# Precipitate evolution and related strengthening during long term ageing of 2618A aluminium alloy

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. Precipitate evolution and related strengthening during long term ageing of 2618A aluminium alloy. Acta Materialia, 2025, 296, pp.121264. 10.1016/j.actamat.2025.121264. hal-05138483

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# Precipitate evolution and related strengthening during long term ageing of 2618A aluminium alloy

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

## ARTICLE INFO

Keywords:

Ageing

precipitation

Phase transformation

High-throughput

Aluminium alloys

## ABSTRACT

The 2618A alloy is used for aerospace applications where high resistance to long-term thermal ageing is required. Being able to predict the evolution of mechanical properties during long-term ageing is therefore crucial to determine the end-of-life of these products. It requires an in-depth understanding of the evolution of hardening precipitates during extended ageing, which happens along a complex sequence of metastable and stable phases. Here we used a high-throughput experimental methodology to gather systematic microstructure and related mechanical properties data resolved in time and temperature, using samples aged within a temperature gradient up to 10,000 h. Hardness maps were used to monitor the evolution of the mechanical properties along samples aged in this temperature gradient. Local transmission electron microscopy (TEM) with scanning precession electron diffraction (SPED) and atom probe tomography (APT) were used to identify the nano-precipitates for selected conditions, while systematic small angle X-ray scattering (SAXS) was used to evaluate the evolution of sizes and volume fractions of the precipitates along the graded samples. Our results evidence for the first time the important contribution of Si-containing L-phase to the initial strength of the T851. In the first stages of long-term ageing up to 5,000h at 200°C the strength loss is controlled by the partial dissolution of this L phase together with coarsening of S precipitates. Subsequently, the Q phase appeared to form, which destabilised partly the S phase and results in an accelerated loss of mechanical properties.

## 1. Introduction

The 2618A alloy is an age-hardenable aluminium alloy known for its good ageing resistance at elevated temperatures, making it suitable for high-performance applications such as racing engine pistons, as well as in the aeronautical and aerospace industries [1]. These applications require the material to be able to withstand thermal ageing for extended periods of time up to 100,000 hours at temperatures around 200°C. Accurate prediction of the properties throughout this long-term ageing is crucial for ensuring safety or avoiding unnecessary replacement of components. This requires an in-depth understanding of the evolution of the hardening precipitates during extended ageing, which can involve a combination of precipitate coarsening and phase transformations from metastable phases to more stable ones.

Precipitation is the primary strengthening mechanism in the 2618A alloy. Given that it is an Al-Cu-Mg alloy with minor Si additions, the principal hardening precipitates are expected to belong to the S-

Al₂CuMg family. The first precipitation sequence for such precipitates was proposed by Bagaryatsky [2]:

$$SSS \rightarrow GPB \ zones \rightarrow S'' \rightarrow S \rightarrow S$$

With SSS standing for the supersaturated solid solution and GPB zones for Guinier-Preston-Bagaryatsky zones. This precipitation sequence has since been discussed and various studies discussed the existence of S'' precipitates [3,4] (also referred to as GPB2 zones) and the composition and crystallography of the S phase and its precursors [5-7]. The S' and S precipitates exhibit minimal differences in crystallographic parameters, raising the possibility that S' is simply a distorted variant of the S phase, which may question the classification of S' as a distinct phase.

Nonetheless, Styles et al. [8,9] showed that two kind of S phases (S₁ and S₂) exist, both exhibiting an orthorhombic structure (space group Cmcm) with small differences in crystallographic parameters (a = 4.049

<footnote><sup>a</sup> University Grenoble Alpes, CNRS, 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>
Å, b = 9.250 Å, c = 7.090 Å for S₁, and a = 4.016 Å, b = 9.27 Å, c = 7.117 Å for S₂). The two S phases also exhibit morphological differences with S₁ having a lath-like morphology and S₂ having a rod-like morphology. Both elongated shapes lie along the [100]Al directions and the rectangular cross-section of the S₁ phase align with the [210]Al directions.

Addition of Si to the Al-Cu-Mg system adds complexity to the precipitation sequence that can be observed in these alloys. Hutchinson and Ringer [10] observed that incorporating 0.1 to 0.5 at% Si into an Al-2.5Cu-1.5Mg alloy (a composition close to the 2618A alloy) significantly enhanced the age-hardening response, leading to an increase in hardness by up to 50% at the peak-aged condition. This improvement was attributed to a finer distribution of the S phase. The Si addition was also found to promote β phase precipitation. Depending on the Si content, precipitation of quaternary Al-Cu-Mg-Si phases, such as Q and C phases, can occur as shown by Li et al. in a 2014 alloy with Si addition [11], and Niu et al. in a Al-3.0Cu-1.8Mg-0.5Si (wt. %) alloy [12]. The Q phase exhibits a rod-like morphology or lath-like morphology, with the long dimension aligned with the [100]Al directions. When a lath-like morphology is observed, the rectangular cross section align with [150]Al directions. The orientation relationship between the Q precipitates and the matrix is given by [0001]Q//[001]Al and (2130)Q//[(020)Al [13]. Several compositions of the Q phase were reported with Cu content varying from 7.1 at% to 22 at% [14–16], with possible evolution during ageing [16].

Besides, the C phase is recognised as a precursor to the Q phase forming as thin plates in the {100}Al planes with a monoclinic structure (P2₁/m) [17]. The L phase, considered a disordered variant of the C phase, can also appear as a precursor to the Q phase in Al-Cu-Mg-Si alloys. The L phase exhibits a rod-like or lath-like morphology aligned with the <100>Al directions. When a lath-like morphology is observed, the rectangular cross-section lies along the [010]Al and [001]Al directions. The compositions of the L and C phases are not well established, but a low Cu content ranging from 2 at% to 7 at% was reported [17–19]. The L, C, and Q phases share a common Si hexagonal substructure, but the orientation of this substructure relative to the Al matrix depends on the specific precipitate. The orientation relationship between the Si network (SN) and the aluminium matrix were described as (110)SN,LC //(100)Al and (001)SN,LC //(001)Al for the L and C phase, and (110)SN,Q //(150)Al and (001)SN,Q //(001)Al for the Q phase [20]. To our knowledge, none of the L, C or Q phases have been identified so far in the 2618A alloy during ageing, although they may be expected to form.

Studies investigating the mechanical and microstructural evolution of the 2618A alloy during long-term ageing reported a degradation in mechanical properties primarily attributed to growth and coarsening of the main hardening S precipitates [21–23]. The development of precipitate-free zones (PFZ) was also noted, potentially impacting mechanical properties [21,24]. These studies typically investigated several ageing temperatures and durations, highlighting the effects of both parameters and revealing only general trends.

Comprehensive datasets for predictive analysis can be obtained using graded samples along high-throughput characterisation techniques. Composition gradients, for instance, are an effective approach to study the effects of alloying elements [25–27]. For investigating the impact of heat treatments, applying a temperature gradient is a powerful method to assess systematically the influence of the heat treatment temperature [28,29]. When it comes to characterising graded samples, small-angle X-ray scattering (SAXS) has proven effective in mapping precipitation states in heterogeneous materials, with welded materials serving as a good example [30,31]. SAXS can provide accurate information on the size and volume fraction of phases when the precipitate morphology and composition are identified. Regarding mechanical properties, hardness maps are useful for evaluating their evolution, as hardness measurements are closely correlated with tensile properties [22,32].

The aim of this paper is first to present a systematic quantitative investigation of the precipitate microstructure evolution during long-term ageing. This will be achieved by using a high-throughput methodology consisting of ageing samples within a temperature gradient to cover an extensive domain of ageing temperatures and times, together with a spatially resolved evaluation of precipitate characteristics and related mechanical properties. It will make it possible to identify the prevailing strengthening mechanisms in a time-temperature map and evidence bifurcations of the ageing mechanisms at critical conditions.

Classical single-temperature heat treatments were first used to establish correlations between hardness and tensile properties during ageing. Long samples were then aged in a temperature gradient ranging from 165°C to 245°C for durations up to 10,000 hours prior to characterisation. The evolutions of mechanical and microstructural properties were systematically evaluated using hardness and small angle X-ray scattering (SAXS). Local transmission electron microscopy (TEM) with energy-dispersive X-ray spectroscopy (EDS) and scanning precession electron diffraction (SPED) was used to identify the precipitates. Atom probe tomography (APT) was also used to complement the identification. Finally, time-temperature equivalences were implemented to allow predictions of the evolution of mechanical properties for a given temperature. A phase transition occurring for extended ageing times at high temperature (5,000 hours at 200°C) was identified, causing an accelerated loss of mechanical properties. A micromechanical model was implemented to quantify the hardening effect of the main strengthening precipitates.

## 2. Material and methods

The alloy investigated is a 2618A alloy produced by Aleris as thick laminated plates. The composition of the alloy measured by inductively coupled plasma atomic emission spectroscopy (ICP) is given in Table 1. The alloy plates were received in a T851 thermomechanical state corresponding to a solution heat treatment at 530°C followed by a water quench, 1% to 3% deformation and 20 hours at 190°C.

Two types of ageing treatments were employed: classical single-temperature heat treatments and temperature gradient heat treatments.

The samples that underwent classical single-temperature heat treatments were used to establish correlations between tensile properties and hardness. Standard TC25 cylindrical tensile specimens were machined along the rolling direction and tested at room temperature following the NF EN 2002-001 standard with a strain rate of $8.3 \times 10^{-5} s^{-1}$ up to 1% strain, followed by a strain rate of $8.3 \times 10^{-4} s^{-1}$ beyond 1% strain. Six samples were tested for each condition. Vickers hardness measurements were conducted using a 500 g load, with thirty indents taken per sample from the single-temperature heat treatments.

The samples subjected to a temperature gradient were aged, starting from the T851 initial state, in a temperature gradient ranging from 165°C to 245°C along a distance of 32 cm. Details on obtaining this temperature gradient can be found in [33]. Concerning hardness measurements, five indents were measured per position, and the hardness maps were conducted with 5 mm between the different positions, corresponding to a temperature increment of 0.5 to 1°C depending on the position.

SAXS measurements were conducted along the length of the graded samples to characterise the evolution of the hardening precipitates. These measurements were performed at the European Synchrotron Radiation Facility (ESRF) in Grenoble, using a 2D photon counting IMXPAD D5 detector with a pixel size of 130 µm. The beam size was set to $100 \times 100 \mu m^2$, with a beam energy of 18 keV and a sample-to-

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

Composition of the alloy measured by ICP.</caption><thead><tr><th>%wt</th><th>Al</th><th>Mg</th><th>Si</th><th>Cu</th><th>Fe</th><th>Ni</th></tr></thead><tbody><tr><td></td><td>B.</td><td>1.6</td><td>0.30</td><td>2.5</td><td>1.0</td><td>1.0</td></tr></tbody></table>
detector distance of 3.5 m. As a consequence, the measured q-range extended from 0.004 to 0.3 Å⁻¹ and data fitting was performed over the entire available range. The sample-to-detector distance was calibrated using a silver behenate standard, while the absolute intensity calibration was carried out with a glassy carbon reference.

Considering the anisotropic morphology and distribution of the studied precipitates (rods or laths along the [100]Al directions), rotations of the samples were implemented as described in [34]. A rotation range from -45° to +45° with a 3° increment and a 1 second acquisition time were used, with a semi-continuous approach as described in [34]. Azimuthal integration of each image (corresponding to an ageing temperature and an angle) was carried out using the PyFAI Python package [35] to obtain an I(q) plot. These curves were then fitted using a model that includes the scattering contributions from the precipitates (as detailed in Section 5.2), as well as Porod and Laue background terms. The resulting fit parameters (precipitate size and volume fraction) can then be plotted as functions of ageing temperature and duration. All data processing and analysis were performed using custom Python scripts developed for batch analysis.

Complementary TEM observations were performed on selected conditions from the graded samples to identify the different phases, using a JEOL 2100F instrument equipped with a field emission gun and operated at 200 kV. SPED was performed using the ASTAR software from Nanomegas with a precession angle varying between 0.5 to 1°. An in-line direct electron detector Medipix 3 in the Cheetah camera from Amsterdam Scientific was used to collect the diffraction patterns. Details on the SPED technique for the identification of precipitates can be found in [36]. A high collection angle SDD Centurio detector was used to obtain EDS maps. To characterise the precipitation in the alloy, all observations were conducted in a [100]Al zone axis as the expected precipitates lie along these directions. At the selected positions, thin sheets approximately 500 µm thick were cut and mechanically ground to a final thickness of 100 µm. Discs with a diameter of 3 mm were then extracted at precise locations and electropolished using a Tenupol-3 device and a solution of 33% nitric acid and 66% methanol at -25 °C.

APT samples were prepared using a standard two-step electro-polishing procedure initially using a solution of 25% perchloric acid in 75% acetic acid, and then a solution of 2% perchloric acid in 2-butoxyethanol. The experiments were performed using a LEAP6000 XR from CAMECA in voltage mode. The specimen temperature was set to 60 K, with a voltage pulse fraction of 30% and a pulse frequency of 125 kHz. The reconstructions and analysis were performed using the IVAS software.

### 3. Temperature gradient heat-treatments

Long samples (325 × 7 × 3.5 mm³) aged in a temperature gradient enabled the characterisation of the effect of over-ageing across a continuous spectrum of ageing temperatures over selected periods. In this study, samples were aged for durations ranging from 210 hours to 10,000 hours in temperature gradients ranging from 165°C to 245°C with one sample per ageing duration resulting in six samples in total. The temperature gradient measurements are shown in Fig. 1, along with the polynomial fit used to determine the ageing temperature as a function of the position on the sample for the different characterisation technics.

Continuous temperature measurements at multiple positions were recorded throughout the 10,000 hours of ageing, revealing a maximum variability of ±2°C. More details on the thermal gradient and stability issues are available in [33].

Due to the geometry of the sample, tensile test could not be machined from the samples to provide the tensile properties after ageing at a given temperature. However, hardness profiles can be straightforwardly obtained, and equivalent tensile properties were derived from correlations obtained using classical isothermal heat treatments.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Temperature gradient measured across the sample, with the corresponding polynomial fit used to predict temperature as a function of position.</figcaption></figure>

### 4. Evolution of mechanical properties

#### 4.1. Correlation between hardness and tensile properties

Before characterising the gradient samples, bulk samples (100 × 60 × 60 mm³) were heat-treated in classical furnaces at three temperatures (150°C, 175°C, and 200°C) with aging durations ranging from 1,000 to 15,000 hours. Hardness tests were conducted on these samples, and tensile test specimens were machined and tested. The evolution of the three main parameters (ultimate tensile strength, yield strength and hardness) are highly correlated, and linear relationships were established between hardness and tensile properties as shown in Fig. 2.

These relationships are in good agreement with similar studies [22].

#### 4.2. Hardness profiles and time-temperature equivalences

Hardness profiles were performed on the graded samples and equivalent $\sigma_y$ values were calculated using the previously established linear correlation. Increasing the ageing time and duration results in a greater loss of mechanical properties (Fig. 3 (a)). For ageing times between 210 h and 3,000 h in the considered temperature range, the same trend is observed with a seemingly linear evolution of the hardness with the ageing temperature and a similar slope for the different ageing times. For longer ageing treatments, an accelerated loss of mechanical properties is observed in the higher range of temperatures. Specifically, an acceleration is observed above 200°C for the sample aged 5,000h with a

<figure><img src="image_4.png" /><figcaption>Fig. 2. Correlation between the ultimate tensile strength (UTS), yield strength ($\sigma_y$) and hardness (HV) measured during long-term ageing.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) Hardness profiles and equivalent yield strength for the graded samples with standard deviation (5 indents were measured per position) and (b) time-temperature equivalences for the hardness and equivalent yield strength with E_a = 138 kJ/mol. The standard deviations are not represented on graph (b) so as not to overcrowd the figure.</figcaption></figure>

steeper slope for greater ageing temperatures. The sample aged 10,000 h seems to exhibit the same evolution at a temperature closer to 180°C. This suggests that a new mechanism is activated at high temperature and long-time of treatment.

To compare the different ageing conditions, the evolution of the mechanical properties can be plotted as a function of an equivalent ageing time at a given temperature. This approach assumes that the ageing process is governed by a single thermally activated mechanism, such as solute diffusion in the alloy. If the solubility of the phases exhibits significant temperature dependence or if a phase transformation occurs, this equivalence would not be valid. According to the TCAL9 database from Thermo-Calc, the solubility in the Aluminium phase of Mg and Cu in equilibrium with the S phase in the 2618A alloy remains nearly constant for temperatures below 270°C. The equivalent ageing time (t<sub>eq</sub>) for a chosen ageing temperature (T<sub>ref</sub>) is given by relation (1):

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

with t and T being the actual ageing time and temperature of the sample, E_a the activation energy of the mechanism, and R the gas constant.

Using the activation energy of copper diffusion in the alloy (138 kJ/mol), Fig. 3 (b) is obtained. A good correlation is observed for the specimens aged up to 5,000 h. Above 5,000 hours of equivalent ageing time at 200°C, two paths are observed corresponding to ageing temperatures respectively below and above ~200°C. Therefore, the

assumption of a single thermally activated phenomenon is not verified in the samples aged 5,000 h and 10,000 h. Still, a good correlation between these two samples is observed, even after the transition. The close alignment, below this transition, of the mechanical data using the activation energy for copper diffusion in the alloy suggests that the ageing mechanism is mainly governed by the diffusion of copper, which is consistent with copper being the slowest diffusing element in the alloy.

The appearance of this transition suggests that a new mechanism is at play for the more extreme ageing conditions. To identify the root cause of this phenomenon, the evolution of the microstructure was characterised.

## 5. Evolution of the microstructure

To explain the hardness evolution and the presence of the two distinct regimes, high-throughput characterisation of the hardening precipitates was conducted using SAXS acquisitions on samples aged from 1,000 to 5,000 hours. Local TEM and APT observations in the graded samples were first needed to identify the precipitates present, their morphology and composition to be able to effectively interpret the SAXS acquisitions. Three conditions were selected to identify the hardening precipitates: the T851 initial state and two aged conditions (5,000 h at 170°C and at 240°C) representing stages before and after the observed acceleration of the hardness evolution (Fig. 3).
## 5.1. Precipitate identification

Fig. 4 shows TEM observations of the specimen in the T851 initial state. The precipitates are mainly present as rods. A bimodal size distribution is observed with large precipitates (approximately 10 nm in equivalent diameter) having nucleated on dislocations and a high density of finer precipitates (2 to 5 nm of equivalent diameter) as seen in Fig. 4 (a). The large precipitates (circled in red on Fig. 4 (b) and (c)) are identified to be S precipitates according to SPED (Fig. 4 (d)). Regarding the fine precipitates, only SPED was effective, as EDS did not have sufficient spatial resolution. Two families are identified at this scale: the S-Al₂CuMg (same structure as the large precipitates) and the L-AlₐMgb. SiₐCuₐ (circled in blue) precipitates.

Due to the partial disorder in the crystal structure of the L phase, its diffraction pattern cannot be reliably simulated. However, comparison with experimental diffraction pattern collected in previous studies [19] allowed to identify those precipitates as possible L precipitates, notably thanks to the orientation of the Si hexagonal substructure. A phase map was obtained by selecting several virtual apertures to differentiate and highlight the two types of precipitates (Fig. 4 (c)). A higher density of L precipitates is observed compared to the S precipitates regarding the fine scale precipitation.

Knowing the composition of the precipitates is crucial for accurately interpreting SAXS measurements. Consequently, APT measurements were conducted. Fig. 5 (a) shows the reconstruction of an APT tip from the T851 initial state displaying the different families identified by TEM. Two precipitate sizes are observed, each with distinct compositions (Fig. 5 (b)). The larger ones are laths with a composition close to Al₂CuMg, slightly enriched in aluminium. The smaller precipitates exhibit a rod-like morphology and with three orthogonal directions. Determining their composition is challenging due to their small sizes and chromatic aberrations as described in [37], and a high variability is observed among these Si-rich precipitates. Nevertheless, those precipitates exhibit a high enrichment in Mg and lower enrichment in Cu and Si, and can be identified to the L phase observed in TEM. When comparing to the composition suggested by Torsæter et al. [17] and Sunde et al. [19], their ratio of solute atoms is close to that of the L phase

of the present work but exhibits higher enrichment in Cu. However, the presently measured Cu content (approximately 5 at%) is in good agreement with another study [18]. The rod-like morphology of the identified L phase differs from the previously reported lath-like morphology, which could be attributed to the small size of these precipitates corresponding to their early stage of precipitation.

TEM observations were also conducted on two specimens extracted from the gradient sample aged for 5,000 h. In the specimen aged 5,000 h at 170°C (Fig. 6), using EDX analysis coupled with SPED, we can identify the S precipitates (circled in red) as form of rods (S₂) or as laths with the cross-section aligned along the [210]Al directions (S₁).

Laths with cross-section aligned along the [100]Al are also observed (in blue). The orientation of the rectangular sections is inconsistent with S precipitates. SPED show that these laths correspond to L precipitates with a low Cu content according to the EDX maps. APT acquisitions were also performed for the specimen aged 5,000 h at 170°C, validating the precipitate identification with L and S precipitates observed within the tip. The L precipitates exhibited a low Cu content close to 4 at% and composite precipitates composed of L and S precipitates were found (Fig. 7).

The specimen aged at 240°C (Fig. 8) contains S precipitates (circled in red), and a Cu-Mg-Si rich phase (circled in yellow) with either a lath-like morphology along the [100]Al direction with a rectangular cross-section oriented along [051]Al, or a rod-like morphology along the [100]Al direction. These precipitates are identified as the Q phase on SPED diffraction patterns. Their morphology and orientation relationship align well with the phase identification, as Q precipitates were shown to exhibit a lath or rod morphology aligned along the [100]Al directions and when a lath-morphology is observed, the rectangular cross-section is aligned along the [051]Al directions. Curved “clouds” visible in the Si map can be attributed to the redeposition of Si-O-H during electropolishing, as observed by Jensen et al. [38] and Wang et al. [39]. This interpretation is supported by the O map, which shows that these streaks are also enriched in oxygen.

No APT measurement was conducted for the specimen aged at 240°C due to the low precipitate density, making it unlikely to capture a Q precipitate in the APT tip.

<figure><img src="image_6.png" /><figcaption>Fig. 4. (a) STEM dark field image showing precipitates having nucleated on dislocations and high magnification STEM bright field showing fine rod-like precipitates, (b) virtual bright field obtained from SPED acquisition of the alloy at the initial T851 state, (c) phase map obtained using various virtual dark-field apertures to select the two kinds of precipitates and (d) typical diffraction patterns from the two families of precipitates identified.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 5. APT acquisition for the 2618A specimen at the initial T851 state displaying (a) 10 at%Cu and 1 at% Si isoconcentration surfaces, with aluminium atoms in blue and identification of two precipitates (P1, P2) and (b) concentration profiles for the two precipitates.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. STEM bright field image with EDX analysis and typical diffraction patterns obtained for the circled precipitates, for the sample aged for 5,000 hours at 170°C.</figcaption></figure>

## 5.2. *High-throughput precipitate characterisation*

SAXS acquisitions were used to monitor the evolution of the

precipitate characteristics. Ex-situ SAXS measurements were performed for samples aged 1,000 h, 2,000 h, 3,000 h and 5,000h. It is important to recall here that the scattering contrast comes from the difference in
<figure><img src="image_9.png" /><figcaption>Fig. 7. (a) APT acquisition of a specimen aged 5,000 h at 170°C exhibiting a composite precipitate with an Si-rich and a Cu-rich part and (b) composition profile along the arrow.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. STEM bright field image with EDX analysis and typical diffraction patterns obtained for the circled precipitates, for the sample aged for 5,000 hours at 240°C.</figcaption></figure>

electron density between the matrix and the precipitates. As the average atomic volumes in the precipitates and the matrix are close, the main source of contrast is the difference in the mean atomic number between the Al-matrix and the precipitates. Therefore, Cu-rich precipitates exhibit high contrast while Al-Mg-Si phases do not display sufficient contrast with the Al-matrix. In our case, only the S and Q phase exhibit sufficient contrast to be observed, while the L phase will not produce a measurable SAXS signal given the too small Cu-content.

Fitting the SAXS signal using appropriate models that account for the morphology of the precipitates allows measuring the mean size of the precipitates and the mean square fluctuation η², which mainly depends on the composition and volume fraction of the precipitates [40,41]. Therefore, if the composition of the precipitates is known, the volume fraction can be determined. The composition of the S precipitates is well identified and is not expected to evolve during ageing. The scattering contrast Δρ² can be estimated to be 0.053 Å⁻³ taking into account the crystallographic parameters of the S phase. However, the unknown Q-composition makes it impossible to quantitatively measure the volume fraction. Here, we will assume that the Q contains 22at% of Cu as

observed by Biswas et al. [16] using APT for the early precipitation of the Q phase. This allows us to have a representative evolution of the volume fraction of the Q phase using a scattering contrast Δρ² of 0.034 Å⁻³, taking into account the crystallographic parameters of this phase.

Selecting the appropriate model to fit experimental SAXS data can be challenging, and results may vary depending on the chosen model. SAXS measurements should be complemented with direct-space characterization whenever possible. In this study, the fit model was chosen based on phase identification from TEM and APT observations. The SAXS data were accordingly fitted using a single family of rod-like morphologies for samples aged for less than 5,000 hours, whereas for the sample aged for 5,000 hours, two distinct families of rod-like morphologies were fitted. The model from Hammouda [42] was used. This model assumes rod-like features which result in a signal that can be divided into three distinct regions: a Porod q⁻⁴ region at high q, a Porod q⁻¹ region for intermediate q and a low-q Guinier region. The coefficient in the intermediate q-range depends on the precipitate's electronic contrast, volume fraction, and radius, while their length influences the transition between the intermediate and low-q regions. Within the investigated
q-range, this boundary is not observed, so only the equivalent radius of the cross-section of the rods can be determined. In accordance with the TEM and APT results, the main precipitate family characterised for the lower range of temperatures is identified as being S precipitates, while the second family also identified in the sample aged 5,000 h is identified with the Q phase.

The results of the SAXS-fit are displayed in Fig. 9 and show that the mean size of the S precipitates increases with both ageing temperature and duration (Fig. 9 (a)). Examples of the I(q)-plots for several conditions are also available in Appendix B. The volume fraction of S precipitates remains nearly constant for ageing durations up to 3,000 hours. However, under more extreme conditions i.e. for the sample aged 5,000 h, dissolution of the S precipitates becomes clear for temperatures higher than 200°C (Fig. 9 (b)). This dissolution coincides with the apparition of the Q phase as shown by the evolution of the volume fraction: the Q phase is virtually inexistant for temperatures lower than 200°C and becomes apparent for higher temperatures. The mean radius of the Q phase precipitates is greater than that of the S phase precipitates and is almost constant regardless of the temperature. The contribution of each precipitate family to the fitted signal is given for two different conditions in Appendix B, showing a noticeable contribution of the Q precipitates to the SAXS signal for the sample aged 5,000 h at 235°C. The appearance of the Q-phase, observed using SAXS, aligns well with TEM observations and correlates well with the dissolution of the S phase observed above 200°C.

Time-temperature equivalences can also be applied to the SAXS results concerning the evolution of the mean radius and volume fraction of the S precipitates (Fig. 10). Again, using an activation energy of 138 kJ/mol gives a very good agreement between the measurements from the samples with ageing times smaller than 5,000 h. A clear separation is also seen for the sample aged 5,000 h, which is consistent with the phase transition.

## 6. Modelling precipitation hardening

A mechanical model of precipitation hardening was implemented to quantify the effect of the dissolution of the S phase and validate that it is

the primary cause of the observed loss in mechanical properties.

For an alloy hardened mostly by precipitation, the yield strength is given by:

$$ \sigma_y = \sigma_{ppt} + \sigma_0 = (M * \tau_{ppt}) + \sigma_0 \quad (2) $$

With $\sigma_{ppt}$ being the contribution of the hardening precipitates and $\sigma_0$ the sum of the other contributions such as grain boundaries, solid solution strengthening, work hardening and the yield strength of the alloy without any defect, and M being the Taylor factor. $\tau_{ppt}$ is the contribution of the hardening precipitates to the critical resolved shear stress.

Regarding the contribution of the solid solution, APT acquisitions allow for precise measurements of the composition of the solid solution. The solid solution compositions were determined using the DIAM method [43] for both the initial T851 condition and after 5,000 hours of ageing at 170°C. In the T851 state, the solid solution contains 0.14 at% Cu, 0.37 at%Mg and 0.02 at%Si, while for the aged condition, a composition of 0.16%atCu, 0.44 at%Mg and 0.03 at%Si was measured. The small differences between the two conditions are not significant, given the measurement uncertainties and potential variations within the material, suggesting that the overall solute element content remains low and nearly constant during ageing. Consequently, the contribution of solid solution strengthening is expected to be minimal and stable over time. Among the solute elements, Mg has been shown to contribute the most to solid solution strengthening compared to Cu and Si [44,45]. Assuming that Cu and Si provide similar strengthening effects as Mg, the maximum solid solution strengthening can be estimated using the commonly applied equation for this phenomenon:

$$ \sigma_{ss} = Hc^n \quad (3) $$

With H and n two constants specific to each element.

For the influence of Mg on the yield strength, H and n were found to be 12.1 MPa(%at)⁻ⁿ and 1.14 respectively [46]. A maximal contribution of the solid solution to the yield strength of 10 MPa can therefore be expected, and this contribution should not evolve during ageing.

Based on the preliminary tensile test data outlined in Section 4.1, an evolution in work hardening is evident in the stress-strain plots (Fig. 11

<figure><img src="image_11.png" /><figcaption>Fig. 9. Evolution of (a) the mean radius and volume fraction of the S precipitates for the different ageing times and (b) the mean radius and volume for the Q precipitates for the specimen aged 5,000 h.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 10. Time-temperature equivalences for the mean radius and volume fraction of S precipitates measured by SAXS for the graded samples, with $E_a = 138$ kJ/mol.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. (a) Examples of the stress-strain curves obtained for samples aged at 200°C for different ageing durations and (b) corresponding strain-hardening plots.</figcaption></figure>

(a)). To assess this evolution, work hardening plots can be generated, as illustrated in Fig. 11(b). A clear difference between the initial T851 state and the overaged states is observed, with a steeper slope and significantly higher initial work-hardening for the overaged states. This kind of transition was attributed by Cheng et al. [47] and Poole et al. [48] to a change in the interaction between dislocations and precipitates, specifically from shearable to non-shearable precipitates. This implies that for aging durations of 1,000 hours or more, the precipitates are non-shearable.

Therefore, we can implement a micromechanical model for precipitate by-passing that links the microstructural properties measured by SAXS and the evolution of the mechanical properties for the gradient samples. Zhu et Starke [49] used computer simulations to extract such a law for rod precipitates, using only the volume fraction ($f_v$) and mean diameter of the precipitates ($D_r$), and other parameters related to the alloy (b) the Burgers vector, G the shearing modulus and $r_0$ the inner cut-off radius for the calculation of the dislocation line tension):

$$ \tau_{ppt} = 0.15G \frac{b}{D_r} \left( f_v^{\frac{1}{2}} + 1.84f_v + 1.84f_v^{\frac{3}{2}} \right) \ln \left( \frac{1.316D_r}{r_0} \right) \quad (4) $$

By considering that precipitation hardening is only achieved by S precipitates, the model can be implemented using parameters summarised in Table 2.

<table><caption>**Table 2**

Values of the parameters used in the model.</caption><thead><tr><th>Symbol</th><th>M</th><th>b</th><th>G</th><th>r<sub>0</sub></th><th>σ<sub>0</sub></th></tr></thead><tbody><tr><td>Value</td><td>2.7</td><td>2.86 Å</td><td>28 GPa [50]</td><td>5.72 Å</td><td>60 MPa</td></tr></tbody></table>

With $\sigma_0$ assumed to remain constant throughout ageing, a good correlation between the experimental data from hardness and the predicted yield strength from SAXS data is achieved with $\sigma_0 = 60$ MPa (Fig. 12).

The low and constant value of $\sigma_0$ implies that solid solution strengthening remains minimal and unchanged throughout the ageing process, as confirmed by the APT acquisitions. Moreover, this constant value also suggests that the evolution of the grain boundaries has a minimal impact on the mechanical properties (see Appendix A for more precision on the evolution of grain boundaries). Nevertheless, as long as the precipitation state is dominated by S phase precipitates, the hardness/yield strength is very well predicted, as shown in Fig. 12. Calculations were also performed to account for the hardening effect of the Q precipitates. When multiple families of precipitates are present, the total contribution to the yield strength is typically considered as the Pythagorean sum of the contributions from each precipitate family. The results indicated a minimal impact of the strengthening of the Q phase, with a maximum difference of only 10 MPa between the yield strength predictions with and without considering the effect of the Q phase.

When applying the same strengthening model to the T851 initial state, the predicted yield strength of 350 MPa is significantly lower than the experimentally measured value of 420 MPa. This deviation can be attributed to the different assumptions of the model. As illustrated in Fig. 11, the work hardening curves suggest that the precipitates in the initial state are likely shearable. Therefore, the predicted bowing stress should be higher than the experimental shearing stress. However, the model predicts a bowing stress lower than what is experimentally observed. Given that the T851 state is close to the peak-aged condition, the shearing and bowing stresses should theoretically be comparable. In
<figure><img src="image_14.png" /><figcaption>Fig. 12. Comparison between the experimental hardness and the predicted yield strength using the mean radius and volume fraction measured by SAXS.</figcaption></figure>

the yield strength prediction, it is assumed that only the S precipitates contribute to precipitation strengthening, thus the underestimation of yield strength strongly suggests that another strengthening mechanism contributes to it. Indeed, TEM observations of the initial state revealed a high density of L precipitates, which are also expected to contribute to the yield strength. This fine distribution of rod-like L precipitates is absent in the aged samples, where only a low density of lath-like L precipitates is observed. Therefore, it can be inferred that L precipitates significantly contribute to precipitation hardening in the initial state, but their contribution is negligible during overageing due to their rapid dissolution and transformation to coarse Q phase. Assuming that the strengthening contributions of the various precipitates are additive using a Pythagorean sum, it can be deduced that L precipitates account for at least 2/5 of the total strength of the alloy in the initial T851 state.

## 7. Discussion

The results obtained from the analysis of the SAXS data indicate a significant dissolution of the S phase in the sample aged for 5,000 hours. It is important to acknowledge that the accuracy of the SAXS fit heavily relies on the initial assumptions, which in this case involve two distinct phases and a simplified rod-like morphology based on TEM observations. Despite these assumptions, clear trends can be observed regarding the evolution of precipitate size and volume fraction. The excellent agreement between the microstructural evolution of the S precipitation and the hardening model, where only the $σ_0$ parameter is fitted, suggests that these measurements closely reflect the actual microstructural changes. A strong linear correlation ($R^2=0.98$) between the volume fractions of Q and S precipitates is observed when plotting their evolution, as shown in Appendix C. The transition from L to Q precipitates is therefore strongly linked to the dissolution of the S phase. Given that the Q phase is richer in copper compared to the L phase, and considering that the copper content in the solid solution was measured to be around 0.1 at% after 5,000 hours of ageing using APT, it is likely that the

formation of the Q phase cannot occur without the prior dissolution of the Cu-rich S phase to release the necessary copper. To the authors' knowledge, there is no report of such interaction between the Q and S phase in Al-Cu-Mg-Si alloys. It is plausible that the Q phase is more stable than the S phase in the considered alloy, meaning that the formation of the Q phase would be responsible for the dissolution of the S phase for these extreme ageing conditions.

Research on the ageing of the 2618A alloy has not documented the formation of the L and Q phase during ageing. Concerning the Q phase, this absence may be attributed to the extreme ageing conditions required for the formation of such precipitates, which might not have been explored in previous studies. Additionally, the identification of the Q phase likely necessitates extensive microstructural analysis using advanced techniques such as SPED. Concerning the extensive presence of the L phase in the T851 state, although it was not explicitly identified yet, a lath-like phase with a similar orientation and rectangular cross-section can be observed in Fig. 7 (c) from [23] and Fig. 5 from [10] in a 2618A alloy and in an alloy with similar composition but no Fe or Ni, respectively. The fine lath morphology with a [100] habit plane does not align with the characteristics of S precipitates, suggesting that these could plausibly be L precipitates. As L precipitates were not identified yet in the 2618A alloy, it was believed until now that the mechanical properties of the alloy during the initial heat treatment were driven by the precipitation of S precipitates while here we showed that L precipitates also significantly contribute to precipitation hardening. During overageing, their contribution becomes negligible compared to S precipitates.

Previous studies of the overageing of the 2618A alloy have also reported the formation of precipitate-free zones (PFZ) along grain boundaries [21,24], which may contribute to the deterioration of mechanical properties during ageing. TEM observations of the grain boundaries on the samples aged at 170°C and 240°C (see Appendix A) actually revealed a substantial evolution of the width of these PFZ, with their volume representing up to 6% in the specimen aged for 10,000
hours at 240°C. The formation of large precipitates associated with PFZ can lead to a slight reduction in the volume fraction of hardening precipitates within the grains. While this reduction is accounted for in the hardening model, since SAXS measures the overall volume fraction of hardening precipitates, the influence of PFZ as localised strain sites [51] is not considered. Given the excellent agreement between the hardening model and the experimental data, this suggests that the impact of such mechanisms on hardness and tensile properties is likely secondary to the effects of precipitate evolution.

## 8. Conclusions

A high-throughput methodology was used to study the effect of long-term ageing on the properties of the 2618A alloy.

* Single-temperature heat treatments allowed to establish linear correlations between hardness and tensile properties during ageing, enabling calculation of the equivalent tensile properties for hardness in the graded samples.

* Using a temperature gradient allowed characterisation of a broad and continuous spectrum of ageing temperatures, enabling the collection of extensive data for both mechanical and microstructural evolutions using hardness and SAXS measurements.

* The implementation of time-temperature equivalences using the activation energy of copper diffusion revealed that ageing is first controlled by Cu diffusion, followed by a change in the ageing mechanism after 5,000 hours of ageing at temperatures greater than 200°C. Two distinct regimes were observed and described by the time-temperature equivalence, allowing prediction of the evolution of the mechanical properties for any ageing conditions in the investigated range and possibly beyond.

* The Si-content of the alloy allows for the late precipitation of the Q phase after 5,000 hours of ageing, together with partial dissolution of the S precipitates, leading to an accelerated degradation of the mechanical properties. The L phase, precursor to the Q phase, was identified in the T851 initial condition and during ageing. This phase

appears to dissolve and transform into the Q phase after 5,000 hours at high temperatures.

* The development of large PFZ was also observed during ageing but the implementation of a micromechanical model of precipitation hardening suggested that the impact of the PFZ on the mechanical properties is secondary.

## Funding

This work was supported by the DGAC, the ‘France Relance’ national stimulus plan and the ‘Nextgeneration EU’ European support program. This work also received support from the DIAMS project of the PEPR DIADEM (ANR-22-PEXD-0005).

## CRediT authorship contribution statement

**Thomas Perrin:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Conceptualization. **Arthur Després:** Writing – review & editing, Validation, 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 experiments. TP would also like to thank Pr. Randi Holmestad for fruitful discussions.

## Appendix A. Evolution of the grain boundaries

Additional observations of grain boundary evolution during aging revealed the formation of precipitate-free zones (PFZ) and large precipitates at the grain boundaries (a). The size of the PFZ appears to be strongly influenced by the ageing temperature (b), with the volume fraction of the PFZ increasing to 6% after 10,000 hours at 240°C (c).
<figure><img src="image_15.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(c)</figcaption></figure>

(a) STEM observations of the grain boundaries during ageing for two temperatures with the same magnification, (b) evolution of the size of the PFZ and (c) hardness evolution as a function of the estimated ratio between the volume of the PFZ and the volume of a grain.

<figure><img src="image_18.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(c)</figcaption></figure>

(a) Examples of experimental scattered intensities for the initial
T851 state and three aged conditions showing the noticeable evolution of the integrated intensity related to the volume fraction and the increase in precipitate size, (b) and (c) SAXS fit for the specimen aged 5,000 h at 180°C and 235°C respectively, with the fitted contributions of the S precipitates, the Q precipitates and the Porod and Laue.

## Appendix C. Correlation between the measured volume fraction of the S precipitates and Q precipitates

<figure><img src="image_21.png" /></figure>

Evolution of the measured volume fraction of Q precipitates as a function of the measured volume fraction of S precipitates for the sample aged 5,000 h, suggesting a direct link between the dissolution of the S phase and the appearance of the Q phase.

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