# High-throughput characterisation of the long-term ageing of an A357+1wt%Cu cast aluminium alloy using temperature gradient

Thomas Perrin, Arthur Després, Pierre Heugue, Alexis Deschamps, Frédéric de Geuser

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Thomas Perrin, Arthur Després, Pierre Heugue, Alexis Deschamps, Frédéric de Geuser. High-throughput characterisation of the long-term ageing of an A357+1wt%Cu cast aluminium alloy using temperature gradient. Materialia, 2025, 39, 10.1016/j.mtla.2025.102378. hal-04957991

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# High-throughput characterisation of the long-term ageing of an A357+1wt %Cu cast aluminium alloy using temperature gradient

Thomas Perrin<sup>a, *, D</sup>, Arthur Després<sup>a</sup>, Pierre Heugue<sup>b, D</sup>, Alexis Deschamps<sup>a, D</sup>, Frédéric De Geuser<sup>a, D</sup>

## ARTICLE INFO

**Keywords:**

High-throughput

Precipitation

Gradient

Ageing

Aluminium alloys

## ABSTRACT

A357 alloy is a widely studied cast aluminium alloy used in applications such as cylinder heads or aerospace applications. The addition of 1wt% copper to this alloy modifies the nanometric precipitation sequence and improves heat resistance. Thermal ageing resistance is a critical property for such applications and the ability to predict the end of life of these products is crucial. In this study, we investigate the effect of long-term ageing on an A357+1wt%Cu alloy. We have developed a combinatorial approach to gather sufficient data to model the evolution of mechanical properties during extended ageing. Samples have been aged in a temperature gradient for durations up to 10,000 h and then characterised using space-resolved Small- and Wide-Angle X-ray Scattering (SAXS & WAXS), as well as hardness mapping. Complementary Transmission Electron Microscopy (TEM) observations were also performed. Finally, a simple approach based on time-temperature equivalence is implemented to predict the evolution of the mechanical properties and the nanometric precipitation during long-term ageing.

## 1. Introduction

Cast aluminium alloys are widely used across diverse industries for their combination of low density, high corrosion resistance, and high mechanical strength [1]. Among them, widely used Al-Si-Mg compositions like A357 and A356 hypoeutectic alloys find particular utility in critical applications such as cylinder heads and aerospace components. Extensive research explored various aspects of these alloys, including heat treatment strategies [2], nucleation and growth kinetics of precipitates [3,4], age hardening mechanisms [5] or fatigue behaviour [6, 7].

In these alloys, addition of copper in relatively modest amount, ranging from 0.5wt%Cu to 4.5wt%Cu, has been shown to significant enhance the mechanical properties in the peak-aged state while simultaneously extending the peak ageing time [8,9]. Depending on the copper content, the precipitation sequence may vary, with the formation of Q'/Q phases, as well as θ'/θ phases [8,10], in addition to the usual β family observed in similar alloys without copper [4,11].

While the initial stages of precipitation hardening leading to the peak-aged state have been extensively studied, fewer investigations

have focused on the long-term ageing of these alloys and the mechanisms involved during thermal ageing from the peak-aged condition. This area of research is crucial, as the microstructure of precipitation-strengthened aluminium alloys undergoes a significant evolution during over-ageing, resulting in detrimental decrease of the mechanical resistance [12–14]. Knowledge of the evolution of mechanical properties during prolonged times at elevated temperatures is necessary to accurately predict the lifetime of products and design parts with appropriate safety margins.

As service conditions involve long periods and a wide range of temperatures, a large amount of data is needed to comprehensively describe the evolution of precipitation and mechanical properties. Graded samples are increasingly recognized as an effective method for measuring a large variety of conditions in a reasonable acquisition time. For example, several studies have used composition gradients to investigate the effect of different solute elements [15–18]. A few studies have also subjected samples of homogeneous compositions to temperature gradients, however those focused mostly on short ageing times [19,20]. In the case of long-term ageing, where each experiment lasts several thousand hours, samples aged in a temperature gradient offer a practical

<footnote><sup>a</sup> Univ. Grenoble Alpes, Grenoble INP, SIMaP, 38000 Grenoble, France</footnote>

<footnote><sup>b</sup> DT/MPE, Safran Transmission Systems, 18 Boulevard Louis Seguin, Colombes 92707, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: thomas.perrin@grenoble-inp.pro (T. Perrin).</footnote>
approach to obtaining a wide range of ageing conditions using a single sample.

The usual approach for characterizing the precipitation state involves characterisation methods such as differential scanning calorimetry (DSC) [21–23] and transmission electron microscopy (TEM) [24–26]. While these methods allow for phase identification and measurement of size or volume fraction, they are local by nature and not suitable for systematically characterising graded samples.

On the other hand, diffraction and scattering techniques such as X-ray diffraction (XRD) / wide angle X-ray scattering (WAXS) [18] and small angle X-ray scattering (SAXS) [16] are better suited for characterizing graded samples, since they can be easily realised repetitively and their analysis can be automatized. XRD / WAXS can provide structural information on the phases present in the microstructure and SAXS on their size or morphology at the nanometre scale. Depending on the exact setup, SAXS and WAXS measurements may be performed simultaneously [27]. SAXS has been extensively used to map the precipitation states in heterogeneous materials, heterogeneity being either introduced as a composition gradient [16] or a gradient of other processing parameters such as plastic deformation [28] or due to specific processes such as welding [29–32]. In contrast, WAXS measurements for mapping studies have been little reported.

In the present study, we present a high-throughput methodology aimed at investigating the influence of long-term ageing on both the mechanical properties and precipitation state of an A357+1wt%Cu alloy. This approach involves submitting samples to an ageing treatment within a temperature gradient from 165 °C to 245 °C for durations up to 10,000 h. The samples are subsequently characterized using hardness mapping and space-resolved SAXS & WAXS. Complementary TEM observations, including Energy-dispersive X-ray spectroscopy (EDS) mapping and scanning precession electron diffraction (SPED), are carried out to refine and validate the results obtained by the scattering techniques. Through this combinatorial methodology, we establish a straightforward approach for predicting the evolution of mechanical properties based on time-temperature equivalences. The same approach is then used to describe the evolution of the main precipitates during overageing.

## 2. Material and methods

### 2.1. Alloy studied and initial thermal state

The material investigated is an A357+1wt%Cu alloy cast by Aviocast. The alloy composition, as determined by inductively coupled plasma atomic emission spectroscopy (ICP), is presented in Table 1.

This composition allows for the precipitation of multiple phases. The stable phases Q, θ and β can be obtained at the equilibrium state according to the diagram in Fig. 1, which means that during ageing, the metastable precursors of these different phases may also precipitate and participate in age hardening. The Si, Al<sub>3</sub>Ti and Al<sub>9</sub>Fe<sub>2</sub>Si<sub>2</sub> phases are coarse particles that cannot dissolve after solidification and do not evolve during ageing in the investigated conditions.

Based on the diagram in Fig. 1, the high solvus temperature of the β-Mg<sub>2</sub>Si phase means that the solution heat treatment needs to be between 520 °C and 550 °C.

Consequently, the initial heat treatment involved a solution heat treatment at 530 °C for 16 h, followed by a water quench. At this stage the casting-related composition fluctuations of the major solute elements are considered to be homogenized. Subsequently the material was artificial aged at 200 °C for 8 h, leading to an equivalent T7 thermal

<table><caption>**Table 1**

Composition of the alloy measured by ICP.</caption><thead><tr><th>%wt</th><th>Al</th><th>Si</th><th>Cu</th><th>Mg</th><th>Fe</th><th>Ti</th></tr></thead><tbody><tr><td>ICP</td><td>91.4</td><td>6.8</td><td>1.0</td><td>0.54</td><td>0.04</td><td>0.10</td></tr></tbody></table>

state.

Samples were artificially aged from this initial thermal state in a temperature gradient using a Carbolite-Gero TG3 12/60/600 tubular gradient furnace and a cooler. Further details on the methodology for generating the temperature gradient are provided in Section 3.

### 2.2. Characterisation techniques

Mechanical properties were assessed using hardness tests conducted on a Presi HZ50-4 machine with a dwell time of 10 s and a 5 kg load, capturing the influence of all the different phases present in the alloy for each indentation. A 5 mm step size was used along the gradient samples, with five measurements taken at each position to determine the mean value.

Complementary tensile tests were conducted following the NF EN 2002-001 standard with six TC25 cylindrical tensile test specimens machined for each ageing condition to obtain mean values and standard deviations for the measurement of yield strength.

Simultaneous SAXS and WAXS measurements were performed on BM02-D2AM beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The beam size was set to 100×100 µm² and a sample-to-detector distance of 15 cm was selected for WAXS, with a concealing mask positioned to shield the 2D IMXPAD WOS detector from the intense diffraction peaks of the aluminium matrix. This limited the WAXS observations to a q-range from 0.75 to 2.6 Å⁻¹. The WAXS detector has a hole in its centre to allow simultaneous SAXS acquisition. A 2D photon-counting detector (IMXPAD D5) was placed at 3.5 m to measure the SAXS signal. Rotations of the sample were implemented as described in [33], considering the anisotropic nature of potential metastable precipitates and the large grain size. This configuration results in more reliable measurements for such precipitates. A rotation range of -45° to +45° was applied with a 3°/s rotation speed. A semi-continuous approach was adopted, where acquisitions occurred during rotations, with each acquisition lasting 1 second. Consequently, each SAXS/WAXS image corresponds to a 3° range, and 30 images were captured for a single position. Normalisation by the effective sample thickness was accounted for each acquisition based on the rotation angle and an average image was then calculated for each position. The azimuthal integration was carried out using the PyFAI Python package to obtain the I(q) plots [34].

Additional TEM observations were performed in STEM mode using a JEOL 2100F with a field emission gun operated at 200 kV. Thin disk specimens were prepared and electropolished using a solution of 33 % nitric acid and 66 % methanol at -20 °C. Energy-dispersive X-ray spectroscopy (EDS) analyses were carried out using a high collection angle SDD Centurio detector. Scanning precession electron diffraction (SPED) was performed using Nanomegas' ASTAR™ software with a precession angle of 0.5° or 1° depending on the sample to identify the various phases in the aluminium matrix. The diffraction patterns were collected with an in-line direct electron detector Medipix 3 in the CheeTah camera from Amsterdam Scientific. The observations were conducted in a [001]<sub>Al</sub> zone axis to better identify and measure the precipitates. More details on the SPED technique are given in [35].

## 3. Temperature gradient

Given the targeted range of possible service conditions, a temperature gradient spanning from 170 °C to 240 °C was selected, along with eight different ageing durations: 120, 210, 500, 1000, 2000, 3000, 5000, and 10,000 h.

### 3.1. Gradient tuning

Slender samples (325 mm x 3.5 mm x 7 mm) were fabricated from the alloy plates. These dimensions were designed to achieve a temperature gradient over a sufficient length and to allow the use of the
<figure><img src="image_3.png" /><figcaption>Fig. 1. The various possible equilibrium phases in the A357+1wt%Cu alloy according to Thermo-Calc using the TCAL9 database.</figcaption></figure>

different characterisation techniques. A single sample was prepared for each ageing condition, meaning a total of eight distinct samples. A sample support, machined from an AA2219 alloy with a thermal conductivity comparable to that of the studied alloy (160 W/m.K for the AA2219 alloy as compared to 170W/m.K for the A357+1wt%Cu alloy at 200 °C), was employed to have a homogeneous temperature for a fixed position in the furnace and limit radiative heat transfer. The geometry of the sample support is illustrated in Fig. 2(a), featuring 15 sample locations and four thermocouple locations. These enable temperature measurements by sliding a thermocouple along the length of the support. More details on the accuracy of these measurements will follow.

To maintain a constant temperature gradient of 70 °C/32.5 cm during the 10,000 h of ageing, a tubular gradient furnace was used. A cooler connected to the support via a copper braid was added to counterbalance the high thermal conductivity of the samples and the support. The cooling circuit employing ethylene glycol cooled at 6 °C was brazed to the end of the braid. Using this cooling circuit with a monitored temperature allowed us to ensure temperature stability throughout the

duration of ageing.

A copper braid with a 4 cm² cross-section was available. Heat transfer calculations were necessary to verify the braid's capacity to extract adequate heat. To do so, the temperature gradient was initially measured without the cooler and then the required heat flow that the braid should extract was calculated. The heat extracted by the copper braid (Q<sub>Cu</sub>) is given by:

$$Q_{Cu} = J_{Cu}S_{Cu} = \lambda_{Cu} \frac{\Delta T_{Cu}}{L_{Cu}} S_{Cu} \quad (1)$$

Where J<sub>Cu</sub> represents the heat flux passing through the copper braid of surface S<sub>Cu</sub> and length L<sub>Cu</sub>, and λ<sub>Cu</sub> denotes the thermal conductivity of the braid.

To obtain a gradient from 170 °C to 240 °C, we want the heat passing through the support (Q<sub>Sup</sub>) to be:

$$Q_{Sup.obj} = \lambda_{Sup} \frac{\Delta T_{Sup}}{L_{Sup}} S_{Sup} = 53 \text{ W} \quad (2)$$

<figure><img src="image_4.png" /><figcaption>Fig. 2. (a) Experimental setup to obtain temperature gradients and (b) examples of experimental temperature gradients, measured in the thermocouple locations, obtained as a function of the maximum temperature set in the furnace. Positions A and B are indicated as reference points for monitoring thermal stability during the ageing process. Temperature measurements for the three instrumented samples are represented for the investigated temperature gradient from 165 °C to 245 °C.</figcaption></figure>
Experimentally, we can measure, without a cold source, QSup,exp = 16 W.

Therefore, we need:

$$Q_{Cu} = Q_{Sup, obj} - Q_{Sup, exp} = 37 \text{ W} \qquad (3)$$

And so:

$$S_{Cu} = \frac{Q_{Cu}}{J_{Cu}} = \frac{Q_{Cu}}{\lambda_{Cu} \frac{\Delta T_{Cu}}{L_{Cu}}} \qquad (4)$$

The values of the different variables are shown in Table 2.

We then obtained a minimal surface for the copper braid of $S_{Cu}=2.2 \text{ cm}^2$ for a braid length of 30 cm. Consequently, the copper braid with an approximate cross-section area of $4 \text{ cm}^2$ could be used to ensure adequate heat extraction. Adjusting the furnace temperature can effectively counterbalance the cooling effect of the braid. The final scheme of the experimental setup is depicted in Fig. 2(a). Photographs of the cooling section are given in Appendix A. Experimentally, various temperature gradients can be achieved by adjusting the central temperature of the furnace, as shown in Fig. 2(b).

Temperature readings were obtained by sliding a thermocouple into the dedicated slot. For this study, the objective was to achieve a temperature gradient from 170 °C to 240 °C. This corresponds to a maximum setpoint of 450 °C. The final experimental temperature gradient ranged from 165 °C to 245 °C.

Instrumented samples with a thermocouple inserted at a fixed position were machined to ensure temperature consistency between the sample and thermocouple locations. Those complementary samples, fabricated from the same alloy, were exclusively used to measure the stability of the temperature gradient. Three depths were investigated (Fig. 2(b)), and the resulting measurements exhibited good agreement with the temperature measured within the thermocouple location, validating the measurements obtained by sliding the thermocouple in the allocated position.

## 3.2. Gradient stability for long heat treatment and during sample exchange

One of the main issues of such complex setup is to ensure a stable temperature gradient throughout the 10,000 h of ageing and during sample exchange.

Measurements taken over the 10,000 h of ageing showed a maximum variation of ± 2 °C compared to the initial temperature gradient. Moreover, to maintain constant thermal mass, a sacrificial sample took place of a removed sample for each ageing time. Stability measurements conducted during sample transitions revealed that the gradient returned to the nominal position within approximately 2 h as shown in Fig. 3 with no temperature overshoot, which is negligible compared to the ageing durations investigated.

# 4. Results

## 4.1. Hardness evolution

The initial state (T7) and all the samples over-aged in the temperature gradient were characterised using hardness mapping. A decrease in mechanical properties with increasing ageing temperature and time is observed (Fig. 4).

For ageing temperatures below 210 °C, both the duration and the temperature of ageing have significant impacts, while for higher

temperatures, the loss of mechanical properties is primarily influenced by the ageing time. To extrapolate tensile properties from the hardness mappings, additional experiments were carried out with an ageing matrix established for three fixed temperatures (150 °C, 175 °C and 200 °C) and durations up to 15,000 h to establish a correlation between hardness and tensile properties. The samples came from the same alloy plates as the slender specimens. These samples subjected to this ageing regime underwent both hardness and tensile tests (as described in Section 2.2), revealing a linear relationship between yield strength ($\sigma_y$) and hardness (Appendix B). Consequently, the equivalent yield strength can be plotted as a function of ageing temperatures and durations (Fig. 4).

## 4.2. Microstructural evolution

### 4.2.1. SAXS/WAXS

Concerning the microstructural evolution, simultaneous SAXS/WAXS measurements were performed on the samples aged 1000 h, 2000 h, and 5000 h, along with a non-aged sample (T7). A step-size of 1 mm to 1.5 mm was chosen, corresponding to a maximum temperature increment of approximately 0.2 °C. The $I(q)$ curves obtained were averaged across five positions, resulting in a step of about 1 °C between each curve.

An evolution of the SAXS $I(q)$-plots is evident during ageing (Fig. 5 (a)), showing a large change of intensity from T7 to the first ageing conditions, followed by a more gradual change towards lower scattering vectors when increasing the temperature, corresponding to an increase in precipitate size. However, the implementation of simple models to extract precipitate size out of each curve proved challenging as fitting the signal with one or two distinct families of precipitates did not yield satisfactory results.

Several factors may contribute to this complexity. Multiple families of precipitates may coexist, potentially exhibiting varying composition and distinct evolution, making their dissociation challenging. Additionally, for the aged samples, the minimum scattering vector $q$ that could be reached by the used set-up was not sufficiently small, as the precipitates were too large and thus a significant part of the signal occurred at scattering angles too small to be detected. Integral parameters can still be calculated to provide a global and semi-quantitative analysis of the evolution of the SAXS signal. One such parameter is the correlation length ($l_c$) as described by Glatter and Kratky [36], which is given by the following equation.

$$l_c = \frac{\int_{0}^{\infty} I(q) q \, dq}{\int_{0}^{\infty} I(q) q^2 \, dq} \qquad (5)$$

As the q-range is limited in the given data, we can compute an approximation of the correlation length ($l_c$) by performing a discrete sum on the measured range:

$$L_c \approx \frac{\sum I(q)q}{\sum I(q)q^2} \qquad (6)$$

This parameter is related to the dimensions of the different precipitates present in the alloy. Fig. 5(b) shows the evolution of this parameter during ageing. $L_c$ increases as a function of ageing time and temperature, indicating an overall growth in the dimensions of the hardening precipitates during ageing. $L_c$ shows a significant increase during the first 1000 h of ageing and a slower evolution for longer ageing times. The precise interpretation of this parameter is difficult as it is highly dependent on the morphology of the precipitates responsible for the signal.

<table><caption>**Table 2**
Values of the different variables.</caption><thead><tr><th>Name</th><th>Q<sub>Cu</sub></th><th>Q<sub>Sup, obj</sub></th><th>Q<sub>Sup, exp</sub></th><th>ΔT<sub>Cu</sub></th><th>ΔT<sub>Sup</sub></th><th>λ<sub>Cu</sub></th><th>λ<sub>Sup</sub></th><th>L<sub>Cu</sub></th><th>L<sub>Sup</sub></th><th>S<sub>Sup</sub></th></tr></thead><tbody><tr><td>Value</td><td>37 W</td><td>53 W</td><td>16 W</td><td>164 K</td><td>70 K</td><td>386 W/m.K</td><td>160 W/m.K</td><td>0.3 m</td><td>0.325 m</td><td>7.8 e-4 m<sup>2</sup></td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Temperature evolution at position A and B (Fig. 2) in the support during sample exchange.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Vickers hardness and equivalent yield strength evolution as a function of the ageing temperatures and the different ageing durations.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Example of SAXS I(q)-plots obtained for different ageing conditions and (b) evolution of the approximate correlation length ($L_c$) as a function of ageing time and temperature.</figcaption></figure>

To better evaluate the microstructural evolution, WAXS acquisitions were performed simultaneously. This characterisation technique allows for the decoupling of the contribution of numerous precipitate families, provided they exhibit crystallographic differences. To facilitate the WAXS interpretation with respect to more classical XRD measurements, the scattered intensity is plotted against the equivalent double diffraction angle for a copper anode ($2\theta_{Cu}$). Peaks corresponding to various precipitate families can be seen and indexed (Fig. 6(a)).

Based on the anticipated phases according to the diagram in Fig. 1, six distinct phases were initially identified in the samples: the aluminium matrix, the Si diamond phase, the Q phase, the L phase (precursor of Q), the θ-phase and the θ'-phase (precursor of θ). Regarding the peaks associated with the phases Q and θ, a noticeable evolution of the peak height is evident for the specimen aged 1000 h (Fig. 6(b)).

As illustrated in Fig. 7, the peak identified as the “Q”-peak for our alloy closely corresponds to the equilibrium Q variant rather than the metastable Q' variant, as indicated by the positions of the (110) and

(100) peaks. Although the Q' and Q phases share the same crystallographic structure, they possess slightly different lattice parameters [37] and the phase observed in the present alloy exhibits closer alignment with the stable variant.

No peaks corresponding to the β phase or its precursors were identified. Furthermore, no peak originating from the $Al_3Ti$ was visible because of the chosen angular range.

For semi-quantitative results, the identified peaks were fitted by a Gaussian function, allowing measurements of the full width at half maximum (FWHM) and the area of each peak. The peak area is linked to the volume fraction of the phase, while the FWHM is inversely correlated to its mean size. For each phase ($\theta'$, θ, L and Q), only the peak of highest intensity was investigated, and the results are shown in Fig. 8. The inverse of the FWHM is plotted to provide a direct indication of size variations.

In the T7 state, the peaks corresponding to the θ phase are not visible, whereas those associated with the Q phase are relatively small. Similarly, the peak related to the θ' precipitates is also small and wide
<figure><img src="image_8.png" /><figcaption>Fig. 6. (a) Section of the WAXS I(2θ<sub>Cu</sub>)-plots of the initial state and the condition aged 1000 h at 190 °C showing the peaks of the different phases present in the alloy and (b) evolution of the peaks related to the θ and Q precipitates in the WAXS I(2θ<sub>Cu</sub>)-plots for the sample aged 1000 h as a function of the ageing temperature. Subtraction of the baseline was performed to highlight the diffraction peaks and compensate for the end of the SAXS signal visible at low diffraction angles.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Evolution of the diffraction angle measured during ageing for the identified “Q”-phase for (a) the (110) peak and (b) the (100) peak compared to the theoretical diffraction angles for the equilibrium Q phase and the metastable Q' phase.</figcaption></figure>

revealing a limited fraction of small precipitates. Additionally, the (101) peak of the L precipitates is also modest in size.

During long-term ageing, the two equilibrium phases (θ and Q) exhibit similar trends. The curves are divided into two distinct stages. The first stage, from 165 °C to 200 °C, shows a notable increase in peak area and decrease in width, particularly pronounced at shorter ageing times. In the second stage, beyond 200 °C, the data corresponding to different ageing times appear to converge onto a single master curve, showing a gradual and consistent increase in peak area alongside a steady reduction in peak width. Consequently, it can be inferred that the Q and θ precipitates undergo growth in size and volume fraction during prolonged ageing, a process expedited by increasing the ageing temperature.

Regarding the evolution of the θ' precipitates, the observed WAXS peak exhibits greater variability from position to position compared to the relatively smooth evolution observed for the equilibrium precipitates. This variability can be attributed to the anisotropic nature of the θ' precipitates, as they are plate shaped structures of high aspect ratio oriented along the <100>Al planes. Such morphology leads to a more anisotropic signal compared to rod precipitates owing to the characteristics of the Fourier transform [33]. Consequently, the WAXS signal originating from these precipitates is highly sensitive to the orientation and number of grains interacting with the X-ray beam. Although the implementation of the rotation setup led to more reliable measurements, noisy variations are still discernible across different positions for this precipitate family. The evolution of the θ'-peak appears

to be roughly independent of the ageing time for the durations investi-
gated. However, a clear impact of the ageing temperature is evident,
with a reduction in peak area and width observed with increasing
temperatures. This trend suggests that the smallest θ' precipitates
dissolve to the profit of the stable phases as the ageing temperature
increases, regardless of the duration of ageing.

The evolution of the L precipitates seems to follow a rapid dissolution
of the precipitates during the first 1000 h of ageing with no significant
change in size. Subsequently, the peak associated with these precipitates
shows minimal evolution over extended ageing periods, with a notably
faint peak persisting throughout the ageing process.

4.2.2. TEM observations

TEM observations have also been carried out in order to confirm the
presence of phases identified by WAXS. TEM observations allow for a
better sensitivity than WAXS to phases in small fraction. Two conditions
were analysed: the initial state (T7) and a condition aged at 200 °C for
1000 h.

The diffraction patterns shown in Fig. 9(a) were taken by SPED with ASTAR, with a probe size of approximately 1 .5nm. By comparing the experimental diffraction patterns to the simulated or experimental patterns of possible precipitates with compositions consistent with the EDS analysis [37–39], two main precipitate families were identified. The first precipitate family (in light grey) corresponds to Q precipitates with rod shapes. The rods are aligned with the [100]Al and their orientation relationship with the matrix is [0001]Q //[001]Al and
<figure><img src="image_10.png" /><figcaption>Fig. 8. Area and FWHM of the peaks of the different families as a function of ageing time and temperature.</figcaption></figure>

[1120]Q/[510]Al. The high number density of these precipitates is in qualitative agreement with the WAXS observations. The average diameter of these precipitates is around 4 nm. The second precipitate family (in orange) is identified as L precipitates with lath morphology. They are present in two variant orientations visible in the [001]Al zone axis. These L precipitates are believed to correspond to a disordered version of the C phase, which is a precursor to the Q precipitates, according to [40]. As its exact crystallographic structure remains unclear, no diffraction pattern could be simulated for this phase but the correspondence of our diffraction patterns with the experimental patterns shown by Sunde et al. [39] is excellent. Additionally, the morphology and orientation with respect to the matrix of these L precipitates are in perfect agreement with previous works [41–43], i.e. the lath shape is aligned with the (001) directions of the aluminium matrix, with the rectangular cross-section along the [100]Al and [010]Al. EDS analysis (Fig. 9(b)) validated the phase identification, revealing that the rod-like (Q) and lath-like (L) precipitates are enriched in Mg, Cu and Si. These results are in good agreement with the WAXS observations that enabled the identification of these precipitates in the initial state. No precipitates from the β or θ family were found in the alloy in the initial state, which is consistent with the WAXS measurements.

For the sample aged during 1000 h at 200 °C, observations in bright-field STEM mode, along with SPED analysis, are shown in Fig. 10(a). The formation of the θ' phase during ageing is confirmed, alongside the phase transformation from L laths to Q rods with an increase in size, as an average diameter of 8 nm is measured for these rod-like precipitates. The θ' precipitates exhibit a mean thickness of 15 nm. The EDS maps (Fig. 10(b)) validate the identification by diffraction as the θ' platelets are Cu-rich, and the Q rods are enriched in Mg, Si and Cu. An additional EDS map acquired in a different area (available in Appendix C) revealed a Cu rich phase with a more globular morphology, that corresponds well

to the θ phase.

Additionally, no L precipitates were identified in the aged sample, suggesting that these precipitates dissolved or transformed into Q precipitates. This also aligns with the WAXS data, as the volume fraction of the L precipitates appeared to sharply decrease during the first 1000 h of ageing.

Further TEM observations confirmed the presence of a Ti-rich phase consistent with Al3Ti (Appendix C), in agreement with the Thermo-Calc prediction (Fig. 1). Al3Ti is a stable phase used as grain refiner and does not undergo evolution during ageing [44].

The microstructural characterizations carried-out by TEM confirm the WAXS measurements and allow for a finer description of the evolution of the precipitation state during long-term ageing. In the T7 condition, precipitates are mostly from the Q phase and the L phase. During ageing, the Q precipitates grow in size, this being likely facilitated by the transformation of the L precipitates. Simultaneously, θ and θ' precipitates appear at a size with a low hardening potential. The absence of precipitates from the β-family was confirmed, despite indications from the Thermo-Calc predictions (Fig. 1) suggesting their potential presence. The formation of θ and θ' precipitates, which exhibit a low hardening effect due to their large size, depletes the solute elements (Cu) required for the precipitation of the hardening phases L and Q.

## 5. Predicting the time-evolution for a given ageing temperature

The extensive database detailed in the previous parts provides by itself valuable insights on the ageing mechanisms for this alloy. In addition, these results can also be used to support a predictive approach for the evolution of mechanical properties during an isothermal heat treatment, which holds significant potential for industrial applications particularly in predicting the service life of components.

### 5.1. Time-temperature equivalence approach

A simple time-temperature equivalence, based on the Arrhenius equation, was implemented to predict the evolution of mechanical properties across various ageing times and temperatures. This approach assumes that the evolution of microstructure and hardness is governed solely by one thermally activated process. While this is a very strong approximation, it will be shown to yield remarkably reliable predictions. The approach relies on fitting an activation energy (Ea) capable of linking ageing time and temperatures giving similar mechanical properties. For two conditions (T1, t1) and (T2, t2), where T represents the ageing temperature and t the ageing duration, resulting in similar hardness, we should have:

$$t_1 \exp\left(-\frac{E_a}{RT_1}\right) = t_2 \exp\left(-\frac{E_a}{RT_2}\right) \quad (7)$$

R being the gas constant.

Consequently, an equivalent time teq for a reference temperature Tref can be calculated as:

$$t_{eq} = t_2 \exp\left(\frac{E_a}{R}\left(\frac{1}{T_{ref}} - \frac{1}{T_2}\right)\right) \quad (8)$$

Ea can then be optimised to obtain a single curve HV(teq) using the data from the different ageing times: the fitted Ea is found to be 130 ± 10 kJ/mol for our alloy.

This approach enables plotting the experimental hardness as a function of an equivalent ageing time at any given temperature within the studied range (165 °C to 245 °C). Predictions of the hardness and the equivalent yield strength evolutions with time for a given ageing temperature can be plotted as illustrated in Fig. 11 for a temperature of 200 °C. In this figure, each data point represents a data point from Fig. 4, converted into an equivalent time using Eq. (6) with an aging
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** TEM observations of the T7 initial state in [001]Al zone axis. (a) STEM image with typical integrated diffraction patterns obtained by SPED acquisitions using ASTAR compared to simulated diffraction patterns for the Q phase. The diffraction pattern of the aluminium matrix is given as reference (grey). (b) EDS analysis illustrating the presence of precipitates enriched in Mg, Cu, and Si with different morphologies.</figcaption></figure>

temperature of 200 °C. Using an activation energy of 130 kJ/mol, we obtain a hardness variation of ± 5 HV corresponding to an equivalent yield strength variation of ± 15 MPa for a given ageing time at 200 °C. This low variability appears to validate the necessary assumptions for a time-temperature equivalence to be effective. Specifically, this implies that a single thermally activated phenomenon governs the evolution of the mechanical properties.

A similar methodology can be applied to the WAXS data and the measured characteristics of the different peaks for the stable families θ and Q (Fig. 12). This approach was not implemented for θ' and L precipitates as their measured characteristics remain unaffected by the ageing duration after 1000 h of ageing. Using the activation energy fitted to the hardness evolution proved satisfying.

This activation energy can be compared to those reported in the literature using the Kissinger method with DSC [45,46]. Caution should be exercised as the activation energy determined through the Kissinger method also considers nucleation effects, whereas our results solely address the coarsening stage. Nevertheless, the activation energy of 130 kJ/mol reported by Gaber et al. for the Q precipitates is similar to our findings [47]. Activation energies found for the θ precipitates vary significantly depending on the alloy composition, ranging from 137 to 330 kJ/mol [23,48–50]. Our activation energy lies in the lower range for this type of precipitate.

The value of the activation energy found for the evolution of mechanical and microstructural properties closely aligns to the activation energy of copper diffusion (133 kJ/mol) according to ThermoCalc using the TCAL9 database. This suggests that the evolution of microstructural and mechanical properties is directly governed by copper diffusion, consistent with copper being the slowest diffusing element among those forming the precipitates.

## 5.2. Extrapolation to ageing temperatures not included in the studied temperature range

The obtained equivalences for the microstructural and the mechanical properties seem valid within the studied temperature range.

This equivalence should theoretically apply at temperatures lower than 165 °C, as no additional phenomena are expected to occur, and the solubility of the alloying elements would not be significantly influenced by temperature in this range.

However, to plot the evolution of the measured properties as a function of an equivalent ageing time at a temperature exceeding 245 °C, it would be necessary to validate the assumptions of the time-temperature equivalence. Phase transformation or significant variations in solubility may render the presented approach inapplicable. At higher temperatures, the θ' precipitates would dissolve and/or transform into θ precipitates. However, this transformation would have a minimal impact on the mechanical properties, as θ' precipitates form at a size with low hardening potential, meaning that their disappearance would cause a negligible reduction in mechanical strength. Moreover, as the Q precipitates are stable, there should be no phase transformation affecting them. Therefore, the equivalence could potentially yield approximate results concerning the mechanical properties for these higher temperatures. However, beyond a certain ageing temperature, the equilibrium volume fraction, which is temperature-dependent (Fig. 1), will start to limit the Q precipitation. This will result in deviations between the results obtained using the equivalence and the experimental mechanical observations. According to the diagram presented in Fig. 1 this should only occur at temperatures higher than 300–350 °C as the equilibrium volume fraction of Q is minimally impacted at lower temperatures.
<figure><img src="image_12.png" /><figcaption>Fig. 10. (a) Examples of the different phases identified by SPED using ASTAR with the simulated patterns for comparison on a sample aged 1000 h at 200 °C in [001]Al zone axis and (b) EDS analysis of the precipitates visible for the same zone.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Time-temperature equivalence plot of the experimental hardness and the equivalent yield strength as a function of the equivalent ageing duration at 200 °C, with E_a = 130 kJ/mol.</figcaption></figure>

## 6. Conclusions

Using an experimental setup based on long-term ageing in a temperature gradient, an extensive amount of data was collected concerning the evolution of both the microstructure and the mechanical properties of an A357+1wt%Cu aluminium alloy for up to 10,000 h.

* The experimental configuration, consisting of elongated samples aged in a gradient tubular furnace connected to a cooler allowed to produce specimens aged within a temperature range of 165 °C to 245 °C for durations spanning up to 10,000 h.

* WAXS provided more useful results compared to SAXS due to its capability to decouple the evolution of multiple precipitates families.
<figure><img src="image_14.png" /><figcaption>Fig. 12. Time-temperature equivalence for the characteristics (area and width) of the θ and Q WAXS-peaks for an activation energy of 130 kJ/mol.</figcaption></figure>

* Mechanical and microstructural characterisations showed that the evolution of the mechanical properties was related to a complex evolution of several precipitate families. Hardening precipitates from the L, Q and θ' families were observed during ageing. L precipitates transformed into Q precipitates, which exhibited an increase in both size and volume fraction over time. Additional θ' precipitates also formed during ageing, but their large size translates in a low hardening potential. Stable θ precipitates also formed during ageing with a low hardening potential due to their large size. Their size and volume fraction were shown to increase during ageing.

* Based on the hardness evolution, a straightforward approach using time/temperature equivalences was developed, allowing the plotting of the evolution of the mechanical data as a function of an equivalent time at a desired temperature. The activation energy fitted to tune this equivalence proved to be consistent with the microstructural evolution of the stable q and Q precipitates measured by WAXS.

* The value of the activation energy (130 ± 10 kJ/mol) suggested that the evolution of the microstructure and mechanical properties of the alloy is directly controlled by copper diffusion within the aluminium matrix.

## Funding

This work was supported by the DGAC, the ‘France Relance’ national

stimulus plan and the ‘Nextgeneration EU’ European support program.

## CRediT authorship contribution statement

**Thomas Perrin:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Conceptualization.
**Arthur Després:** Writing – review & editing, Visualization, Supervision, Investigation, Conceptualization.
**Pierre Heugue:** Writing – review & editing, Supervision, Resources, Project administration.
**Alexis Deschamps:** Writing – review & editing, Visualization, Supervision, Investigation, Conceptualization.
**Frédéric De Geuser:** Writing – review & editing, Supervision, Software, Project administration, Investigation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors would like to express their gratitude to the scientific and technical team of the D2AM-BM02 beamline at the ESRF synchrotron for their assistance with the SAXS/WAXS experiments.

## Appendix A. Photographs of the cooling section

Fig. A.1
<figure><img src="image_15.png" /><figcaption>Fig. A.1. Photographs of (a) the connection between the copper braid and the sample support and (b) the cooling circuit brazed to the copper braid coming out from the gradient furnace. The different components are labelled as follows: (1) copper braid, (2) sample support, (3) end of the gradient furnace and (4) cooling circuit brazed to the copper braid. Thermal paste was applied at the interface between the copper braid and the sample support.</figcaption></figure>

## Appendix B. Correlation between yield strength and hardness during ageing

A database of ageing treatments at three temperatures (150 °C, 175 °C and 200 °C) for durations up to 15,000 h allowed to plot the evolution of the yield strength measured by uniaxial tensile tests as a function of the hardness throughout ageing. A linear correlation is observed between the two properties.

<figure><img src="image_16.png" /><figcaption>Fig. B.1. Correlation between the yield strength and hardness during long-term ageing.</figcaption></figure>

## Appendix C. Additional EDX mappings of Cu-rich phase and Ti-rich phase

<caption>Fig. C.1</caption>
<figure><img src="image_17.png" /><figcaption>Fig. C.1. (a) Cu-rich phase identified as θ precipitate and (b) Ti-rich phase identified as Al₃Ti.</figcaption></figure>

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