1. Introduction
Structural aluminum alloys have gained increasing relevance in various sectors, and the automotive industry is one of its leading promoters. These alloys have found extensive applications; firstly, high-end vehicles have embraced their use for chassis and doors, but nowadays, other manufacturers have incorporated structural parts. The main advantage of aluminum alloys is weight reduction; when vehicles become lighter, they reduce energy consumption and improve fuel efficiency. Consequently, this is translated into cost savings for vehicle owners and significantly decreases CO
2 and other greenhouse gas emissions, positively impacting the environment [
1,
2,
3].
One of the most-used aluminum alloys is the 6xxx series, a precipitation-hardening type. These alloys gain enhanced mechanical properties through heat treatment processes based on age hardening. 6xxx alloys are characterized by a main β hardening phase primarily composed of Mg
2Si, dispersed within the aluminum matrix. Various studies have determined the precipitation sequence of the β hardening phase by conducting solutionizing and aging heat treatments [
4,
5,
6,
7]. It is described as follows: supersaturated solid solution (SSSS) → Si/Mg cluster → Guinier–Preston (GP) zones → β″ → β′ → β. The β phase is the primary mechanism for strengthening these alloys.
Naronikar et al. [
8] worked with 6061 alloys, implementing heat treatments by varying the temperature and treatment duration to improve the formability of sheets and plates. In their experimentation, they employed two types of heat treatments. First, a solutionizing treatment was conducted at 530 °C for 1 h, followed by water quenching. Then, an annealing heat treatment was performed at 415 °C for 2 h, followed by furnace cooling (according to the authors, this process is intended to avoid fractures during mechanical forming). After conducting an artificial aging process at 120 °C for 6 h, they reported 354 MPa as the alloy’s ultimate tensile strength (UTS). The authors confirmed that heat treatment influences grain size and precipitate distribution, thereby improving the tensile mechanical properties of the alloy. In another example, Subba Rao et al. [
9] performed a solutionizing treatment on a MoS
2-modified alloy at 520 °C for 1 h, followed by water quenching and aging at 180 °C for 12 h, obtaining a UTS = 246 MPa. These findings highlight the significance of carefully selecting heat treatment parameters to achieve the desired mechanical performance in aluminum alloys.
Using X-ray diffraction (XRD) and scanning electron microscopy (SEM), Aydia et al. [
10] investigated an alloy after a solutionizing treatment at 580 °C for 5 h and aging at 185 °C for 6 h. The SEM analysis revealed the presence of structures such as Al-Fe-Si and the primary hardening phase (Mg
2Si), previously identified by Jacobs as the β phase [
11]. Moreover, recent studies have determined that the precipitates in the 6xxx alloys are (a) precipitates of Mg
2Si, identified in optical microscopy as small, dark particles with an angular or globular shape, depending on the stage of aging; (b) precipitates of AlFeSi, which usually appear as elongated particles or plates, exhibiting an acicular (needle-like) or lamellar shape, and are typically larger than Mg
2Si precipitates; and (c) precipitates of AlMnSi, which are usually thicker and less numerous, appearing as spherical or irregularly elongated particles, and are generally larger than Mg
2Si precipitates but smaller than AlFeSi precipitates [
12,
13,
14]. The main β phase distributed within the aluminum matrix favors tensile mechanical strength, achieving up to 206 MPa of UTS, but decreases corrosion resistance. Furthermore, fracture analysis of alloys subjected to solutionizing and aging heat treatments revealed a ductile fracture mechanism, typically characterized by dimples, as some researchers have demonstrated previously [
15,
16,
17].
The mechanical properties of aluminum alloys are closely related to heat treatment parameters, as evidenced by the studies reviewed previously. In optimizing heat treatment conditions, employing specialized methodologies becomes helpful in effectively assessing the critical variables inherent in these processes. Among the techniques available, the Taguchi design of experiments (DOE) is a robust methodology devised by the Japanese engineer Genichi Taguchi. This approach simplifies processes and elevates product quality by highlighting the factors influencing performance and variability [
18]. Its efficacy becomes particularly important in scenarios necessitating meticulous tests and measurements to comprehend and predict mechanical properties, including tensile strength.
Several remarkable applications of Taguchi DOE in optimizing mechanical properties in materials have been documented. For instance, Leisk and Saigal [
19] optimized the critical parameters of an aluminum heat treatment process to improve alumina/aluminum metal matrix composites, resulting in a notable increase in yield strength. Similarly, Yang et al. [
20] utilized the Taguchi method to optimize heat treatment parameters for enhanced mechanical properties in a 2219 aluminum alloy produced via wire-arc additive manufacturing. Their findings emphasized the significant impact of solution temperature on alloy strength. Moreover, in the study undertaken by Afrasiabi et al. [
21], the Taguchi DOE was employed to enhance the corrosion resistance of a 6061 aluminum alloy. By optimizing heat-treatment process parameters and investigating the effect of NaCl (sodium chloride) concentration, researchers successfully improved the alloy’s resistance to corrosion. Another notable application was performed by Alphonse et al. [
22], in which the Taguchi DOE was instrumental in identifying optimal heat-treatment parameters for a forged 2219 aluminum alloy, improving tensile strength and elongation percentage. These examples highlight the versatility and efficacy of the Taguchi DOE in optimizing mechanical properties across various materials and fabrication processes.
Our investigation was conducted to determine the phases present and the influence of the strengthening β phase on the tensile and hardness properties of a 6061-aluminum alloy. Solutionizing and artificial aging heat treatments were applied at various temperatures and for various durations based on a Taguchi experimental design. Characterization techniques such as XRD and SEM were employed to identify the phases and assess the tensile properties after the heat treatments. The Taguchi experimental design, through analysis of variance (ANOVA), facilitated the systematic selection of the heat treatment parameters, allowing for a comprehensive understanding of the relationship between the β phase and the mechanical properties of the alloy.
3. Results
3.1. Tensile Strength Evaluation
Table 4 presents the tensile test results (average of three repetitions) after the experimental series from the combination of parameters exhibited in
Table 3 was conducted (DOE). The analysis begins by explaining and interpreting the tensile test results because they serve as the starting point for the microstructural analysis of the samples and the further investigation of fracture behavior. Also, the ultimate tensile strength is an indicator or reference for the study of the Taguchi DOE and ANOVA.
As a reference, we measured the tensile strength of the as-received alloy, which was found to be 274 MPa with a standard deviation (SD) of 10 MPa. Although a mechanical strength of 290–310 MPa is often mentioned in the literature as a typical value for 6061-T6 alloy, the ASTM B209 standard [
32] specifies a minimum UTS value of 42 ksi (approximately equivalent to 289 MPa). Then, our measured UTS of 274 MPa (SD = 10 MPa) for the as-received material is, to some extent, slightly below this minimum specification.
However, it is important to note that we purchased the commercial plate from a local supplier and assumed inherent variations as accounted for in the ASTM E8 standard, particularly Table X1.1 in [
30], where a repeatability and reproducibility (R&R) value of 12.1 MPa is reported, indicating variability due to sampling. Given this context, our measurement of 274 MPa falls within the acceptable range when considering the reported tolerance value and our measurement precision.
Furthermore, the UTS of 293.7 MPa (SD = 1.5 MPa) obtained from our best condition after the heat treatment study indeed shows an improvement compared to the original strength of the as-received alloy. This result emphasizes the main point of our research: the significant influence of solutionizing and aging parameters on the mechanical properties of the alloy, from a Taguchi DOE perspective.
Thus, UTS was chosen as the primary output response, and a criterion of the larger-the-better approach was selected. The signal-to-noise (S/N) ratio for each run is calculated as the negative logarithm of the reciprocal of the squared output value. The average S/N ratio for a particular factor level combination is then determined as follows:
where
is the number of replicates, 3 for our L27 (3^4) design; and
is the response variable value for the
-th replicate. Once the S/N ratios for each combination of factor levels are calculated, they can be compared and analyzed to determine the optimal factor level settings that maximize the S/N ratio for the specific objective.
The samples that exhibited the best mechanical tensile properties among the tested samples were those in the 7th run (see
Table 4); also, this run showed the maximum S/N ratio of 49.357 dB, according to the criterion of “the larger, the better”. These samples were processed at a solutionizing temperature of 540 °C or 3 h, followed by aging at 170 °C for 18 h, resulting in an average ultimate tensile strength of 293.7 MPa. In contrast, samples from the 1st run exhibited the lowest mechanical properties; they were subjected to a solutionizing temperature of 520 °C for 3 h and aging at a temperature of 150 °C for 12 h, yielding a significantly lower UTS, of only 193.7 MPa. The sample comparison demonstrates the considerable influence of the solutionizing and aging parameters on the resulting mechanical properties, as can be inferred from
Table 4. Stress vs. strain curves for selected samples are exhibited in
Figure 1 (only the 3 best and the worst samples were plotted); please note that numerical values of UTS for each individual combination of factors are exhibited in
Table 4.
3.2. Analysis of Variance and the Fit Result of the Model
Once UTS was determined to be the primary output parameter, the models’ behavior and their variables were analyzed by constructing an ANOVA table. We proposed a design of experiment (DOE) using a Taguchi L27 (3^4) array (see the experimental parameters of DOE in
Table 3 and the results of the experiments in
Table 4), using the residuals and the total sum of squares to calculate the source of variation of the models (as specified in
Table 1).
Table 5 shows the ANOVA performed for the regression model, considering all 27 experiments that were realized based on the combinations of levels and factors previously specified in
Table 3. The model is representative by having a
p-value < 0.05; i.e., the model adequately represents the variability that occurs in the process. This comprehensive analysis allows us to assess the significance and contribution of each factor and its interactions across the entire experimental matrix.
The probability
p-value is an approach for making decisions in hypothesis tests. One way to report the results of a hypothesis test is to state that the null hypothesis (usually denoted
Ho) was or was not rejected at a specified
α-value or significance level; this α-value is typically 0.05. The
p-value is the probability that the test statistic will take on a value that is at least as extreme as the observed value of the statistic when the null hypothesis
Ho is true [
33]. A
p-value conveys a lot of information about the weight of evidence against
Ho so that a decision-maker can draw conclusions at any significance level. Thus, the
p-value is the smallest level of significance that would lead to the rejection of the null hypothesis
Ho with the given data. It is customary to call the test statistic (and the data) significant when the null hypothesis
Ho is rejected; therefore, we may consider the
p-value the smallest level at which the data are significant. Once the
p-value is known, the decision maker can determine how significant the data are without the data analyst formally imposing a preselected significance level (in this case,
α = 0.05). Please note that a
p-value of approximately zero implies that it is much lower than the significance level (see
Table 5).
The ANOVA for the regression model using the Taguchi L27 (3^4) array method can be seen in
Table 5. This adequately represents what happens in the process by having a
p < 0.05, and the calculated F is higher than the F distribution in 1 −
α =
P(
F ≤
fα, 4, 12) with
α = 0.05, indicating that the model rejects the null hypothesis and concludes that the ultimate tensile strength of the alloy is linearly related to four factors: (A) solutionizing temperature, (B) aging temperature, (C) solutionizing time, and (D) aging time. Additionally, we intend to identify which variables have a greater weight in the model and process, where it is observed that the tensile strength model is less affected by the variable aging temperature with a value
p = 0.109 (
p > 0.05) and a calculated F of 2.79, noting that this has a lower weight in the model. Therefore, this variable does not have statistical significance to the ultimate tensile strength value when compared with the
p-value of the other parameters. This observation is supported by the
p-value reported for the aging temperature variable, which was found to be
p = 0.109. In contrast, the
p-values for the other variables (solutionizing temperature, solutionizing time, and aging time) were all below the significance threshold of 0.05, indicating their statistical significance with respect to the response variable.
The linear regression model was fitted using the data collected by the Taguchi array method from the 27 performed experiments (see
Table 4). As a result of this process, the resultant model is shown in Equation (11):
where the intercept
and slope (
) of the line are called regression coefficients, and
are the factors (or regressors) involved in the DOE (solutionizing temperature, aging temperature, solutionizing time, and aging time, respectively) affecting the predicted output
, i.e., the UTS value.
In that case, the ultimate tensile strength (UTS) can be expressed as (12):
It is reasonable to assume that the mean of the random variable
is related to
by Equation (11) as a straight-line relationship, and its solution is given by Equation (12). While the mean of
is a linear function of
, the actual observed value
does not fall exactly on a straight line. The appropriate way to generalize this to a probabilistic linear model is to assume that the expected value of
is a linear function of
, but that for a fixed value of
the actual value of
is determined by the mean value function (the regression linear model) [
34]. This is a multiple linear regression model because it has various independent variables or regressors. Sometimes, a model like this will arise from a theoretical relationship. At other times, we will have no theoretical knowledge of the relationship between
and
.
Thus, the regression model in (11) is a line of mean values; that is, the height of the regression line at any value of is just the expected value of for that . (in this case ) is the value of the predicted variable when all regressors are equal to zero, while can be interpreted as the change in the mean of for a unit change in . Furthermore, the variability of at a particular value of is determined by the error variance . This implies that there is a distribution of at each and that the variance of this distribution is the same at each .
In this case, , the intercept , and the slopes are . The input variables are in as follows: solutionizing temperature = , aging temperature = , solutionizing time = , and aging time = (see Equation (12)). Consequently, the regression model shows that the relationship between and the input variables are at a level . Then this fitted regression equation or model can be used in prediction of future observations of or for estimating the mean response at a particular level of .
3.3. Hardness Evaluation
After the heat-treatment process, the hardness of the samples was also assessed. The investigation revealed that fluctuations in hardness primarily depend on the solutionizing temperature. The summarized results are presented in
Figure 2, representing the hardness of all samples treated at a specific solutionizing temperature; it provides valuable insights into the microhardness’s behavior.
Previous authors [
10,
35] have determined that hardness depends on the presence of alloying elements such as Mg and Si, which form intermetallic phases in the presence of Fe, among other elements, as well as the time and temperature of the aging process. With a solutionizing temperature of 540 °C for 3 h, followed by artificial aging at a temperature of 170 °C for 18 h, hardness of up to 98 HV (SD = 2 HV) was achieved. At these solutionizing temperatures, a more significant quantity of alloying elements can be retained as a solid solution, allowing for the precipitation of alloying elements during artificial aging, which forms strengthening phases.
The hardness of an alloy is primarily attributed to the presence of GP zones and strengthening phases, as reported previously [
36,
37,
38,
39]. Notably, at a temperature of 540 °C, the precipitation of Mg
2Si phases and GP zones is favored; then, microhardness values of up to 98 HV (SD = 2 HV) were obtained for these samples. In contrast, the lowest microhardness was observed for a solutionizing temperature of 520 °C.
The initial microhardness of the as-received sample was measured as 101 HV (SD = 4.5 HV), but it is worth noting that a slightly increased hardness does not necessarily enhance the maximum mechanical strength [
38,
39].
Although the change from an average of 101 HV (SD = 4.5 HV) for the as-received material to 98 HV (SD = 2 HV) is not significant, it is important to understand that a slight decrease in hardness does not necessarily correlate with a reduction in mechanical strength. As described by various authors [
15,
16,
17], the β phases (Mg
2Si) present in the as-received material become more voluminous and well-distributed after artificial aging. During the aging process, the β phases precipitate and re-distribute within the aluminum matrix, a phenomenon we confirmed using X-ray diffraction (see
Section 3.5).
According to Demir and Gündüz [
40], increasing the aging time enhances re-precipitation, resulting in increased hardness due to the impeded mobility of dislocations caused by precipitate formation. However, prolonged aging can lead to the coarsening of precipitates, reducing their effectiveness as obstacles to dislocation movement and, consequently, decreasing hardness. This balance between precipitate distribution and size significantly influences the material’s mechanical properties (see
Section 3.4).
In our case, the observed increase in UTS in the 7th run sample (293.7 MPa) compared to the as-received material (274 MPa) can be attributed to the better re-distribution and size of the precipitates achieved through our specific heat-treatment regimen. The artificial aging process used in our experiments led to a favorable precipitate structure that enhanced tensile strength without a corresponding increase in hardness. The reduced hardness (98 HV) indicates a more refined precipitate distribution, which can improve the tensile strength by effectively blocking dislocation motion, thereby increasing UTS.
While the hardness change was minimal, the substantial increase in UTS reflects the successful optimization of the precipitate structure through our heat-treatment process, leading to improved mechanical performance of the alloy.
3.4. Microstructural Analysis
After the heat-treatment, the samples were removed from the furnace, and cross-sections were prepared to analyze their microstructure utilizing SEM. The microstructural results presented here correspond to selected samples from the tensile tests shown in
Table 4.
Figure 3 depicts the microstructure of the as-received alloy material. Equiaxed grains, characteristic of the 6061-T6 alloy, can be observed in
Figure 3a; additionally,
Figure 3b shows the presence of Al-Fe-Si dispersoids.
As-received material was also analyzed by EDS, and its spectrum is exhibited in
Figure 4. It is worth mentioning that the sample exhibited some particles of Al-Fe-Si, as observed previously in
Figure 3. However, EDS analysis revealed that Mg is also present in the metallic matrix, as well as traces of Si. The latter suggested the presence of other phases, mainly the β phase, as would be further confirmed by XRD (see
Section 3.5). Small traces of Fe were also detected by the equipment.
Figure 5a shows the micrograph of a selected sample from the 7th run of the DOE, where equiaxed grains are visible. Also,
Figure 5b exhibits strengthening precipitates, precipitate clusters, and β precipitates alongside Fe-Al-Si dispersoids [
12,
14].
The presence of β phases and dispersoids in the sample with the best mechanical condition (7th run) was confirmed using EDS in
Figure 6. The representation of EDS spectra was performed in an energy range from 0 to 4 keV to highlight traces of Mg (at 1.2 keV), Si (1.75 keV), and Fe (0.65 keV) precursor elements. These elements exhibit much lower relative intensities compared to the characteristic peak of Al, which is at 1.5 keV. Although the original test was conducted in a range of 0 to 7.5 keV, no traces of Mg, Si, or Fe were identified at other energy values, leading to the decision to more clearly display the peaks that are most visible near the characteristic peak of Al.
3.5. XRD Phase Identification
We utilized XRD analysis to identify the β phase. The identification of the strengthening phase presents challenges because the predominant peaks of aluminum from the aluminum matrix complicate intensity measurements, leading to potential confusion between the crystallographic planes of hexagonal aluminum corresponding to the β phase and the FCC structure of the aluminum matrix. However, it is still possible to distinguish the β phase with careful analysis, as explained in the following paragraphs.
Figure 7a presents the XRD pattern of the as-received sample; the highest peak corresponds to aluminum with (200) orientation. By zooming in on the spectrum in
Figure 7b, the presence of the β phase (Mg
2Si) with (220) orientation becomes more evident. Traces of the aluminum matrix with orientations (111) and (311) are also observed [
41].
Figure 8 shows the XRD spectrum corresponding to the sample that exhibited the lowest mechanical properties (1st run), in which the presence of the β phase with orientation (220) is observed. The presence of aluminum peaks having the orientations (111), (220), and (311) is noticeable with greater relative intensity compared to the as-received sample.
Figure 9 presents the XRD pattern of a representative sample from the 7th run, subjected to a solubilization temperature of 540 °C for 3 h and aging at 170 °C for 18 h. It can be confirmed that the thermal treatment has induced recrystallization in the aluminum matrix. This is evident from the altered orientation of the aluminum diffraction peak initially observed at (200) in
Figure 7. Furthermore,
Figure 9 demonstrates a change in the relative intensity of other peaks, indicating the presence of the β phase in the alloy. According to the literature, the morphology of the β phase is typically observed in the form of plates or needles [
11], as previously depicted in
Figure 5, which corroborates the XRD findings. It is important to note that increasing the solution time can result in the dissolution of a more significant amount of the β strengthening phase, leading to increased hardening after the solution treatment [
42]. Therefore, traces of the beta phase can be observed in
Figure 7,
Figure 8 and
Figure 9.
The recrystallization of the aluminum matrix after the thermal treatment is a significant phenomenon in alloy processing. Recrystallization refers to forming new grains with a lower dislocation density and improved structural stability. In this case, the observed shift in the diffraction peak of aluminum (200) suggests a realignment of crystallographic planes, indicating the occurrence of recrystallization. The recrystallization process promotes the development of a more uniform and fine-grained microstructure, which can contribute to enhanced mechanical properties, such as increased strength and improved formability.
3.6. Fracture Mechanisms
An interesting aspect of this study is the evaluation of the fracture mechanisms in the different experimental samples. First, we present the fractography shown in
Figure 10, which corresponds to the sample from run 1, which exhibited the lowest UTS among all the samples. The fractographic analysis reveals the presence of microvoids, characteristic of ductile fracture. However, we also observe traces of cleavage, indicative of brittle fracture. Therefore, this sample exhibited a mixed fracture mechanism, combining both ductile and brittle features [
43,
44].
In contrast, samples in the best condition (7th run, which reported the best performance in the tensile test, achieving the highest UTS result) exhibited different fracture mechanisms. The fracture was predominantly ductile, as indicated by the white arrows highlighting the presence of dimples and micro-cracks, which are characteristic of ductile fracture, as depicted in
Figure 11a. Furthermore,
Figure 11b, captured at 300× magnification, illustrates the presence of dimples and microvoids, reinforcing the observation that the specimen exhibits good ductility [
8]. The rest of the samples, including the as-received materials, exhibit similar fracture behavior, demonstrating consistent ductile fracture characteristics across these conditions.
The existence of distributed microvoids throughout the fractured aluminum matrix indicates good ductility and a favorable distribution of the strengthening β phase (Mg
2Si). The formation of microvoids occurs due to various mechanisms, including grain boundary sliding and dislocation movement [
16]. During tensile deformation, stress concentrations can lead to the nucleation and growth of microvoids, which subsequently coalesce and form larger voids. These voids are then observed as dimples on the fracture surface. The localized coalescence of microvoids into larger dimples results from the interaction between the plastic deformation mechanisms and the material microstructure. Grain boundaries, as well as dislocations, play a crucial role in this process. The sliding of grain boundaries and the movement of dislocations promote stress concentration around certain regions, leading to the nucleation and growth of microvoids. As deformation continues, these microvoids coalesce and form dimples, which are energy-absorbing features during the fracture process. A significant note is that fractographs obtained from tensile testing are more likely to reflect the plastic deformation ability of the material, corresponding to its elongation property, rather than solely indicating its strength. It is essential to consider that numerous factors, including the phases present within the material, influence the stress experienced by the material during testing.
4. Discussion
The mechanical testing results obtained through the DOE analysis (
Section 3.1) start from the essence of the Taguchi DOE, which is the ability to construct an efficient and informative experimental design. By selecting fewer factors and levels, we aimed to simplify the experimental process and focus on the most influential variables while maintaining statistical robustness (as the ANOVA exhibited in
Section 3.2). This approach allows us to achieve reliable results with fewer experiments than traditional full factorial designs, making the Taguchi DOE a valuable tool for experimental optimization. This approach is inherent to the Taguchi DOE’s capabilities and aligns with the principles of sound experimental design. To analyze the results of evaluating the selected parameters on the ultimate tensile strength, we analyzed the hardness (
Section 3.3) and the microstructure (
Section 3.4); also, we conducted a hardening phase study (
Section 3.5) and performed a fracture evaluation (
Section 3.6).
Yield strength is relevant in mechanical testing evaluation, especially when the material’s response to plastic deformation is predominant. However, we focus on UTS from the specific nature of processes such as welding and similar procedures, where the tensile strength often determines the final response due to several factors, including the variability in the 0.2% yield strength resulting from the mixture of microstructures generated during the cooling process. This variability can significantly impact the material’s performance, particularly its ability to withstand applied stresses and resist deformation. In welding, the capacity of joints to withstand stress emphasizes the importance of considering the ultimate tensile strength in evaluating weldability and joint integrity [
27]. Furthermore, in applications such as wear-resistance assessments, where hardness measurements serve as an initial indicator, ultimate tensile strength plays a crucial role, as it is directly correlated with hardness. Similarly, in phase transformation processes, the material’s tensile strength is a key indicator of its response to heat-treatment, which is a critical consideration in various industries.
The Taguchi design of experiment is a potent and efficient methodology distinctively adept at discerning crucial factors, minimizing variability, enhancing performance, and conserving resources [
18]. Particularly in assessing mechanical properties such as tensile strength, its application transcends traditional testing and measurement approaches (often performed as a trial-and-error procedure), offering a proficient and cost-effective means of optimization. Moreover, this methodology is evaluated using ANOVA to propose a prediction model that explains the contribution of each variable in the heat-treatment process to the final UTS value.
After ANOVA was applied to the Taguchi DOE, we obtained a regression model where the ultimate tensile strength of the alloy was linearly related to four factors: solutionizing temperature, aging temperature, solutionizing time, and aging time. It is important to note that the variable “aging temperature” was the least influential factor according to the analysis of variance, referring specifically to its relationship with the model and its generalization capability. This does not imply that aging temperature does not influence the outcome of the heat-treatment process because aging temperature is crucial in determining the final tensile strength.
Comparing the determination coefficient, the regression model obtained R2 = 93.18%. Thus, the model accounts for about 93% of the variability in the tensile strength response. Note that for the multiple regression model for the tensile strength data, = 91.95%. Therefore, we would conclude that adding the variable of aging temperature to the model does result in a meaningful reduction in unexplained variability in the response.
A cross-validation approach was employed to assess how well the model can predict results in different datasets. The was reserved for assessing the model’s predictive ability. The obtained fitting results () was 89.75%, indicating that the model can explain approximately 90% of the variability observed in the test data for prediction and to evaluate the model’s predictive capacity.
Therefore, at this point, it is crucial to explain the combined role of the variables involved in the heat-treatment process and the resulting ultimate tensile strength values in terms of the specific characteristics of this alloy. Increasing the solutionizing temperature to 540 °C allows more alloying elements, such as Mg, Si, and Cu, to remain in a solid solution [
10,
45]. Subsequently, these elements precipitate during artificial aging at high temperatures to form the Mg
2Si (β) phase [
3,
17]. In a study on various 6XXX-type alloys, Mrówka-Nowotnik and J. Sieniawski [
36] determined that tensile strength in such alloys is influenced by the amount of Mg and Si present in a supersaturated solution, with Mg
2Si being the primary strengthening phase.
The reinforcement of the tensile strength of the alloy after the heat-treatment process can also be attributed to the movement of dislocations due to the presence of foreign particles from any other phase. However, if the temperature increases, as observed in run 7, with aging at 170 °C and a solutionizing temperature of 540 °C, when we relate hardness to tensile strength, samples treated at 530 °C exhibited lower hardness. This is reflected in decreased tensile strength or strengthening due to the coalescence of precipitates within a larger particle. Additionally, the annealing of defects occurs, which causes a reduction in obstacles to the movement of dislocations.
Ternary systems like Al-Mg-Si and alloys without an excess of Si exhibit a well-established precipitation sequence, as was demonstrated in previous studies using transmission electron microscopy (TEM) [
37,
46]:
Solid solution
GP (Guinier–Preston) zones
Needle-shaped precipitates aligned with the (100) direction of the matrix and coherent with the Al matrix along their major axes
β′ phase (rod-shaped precipitates, semi-coherent with the matrix)
β phase (Mg2Si, plate-shaped equilibrium precipitates)
This sequence illustrates the compositional changes during precipitation, contributing to understanding the alloy’s mechanical properties. It is worth noting that numerous studies in the literature have effectively utilized TEM to explain the microstructural evolution during aging treatments. Notably, research compiled by Ding [
5] has provided comprehensive insights into the transformation sequence, including observing GP zones and the evolution of the beta phase through applying TEM. Additionally, references such as those by Jacobs [
11], Saito [
6], and Matsuda [
47] have extensively investigated the phenomenon of beta dissolution utilizing TEM techniques, further supporting the efficacy of TEM in studying microstructural evolution during aging treatments. These findings align with the precipitation sequence previously reported [
6,
15]: super-saturated solid solution (SSSS) → Si/Mg clusters → Guinier-Preston (GP) zones → β″ → β′ → β.
Despite recrystallization (during the solutionizing stage), the β phase is still evident in the alloy after the thermal treatment, as we observed by XRD examination. The β phase is known for its strengthening effect on aluminum alloys, as it precipitates from the supersaturated solid solution during aging. The indexation of the diffraction peak at (220) confirms the existence of the β phase in the alloy (see
Figure 9). It is worth noting that the morphology of β can vary, and in this alloy, it appears to exhibit plate-like or needle-like shapes (see
Figure 5). These precipitates contribute to the overall strengthening mechanism by impeding dislocation movement and enhancing the alloy’s resistance to deformation. Thus, XRD analysis confirmed the microstructural changes that occur during the thermal treatment of the alloy. It also confirms the recrystallization of the aluminum matrix and the persistence of the strengthening β phase, being important in understanding the alloy’s microstructural evolution and optimizing its mechanical properties.
Finally, the presence of dimples and microvoids on the fracture surface is desirable because it implies that the material has undergone plastic deformation before failure. This indicates that the alloy possesses good ductility and can withstand significant strains without sudden brittle failure. The favorable distribution of the β phase within the aluminum matrix further enhances the mechanical properties, contributing to the material’s ability to deform plastically and absorb energy during fracture. This highlights its favorable mechanical behavior and ability to withstand deformation under tensile loading conditions.