Experimental Investigation on Tensile Properties and Yield Strength Modeling of T5 Heat-Treated Counter Pressure Cast A356 Aluminum Alloys

Abstract

In the present study, experimental investigations on microstructures and tensile properties of an counter-pressure cast (CPC) A356 aluminum alloy under different T5 heat treatment conditions were conducted in the temperature range of 160–200 ${}^{\circ }$C for 1–48 h. As the T5 heat treatment time increased, both tensile and yield strength of the CPC A356 alloy either continuously increased at 160 ${}^{\circ }$C until 48 h of heat treatment time or increased until the maximum strength values were achieved and then decreased, showing peak aging behavior at 180 and 200 ${}^{\circ }$C. Changes in microstructural aspects, such as size and aspect ratio, of the eutectic Si, Mg and Si distribution in the $\alpha$-Al grain and the stability of intermetallic compounds were found to be negligible during the T5 heat treatments employed in the present study. From high resolution-transmission electron microscope (HR-TEM) analysis, nanosized needle-like ${\beta }^{″}$ precipitates were identified in the specimens, showing a significant increase in strength after the T5 heat treatment. Based on the measured tensile properties and observed microstructure changes, a yield strength model was proposed to predict yield strengths of CPC A356 alloys at arbitrary T5 heat treatment conditions. The calculation results of the model showed good agreement with the experimental data obtained in the present study. From the model calculations, the optimal T5 heat treatment time or temperature conditions were suggested.

1. Introduction

The consumption of aluminum alloys in the automotive industry has been increased for weight reduction in order to improve mileage or reduce emissions of vehicles. Specifically, the A356 aluminum alloy, one of the Al-Si-Mg casting alloys designated by the Aluminum Association in the United States, has been widely used for automobile parts due to its high strength, corrosion resistance, and excellent castability [1]. Mass productions of automobile parts using the A356 aluminum alloy are based on various casting processes, such as gravity die casting, low-pressure die casting, and counter-pressure die casting. In particular, the counter-pressure die casting process pressurizes both the lower chamber containing molten aluminum and the upper chamber containing casting molds so as to fill the mold under a working pressure higher than the atmospheric pressure. This filling process is beneficial in terms of less melt turbulence, higher heat transfer efficiency between mold and casting, less gas porosity, etc. [2]. Furthermore, undercooling of the molten metal could occur during the solidification under the increasing external pressure, resulting in further refinement of the microstructure [3].

Meanwhile, A356 alloy castings are generally followed by a heat treatment process in order to improve mechanical properties. The most widely used heat treatment for A356 alloy is the so-called T6 heat treatment process, which consists of a solution heat treatment and a subsequent artificial aging treatment. The A356 alloy could be also subjected to the T5 heat treatment process (artificial aging without solution treatment after casting) if a moderate level of strength and elongation is sufficient or the distortion of the casting after solution treatment and subsequent rapid quenching is critical for a specific automotive part. Tensile properties data of counter-pressure cast (CPC, hereafter) A356 alloys after T5 heat treatment, however, were scarce, and a few available studies were only focused on squeeze casting [4] or semi-solid casting processes [5].

When it comes to the optimization issue of heat treatment conditions, it is the typical method to conduct a number of heat treatment experiments at different times and temperature conditions, followed by microstructure observation and mechanical tests. This experimental approach, however, is time-consuming and expensive. Therefore, it is efficient to optimize the heat treatment process by utilizing numerical simulation techniques, such as modeling of tensile behavior of the aluminum alloy, with consideration of various strengthening mechanisms and microstructural changes during heat treatments [6,7,8,9].

In the present study, experimental investigations on the microstructure and mechanical properties of a CPC A356 aluminum alloy after a T5 heat treatment were conducted in the temperature range of 160 to 200 ${}^{\circ }$C for 1 to 48 h. Furthermore, a yield strength model was proposed based on the measured tensile properties and observed microstructure changes in the CPC A356 specimens after T5 heat treatments.

2. Experiments

2.1. Material and Heat Treatment

A CPC A356 aluminum alloy in the form of automotive knuckles manufactured by Myunghwa Co., Ltd., Seoul, Rep. of Korea was selected in the present study. The A356 automotive knuckles were counter-pressure cast into a permanent mold, quenched into warm water (∼40 ${}^{\circ }$C), and naturally aged longer than a week at room temperature before the T5 heat treatment. The chemical composition of the CPC A356 aluminum alloy used in the present study is shown in

Table 1. The chemical composition of CPC A356 aluminum alloy (wt%).

Element	Si	Mg	Ti	Fe	Sr	Al
Content	7.01	0.40	0.12	0.11	0.0057	Balance

. Bar-type specimens (18 × 13 × 110 mm) were machined from the knuckles, followed by artificial aging heat treatment in a muffle furnace. The heat treatment temperatures were controlled from 160 to 200 ${}^{\circ }$C, and the heat treatment time varied from 1 to 48 h. After the desired time of heat treatment, the specimens were air-cooled out of the furnace.

2.2. Mechanical Properties

Tensile properties of T5 heat-treated CPC A356 alloys were determined from the tensile test samples machined in the form of ASTM E8 sub-size which have a gauge length of 25 mm. Uniaxial tension tests were performed using a universial testing machine (Model 8801, Instron Co., Norwood, MA, USA) under a constant crosshead speed of 1 mm/min. At least three tensile tests were conducted for each heat treatment condition to ensure the reproductivity of the test results.

2.3. Microstructure Observation

In order to perform microstructure observation, square samples (10 × 10 × 10 mm) were cut from T5 heat-treated bar-type specimens, and the cross-section was ground and polished up to 0.04 μm alumina suspension. Morphologies of $\alpha$-Al, eutectic Si, and intermetallics were observed by an optical microscope (Eclipse MA 200, Nikon, Tokyo, Japan). The size and aspect ratio of eutectic Si were quantitatively measured from optical microscope images at 100× magnification with image analysis software (iSolution DT, IMT iSolution Co., Seoul, Korea). The size of a Si particle was defined according to the following equation:

$$r=\sqrt{A/\pi }$$

(1)

where r and A are the equivalent radius and area of a Si particle, respectively. The aspect ratio of a Si particle was determined as the ratio of the major axis to the minor axis of the fitted ellipse to the Si particle. At least 500 particles of eutectic Si were analyzed for accuracy. Furthermore, the chemical compositions of $\alpha$-Al and intermetallics were determined by energy dispersive spectroscopy (EDS) with a field emission-scanning electron microscope (FE-SEM, JSM-7100F, JEOL, Tokyo, Japan). For the investigation of nanosized precipitates, tiny specimens prepared by a focused ion beam (FIB, JIB-4601F, JEOL, Japan) were subjected to nanoscale observation via a high-resolution-transmission electron microscope (HR-TEM, JEM-2010, JEOL, Japan).

3. Yield Strength Modeling of T5 Heat-Treated CPC A356 Alloy

A yield strength model of T5 heat-treated CPC A356 alloy was suggested by considering various strength contributions from different microstructures, such as $\alpha$-Al, eutectic Si, and nanosized precipitates. As will be described in Section 4.1, the precipitation of ${\beta }^{″}$ after T5 heat treatment was remarkable in the present CPC A356 alloy, whereas negligible microstructural changes of eutectic Si and intermetallics and insignificant composition changes of solutes in $\alpha$-Al were observed in the same specimens. Therefore, precipitation kinetics of ${\beta }^{″}$, which significantly affects the yield strength after heat treatment, were mainly described as simple equations in order to predict the size and fraction of ${\beta }^{″}$ precipitates during the T5 heat treatment. The yield strength of the T5 heat-treated CPC A356 alloy was then calculated based on several strengthening mechanisms, including precipitation hardening by ${\beta }^{″}$. For simplicity, the effect of intermetallics on the mechanical properties of the alloy was not considered in the present study.

3.1. Precipitation Kinetics Model

The precipitation sequence of the A356 alloy is generally accepted as below [10,11,12,13]:

$$\mathrm{SSS}\to \mathrm{clusters}(\mathrm{involving}\mathrm{Mg}\mathrm{and}/\mathrm{or}\mathrm{Si})\to \mathrm{GP}\mathrm{zones}\to {\beta }^{″}\to {\beta }^{\prime }\to \beta$$

(2)

where SSS is the supersaturated solid solution. In the present study, the significant strength increase in CPC A356 alloys after the T5 heat treatment was confirmed with the formation of ${\beta }^{″}$ particles. Therefore, a mathematical model for microstructure changes in A356 alloy during T5 heat treatment was described with a focus on the precipitation kinetics of ${\beta }^{″}$.

In order to briefly describe nucleation and growth behavior of ${\beta }^{″}$, the Johnson–Mehl–Avrami–Kolmogorov (JMAK) Equation [14,15,16] was introduced in the present study:

$$f_{{\beta }^{″}}=1-\exp (-k_{{\beta }^{″}}^{\mathrm{NG}}{t}^n)$$

(3)

$$k_{{\beta }^{″}}^{\mathrm{NG}}=k_{{\beta }^{″}}^{\circ ,\mathrm{NG}}\exp \left(\frac{-Q_{{\beta }^{″}}^{\mathrm{NG}}}{\mathrm{R}T}\right)$$

(4)

where $f_{{\beta }^{″}}$, $k_{{\beta }^{″}}^{\mathrm{NG}}$, $\mathit{n}$, $Q_{{\beta }^{″}}^{\mathrm{NG}}$, and R are the relative volume fraction of ${\beta }^{″}$, the JMAK kinetic parameter of ${\beta }^{″}$, the time exponent, the activation energy of nucleation and growth of ${\beta }^{″}$, and the gas constant (8.314 J/mol · K), respectively. Meanwhile, the average radius of ${\beta }^{″}$ precipitate ($r_{{\beta }^{″}}$) was calculated by assuming the size of ${\beta }^{″}$ precipitate is proportional to its volume fraction:

$$r_{{\beta }^{″}}^3=\frac{f_{{\beta }^{″}}}{f_{{\beta }^{″}}^{\mathrm{peak}}}{\left(r_{{\beta }^{″}}^{\mathrm{peak}}\right)}^3$$

(5)

where $f_{{\beta }^{″}}^{\mathrm{peak}}$ and $r_{{\beta }^{″}}^{\mathrm{peak}}$ are the volume fraction and radius of ${\beta }^{″}$ at the peak aging condition, respectively. In the present modeling of precipitation kinetics of ${\beta }^{″}$, several assumptions were made for simplicity:

• Precipitation kinetics of the needle-like ${\beta }^{″}$ are not much different from those of a spherical precipitate with similar volume so that the size of the needle-like ${\beta }^{″}$ could be expressed as equivalent radius $r_{{\beta }^{″}}$;
• Precipitation kinetics of ${\beta }^{″}$ are dominantly controlled by nucleation and the growth mechanism until its radius reaches to $r_{{\beta }^{″}}^{\mathrm{peak}}$;
• After the peak aging condition, coarsening of existing ${\beta }^{″}$ precipitates occur rather than simultaneous nucleation and growth of ${\beta }^{″}$.

Coarsening of ${\beta }^{″}$ is mathematically described based on the LSW theory [17,18] as below:

$$r_{{\beta }^{″}}^3={\left(r_{{\beta }^{″}}^{\mathrm{peak}}\right)}^3+k_{{\beta }^{″}}^{\mathrm{C}}(t-t_{\mathrm{peak}})$$

(6)

$$k_{{\beta }^{″}}^{\mathrm{C}}=\frac{k_{{\beta }^{″}}^{\circ ,\mathrm{C}}}{T}\exp \left(\frac{-Q_{{\beta }^{″}}^{\mathrm{C}}}{\mathrm{R}T}\right)$$

(7)

where $t_{\mathrm{peak}}$, $k_{{\beta }^{″}}^{\mathrm{C}}$, and $Q_{{\beta }^{″}}^{\mathrm{C}}$ are the time required to reach the peak aging condition, coarsening parameters of ${\beta }^{″}$, and activation energy of coarsening of ${\beta }^{″}$, respectively. The model parameters for the precipitation kinetics model of ${\beta }^{″}$ are summarized in

Table 2. Model parameters for the precipitation kinetics of ${\beta }^{″}$.

Parameter	Unit	Value	Remark
n	-	1.8	Optimized in the present study
$r_{{\beta }^{″}}^{\mathrm{peak}}$	m	1.75 × 10${}^{-9}$	From the literature [19]
$f_{{\beta }^{″}}^{\mathrm{peak}}$	-	0.0072	From the literature [19]
$k_{{\beta }^{″}}^{\circ ,\mathrm{NG}}$	1/sec	4.65644 × 10${}^{16}$	Optimized in the present study
$Q_{{\beta }^{″}}^{\mathrm{NG}}$	kJ/mol	181.384	Optimized in the present study
$k_{{\beta }^{″}}^{\circ ,\mathrm{C}}$	m${}^3$/sec	8 × 10${}^{-7}$	Optimized in the present study
$Q_{{\beta }^{″}}^{\mathrm{C}}$	kJ/mol	125	Optimized in the present study

.

3.2. Yield Strength Model

Yield strength of the T5 heat-treated A356 alloy (${\sigma }_{\mathrm{YS}}$) could be expressed as below:

$${\sigma }_{\mathrm{YS}}={\sigma }_{\mathrm{int}}+{\sigma }_{\mathrm{SS}}+{\sigma }_{\mathrm{Si}}+{\sigma }_{{\beta }^{″}}$$

(8)

where ${\sigma }_{\mathrm{int}}$, ${\sigma }_{\mathrm{SS}}$, ${\sigma }_{\mathrm{Si}}$, and ${\sigma }_{{\beta }^{″}}$ are yield strength contributions from pure Al matrix, solute elements, eutictic Si, and precipitation hardening by ${\beta }^{″}$, respectively. ${\sigma }_{\mathrm{int}}$ and ${\sigma }_{\mathrm{SS}}$ are adapted from the literature [19], and ${\sigma }_{\mathrm{Si}}$ was calculated from the yield strength of as-cast specimen (${\sigma }_{\mathrm{YS}}^{\mathrm{AC}}$) by assuming ${\sigma }_{{\beta }^{″}}$ is negligible at the as-cast condition:

$${\sigma }_{\mathrm{Si}}={\sigma }_{\mathrm{YS}}^{\mathrm{AC}}-{\sigma }_{\mathrm{int}}-{\sigma }_{\mathrm{SS}}$$

(9)

Generally, precipitation hardening could occur by either dislocation by-passing (strong obstacle) or dislocation shearing (weak obstacle) depending on the size of precipitates. In the present study, precipitation hardening by ${\beta }^{″}$ precipitates at their nucleation and growth mode is formulated as precipitate shearing [19]:

$${\sigma }_{{\beta }^{″}}^{\mathrm{SH}}=\frac{M{\left(F^{\mathrm{peak}}\right)}^{2/3}{\left(f_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{1/2}}{b{\left(2\sqrt{3}\pi \right)}^{1/2}{\Gamma }^{1/2}{\left(r_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{3/2}}{\left(f_{{\beta }^{″}}{r}_{{\beta }^{″}}\right)}^{\frac{1}{2}}$$

(10)

where M, $F^{\mathrm{peak}}$, b, and $\Gamma$ are the Taylor factor, interaction force between the average size precipitate and the dislocation at peak-aged condition, the magnitude of Burgers vector, and the dislocation line tension, respectively. In the present study, all the variables in Equation (10), except for size and fraction of ${\beta }^{″}$, were defined as a constant model parameter $C_{{\beta }^{″}}^{\mathrm{SH}}$:

$$C_{{\beta }^{″}}^{\mathrm{SH}}=\frac{M{\left(F^{\mathrm{peak}}\right)}^{2/3}{\left(f_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{1/2}}{b{\left(2\sqrt{3}\pi \right)}^{1/2}{\Gamma }^{1/2}{\left(r_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{3/2}}$$

(11)

As ${\beta }^{″}$ precipitates become bigger, precipitation hardening behavior of ${\beta }^{″}$ might change to dislocation by-passing. In this case, the yield strength contribution from non-shearable ${\beta }^{″}$ precipitate is expressed as [19]:

$${\sigma }_{{\beta }^{″}}^{\mathrm{NS}}=\frac{M\Gamma {\left(f_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{1/2}}{b{(\pi /2)}^{1/2}}\frac{1}{r_{{\beta }^{″}}}$$

(12)

Similar to $C_{{\beta }^{″}}^{\mathrm{SH}}$, a single parameter $C_{{\beta }^{″}}^{\mathrm{NS}}$ is defined as a model parameter to be optimized:

$$C_{{\beta }^{″}}^{\mathrm{NS}}=\frac{M\Gamma {\left(f_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{1/2}}{b{(\pi /2)}^{1/2}}$$

(13)

$C_{{\beta }^{″}}^{\mathrm{SH}}$ and $C_{{\beta }^{″}}^{\mathrm{NS}}$ are dependent on each other due to the same magnitude of ${\sigma }_{{\beta }^{″}}^{\mathrm{SH}}$ and ${\sigma }_{{\beta }^{″}}^{\mathrm{NS}}$ at the peak aged condition:

$$C_{{\beta }^{″}}^{\mathrm{NS}}=C_{{\beta }^{″}}^{\mathrm{SH}}{\left(f_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{1/2}{\left(r_{{\beta }^{″}}^{\mathrm{peak}}\right)}^{3/2}$$

(14)

In the present study, precipitation harderning is assumed to occur in the precipitate shearing mode if the average radius of ${\beta }^{″}$ is smaller than that at the peak aged condition. After the peak aged condition, precipitate by-passing becomes the dominant strengthening mechanism with the coarsening of ${\beta }^{″}$ precipitates in the present yield strength model. The parameters for yield strength model are summarized in

Table 3. Parameters for the yield strength model proposed in the present study.

Parameter	Unit	Value	Remark
${\sigma }_{\mathrm{int}}$	MPa	10	From the literature [19]
${\sigma }_{\mathrm{SS}}$	MPa	50	From the literature [19]
${\sigma }_{\mathrm{Si}}$	MPa	48	Optimized in the present study
$C_{{\beta }^{″}}^{\mathrm{SH}}$	MPa/$\sqrt{m}$	131.384	Optimized in the present study

and overall model structure for the calculation of precipitation kinetics and yield strength is schematically described in Figure 1.

4. Results and Discussion

4.1. Experimental Results

4.1.1. Tensile Properties of the T5 Heat-Treated CPC A356 Alloy

Figure 2 shows the tensile properties of the T5 heat-treated CPC A356 alloys measured in the present study. As the heat treatment time increased, both the tensile and yield strength of the CPC A356 alloy either continuously increased at 160 ${}^{\circ }$C until 48 h of heat treatment time or increased until the maximum strength values were achieved and then decreased, showing peak aging behavior at 180 and 200 ${}^{\circ }$C. The heat treatment time required to reach the peak aged condition was shorter at 200 ${}^{\circ }$C compared with that at 180 ${}^{\circ }$C. Furthermore, the time required to obtain the maximum strength of the CPC A356 alloy after the T5 heat treatment at 160 ${}^{\circ }$C might be longer than 48 h. The maximum tensile strengths of the CPC A356 alloy after T5 heat treatments at 180 and 200 ${}^{\circ }$C were 280 and 278 MPa, respectively. The maximum yield strengths after 180 and 200 ${}^{\circ }$C of the T5 heat treatment were also similar to each other (208 MPa at 180 ${}^{\circ }$C and 209 MPa at 200 ${}^{\circ }$C). Those maximum strength values obtained in the present T5 heat-treated CPC A356 alloys were about 30–40 MPa smaller than the reported peak strengths of a A356 alloy after a T6 heat treatment [20]. The elongation of the T5 heat-treated CPC A356 alloy increased at the initial stage of heat treatment (1 hr) but kept decreasing as the T5 heat treatment time increased. At higher temperatures of the T5 heat treatment, a decrease in elongation of the CPC A356 alloy occurred faster.

4.1.2. Microstructural Analysis in T5-Heat-Treated CPC A356 Alloys

Figure 3 shows the as-cast microstructure of the CPC A356 alloy. The microstructure consists of $\alpha$-Al, eutectic Si, and intermetallic compounds, which are typical stable phases in Al-Si-Mg alloys. Furthermore, grain refinement of $\alpha$-Al and the modification of eutectic Si were achieved in the specimen due to addition of Ti and Sr in the alloy, respectively.

Microstructures of T5 heat-treated CPC A356 alloys at different heat treatment conditions are summarized in Figure 4. From the figure, it seems that during the T5 heat treatment up to 9 h, the size or morphology of eutectic Si phases did not change remarkably.

In order to quantitatively measure the size and morphology changes in eutectic Si particles, image analysis of the micrographs from the optical microscope was performed. As the T5 heat treatment proceeds, the equivalent radius of eutectic Si slightly increases regardless of heat treatment temperatures, as shown in Figure 5. For example, the average value of the equivalent radius of eutectic Si after 9 h of T5 heat treatment at 160 ${}^{\circ }$C was 0.73 μm as compared to 0.61 μm at as-cast condition. When the T5 heat treatment temperature increased from 160 ${}^{\circ }$C to 200 ${}^{\circ }$C, the average value of the equivalent radius of eutectic Si after 9 h of heat treatment increased from 0.73 μm to 0.80 μm. Furthermore, the equivalent radius of eutectic Si at 200 ${}^{\circ }$C shows a wider distribution than that at 160 ${}^{\circ }$C, indicating the growth of the eutectic Si phase was more active at higher T5 heat treatment temperatures. Meanwhile, a significant change in the average value of the eutectic Si aspect ratio was not found in T5 heat-treated CPC A356 alloys, showing similar values around 2 regardless of heat treatment time and temperature. At 200 ${}^{\circ }$C, the distribution of the aspect ratio of eutectic Si particles became narrow as the T5 heat treatment time increased. It suggests spherodization of eutectic Si occurred more significantly at higher T5 heat treatment temperature.

In order to check the possible homogenization of solute distribution in the $\alpha$-Al matrix during T5 heat treatment, composition analysis on $\alpha$-Al was also conducted using FE-SEM-EDS on the specimens under different heat treatment conditions. As shown in Figure 6, the Si concentration at the center of an $\alpha$-Al dendrite was higher than that at the edges of an $\alpha$-Al dendrite. On the contrary, the Mg concentration at the center of an $\alpha$-Al dendrite seems lower than that at the edges an $\alpha$-Al dendrite. Similar microsegregation of Si and Mg in A356 dendrites was observed from electron probe microsnalyses on as-cast low-pressure die-cast automotive wheels [21]. It was reported in the literature that the microsegregation of solutes in A356 dendrites was eliminated after 15 min of solution treatment at 540 ${}^{\circ }$C [21]. On the contrary, the microsegregation of Si and Mg in $\alpha$-Al grains in an as-cast CPC A356 specimen was not eliminated after the T5 heat treatment conditions employed in the present study.

In the present study, two different intermetallic phases were observed in T5 heat-treated CPC A356 specimens under all heat treatment conditions. For the identification of those intermetallic phases, EDS point analysis and mapping analysis of FE-SEM were conducted to check their chemical compositions. As shown in Figure 7, it was determined that the intermetallic phases have either significant amount (∼16 at%) of Mg or negligible amount of Mg at 180 ${}^{\circ }$C-6 h heat treatment condition. Meanwhile, it was already confirmed from the literature [22] that stable intermetallics in A356 alloys were $\pi$-Al${}_8$FeMg${}_3$Si${}_6$ and $\beta$-Al${}_5$FeSi. The stoichiometry of two different intermetallics determined from EDS analysis was similar to Al${}_8$FeMg${}_3$Si${}_6$ and Al${}_5$FeSi. Therefore, stable intermetallics observed in the present T5 heat-treated A356 alloys were concluded to be $\pi$-Al${}_8$FeMg${}_3$Si${}_6$ and $\beta$-Al${}_5$FeSi.

Figure 8 shows SEM images of $\pi$-Al${}_8$FeMg${}_3$Si${}_6$ and $\beta$-Al${}_5$FeSi intermetallics in CPC A356 specimens at different T5 heat treatment conditions. After 9 h of T5 heat treatment at 200 ${}^{\circ }$C, those intermetallics were still observed in the sample.

It is well-known that an increase in the A356 alloy’s strength after artificial aging mainly occurred by nanosized precipitates, and this precipitation strengthening becomes maximized when ${\beta }^{″}$ precipitates were formed [23,24]. In the present study, peak aging behavior during 48 h of the T5 heat treatment was observed at 180 and 200 ${}^{\circ }$C conditions. Therefore, the possible formation of nanosized precipitates that contributes to precipitation hardening was investigated using HR-TEM. As can be seen in Figure 9, needle-like precipitates were found in the specimens with 8 and 9 h of T5 heat treatment at 200 ${}^{\circ }$C. In contrast, the microstructure of as-cast specimens did not have any precipitates with a needle-like shape. The size of those precipitates detected from HR-TEM had a maximum diameter of 3.92 nm and maximum length of 91.2 nm, showing a similar size of ${\beta }^{″}$ reported in the literature [25,26] (see

Table 4. Precipitation phases in the A356 alloy [25,26,27,28,29,30].

Phase	GP Zone	${\mathit{\beta }}^{″}$	${\mathit{\beta }}^{\prime }$	$\mathit{\beta }$
Shape	fine plate [27]	Needle-like [28]	Rod-like [29]	Platelets [30]
Composition	MgSi [27]	Mg${}_5$Si${}_6$ [28] Mg${}_5$Al${}_2$Si${}_4$ [31]	Mg${}_{1.6}$Si [29]	Mg${}_2$Si [30]
Structure	fcc based cubic [27]	Monoclinic (C2/m) [28]	Hexagonal (P6${}_3$/m) [29]	Cubic (CaF${}_2$) [30]
Lattice Parameters	a = 4.05 Å [27]	a = 15.16 Å b = 4.05Å c = 6.74 Å $\beta$ = 105.3${}^{\circ }$ [28]	a = 7.1 Å c = 4.05 Å [29]	a = 6.39Å [30]
Size	1–3 nm [25,26]	4 × 4 × 35–50 nm [25,26]	20 × 20 × 500 nm [26]	10–20 nm diameter [25]

). Furthermore, the needle-like precipitates lie on the [001]${}_{\mathrm{Al}}$ direction, which is another crytallographic characteristic of the ${\beta }^{″}$ phase. Therefore, the needle-like nanosized precipitates detected in the present study were determined to be ${\beta }^{″}$.

4.1.3. Relationship between Tensile Properties and Microstructures of T5 Heat-Treated CPC A356 Alloys

From the tensile test of T5 heat-treated CPC A356 specimens, it was concluded that both the tensile and yield strength of specimens increased as the T5 heat treatment time increased in the case of the 160 ${}^{\circ }$C condition or became maximized at peak aged condition and then decreased at 180 and 200 ${}^{\circ }$C conditions. Those improvements in strength during the T5 heat treatment were closely related to microstructural changes in CPC A356 specimens.

Si particles in hypoeutectic Al-Si alloys could increase the strength of the alloy by the Orowan dislocation bowing mechanism, which could be expressed as [32]:

$${\sigma }_{\mathrm{Si}}={\sigma }_0+k{\lambda }^{-0.5}$$

(15)

where ${\sigma }_0$ and k are constants, and $\lambda$ is the mean particle interspacing. The strengthening by Si particles could be affected by the size and density of Si particles. Therefore, strengthening effect by Si particles did not contribute to an improvement in strength of CPC A356 alloys after the T5 heat treatment because the size and morphology of eutectic Si did not significantly change regardless of T5 heat treatment conditions (Figure 5 and Figure 10).

In terms of solid solution strengthening, alloying elements, such as Mg, Si and Cu, give rise to a remarkable strengthening effect [33]. Provided that the contribution from each solute element to the solid solution strengthening is additive, the strength contribution from solid solution strengthening, ${\sigma }_{\mathrm{SS}}$, can be expressed as [34]:

$${\sigma }_{\mathrm{SS}}=\sum k_j{C}_j^{2/3}$$

(16)

where $k_j$ and $C_j$ is the scaling factor and the concentration of a specific element j in solid solution, respectively. In the present study, the existence of microsegregation of Si and Mg in $\alpha$-Al dendrites was confirmed by SEM-EDS analysis. However, dissolved Si and Mg content in the $\alpha$-Al was not changed during T5 heat treatments (Figure 6). Therefore, tensile property changes in T5 heat-treated CPC A356 alloys were not affected by solid solution strengthening of the $\alpha$-Al phase.

Meanwhile, $\beta$-Al${}_5$FeSi and $\pi$-Al${}_8$FeMg${}_3$Si${}_6$, typical intermetallics in Al-Si-Mg alloys, are known to have harmful effects on both strength and ductility [35]. In the present study, the decomposition of those intermetallics was not observed during T5 heat treatment (Figure 8), which suggests a negligible effect of intermetallics on changes in tensile properties of CPC A356 alloys after the T5 heat treatment.

Precipitation hardening of A356 alloys is related to the nanosized precipitates (such as GP zones, ${\beta }^{″}$ and ${\beta }^{\prime }$) formed during isothermal aging treatment [20]. Chen et al. found that the strength of the A356 alloy dramatically increased when a high density of needle-like ${\beta }^{″}$ was observed [20]. During the over-aging stage, the yield strength of the A356 alloy decreased as the transformation from the coherent ${\beta }^{″}$ to semi-coherent ${\beta }^{\prime }$ occurred [20]. In the present study, the formation of ${\beta }^{″}$ precipitates was also observed when both tensile strength and yield strength were remarkably improved at 8 and 9 h of T5 heat treatment at 200 ${}^{\circ }$C (Figure 9). In summary, the increase in the strength of CPC A356 specimens after the T5 heat treatment was mainly contributed by precipitation hardening with ${\beta }^{″}$ formation.

4.2. Calculation Results of Yield Strength Model

Based on the ${\beta }^{″}$ precipitation kinetics model suggested in the present study, changes of radius and relative volume fraction of ${\beta }^{″}$ were calculated at 160 ${}^{\circ }$C, 180 ${}^{\circ }$C, and 200 ${}^{\circ }$C, as shown in Figure 11. When the T5 heat treatment temperature increased, the growth of ${\beta }^{″}$ precipitates became faster, resulting in a bigger radius at the same heat treatment time. Similarly, the relative volume fraction of ${\beta }^{″}$ reached the peak aging condition ($f_{{\beta }^{″}}$ = 1) faster in a higher heat treatment temperature condition.

The calculated results of yield strength at the temperature conditions employed in the present study are shown in Figure 12 with the experimental data of the present study. The calculation results showed a good agreement with experimental data even though some discrepancies were inevitable at the initial stage (1 h) of T5 heat treatment. Furthermore, peak aging behavior is obviously predicted from the S-shape of the strength curve. Figure 13 shows the contributions of the calculated yield strength at different temperature conditions. At the early stage of heat treatments, the yield strength is mainly affected by strength contributions of both eutectic Si (${\sigma }_{\mathrm{Si}}$) and solute elements in $\alpha$-Al (${\sigma }_{\mathrm{SS}}$). As the heat treatment goes on, precipitation hardening by ${\beta }^{″}$ (${\sigma }_{{\beta }^{″}}$) becomes dominant around the peak aged conditions, and the combined effect of precipitate shearing (${\sigma }_{{\beta }^{″}}^{\mathrm{SH}}$) and by-passing (${\sigma }_{{\beta }^{″}}^{\mathrm{NS}}$) enables the model to reproduce the yield strength curve showing peak aging behavior.

The present yield strength model could be utilized to estimate the heat treatment time required to maximize the yield strength at an arbitrary temperature of T5 heat treatment. The model calculations could also be useful to optimize T5 heat treatment temperatures to achieve a desired yield strength of the CPC A356 alloy in a shorter heat treatment process. Figure 14 shows the calculated yield strength at various temperatures from 150 to 200 ${}^{\circ }$C. In order to achieve the maximum yield strength, for instance, the necessary heat treatment time is estimated to be about 9.5 h at 190 ${}^{\circ }$C. Furthermore, about 210 MPa of yield strength after 9 h of heat treatment at 180 ${}^{\circ }$C could be obtained from 4 h of a shorter heat treatment process at 200 ${}^{\circ }$C. From those calculations by the present yield strength model, the T5 heat treatment process could be optimized efficiently with subsequent experimental confirmation.

5. Conclusions

In the present study, tensile properties and microstructures of T5 heat-treated CPC A356 alloys were investigated experimentally. As the T5 heat treatment time increased, both the tensile and yield strength either continuously increased at 160 ${}^{\circ }$C until 48 h of heat treatment time or increased until the maximum strength values were achieved and then decreased at 180 and 200 ${}^{\circ }$C (peak aging behavior). In terms of microstructures of the T5 heat-treated CPC A356 alloy, eutectic Si particles and intermetallic compounds ($\pi$-Al${}_8$FeMg${}_3$Si${}_6$ and $\beta$-Al${}_5$FeSi) were not changed remarkably during T5 heat treatments. The solute redistribution of Si and Mg in $\alpha$-Al dendrite were also negligible during the present T5 heat treatment conditions. From HR-TEM analysis, needle-like nanosized ${\beta }^{″}$ precipitates, which were not detected in as-cast samples, were observed in the specimens heat-treated at 200 ${}^{\circ }$C for 8 and 9 h.

The present yield strength model was designed to calculate yield strength changes during T5 heat treatments with a consideration of the combined effect of precipitation shearing and by-passing depending on the size of ${\beta }^{″}$ estimated by a simple precipitate kinetics model. The measured yield strength data and model calculations showed a good agreement with each other. From the model calculations at arbitrary T5 heat treatment conditions, the optimal heat treatment time or temperature could be estimated to achieve a higher strength of the CPC A356 alloy or to shorten the T5 heat treatment process.