*Article* **Comparative Study and Multi-Objective Crashworthiness Optimization Design of Foam and Honeycomb-Filled Novel Aluminum Thin-Walled Tubes**

**Yi Tao 1, Yonghui Wang 2, Qiang He 2,\*, Daoming Xu <sup>1</sup> and Lizheng Li <sup>2</sup>**


**Abstract:** Due to their lightweight, porous and excellent energy absorption characteristics, foam and honeycomb materials have been widely used for filling energy absorbing devices. For further improving the energy absorption performance of the novel tube proposed in our recent work, the nonlinear dynamics software Abaqus was firstly used to establish and verify the simulation model of aluminum-filled tube. Then, the crashworthiness of honeycomb-filled tubes, foam-filled tubes and empty tube under axial load was systematically compared and analyzed. Furthermore, a comparative analysis of the mechanical behavior of filled tubes subjected to bending load was carried out based on the study of dynamic response curve, specific energy absorption and deformation mechanism, the difference in energy absorption performance between them was also revealed. Finally, the most promising filling structure with excellent crashworthiness under lateral load was optimized. The research results show that the novel thin-walled structures filled with foam or honeycomb both show better energy absorption characteristics, with an increase of at least 8.8% in total absorbed energy. At the same time, the mechanical properties of this kind of filled structure are closely related to the filling styles. Foam filling will greatly damage the weight efficiency of the novel thin-walled tube. However, honeycomb filling is beneficial to the improvement of *SEA*, which can be improved by up to 18.2%.

**Keywords:** thin-walled structure; filling structure; numerical simulation; crashworthiness optimization; energy absorption performance

#### **1. Introduction**

Thin-walled structures have been widely used in automobiles, aviation and other industrial fields, due to their excellent mechanical properties. Therefore, the research on their mechanical properties has always been a hot topic for scholars [1–5]. Galib et al. [6] conducted a comprehensive experimental and numerical study on circular tubes subjected to dynamic load. Zhang et al. [7,8] pointed out that multi-cell square tubes showed better mechanical properties. Alavi Nia et al. [9] conducted axial impact tests on structures with different polygonal cross-sections, and proposed that the multi-cell cross-section was conducive to the improvement of energy absorption performance.

Considering that the traditional thin-walled structure has limited room to improve energy absorption efficiency and stability, it can no longer meet current requirements. Researchers have found that applying biological structural features to structural design can effectively enhance its energy absorption performance [10–13]. Song et al. [14] designed a novel bionic tube with grooves and studied its crashworthiness under lateral impact. The study demonstrated that the innovative design is conducive to improving the energy absorption efficiency of regular structures. Based on the structural characteristics of bamboo, Zou et al. [15] designed a bionic tube and solved its numerical examples under axial/transverse impact. Palombini et al. [16] mechanically explored the special geometry of a

**Citation:** Tao, Y.; Wang, Y.; He, Q.; Xu, D.; Li, L. Comparative Study and Multi-Objective Crashworthiness Optimization Design of Foam and Honeycomb-Filled Novel Aluminum Thin-Walled Tubes. *Metals* **2022**, *12*, 2163. https://doi.org/10.3390/ met12122163

Academic Editor: Amir M. Yousefi

Received: 15 November 2022 Accepted: 14 December 2022 Published: 16 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 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/).

single vascular bundle in bamboo, and the new design proposed has a better improvement in its strength and crashworthiness under dynamic loads. Ferdynus et al. [17] proposed a new type of trigger for the square tube and focused on its effect on the energy absorption indicators achieved (triggering effect).

Metal matrix syntactic foams are high-performance foams consisting of a light-weight matrix and a set of porous fillers. Orbulov and Szlancsik et al. [18–20] carried out a lot of experimental work to characterize its structure–mechanical property relationship. Fiedler et al. [21] analyzed the mechanical properties of the foam with gradient characteristics. Rabiei et al. [22,23] manufactured steel composite metal foam core sandwich panels and studied their quasi-static mechanical properties. These studies show that metal foam has superior mechanical properties and can be used as energy absorption materials.

In order to further enhance the crashworthiness, some scholars fill the regular tubes with lightweight porous materials such as metal foam and honeycomb [24–28]. Li et al. [29,30] conducted bending experiments on foam-filled tubes with different structures. Qi et al. [31] conducted a numerical analyzed mechanical behavior investigation of empty and foamfilled hybrid beams, and optimized their design. Pandarkar et al. [32] elaborated on foamfilled pipes, and the main conclusion was that filling thin-walled structures can improve the stability of the structure. Cakıroglu [33] focused on the quasi-static mechanical properties of honeycomb-filled round pipes and optimized their crashworthiness design. Inspired by biology, Nian et al. [34] proposed a new type of gradient honeycomb-filled round tube and systematically studied its crashworthiness under lateral load. Yao et al. [35] mainly analyzed the dynamic responses of honeycomb-filled structure under various conditions.

In summary, the novel thin-walled tube obtained by filling with foam and honeycomb material has better crashworthiness. Although there are a large number of studies on the foam or honeycomb filling structures, comparative studies of these two filling methods are rarely reported. Therefore, it is important to conduct in-depth research of the mechanical behavior of the novel thin-walled tubes filled with foam and honeycomb, and then to understand the collision behavior and energy absorption characteristics between them more thoroughly. The difference in the dynamic response of the foam and honeycomb-filled novel thin-walled tubes under different filling styles is systematically studied, specifically involving the energy absorption characteristics, peak impact force, deformation mode and load displacement characteristics. The optimization design of the most promising filling structure with excellent crashworthiness is further conducted to maximize the specific energy absorption and minimize the peak collision force.

#### **2. Numerical Model**

#### *2.1. Geometric Model of the Filling Structure*

Figure 1 gives the geometric model of the filling structure. *Rinner*, *Router* and *T* are the radius and wall thickness of the inner and outer round tubes, respectively. The dotted line in the picture is the angle bisector of the angle α, and the intersection of two adjacent oblique lines falls on the intersection of the angle bisector and the section line of the outer tube. The sizes of *Rinner*, *Router*, *T* and *α* are, respectively, 15 mm, 30 mm, 1 mm and 90◦. Figure 2b exhibits the different filling methods of these novel thin-walled structures. Among these seven filling styles, G is a full filling style and A–F are partial filling styles. The filling structure adopts the following naming rules: F and H indicate foam and honeycomb, and the second letter indicates the filling style. For example: FA means using foam to fill in A style of filling, HA uses honeycomb to fill in style A.

**Figure 1.** Geometric configuration of the filling structure: (**a**) novel thin-walled structure; (**b**) filling styles.

**Figure 2.** Finite element model of the filled structure. (**a**) the calculation model of the axial compression; (**b**) the calculation model of the axial compression; (**c**) Finite element mesh model of thin-walled tube.

#### *2.2. Finite Element Model*

To study the impact behavior of the infill structure under impact load, a model of the infill structure was constructed by the nonlinear dynamic finite element method for simulation. Figure 2 is the numerical simulation model of infill structure. Part a in Figure 2 is the calculation model of the axial compression of the filling structure. The tube wall and honeycomb are treated as shell, the foam is treated as solid. The impact block and rigid wall are set as rigid bodies. When the impact block impacts the thin-walled tube axially at a speed of 20 m/s, the rigid wall at the bottom is fixed. The contact settings in the dynamic compression process are as follows: the thin-walled tube adopts automatic single-surface contact and the contact between thin-walled tube and the rigid wall is set as surface-to-surface contact. The sensitivity analysis of the mesh shows that the mesh size of the element of 1.5 mm × 1.5 mm is sufficient to produce reliable results. In these contacts, the dynamic and static friction coefficients are set to 0.2 and 0.3. The right side of part a in Figure 2 is the model of the filling structure under different filling methods, with a length of 150 mm.

Part b is the finite element model of the filling structure under lateral load. The indenter and the supports are treated as rigid bodies. The indenter impacts the thin-walled structure vertically downward at 4.4 m/s and the supports are fixed during the impact. The settings of contact properties, mesh size and thin-walled tube length are the same as part a.

#### *2.3. Material Properties*

The material of the new thin-walled tube and honeycomb filler is aluminum alloy AlMgSi0.5F22 with density *<sup>ρ</sup>* = 2.7 × 103 kg/m3, elastic modulus *<sup>E</sup>* = 68.566 GPa, Poisson's ratio *ν* = 0.29, yield stress *σ<sup>y</sup>* = 231 Mpa and ultimate stress *σult* = 254 Mpa. Considering that aluminum is not sensitive to strain rate, material strain-rate effect can be ignored during simulation analysis [36]. The foam filling is made of foamed aluminum. In order to save calculation cost and ensure sufficient calculation accuracy, crushable foam is used for modeling. The platform stress of lightweight porous materials is very important for its energy absorption. The calculation formula of foam aluminum platform stress *σ<sup>p</sup>* [31,37] is as follows:

$$
\sigma\_p = \mathbb{C}\_{\text{pww}} \left( \frac{\rho\_f}{\rho\_0} \right)^n \tag{1}
$$

In the formula, *ρ<sup>f</sup>* and *ρ*<sup>0</sup> are the density of the foam and foam substrate, respectively. The density of aluminum is *<sup>ρ</sup>*<sup>0</sup> = 2.7 × <sup>10</sup><sup>3</sup> kg/m3. *Cpow* and *<sup>n</sup>* are constants. According to the test results in literature [38], *Cpow* = 526 Mpa and *n* = 2.17. The simplified functional relationship of the foam stress–strain curve is used for simulation, as shown in Table 1 [39]. The Young's modulus of the foam is *E* = 64.8 GPa, the tensile stress cut-off value is 1.11, the rate-sensitive damping is 0.05 and the Poisson's ratio is 0.01 [31].

**Table 1.** Simplified stress–strain relationship of aluminum foam.


#### *2.4. Evaluation Index*

Generally, energy absorption (*EA*), average crushing force (*MCF*), maximum collision force (*MIF*), specific energy absorption (*SEA*) and crushing force efficiency (*CLE*) are commonly used evaluation indicators. As a key indicator, specific energy absorption (*SEA*) is often used to evaluate the mechanical performance of thin-walled structures. A larger *SEA* means better crashworthiness. The calculation formula is as follows:

$$SEA = \frac{EA}{M} \tag{2}$$

Among them, *M* is the total mass and *EA* indicates the total absorbed energy of the structure. The calculation formula of *EA* is as follows:

$$EA = \int\_0^s F(x)dx\tag{3}$$

In the formula, *S* indicates the displacement of impact force and *F*(*x*) represents the instantaneous collision force.

*CLE* is an index for evaluating the uniformity and consistency of the collision force. It is another very important evaluation index for crashworthiness. It can be calculated as:

$$\text{CLE} = \frac{\text{MCF}}{\text{PCF}} \times 100\% \tag{4}$$

Among them, *MCF* is the average crushing force, *PCF* is the maximum collision load and the calculation formula of *MCF* is as follows:

$$\text{MCF} = \frac{1}{s} \int\_0^s F(\mathbf{x}) d\mathbf{x} \tag{5}$$

#### *2.5. Validation of the FE Model*

To verify the effectiveness of the numerical model, the results of the axial compression simulation of foam-filled multi-cell square tube (F01, F40) are compared with the reference results in literature [40]. Figure 3 shows that the simulation values in this paper are consistent with the results in reference [40], which have been verified by the theoretical results. Subsequently, the bending behavior of foam-filled square tube in reference [41]

was simulated. Figure 4 shows the comparison between the test results and the numerical results. Both the force–displacement curve and the deformation mode show a high consistency feature. In summary, the finite element model of axial and lateral impact is sufficiently reliable.

**Figure 3.** The present FE and reference.

**Figure 4.** Comparison of test results and numerical results.

#### **3. Numerical Results**

#### *3.1. Axial Compression Analysis*

In this section, the mechanical behavior of filled structures subjected to axial impact will be studied. The unfilled novel thin-walled tube is also introduced for comparison. Figure 5 shows the *EA* and *SEA* of the filling structure in different filling styles. The *EA* values of the honeycomb- and foam-filled tubes under different filling styles are higher than that of empty tubes (red dotted line) in Figure 5a. In addition, the *EA* of honeycomb/foamfilled tubes shows obvious differences between different filling styles. Partially filled HB/FB has the smallest *EA*, which is, respectively, 8.8% and 17.6% higher than that of empty tube. This shows that whether it is honeycomb or foam filling, the different filling methods of novel thin-walled tube are all conducive to total energy absorption. Additionally, the foam-filling method has better enhancement effect.

**Figure 5.** *EA* and *SEA* of the filling structure under different filling styles. (**a**) *EA* of filling structure. (**b**) *SEA* of filling structure.

Considering that foam and honeycomb filling may compromise the weight efficiency of the novel structures, Figure 5b compares the *SEA* of the filling structures. As shown in the picture, the *SEA* of the foam-filled tube is relatively low, regardless of the filling method. By contrast, the honeycomb filling method increases the *SEA*. Among the foam/honeycombfilled tubes, partially filled FB/HA has the largest *SEA*, which is 40.4% lower and 18.2% higher than that of the empty 20.86 KJ tube. Although foam filling plays a positive role in improving mechanical properties, it greatly impairs the weight efficiency. It is worth noting that honeycomb filling just compensates for this defect. Figure 6 shows the peak impact force of the filling structure with different filling methods. The foam-filled structure has the greatest peak force, while the empty tube has the least. This shows that honeycomb is more conducive to reducing peak force than foam filling. Among foam/honeycomb-filled tubes, fully-filled FG/HG has the largest *PCF*, followed by partially filled FE/HD, and partially filled FB/HA is the smallest.

**Figure 6.** *PCF* of filling structure under different filling styles.

From the above analysis, we can see that FB/HA has the best crashworthiness among these novel thin-walled tubes. To have a better understand, Figure 7 exhibits deformation modes of FB, HA and the unfilled thin-walled structure. These three thin-walled structures have all undergone orderly and progressive folding. However, they have different folding characteristics. As shown in the partial enlarged cross-sectional view on the right, the honeycomb-filled tube outside (black solid line ellipse) and the number of internal folds (black solid line box) are larger than foam-filled and empty tubes. Although the number of folds on the outside of the foam-filled tube is the same as that of empty tube, there are more folds on the inside of the foam-filled tube. Meanwhile, the whole structure of the foam-filled structure has a certain degree of plastic deformation (such as the blue solid line box) when the compression displacement is 60 mm, while more plastic deformation means that more impact energy is absorbed, which explains why the *EA* of FB is greater than that of HA.

**Figure 7.** Deformation mode of filling structure.

#### *3.2. Three-Point Bending Analysis*

The thin-walled structures will also be subjected to lateral loads in actual use. Thinwalled structures are not only impacted by axial loads, but are sometimes also impacted by lateral loads. Therefore, the bending performance of the structure is very important for its application. Figure 8 shows the *EA*, *SEA*, *PCF* and *CLE* of the filling structure under different filling styles. As shown in Figure 8a, the *EA* of foam- and honeycomb-filled structures are both larger than that of empty tube. Fully filled FG and HG have the largest *EA*, followed by partially filled FA and HD. In particular, under the same filling style, just the *EA* of the honeycomb-filled tube in the filling style C exceeds that of foam-filled tube. This shows that both foam and honeycomb filling will cause the increase in total absorbed energy, and foam filling is more conducive to the growth of *EA* than honeycomb filling. However, it does not represent an increase in its energy absorption efficiency. The *SEA* of honeycomb-filled tube is higher than that of empty tube. The *SEA* of foam/honeycombfilled pipes showed significant differences. The partially filled FB/HF has the largest *SEA*, which is 27.4%/26.8% lower/higher than the empty tube. The results indicate that the honeycomb filling is an extremely effective means to enhance energy-absorption capacity, and the F filling method may be the best choice.

**Figure 8.** *Cont*.

**Figure 8.** The performance indicatorsof the filling structures under different filling methods: (**a**) *EA*; (**b**) *SEA*; (**c**) *PCF*; (**d**) *CLE*.

The *PCF* of the filling structures is also compared in Figure 8c. The *PCF* of foam and honeycomb filling is greater than that of empty tube, and *PCF* of the foam filling tube is the highest. At the same time, the *PCF* of foam and honeycomb tubes are affected by filling method. In Figure 8d, filling techniques do not make *CLE* of the empty tube change too much and the *CLE* did not change significantly with the change of the filling method.

Based on the above, FB/HF has the best energy absorption characteristics among foam/honeycomb-filled tubes. For further understanding the difference in bending performance, the force–displacement curves, specific energy absorption–displacement curves and deformation modes are selected for comparative analysis, as shown in Figure 9. The impact force for the honeycomb filling tube and the empty tube presents the same trend. It first increases sharply and then slowly decreases, while the collision force of the foam-filled tube shows a monotonous increasing trend. The collision force of foam- and honeycomb-filled structures is bigger, and when the loading displacement is equal to 120 mm, the collision force of foam-filled pipes is the largest. This means that foam and honeycomb-filled tubes can withstand a higher level of lateral impact and transmit greater bending moments. In order to better illustrate this point, Figure 9c shows their deformation modes. It can be seen from the map that the partially recessed area of the foam-filled tube is arc-shaped. The effective contact area is larger than that of the honeycomb-filled and empty tube. Although honeycomb filling and empty tube both have the phenomenon of concentrated deformation area, the local recessed area is V-shaped. However, the cross-sectional deformation of the partially recessed area of the honeycomb-filled tube is more obvious than that of empty tube. As shown in the *SEA*-displacement curve in Figure 9b, the *SEA* of honeycomb-filled tube is the largest. This is just the opposite for foam-filled tube. Therefore, foam-filled tubes are not the best choice for crashworthiness.

**Figure 9.** *Cont*.

**Figure 9.** Comparison of filled structures: (**a**) force–displacement diagram; (**b**) SEA-displacement diagram; (**c**) deformation mode.

#### **4. Multi-Objective Optimization Design**

*4.1. Optimization Problem Set-Up*

It is often required that thin-walled structures can absorb the most energy in a certain range of peak stress. Therefore, *SEA* and *PCF* are selected as two objectives of this optimal design. Crashworthiness optimization aims to maximize *SEA* and minimize *PCF*. However, *SEA* and *PCF* are in conflict with each other. Therefore, a multi-objective optimization design is selected to solve this contradictory objective problem [42–45]. From the analysis in Section 3.2, FB and HF have better crash resistance. Moreover, the crashworthiness of HF is better than that of FB. However, the optimal crashworthiness of these structures still depends on different structure and material parameters. Therefore, in this section, the novel thin-walled tube wall thickness *T*, honeycomb wall thickness *t* and foam density *ρ<sup>f</sup>* are used as design variables. The crashworthiness optimization problem is described as follows:

The optimized expression of FB is as follows:

$$\begin{cases} \text{Minimize } [PCF(T, \rho\_f)\_\prime - SEA(T, \rho\_f)]\\ \text{s.t} \begin{cases} 0.5 \text{ mm} \le T \le 1.5 \text{ mm} \\ 170 \text{ Kg/m}^3 \le \rho\_f \le 340 \text{ Kg/m}^3 \end{cases} \end{cases} \tag{6}$$

The optimized expression of HF is as follows:

$$\begin{cases} \text{Minimize } [PCF(T, \,\rho\_f), -SEA(T, \,\rho\_f)]\\ \text{s.t} \begin{cases} 0.5 \text{ mm} \le T \le 1.5 \text{ mm} \\ 0.01 \text{ mm} \le t \le 0.1 \text{ mm} \end{cases} \end{cases} \tag{7}$$

The optimized expression of empty tube is as follows:

$$\begin{cases} \text{Minimize } [PCF(T, \,\rho\_f)\_\prime - SEA(T, \,\rho\_f)]\\ \text{s.t.} \{0.5 \text{ mm} \le T \le 1.5 \text{ mm} \end{cases} \tag{8}$$

#### *4.2. Experimental Design*

The main experimental design methods include central composite design, Taguchi orthogonal experiment method [45], Latin hypercube design and full-factor experiment. Because the full-factor experiment has good uniformity [10,39], this paper uses the fullfactor design to generate 16 sample points (four levels for design variables *T*, *t*, *ρf*), as shown in Figure 10. Subsequently, numerical simulation on these sample points is carried out and corresponding response values are obtained.

**Figure 10.** Design sample points of FB and HF.

#### *4.3. Predictive Model*

Since the construction of *SEA* and *PCF* forecasting models is important for the crashworthiness optimization, the accuracy of forecasting models needs to be verified. Firstly, through polynomial regression analysis (PR), the functional relationship between the optimization objective and design parameters is established, and the corresponding prediction model is obtained. Then, the square value of index *R* (*R*2), adjusted *R<sup>2</sup>* (*R*<sup>2</sup> *adj*), root mean square error (*RMSE*) and maximum relative error (*MARE*) are used to evaluate the accuracy of this prediction model. The corresponding expression is as follows:

$$R^2 = 1 - \frac{\sum\_{i=1}^{n} (y\_i - \hat{y}\_i)^2}{\sum\_{i=1}^{n} (y\_i - \hat{y})^2} \tag{9}$$

$$R\_{adj}^2 = 1 - \left(1 - R^2\right) \frac{n-1}{n-k-1} \tag{10}$$

$$RMSE = \sqrt{\frac{\sum\_{i=1}^{n} (y\_i - \hat{y}\_i)^2}{n}} \tag{11}$$

$$MARE = \max\_{i=1,2,\ldots,n} (\frac{|y\_i - \mathcal{Y}\_i|}{|y\_i|}) \tag{12}$$

Among them, *yi* represents the value of the design points obtained by experiment and numerical analysis, *y*ˆ*<sup>i</sup>* is the predicted value of prediction model, *n* is the number of experimental sample points, *y* represents the average value of *yi* and *k* is the number of non-constant items. Normally, the closer *R*<sup>2</sup> is to 1, the higher the degree of fit; the smaller the *RSME* and *MARE*, the more accurate the prediction model. Table 2 gives the accuracy index of the forecasting model of FB, HF and empty tube. From Table 2, we can see that all *R*<sup>2</sup> values are close to 1, and all *MARE* values are less than 6%. Therefore, it can be considered that these PR mathematical models are accurate enough to be used in crashworthiness optimization.

**Table 2.** Accuracy of the prediction model.


*4.4. Particle Swarm Algorithm and Optimization Process*

Since the particle swarm algorithm has the advantages of easy implementation, high accuracy and fast convergence [46,47], this paper uses the particle swarm algorithm to obtain a Pareto relatively optimal solution of the prediction model. Ten particles are set for tracking and each particle moves 100 times in the constrained space for accuracy. The inertia weight *w* is an important parameter that affects the pros and cons of the particle swarm algorithm. The solution of the HF prediction model obtained by the particle swarm algorithm under different inertia weights is shown in Figure 11. It can be seen from the picture that when the inertia weight is equal to 0.7, the solutions of the *SEA* and *PCF* prediction models have undergone large oscillations at first, and then stabilized in a certain area. Therefore, when the inertia weight is equal to 0.7, the convergence is best. The specific parameters of the particle swarm algorithm are shown in Table 3. Figure 12 is the flow chart of the optimized design. First, the full-factor experimental design is carried out on the problem of clear optimized design. Further, perform simulation analysis on the sample points to obtain the target response value. Then, the prediction models of *SEA* and *PCF* were constructed through polynomial regression analysis. Finally, the Pareto optimal solution set is given after the calculation of the prediction model by the optimized algorithm.

**Figure 11.** The solutions of *SEA* and *PCF* under different inertia weights.


**Table 3.** Parameters of particle swarm algorithm.

**Figure 12.** Optimization design flow chart.

#### *4.5. Multi-Objective Optimization Results*

To comprehensively analyze the crashworthiness difference between FB, HF and empty tube more, the Pareto boundary obtained after particle swarm optimization is compared and shown in Figure 13. It can be found from the figure that when the *PCF* is constant, the closer the Pareto boundary is to the left, the greater the specific energy absorption (*SEA*). The Pareto optimal solution set of HF is closest to the left, followed by the empty tube. Therefore, the crashworthiness of HF is better than that of FB and empty tube, and the crashworthiness of FB is the worst. In engineering applications, designers can choose based on requirements of *PCF*. When the *PCF* is less than or equal to 15 KN, the red five-pointed star in the map is the optimal design point of each structure. Figure 14 shows the force–displacement diagrams and deformation modes of these three optimal structures. The *PCF* of the three structures in Figure 14a is less than 15 KN, and HF has the largest *PCF*. In Figure 14b, local recessed area of the HF optimal structure presents an arc shape, while both FB and empty tube present V shapes.

**Figure 13.** Comparison of the Pareto boundary of FB, HF and empty tube.

**Figure 14.** Comparison of the optimal structure: (**a**) force–displacement diagram; (**b**) deformation mode.

#### **5. Conclusions**

To further enhance the crashworthiness of the novel thin-walled structure, foam and honeycomb are used to fill it. The numerical simulation model of the filled structure was first built and verified using the nonlinear dynamic Abaqus software. Then, the impact resistance of honeycomb-filled tubes, foam-filled tubes and empty tube under axial load was systematically compared and analyzed. Furthermore, based on the force–displacement curve, specific energy absorption and deformation model, a comparative analysis of the mechanical behavior of filled tubes subjected to lateral impact was carried out. The optimization design of the most promising filling structure with excellent crashworthiness was finally conducted to maximize the specific energy absorption and minimize the peak collision force. The results of this study show that:

(1) The introduction of honeycomb filling and foam filling enabled the thin-walled structures to absorb more energy. The total absorbed energy increases at least 8.8% compared with the empty tube. At the same time, the crashworthiness of the filling structure was closely related to the filling styles. The foam filling will greatly impair the weight efficiency of the novel thin-walled tube. However, honeycomb filling was beneficial to the improvement of *SEA*, which can be improved by up to 18.2%.

(2) Honeycomb filling was more conducive to the reduction of *PCF* than foam filling under axial load. Among foam/honeycomb-filled tubes, fully filled FG/HG had the largest *PCF*, followed by partially filled FE/HD and FB/HA was the smallest.

(3) Under the action of lateral load, foam- and honeycomb-filled tubes could withstand a higher level of lateral impact and transmit greater bending moments than empty tube. Among foam/honeycomb-filled tubes, FB/HF was the most promising structure with excellent crashworthiness.

(4) The particle swarm algorithm was further used for crashworthiness optimization design of FB and HF, and the Pareto boundaries were obtained and compared. By way of contrast, the optimal structure of HF showed the best crashworthiness. In practical engineering applications, the use of honeycomb-filled novel thin-walled tube may be the best choice.

**Author Contributions:** Conceptualization, Y.T.; resources, L.L.; software, Y.W.; writing—review and editing, Y.W. and D.X.; methodology, Q.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is supported by The National Natural Science Foundation of China (No. 51705215), The Chinese Postdoctoral Science Foundation (2022M712932) and the Natural Science Fundamental Research Project of Jiangsu Universities (No. 22KJA460003).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare there is no conflict of interest regarding the publication of this work.

#### **References**


## *Article* **Microstructural Evolution and Mechanical Properties of Al-Si-Mg-Cu Cast Alloys with Different Cu Contents**

**Pengfei Zhou 1,2,3, Dongtao Wang 1,2,\*, Hiromi Nagaumi 1,2,\*, Rui Wang 1,2, Xiaozu Zhang 1,2, Xinzhong Li 1,2, Haitao Zhang 1,4 and Bo Zhang <sup>5</sup>**

	- <sup>4</sup> Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China
	- <sup>5</sup> Shandong Weiqiao Aluminum & Electricity Co., Ltd., Binzhou 256200, China
	- **\*** Correspondence: dtwang@suda.edu.cn (D.W.); zhanghai888jp@suda.edu.cn (H.N.)

**Abstract:** The mechanical properties of Al-Si-Mg-Cu cast alloys are heavily determined by Cu content due to the precipitation of relating strengthening precipitates during the aging treatment. In this study, the microstructures and mechanical properties of Al-9Si-0.5Mg-*x*Cu (*x* = 0, 0.9, 1.5, and 2.1 wt.%) alloys were investigated to elucidate the effect of Cu content on the evolution of their mechanical properties. After T6 (480 ◦C+6h − 530 ◦C + 4 h, 175 ◦C + 10 h) treatment, Mg-rich and Cu-rich phases were dissolved in the matrix; the main aging-precipitates of the alloys change from the needle-like β phases in the base alloy to the granular Q phases in the 0.9Cu alloy, the granular Q phase in the 1.5Cu alloy, the granular Q phase, and θ platelets in the 2.1Cu alloy. The increase of Cu level results in difference of the type, number density, and morphology of the nanoscale precipitated phase. Because of precipitation strength, the yield strength was increased by 103–130 MPa depending on the Cu contents. The precipitation strengthening effect of the precipitates was quantitatively evaluated by the Orowan mechanism. The aging-treated Al-9Si-0.5Mg-2Cu alloy shows the good strength and ductility: yield strength 351 MPa, ultimate tensile strength 442 MPa, and elongation 8.4%. The morphologies of fracture surfaces of the alloys also were observed.

**Keywords:** Al-Si-Mg-Cu alloy; Cu content; microstructure; precipitate; mechanical properties

#### **1. Introduction**

Al-Si cast aluminum alloys are extensively used in the automobile field due to their superior castability, satisfactory mechanical and physical properties, and low coefficient of thermal expansion [1–4]. Adding Mg to Al-Si alloys plays a role in solid solution strengthening and precipitation hardening of aging treatment [5–7]. Cu can significantly increase the mechanical properties of Al-Si-Mg alloys with the formation of nanoscale θ and Q precipitates during aging [7–10]. Unlike that of Al-Si-Mg and Al-Si-Cu cast alloys, the precipitation strengthening of the Al-Si-Mg-Cu alloy is mainly related to the β, θ , and/or Q phases; meanwhile, the type and volume fraction of Mg and/or Cu-rich precipitates are closely related to heat-treatment conditions and Cu level [7,9,10]. However, the enhanced strength of the Al-Si-Mg alloys with Cu addition is usually at the expense of their ductility. In addition, the addition of Cu can decrease the melting point and eutectic temperature of Al-Si-Mg alloys, leading to an increase in the solidification range of the alloys and facilitating porosity formation. Simultaneously, with the increase in Cu content, the precipitates in Al-Si-Mg alloys constantly change in type, morphology, quantity, and size [7,9–13]. Some useful understandings have been reported in the properties and precipitation behavior change with Cu addition in these quaternary alloys [4,7,8]. Shang [12] systematically

**Citation:** Zhou, P.; Wang, D.; Nagaumi, H.; Wang, R.; Zhang, X.; Li, X.; Zhang, H.; Zhang, B. Microstructural Evolution and Mechanical Properties of Al-Si-Mg-Cu Cast Alloys with Different Cu Contents. *Metals* **2023**, *13*, 98. https://doi.org/10.3390/ met13010098

Academic Editor: Francesco Iacoviello

Received: 5 December 2022 Revised: 27 December 2022 Accepted: 28 December 2022 Published: 2 January 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/).

analyzed the phase component of these alloys with a wide Cu level (0.01–4.5 wt.%) and discussed the effect of precipitates on mechanical properties. The previous works mainly focus on the strengthen effect of θ precipitates in high-Cu/low-Mg Al-Si-Mg-Cu alloy. When Mg content increases and ratio of Cu/Mg decreases, the Q nano-phase may show a high fraction after aging treatment, which may change the aging-strengthen effect. However, the work on systematic observation and characterization needs to be conducted in greater detail in low-ratio of Cu/Mg alloy, including the effects of precipitates on the hardening behavior of these alloys.

Therefore, the current study mainly evaluates the effect of Cu content on the microstructural evolution and mechanical properties of Al-9Si-0.5Mg-*x*Cu alloys (Cu/Mg: 0–4) and discusses the contribution of precipitates to the hardening behavior of Al-Si-Mg*x*Cu alloys.

#### **2. Materials and Methods**

#### *2.1. Material Preparation*

Commercial-purity Al (99.9%), pure Mg (99.95%), pure Cu (99.9%), Al-20%Si master alloys (all compositions quoted in this article are in weight percentage unless otherwise mentioned), and Al-10%Sr alloy as metamorphic eutectic Si were used to prepare Al-Si-Mg-Cu alloys in a 50 kW resistance furnace. Commercial-purity Al and Al-20%Si were first melted in the resistance furnace. The melt was heated to 740 ◦C and held at that temperature for 30 min to ensure all components were sufficiently mixed. Then, pure Cu and Mg were added into the melt at 750 ◦C and held for 20 min, followed by slag removal. The Al-10%Sr alloy was added into alloy melts at 730 ◦C. The alloy melt was ultimately poured into a water-cooled copper mold (25 × <sup>100</sup> × 200 mm3, Figure 1) to form an as-cast ingot [14–16].

**Figure 1.** Schematic of the sample position for microstructural and tensile tests.

#### *2.2. Material Characterization*

The measured compositions of the designed Al-Si-Mg-*x*Cu alloys, which were noted as A1, A2, A3, and A4 were measured using an SPECTROLAB stationary metal analyzer (SPECTROLAB M12, Kleve, Germany). The results are listed in Table 1.

**Table 1.** Composition of the Al-Si-Mg-Cu alloys [wt.%].


Compositional analysis and microstructural evaluation were conducted on samples near the center of the Φ10 mm tensile rods (the red area in Figure 1). The phase compositions of the as-cast alloys were analyzed using a X-ray diffraction (XRD) to identify the phase composition of the alloys with CuKα1 radiation by using PW3040/60X diffractometers. The samples were etched for 2–10 s by using 0.5% hydrofluoric acid for scanning electron microscopy (SEM) characterization using a Phenom X1 scanning electron microscopy (SEM) equipped with X-ray energy dispersive spectroscopy (EDS). The secondary dendrite arm spacing (SDAS) was measured by the intercept method. Quantitative measurements of the SDAS were conducted by optical microscopy using image analysis software (MEDIA CYBERNETICS, Rockville, MD, USA), at least 50 dendrites were measured and their average value is considered as the representation of SDAS [17].

Transmission electron microscope (TEM) samples of the region near the fracture were prepared by sectioning the tensile specimens in the transverse direction. The section near the center of the specimen was polished by hand to approximately 50 μm before a standard 3 mm disc was punched out. Then, the samples were placed on a Gatan 695 PIPS ion beam thinner (Gatan, Inc., Pleasanton, CA, USA). A FEI Tolos F200x (TEM, Tolos F200x, FEI Ltd., Pleasanton, CA, USA) transmission electron microscope equipped with the energy dispersive X-ray spectrometer was operated at an accelerating voltage of 200 kV. All images were taken along the <001>Al zone axis in order to characterize the cross-sections and side views of the precipitates. The average length (l) was calculated using 500 precipitates growing along [100] Al and [010] Al in total. The average area of cross-section of the precipitates (Acs) were calculated in 60 HRTEM images.

#### *2.3. Mechanical Testing*

All samples were treated with the solution at 480 ◦C − 6 h + 530 ◦C − 4 h, followed by cold water quenching (about 20 ◦C). Aging treatments were then performed at 175 ◦C for 10 h. The tensile property of the samples was tested on a DNS-300 universal experimental machine produced by Changchun Machinery Research Institute at a tensile rate of 1 mm/min. The extensometer with a gauge length of 25 mm was used. At least five tensile test specimens were tested for each alloy.

#### **3. Results and Discussions**

#### *3.1. As-Cast Microstructures*

Figure 2 presents the backscattered SEM images of the as-cast alloys. All alloys have α-Al dendritic microstructure, eutectic Si, and eutectic Mg/Cu-containing phases. Secondary dendrite arm spacing was calculated by Image-Pro Plus (6.0, Media Cybernetics, Inc, Rockville, MD, USA), and the values of the A1–A4 alloys were 22.76 mm, 18.66 mm, 18.02 mm, and 18.25 mm, respectively. As shown in Figure 2a, in the absence of Cu, several black Chinese character-shaped phases are present in the as-cast A1 alloy, and the Energy Dispersive Spectrometer (EDS) result indicates that the composition of the back phase is Al-1.79 at.%Mg-6.06 at.%Si, indicating the Mg2Si phase [4,5]. With Cu content increasing to 0.9 wt.%, the quantity of Mg2Si phase decreases. The bright phases are observed in the A2 alloy. The bright phases are dispersed in the eutectic silicon region (Figure 2b). The EDS analysis indicates that the bright phase is Al-15.69 at.%Cu-12.46 at.%Mg-12.05 at.%Si. In A3 alloy, the bright phases increase and the Al2Cu phases are observed, the composition is Al-29.01 at.%Cu. With the Cu content further increasing from 1.5 to 2.1 wt.%, the bright Al2Cu phase increases (Figure 2d). Moreover, the Fe-containing phases were observed in the four alloys (Figure 2), the composition of the Fe-rich phase are: Al-26.38 at.%Si-12.13 at.%Mg-3.78 at.%Fe in A1 alloy, Al-26.22 at.%Si-14.76 at.%Mg-4.29 at.%Fe in A2 alloy, Al-25.45 at.%Si-17.19 at.%Mg-5.59 at.%Fe in A3 alloy, and Al-27.56 at.%Si-11.35 at.%Mg-3.42 at.%Fe in A4 alloy.

**Figure 2.** SEM-BSE images of as-cast alloy (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4.

XRD patterns of the as-cast alloys are presented in Figure 3. The A1 alloy consisted of α-Al, Si, and Mg2Si phases, which is consistent with the microstructural observation in Figure 2a. Compared with that of the A1 alloy, in A3 and A4 alloys, the diffraction peaks of Q-AlCuMgSi and θ-Al2Cu phases were observed, indicating that the Cu addition results in the formation of Q and θ phases. These results are consistent with Figure 2c,d. Therefore, the phase composition of the Al-Si-Mg-Cu alloy system was closely related to the Cu content; meanwhile, the content of each phase was also determined by the Cu and Mg contents [6–10]. In A2 alloys, the XRD results do not show the diffraction peaks of Q and θ phases, but the microstructure in Figure 2b indicates the presence of Q and θ phases. The low fractions of Q and θ phases in low-Cu A2 alloy may result that they hardly be detected by XRD. Moreover, the XRD results indicate the presence of Al8Mg3FeSi6 phase in A1–A4 alloys.

#### *3.2. Microstructures after T6 Treatment*

Heat treatment can affect the microstructural features of Al-Si-Cu-Mg alloys [4,11]. Figure 4 presents the SEM-mapping images of the alloys after T6 treatment. Compared with the as-cast state (Figure 2), the Cu-containing phases were mostly dissolved into the α-Al matrix after solid solution treatment. The residual bright phases after solution treatment are mainly Fe-containing phases, which show the same distribution of Mg and Fe in Figure 4a,b and can be identified as the AlFeMgSi phase. In Figure 4c,d, it indicates that the other Fe-containing phase of small quantity show in A3 and A4 alloys. Moreover, the slight

Cu/Mg-containing phases is residual in high-Cu level A4 alloy. Except the dissolution of Mg and Cu into the matrix, the eutectic Si happens evident spheroidization and dispersion, as shown in Si mapping images of Figure 4.

**Figure 3.** XRD image of as-cast alloys.

**Figure 4.** SEM-mapping images of the alloys after aging treatment (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4.

The TEM micrographs of the alloys after aging treatment are shown in Figure 5. The comparison of the TEM images of the A1–A4 alloys indicates that the nano-precipitates precipitated during aging process show a higher number density with increasing Cu level. By contrast, the lamellar precipitates were observed in A4 alloy. Here, the lamellar precipitates are mainly Cu-containing phases, may be the sheet θ platelets specifically [7,8]. The number density of precipitates is listed in Table 2. The number density of the precipitates was estimated by η = 3 N, where N is the precipitate cross-section in the image. The factor 3 comprises the three growth directions of the precipitates [13]. In Table 2, the increase in Cu content improves the number density of the precipitates in the aging-treated alloys.

**Figure 5.** Bright-field TEM images of the alloys after aging treatment (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4. **Table 2.** Number density of precipitate in aging-treated samples.


Figure 6 presents the TEM results for the precipitates in A1 alloy after aging treatment. This precipitate shows the monoclinic structure with lattice parameters of a = 1.51 and

c = 0.67 nm (Figure 6b), in addition to the orientation relationships of (200)precipitate//(301)Al (Figure 6b) and [010]precipitate//[010]Al (Figure 6c,d). These results indicate that these precipitates are β" phases [13,18], and no other precipitates are observed. This precipitate is regarded as the most common one in the aged Al alloy. HRTEM images (Figure 6b–d) show that the precipitate is coherent with the Al matrix.

**Figure 6.** β" phase in A1 alloy in the <010>Al axis after aging treatment: (**a**) TEM image, (**b**) HRTEM image, (**c**) corresponding FFT, (**d**) schematic pattern.

Figure 7 shows the TEM image and the corresponding FFT pattern of the precipitate in A2 alloy. The HRTEM image and FFT pattern indicate that β" precipitates are in the aged A2 alloy. A closer check of A2 alloy reveals that the precipitation of another nanophase (Figure 8) in addition to the extensive β" phase (Figure 7). This precipitate shows an angle of 120◦ between its a and b axes, and exhibits a typical dense stacked hexagonal lattice (HCP) crystal structure. The lattice parameter of this precipitate is a = 1.032 nm, which is obtained using an internal standard method. The precipitate interface was largely parallel to the three crystal faces of the Al matrix—(501)Al, (103)Al, and (506)Al—but was mostly distributed along <510>Al with an orientation relationship of (2110)precipitate//(501)Al, [0001]precipitate//[010]Al. On the basis of previously reported literature data [19], this precipitate in A2 alloy is identified as granular Q phases. In general, the main precipitates in A2 alloy are the needle-like β" phase and the granular Q phase. It can be seen from Figures 7 and 8 that the precipitates are coherent with the Al matrix.

**Figure 7.** β" phase in A2 alloy in the <010>Al axis after aging treatment: (**a**) TEM image, (**b**) HRTEM image, (**c**) corresponding FFT, (**d**) schematic pattern.

Figure 9 shows the TEM images and the corresponding FFT pattern of the granular precipitate in the aged A3 alloy. The Q nano-phase also can be observed, but no precipitate of other type was observed. Combined with the results in Figure 8, this result indicates that large quantity of Q phases can be identified in A3 alloy. The size of the Q phase is approximately the same as in A2 alloy, and the predominant precipitates in the aged A3 alloy are the granular Q phases, and it is coherent with the Al matrix. As can be seen in Figure 10, the precipitates in A4 alloy have a crystal structure, lattice parameter, and orientation relationship similar to those of the Q phase.

**Figure 8.** Q phase in A2 alloy in the <010>Al axis after aging treatment: (**a**) TEM image, (**b**) HRTEM image, (**c**) corresponding FFT.

**Figure 9.** Q phase in A3 alloy in the <010>Al axis after aging treatment: (**a**) TEM image, (**b**) HRTEM image, (**c**) corresponding FFT.

**Figure 10.** Q phase in A4 alloy after aging treatment along the <010>Al axis: (**a**) HRTEM image, (**b**) corresponding FFT.

Figure 11 shows the TEM images of the lamellar precipitates in A4 alloy, which indicates that these precipitates are distributed along {200} Al. A closer examination shows that the precipitates exhibit the crystal structure and lattice parameters: a = 0.404 nm, c = 0.58 nm, and an orientation relationship of (200)precipitate//(200)Al, [010]precipitate//[010]Al. Therefore, this nano-phase is identified as θ [7,20], and the predominant precipitates in the aged A4 alloy are Q and θ . Additionally, normally, the reduction of interfacial energy causes the precipitates to be compact, while reduction of elastic energy leads to the formation of the plate shape. The ratio between the bulk elastic driving force and the interfacial energy is size dependent, and thus, the tendency towards plate formation depends on the precipitate size. The shape formation of smaller precipitates is mostly driven by interface reduction and therefore the precipitates tend to be more spherical when the interfacial energy is assumed to be isotropic. Combined with Figure 5, the precipitated phase was gradually changed from short rod to granulate to lamellar with increasing Cu content.

**Figure 11.** θ phase in A4 alloy after aging treatment, observed along the <010>Al axis: (**a**) TEM image, (**b**) HRTEM image, (**c**) corresponding FFT.

In summary, the types of aging-precipitate changes with the change of Cu level in alloys, which transforms from needle-like β in A1 alloy to granular Q and needle-like β in A2 alloy. A3 alloy mostly consists of granular Q phase. When Cu level increases to 2.08%, the Q and θ are the main precipitates in aged A4 alloy.

#### *3.3. Tensile Properties*

The ultimate tensile strength (UTS), 0.2% yield strength (YS), and the elongation to fracture of the solution- and aging-treated alloys are listed in Table 3. The strength of the studied alloys increases, and the elongation slightly decreases with increasing of Cu level. Figure 12 presents the engineering stress–strain curves of the alloys under quenching and aging conditions. Under solution-treated state, the YS increases from 161 to 221 MPa and the UTS increases from 275 to 363 MPa when Cu content increases from 0–2%. Meanwhile, the solution-treated alloys of A1–A4 show the high elongations of 16–18%. After aging treatment, the YS and UTS markedly improve in A1–A4 alloys. With increasing Cu content, the YS increases from 264 to 351 MPa, UTS increases from 322 to 442 MPa, and the elongation decreases from 10 to 8.4%.


**Table 3.** Tensile properties of the designed alloys under different conditions.

**Figure 12.** Engineering stress–strain curves of the alloys after solid solution and aging treatment.

Comparing the tensile properties of the alloys treated under different conditions, the change in strength of the alloys with different Cu contents can attribute to solid-solution and aging strengthening. In solution-treated samples, the increase of Cu content results in a higher solution content, which shows a higher solution strengthen effect. The YS and UTS of solution-treated samples gradually increase when Cu content increases. After aging treatment, the mechanical properties of the alloys markedly increase; the aging-treatment is more effective than solution treatment on influence of strength in the Al-Si-Mg-*x*Cu cast alloy. Moreover, it indicates that the elongations of aging-treatment samples decrease due to the inverted relationship between strength and ductility.

Notably, the yield strengths of the Al-Si-Mg-*x*Cu alloys markedly improve after aging treatment. The improvement in yield strength can be attributed to the nano-precipitates of the β", Q , and θ phases. The contribution of the precipitates to yield strength can be calculated by the Ashby–Orowan equation [13]:

$$
\sigma\_D = \frac{0.84MGb}{2\pi(1-\upsilon)^{1/2}\lambda} \ln \frac{r}{b'} \tag{1}
$$

where *<sup>M</sup>* is the Taylor factor, *<sup>M</sup>* = 3.1, *<sup>G</sup>* and *<sup>b</sup>* were the shear modulus (2.65 × 1010 N/m2) and the Burgers vector of dislocations in the Al matrix (2.84 × <sup>10</sup>−<sup>10</sup> m), and *<sup>v</sup>* is the Poisson's ratio for Al (0.33). The interspacing of the precipitates *λ* depends on the radius r and volume fraction *Vf* of the precipitates, as follows:

$$
\lambda = r \left(\frac{2\pi}{3v\_f}\right)^{\frac{1}{2}},\tag{2}
$$

Volume fraction (*Vf*) of precipitates:

$$V\_f = n!A\_{c\star\prime} \tag{3}$$

where *n* is the number density of precipitates, *l* is the average length of dispersoids, and *Acs* is the average area of the cross-section of precipitates. According to Equations (2)–(4), the increase of yield strength caused by precipitates is calculated, which is listed in Table 4.

**Table 4.** Differences in the yield strength of the samples between quenching and aging and the contribution to yield strength from precipitates calculated by the Orowan mechanism.


As can be seen from Table 4, the calculated data agree well with the improved experimental data of yield strength after aging process. However, the measured increase is a little bit lower than the calculated increase in yield strength contributed by the precipitates. This difference can be explained by the decrease of solute strengthening, since the solute concentration in solid solution decreases during aging process [13,21,22].

According to the Orowan bypass mechanism, the yield strength increment (Δ*σs*) shows the relationship with the *f* and *r* (Equation (4)), where α is a constant for the material, *f*

is the second-phase particle (aging precipitates) volume percentage, and *r* is the average radius of the second phase particle (aging precipitates) [13,22]:

$$
\Delta \sigma\_s \propto a \cdot f^{1/2} \cdot r^{-1} \tag{4}
$$

This relationship was used to analyze variation tendency of yield strength increment with the precipitate size, as shown in Figure 13. It indicates that the increasing effect of the aging precipitates on the yield strength is proportional to *<sup>f</sup>* 1/2·*r*<sup>−</sup>1. Therefore, the increment of the yield strength is increased with the increase of *<sup>f</sup>* 1/2·*r*−<sup>1</sup> in Figure 13, which is consistent with the Orowan mechanism.

**Figure 13.** The variation tendency of yield strength increments with the *<sup>f</sup>* 1/2·*r*<sup>−</sup>1.

Figure 14 shows the fracture surfaces of the alloys after T6 treatment. The casting defect does not be observed in the fracture surfaces. The fracture surfaces of the four alloys are occupied by dimples formed by spheroidizing and dispersive Si particles. These dispersive Si particles can result in the fine and homogeneous dimples during one-axis loading process, which is important for high ductility of Al-Si-Mg-Cu cast alloy. In the loading-bearing process, most granular Si particles were pulled out in dimples, and dimples formed in the Al matrix, represented by the yellow arrows in Figure 14. Moreover, the fracture surfaces in T6-treated samples do not show the residual Cu- and Fe-containing phases, avoiding adverse effect on the ductility by coarse intermetallic. Therefore, the elongations of aging-treated samples are higher than 8%, which can meet the engineering application requirements of Al-Si-Cu-Mg casting alloy.

**Figure 14.** Fracture surfaces of the alloys after T6 treatment: (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4.

#### **4. Conclusions**

The microstructures and mechanical properties of Al-9Si-0.5Mg alloys with Cu addition were investigated. The following conclusions are drawn from this study.


**Author Contributions:** Conceptualization, D.W. and H.N.; Methodology, P.Z., D.W. and X.Z.; Validation, X.Z., X.L. and B.Z.; Formal Analysis, R.W. and B.Z.; Investigation, H.N., H.Z. and R.W.; Resources, D.W., B.Z. and R.W.; Data curation, P.Z., B.Z. and X.Z.; Writing—Original draft preparation, P.Z. and D.W.; Writing—Review & Editing, P.Z., D.W., X.Z. and R.W.; Visualization, X.L., H.Z. and B.Z.; Supervision, D.W., H.N. and H.Z.; Project administration, X.L., H.N. and H.Z.; Funding acquisition, X.L., D.W. and H.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grants no. 52004168), The Research Fund for International Senior Scientists (Grants no. 52150710544), the National Natural Science Foundation of China (Grants nos. U1864209 and 51771066), the Aluminumbased Transportation Lightweighting Technology Demonstration Project (Grants no. 2021SFGC1001), and the National Foreign Expert Project 2022 (Grants no. G2022014146L). And The APC was funded by The Research Fund for International Senior Scientists (Grants no. 52150710544).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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

#### **References**


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