In order to quantify precipitate microstructures and monitor precipitation kinetics, small angle X-ray scattering (SAXS) has been extensively used in the last 50 years both ex
situ and in situ for heat treatable aluminium alloys (except AA6xxx due to their low
contrast in atomic number) [80]. In SAXS experiments, the radius of gyration (Guinier radius), rg is usually given as an estimate of the size of the scattering objects. Indeed,
Deschamps and De Geuser [81] showed that rg provides an estimate with a precision
lower than 10% of the average precipitate (moderate aspect ratio) radius,
r
when the precipitate size distribution (PSD) dispersion is 0.2. The Guinier radius being sensitive to the larger precipitates, it overestimates the average precipitate radius for broad PSDs (dispersion > 0.2). The volume fraction of precipitates can be calculated from the scattering signal provided the chemical composition of the precipitates is known. Therefore, the precision on the volume fraction can be estimated to ± 10% due to the uncertainties on composition [82].In the literature, most SAXS experiments are reported in precipitation states different from as-quenched states.
Deschamps et al. [43] monitored the precipitation kinetics of AA2618 during artificial ageing at 200°C to understand its two hardening responses: i) a very rapid (within 2 min) increase in strength [68] followed by ii) an extended yield strength plateau that exists until a rise to peak hardness (at 200°C after ca. 2h) [67]. Thanks to SAXS experiments, these features were attributed to i) the formation of Cu-Mg-rich hardening clusters and ii) their continuous domination of the microstructure associated with a compensation of the small loss of cluster by an increase in their size and the formation of the first stable S precipitates [43].
Fribourg et al. [82] performed in situ SAXS experiments to monitor the precipitation kinetics during artificial ageing of AA7449 to calibrate a precipitation model [42].
Ex situ SAXS experiments on AA7040 were performed by Dumont et al. [8] after slow
(~7 K/si) and fast (~850 K/si) quenches followed by 84 hours at room temperature and artificial ageing. The measured radius and volume fraction of ’ phase during artificial ageing was found to be identical for both quenches, due to the low quench-sensitivity of AA7040 (critical cooling rate lower than 7 K/s according to Dumont’s experiments). In the recent paper of Schloth et al. [10], in situ SAXS experiments on AA7449 during fast coolings similar to the ones in thick plates were performed for the first time. These
i
58 SAXS results are presented hereafter and will be used in the present work for calibration of the yield strength model.
Preliminary SAXS measurements performed by P. Schloth during coolings of AA2618 (not shown here) revealed anisotropic scattering of large objects around 400°C attributed to the formation of S phase. Isotropic scattering of subnanometer-size objects (Guinier radius ~0.4-0.5 nm) was measured below ca. 300°C. A cluster volume fraction of ca. 0.4% was reached after cooling similar to the measured ones in forgings [83].
Early precipitation during cooling of AA7449
The results (Guinier radius and volume fraction of precipitates) of the SAXS measurements for AA7449 are shown in Figure 3-1. For the sake of brevity, the average radius and the volume fraction of small precipitates calculated using a precipitation model calibrated by P. Schloth in his PhD work [50] are also shown along with the measurements.
Figure 3-1 – Results of in situ SAXS experiment for AA7449. Measured volume fraction of phase (a) with corresponding cooling rate (c). Measured and simulated volume fraction (b) and experimental Guinier radius and average simulated radius (b). The legend of the measurements is given in (a) and the legend of the simulations in (b). Adapted from Schloth et al. [10].
During cooling, the scattering of large objects corresponding to the phase and small objects corresponding to clusters has been recorded. Figure 3-1-a shows that precipitation of starts at ca. 400°C and reaches a maximum volume fraction at about 200°C. Precipitation of clusters starts at ca. 250°C with a continuous increase of volume
3. Characterisation and modelling of precipitation during quenching
59 fraction down to room temperature (Figure 3-1-b) while the Guinier radius is fairly constant below ca. 150°C (Figure 3-1-d).
During fast SAXS cooling, Figure 3-1-a and c show that a cooling rate of ca. 25 K/s is not fast enough to avoid precipitation of the phase. Therefore, the high temperature critical cooling rate of AA7449 is higher than 25 K/s. The volume fraction of phase is higher after slow than after fast SAXS cooling which was expected since the slower the cooling is, the more time is available to form large precipitates at high temperature. Nevertheless, for the two coolings, the volume fraction of is small compared to the value of ~0.08 corresponding to the maximal volume fraction that can be formed after slow cooling (calculated under equilibrium [50]). This, together with the fact that precipitation softening does not have a significant effect on RS as shown by Godard et
al. [7], justified the choice of P. Schloth to model only one type of precipitates, namely
the small ones.
A precipitation model has been calibrated by P. Schloth. The calculated volume fraction and average radius of clusters shown in Figure 3-1-b and d respectively compares well with the measurements. The average radius calculated by the precipitation model slightly underestimates the measured Guinier radius. This is due to the broader precipitate size distribution (PSD) measured by SAXS compared to the simulated one by the precipitation model as shown in Figure 3-2.
Figure 3-2 – Measured and simulated precipitate size distribution in AA7449 after fast (a) and slow (b) SAXS cooling. Vertical dashed lines: average radius from simulation and Guinier radius from measurements. Adapted from Schloth [50].
The measured PSD is broader after slow than after fast SAXS cooling. Although this was expected due to fact that the slower the cooling, the larger the precipitates, this result is not predicted by the simulation. The larger precipitates of the PSD are not predicted because no precipitation arises above 180°C due to the thermodynamic description used in the model (see section 3.4.1) which considers only GP(I) zones and not ', that might
60 Early precipitation during cooling of AA7040
Similar SAXS measurements were also performed by P. Schloth on AA7040. The results of these measurements for AA7040 are shown in Figure 3-3 together with the simulations using the precipitation model which considers only GP(I) zones [50].
Figure 3-3 – Results of in situ SAXS experiment for AA7040. Measured volume fraction of phase (a) with corresponding cooling rate (c). Measured and simulated volume fraction (b) and experimental Guinier radius and average simulated radius (d) of clusters. The legend of the measurements is given in (a) and the legend of the simulations in (b). Adapted from Schloth [50]. For AA7040, precipitation of starts at ca. 350°C and reaches a maximum volume fraction at about 150°C. Precipitation of clusters starts at ca. 250°C with a continuous increase in volume fraction down to room temperature while the radius is fairly constant below ca. 100°C. The volume fractions of small and large precipitates are lower for AA7040 than for AA7449 since the latter alloy contains more solute elements available for precipitation. During fast SAXS cooling, it seems that the cooling rate of ~40-50 K/s is high enough to avoid precipitation of the phase at high temperature (Figure 3-3-a and
c). Therefore, the high temperature critical cooling rate of AA7040 should be close to 50
K/s.
As expected, the volume fraction of phase is higher after slow than after fast SAXS cooling (Figure 3-3-a). Again, for the two coolings, the volume fraction of phase is small compared to the value of 0.071 corresponding to the maximal volume fraction that can be formed after slow cooling (equilibrium). The simulated volume fraction and average radius of clusters shown in Figure 3-3-b and d respectively compare very well with the measurements during slow SAXS cooling. The agreement is poor for the volume
3. Characterisation and modelling of precipitation during quenching
61 fraction of clusters during fast SAXS cooling which is overestimated by a factor 2 by the simulation with the precipitation model. A better agreement could be found by adjusting the precipitation model parameters to better fit the volume fraction of clusters after fast SAXS cooling. Instead, it has been chosen to use the same calibrated parameters of clusters GP(I) zones in AA7449 and AA7040 (see section 3.4.1). This is physically sound but it overestimates the volume fraction of clusters after AA7040 fast SAXS cooling. This cooling being very close to that experienced by the surface of a 75 mm plate, this means that the yield strength predicted by the yield strength model and hence residual stresses will be overestimated by the thermo-metallurgical-mechanical model for 75 mm thick AA7040 plate.
The Guinier radii and volume fractions of clusters measured during slow and fast SAXS coolings for AA7449 and during slow SAXS cooling for AA7040 will be used in section 4.3.6 to calibrate the yield strength model. Furthermore, these three cooling conditions representative of industrial quenches will be reproduced in the Gleeble to obtain the corresponding yield strength values necessary for the calibration of the yield strength model.