Writing—original draft, P.C.; Software and Writing—original draft, G.X.; Conceptualization, and Methodology, C.L.; Supervision and Funding Acquisition, D.Z.; Validation, Data curation and Formal analysis, D.F., B.X. and C.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the National Natural Science Foundation of China (52205421), Guangxi Science and Technology Major Project (AA23023028), the Key laboratory open project of Guangdong Province (XF20230330-XT), the school-enterprise, industry-university-research cooperation project (2023XF-FW-32), the science and technology innovation Program of Hunan Province, China (2021RC2087, and 2022JJ30570), and the Key Research and Development Program of Zhenjiang City (GY2021003 and GY2021020).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data will be made available on request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

**Di Feng 1,\*, Qianhao Zang 1, Ying Liu <sup>2</sup> and Yunsoo Lee <sup>3</sup>**


#### **1. Introduction and Scope**

Due to air pollution and energy shortages in the contemporary world, weight lighting for transportation vehicles and energy conservation, as well as emission reductions, are necessary to achieve carbon neutrality and fuel conservation. As a structural material with high specific strength, good process performance, and abundant reserves, aluminum alloy is undoubtedly becoming a substitute for steel materials.

Since the invention of electrolytic aluminum technology, aluminum alloys have been widely used in the fields of aviation and automobiles. The aerospace industry mainly develops aluminum alloys with high strength, high toughness, and excellent stress corrosion resistance to meet the strict usage conditions. 2xxx series and 7xxx series aluminum alloys are typical structural materials for aviation [1]. The current research hotspot lies in the optimization of processing technology and improving the material composition. Powder metallurgy and spray deposition are typical innovative technologies that can avoid compositional segregation and obtain higher element contents. Research on aluminum matrix composites and superplastic aluminum alloy materials is also ongoing. In the industries of new energy vehicles and intelligent connected vehicles, 4xxx and 6xxx series aluminum alloys are widely used. The application of aluminum alloys in a vehicle body and chassis can reduce the weight of the entire vehicle by 20–40%, which effectively extends its range. For car wheels with a complex shape, high-pressure die-casting technology is now commonly used. Compared to steel wheels, the weight of Al-Si series wheels is greatly reduced, effectively reducing the vehicle's fuel consumption and carbon dioxide emissions. Automotive power battery shells made of aluminum alloy can reduce the weight by nearly 20%. The front and rear anti-collision beams made of optimized 7xxx aluminum alloy profiles have energy absorption values of no less than those of steel, achieving weight reduction and improving safety. In addition, aluminum alloys can also be used to manufacture components such as cylinder blocks, cylinder heads, crankshafts, connecting rods, and pistons for automotive engines. Plate and profile goods are commonly used products of aluminum alloys. Different deformation technologies are required to obtain the various shapes. The hot deformation behavior or the thermal deformation constitutive equation is a useful tool to obtain the optimized process parameters. Based on these mathematical models, the deformation defects, and even the service performances, of certain aluminum alloys can be predicted. Computational materials science can greatly shorten the cycle of material preparation processes. This Special Issue's scope embraces several types of aluminum alloys and the interdisciplinary work aimed at introducing the emerging area of technologies and theories.

**Citation:** Feng, D.; Zang, Q.; Liu, Y.; Lee, Y. Aluminum Alloys and Aluminum-Based Matrix Composites. *Metals* **2023**, *13*, 1870. https:// doi.org/10.3390/met13111870

Received: 30 October 2023 Accepted: 3 November 2023 Published: 10 November 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **2. Contributions**

Ten articles have been published in the current Special Issue of *Metals*, encompassing the fields of hot deformation behavior, constitutive modeling, performance prediction modeling, structure designation, composition designation and quenching sensitivity. Current Special Issue papers can also be classified based on material composition, including AlZnMgCu, AlMg, AlSi, and AlLi alloys.

#### *2.1. Hot Deformation Behavior*

The stress–strain curve helps scholars understand the dynamic hardening and dynamic softening behaviors during hot deformation, such as dynamic recovery and dynamic recrystallization [2], which are the basis for optimizing hot-working process parameters. In addition, the constitutive models can also be established based on stress–strain curves under different temperatures and strain rates. The constitutive equation is a necessary model for finite element simulation of plastic deformation to obtain the deformation state, temperature distribution, and the stress concentration during processing. This Special Issue presents two typical constitutive models, which are often used to describe warm forging and hot compression, respectively.

#### *2.2. Performance Prediction Modeling*

The prediction of processing defects and performance is an important step during component production. An accurate damage model or state equation under a complex loading environment can precisely calculate the service life of components, laying a theoretical foundation for material selection and structural designation [3], effectively avoiding material failure and shortening the product development cycle. The Special Issue also presents two prediction models, which are applicated to the real-time monitor of surface defects and the performance life under a cyclic tension–compression condition, respectively. The first-principle investigation for the mechanical properties of an Al-Mg-Zr alloy under uniaxial tension is also presented.

#### *2.3. Composition Designation*

The Zn/Mg ratio and Mg/Si ratio determine the strength of 7xxx and 6xxx aluminum alloys [4], respectively. The increase in Cu content is conducive to improvements in the aging hardening rate and the corrosion resistance. The element Cu is also one of the constituent elements of the nano strengthening phase in AlCu and AlCuLi alloys. For high-strength aluminum alloys, Fe and Si are impurities that can cause a sharp decrease in plasticity. However, Si is the main alloying element in a 4xxx alloy. The increase in Si content improves the fluidity of a AlSi alloy. Adding Cu and Mg to AlSi can also form the θ, β or Q phases, similar to those in AlCu and AlMgSi alloys [5]. Of course, the plasticity will be deteriorated when Si exceeds the eutectic composition. At this point, it is necessary to combine this with rapid solidification technology to improve the morphology of primary Si. It should be pointed out that there is a suitable content for any alloying element. Too little addition does not have a strengthening effect, while too much addition may lead to precipitation of the coarse second phase at the interface, reducing the strength, plasticity, and even corrosion resistance.

#### *2.4. Quenching Sensitivity*

Quenching is one heat treatment technology that obtains excellent strength, toughness and corrosion resistance, and so on. For high-performance aluminum alloys with a high alloying element content, a lower quenching cooling rate will cause a large number of alloying elements to precipitate along grain boundaries during the cooling, forming coarse and incoherent compounds [6]. Quenching precipitation greatly reduces the mechanical properties of the alloy while also deteriorating the corrosion resistance. Where are these coarse compounds formed? What are the ingredients? How does it affect the material properties? At what quenching rate level can cooling precipitation be suppressed? The answers

to the above questions form the foundation for obtaining a high-quality supersaturated solid solution, which results a high-aging strengthening effect. Quenching sensitivity is particularly prominent in AlZnMgCu alloys. The 7085 aluminum alloy is currently known as the most excellent hardenability aluminum alloy.

#### *2.5. Structure Designation*

Even with the same material, different structural designations can be used to achieve different performances, such as increasing stiffness and improving a material's resistance to external loads [7]. In this research neighborhood, computational materials science is also an important application technology that can help researchers quickly judge the rationality of structures and reduce the number of physical experiments.

#### *2.6. External Field-Assisted Manufacturing*

External field-assisted manufacturing is a highly innovative technology that can be used to compensate for the shortcomings of traditional techniques, thereby obtaining a better processing experience or a superior performance. Lasers, magnetic fields, and ultrasound are commonly used external media [8]. The input of these external energy fields changes the processing rate and may also alter the law of the microstructure evolution, resulting in unexpected performances.

#### **3. Conclusions and Outlook**

With the vigorous development of the manned aerospace and intelligent driving vehicle industries, aluminum alloys have shown increasingly vigorous vitality. Whether it is the breakthrough in composition design concepts or the endless emergence of new technologies and processes, something has greatly expanded the application breadth and depth of aluminum alloys. This Special Issue gathers multiple related topics and provides an overview of the latest developments in aluminum alloys, with different compositions and their related technologies.

As Guest Editors of this Special Issue, we hope that these published papers can be helpful to scientists and engineers engaged in the research and development of highperformance aluminum alloys. We also hope that these contributors can establish connections, accomplish interdisciplinary and professional complementarity work, and then achieve greater successes. At the same time, we would like to warmly thank all the authors for their contributions, and all of the reviewers for their efforts in ensuring a high-quality publication. We offer our sincere thanks to the Editors of *Metals* for their continuous help and support during the preparation of this issue. In particular, my sincere thanks goes to Toliver Guo for his help and support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **List of Contributions**


#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

MDPI St. Alban-Anlage 66 4052 Basel Switzerland www.mdpi.com

*Metals* Editorial Office E-mail: metals@mdpi.com www.mdpi.com/journal/metals

Disclaimer/Publisher's Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Academic Open Access Publishing

mdpi.com ISBN 978-3-0365-9613-6