The Benefits of Trace Cu in Wrought Al-Mg Alloys

As a first insight into the aging response, Figure 2 shows the evolution of the yield strength for three conditions; the material with no pre-deformation and the two pre-deformed cases aged at 160^∘C and 200^∘C. In the case of aging starting from the as-solution treated material, it has been shown [6] that the hardening is the result of increasing cluster/GPB zone size. For the material pre-deformed to $\Delta\sigma=44$ MPa ($\sim$ 2% strain) the evolution of the yield stress is nearly the same as that found when aging starts from the solution treated material, the offset between the two sets of data being approximately 15 MPa. In the case of the material pre-deformed by $\Delta\sigma=176$ MPa ($\sim$ 10% strain) an initial drop in yield stress is observed if one compares the as-deformed yield stress to the yield stress after 2 minutes of aging. Further aging, however, leads to continuous strengthening, the rate being very close to that of the material starting from the solution treated state and the samples pre-deformed to $\Delta\sigma=44$. The aging temperature (160^∘C or 200^∘C) makes no significant change in the response for the pre-deformed samples, this being consistent with what was shown for a range of alloy compositions for the as annealed material [6].

The similarity of the increase in yield strength for all of the conditions at times longer than 2 min suggests that recovery dominates the flow stress at short times (particularly for $\Delta\sigma=176$ MPa) but that precipitation hardening dominates the yield strength evolution at longer times. In the case of the solution treated and aged samples, it has been shown that the hardening is dominated by a high density of small clusters/GPB zones, similar in morphology and density to those found in 2xxx series alloys but containing much lower Cu contents [6]. It was shown that the volume fraction of these features did not change significantly over the aging times shown in Figure 2 but that the size of the particles did, this leading to the observed strengthening.

Figure 3 shows illustrative atom probe tomography analyses for two samples aged at 200^∘C for 160 min with a) no pre-deformation and b) pre-deformation to 176 MPa ²²2A more detailed analysis of samples aged with no-predeformation can be found in [6]. The tomographic reconstructions are displayed at the same scale. For both, sets of iso-contour plot are superimposed onto the point cloud (only approx. 1% of the detected Al ions are shown), in order to highlight the population of clusters/GPB zones. In the aged sample 3 variants of small, elongated precipitates are visible. One-dimensional composition profiles calculated in 5-nm-diameter cylinders positioned perpendicular to the long axis of the feature (indicated by coloured arrows) are also shown. The particles are mostly Mg-rich, reaching typically close to 25 at.% Mg, with 2-5 at % Cu (i.e. 22 wt.% Mg and 5-6.5 wt.% Cu).

In contrast, for the pre-deformed material, the distribution of the solute elements is much more heterogeneous, both spatially and compositionally, as highlighted by the iso-contours showing solute rich regions. The geometry of the features suggests segregation and/or precipitation along dislocations. Indeed, some regions along these features appeared to have Mg:Cu ratios close to those observed for clusters/GPB zones in the solution treated and aged samples (e.g. Figure 3a) while others had a Mg:Cu ratio closer to 1. Generally, the particles are larger and less well dispersed in the pre-deformed and aged sample compared to the sample aged directly from the as-solutionized state.

Aging of pre-deformed samples leads to the formation of S-phase precipitates preferentially along dislocations, by-passing the more typical sequence of clusters/GPB zone formation followed by S-phase formation [9]. A similar process has also been reported for other alloys, including an Al-Cu-Li alloy [10]. This is visible in samples prepared here, where lath-like S-phase can be seen along dislocations in Figure 4. The composition of some of the larger particles imaged by APT in Figure 3b is consistent with the S-phase as well.

The microstructural differences between the solution treated+aged and pre-deformed+aged samples belies the very similar rates of hardening shown in Figure 2. While in our previous work on the hardening response of solution treated and aged samples we were able to use information directly from APT experiments to parameterize a precipitation hardening model, here the complexity of the segregation/precipitation in the pre-deformed samples does not allow for such an approach. Rather, to more quantitatively evaluate the precipitation hardening we can look at the work hardening behaviour (Figure 5).

A cursory observation of Figure 5 shows that the real response of the alloy is more complex than the idealized response illustrated in Figure 1. The most noticeable discrepancy between Figures 1 and 5 is the (transient) low work hardening rate ($d\sigma/d\epsilon$) at the onset of yielding. A more careful inspection of Figure 5 also shows that, unlike the idealized response, the work hardening vs. flow stress curves for the as-solution treated and pre-deformed and aged samples are not parallel to one another. Rather, it appears that parallelism is approached asymptotically at high flow stresses. This is particularly notable in Figure 5d.

Very similar behaviour has been recently reported and discussed for a non-precipitation hardenable Al-Mg alloy pre-deformed and aged under very similar conditions to those used here [17]. Therein, a simplified version of the Kubin and Estrin [18] two-internal state variable model was developed. In that case, it was argued that solute-dislocation interactions amplified by the low temperature aging treatment led to changes in the static and dynamic recovery response of forest dislocations. Here, we adapt this model to the case of Al-Mg-Cu alloys. The precipitates are considered as shearable particles and we retain the basic concept outlined in Figure 1 as our method for separating the effects of recovery and precipitation hardening on the yield and flow stress. Here we present the most salient aspects of the model, including the modifications to include the effect of precipitation hardening. We start by writing the flow stress as a function of the strain rate and forest dislocation density ($\rho_{f}$).

In this expression $\sigma_{0}$ is a friction stress including effects of lattice resistance and the grain size. The next two terms $\sqrt{\sigma_{ss}^{2}+\sigma_{ppt}^{2}}$ are the contributions of solid solution strengthening and precipitation strengthening, these being added based on the density of obstacles based on the expectation that the contributions from these two terms will be similar [6].

The reference strain rate, $\dot{\epsilon}_{0}$ is assumed to be proportional to the mobile dislocation density $\dot{\epsilon}_{0}=\beta\rho_{m}$ and was assumed to evolve as,

Where $\eta$ is a parameter related to the rate of mobile dislocation density generation and $\rho_{m}^{s}$ is a saturation mobile dislocation density. The mobile dislocation density will rise with strain to $\rho_{m}^{s}$ corresponding to $\dot{\epsilon_{0}}=\dot{\epsilon}$, or $\rho_{m}^{s}=\beta^{-1}\dot{\epsilon}$. Note that in eqn. 2 one only needs to identify the ratio $\rho_{m}/\rho_{m}^{s}$, not the absolute value of $\rho_{m}$.

In equation 1, two separate forest dislocation densities are introduced, $\rho_{f}$ and $\rho_{f}^{*}$. During pre-deformation at low temperature we expect to generate forest dislocations $\rho_{f}$, which have interacted with approximately immobile solute (due to the low temperature of pre-deformation). Upon aging, two processes will be activated. First, some of these forest dislocations will be lost due to static recovery. At longer times, we anticipate some fraction of these dislocations to be modified due to solute segregation to them and/or precipitation on them. These phenomena are anticipated to change both the rate of static recovery as well as the rate of dynamic dislocation storage and annihilation on reloading following aging. The density of dislocations identified by $\rho_{f}^{*}$ are those that have been decorated by solute (or precipitates) during artificial aging. The total forest dislocation density and the end of aging ($\rho_{f}+\rho_{f}^{*}$) is expected to be less than that at the end of pre-straining due to recovery.

The low temperature deformation after aging is expected to only reduce $\rho_{f}^{*}$, this having been taken in [17] to follow,

The important concept here is that the density $\rho_{f}^{*}$ recovers (dynamically) more slowly than those dislocations generated by deformation ($\rho_{f}$), this leading to an enhanced rate of work hardening over the initial portion of the stress-strain curve.

During deformation, the evolution of $\rho_{f}$ is assumed to obey,

where different rates of storage are attributed due to the interaction with ‘solute loaded’ and ‘solute unloaded’ forest dislocations.

In the above system of equations, there are several parameters that need to be set to predict the mechanical properties. In the case of a solution treated sample it is assumed that $\rho_{f}^{*}$ can be approximated as zero meaning that eqn. 4 depends only on $k_{2}$, $k_{3}$ and $k_{4}$. In the limit where $\rho_{m}=\rho_{m}^{*}$ then this further simplifies as the first term in eqn. 4 becomes a constant, this reducing to the classic Kocks-Mecking analysis (Figure 1 with an initial non-linearity (at low stress) controlled by the value of $k_{2}$ .

The value of $\sigma_{ss}$ can be obtained directly from the alloy content of the sample, the value used here being the same as the value used in [6]. One complicating factor is the fact that precipitation can act to deplete solute from the matrix, this making $\sigma_{ss}$ a function of the aging condition. In our work on aging starting from the as-solution treated state [6] it was shown that the solid solution strengthening was dominated by Mg and that the amount of Mg and Cu found in clusters/GPB zones was insufficient to lead to a significant change in $\sigma_{ss}$. Here, for simplicity, we also assume that $\sigma_{ss}$ can be taken to be constant, independent of the aging condition.

Taking the above points into consideration, a single test on a solution treated sample, allows one to establish values for $\sigma_{0}$, $k_{2}$, $k_{3}$ and $k_{4}$, the values found for the alloy studied here being given in Table 2.

The remaining parameters in eqn. 4, $k_{3}^{*}$ and $k_{4}^{*}$, were obtained as a single best fit to all of the pre-deformed and aged conditions used in this study. Following the findings in [17], we restrict the values of $k_{3}^{*}$ and $k_{4}^{*}$ to be of the same order of magnitude as $k_{3}$ and $k_{4}$. The remaining global parameter to identify is $\eta$ in eqn. 2. As was shown in [17] the exact value is not sensitive to the resulting fit, therefore this parameter was taken to be identical to the value used in [17].

The remaining parameters that are required, and which depend on the level of pre-strain and the aging time/temperature are, i) the density of forest dislocations following aging ii) the ratio of the density of mobile dislocations ($\rho_{m}/\rho_{m}^{s}$) following aging and iii) the precipitate contribution to the flow stress, $\sigma_{ppt}$. The density of dislocations (mobile and forest) following pre-straining are estimated from the fit to the solution treated stress-strain curve at $\Delta\sigma=176$ MPa. Following aging, the density of mobile dislocations is expected to be reduced as some mobile dislocations are locked and converted to forest dislocations while others are lost due to recovery. In the case of the forest dislocation density following aging, we need to distinguish between solute locked forest dislocations ($\rho_{f}^{*}$) and non-solute locked forest dislocations ($\rho_{f}$). Owing to recovery, we expect that $\rho_{f}$ + $\rho_{f}^{*}$ will be less than the density of forest dislocations present at the end of pre-straining.

As described in [17], the value of $\rho_{m}$ following pre-straining and aging affects mainly the value of the (low) work hardening rate at the onset of yielding and does not significantly impact the stress-strain response beyond $\sim$ 1% strain. Indeed, according to eqn. 2, mobile dislocations are rapidly generated with the onset of plasticity for the parameters used here. The value of $\sigma_{ppt}$ only impacts on the yield strength after aging while the values of $\rho_{f}$ and $\rho_{f}^{*}$, have a significant impact on both the yield strength and work hardening rate.

The values of $\sigma_{ppt}$ and $\rho_{f}+\rho_{f}^{*}$ can be established by fitting to the yield strength of the material as well as the initial (high) work hardening rate following the initial (transient) minimum in the work hardening rate. A more direct estimate of $\sigma_{ppt}$ can be obtained from the flow stress-work hardening relationship at high flow stress. At high flow stress, the effect of $\rho_{f}$ dominates that from $\rho_{f}^{*}$ leading to the recovery of a linear relationship between flow stress and work hardening rate, as obtained in a classical Kocks-Mecking analysis. As pointed out before, this behaviour is clear in Figure 5d where the solution treated and aged samples are seen to become parallel at high stress.

Under these conditions, $\sigma_{ppt}$ is recovered unambiguously from the separation between the parallel solution treated and aged work hardening curves, as illustrated in the case of the simplified analysis presented in Figure 1. Knowing $\sigma_{ppt}$, one can then use the yield strength to obtain $\rho_{f}+\rho_{f}^{*}$. To separate these two values, one can then use their distinctly different effect on the work hardening response.

To capture the results found here, it was found necessary to take $\rho_{f}^{*}>>\rho_{f}$ following aging. This would suggest that nearly all dislocations that do not recover during the aging treatment are segregated to and/or precipitated on, a result that would seem intuitive given the similarity of the segregation profile to split edge and screw dislocations in Al-Mg alloys [19].

Figure 6 shows experimental data and modelling fits for the material that had been pre-deformed by $\Delta\sigma=176$ MPa and aged for 10 minutes at 200^∘C. Here one can explicitly see how, at high flow stresses, the work hardening rates of the solution treated and aged materials become parallel, the separation between the two giving the value of $\sigma_{ppt}$.

Following the approach outlined above, we have deduced a best fit to the stress-strain response of the materials pre-deformed to $\Delta\sigma$ = 176 MPa and aged at 160^∘C and 200^∘C for various times. Figure 7 shows the experimental stress-strain curves (solid lines) along with the fits of the model (symbols).

As can be seen, the fits reproduce the stress-strain response very well, the two main parameters that need to be adjusted with aging time being the forest dislocation densities directly after aging ($\rho_{f}$ and $\rho_{f}^{*}$) and the precipitation contribution to the strength, $\sigma_{ppt}$. It was found that the combined best fit values of $\rho_{f}+\rho_{f}^{*}$ were nearly identical for all but the two shortest annealing times at 160^∘C (Figure 8). This would suggest that recovery happens much more quickly than precipitation, reducing the forest dislocation density to $\sim$ 37% the value that was present directly after reloading.

The fact that further recovery seems not to take place may be a consequence of solute segregation and precipitation on those dislocations that had not recovered earlier. This should be contrasted with the results obtained from applying the same model to very similar experimental results for a binary (non-precipitation hardening) Al-Mg alloy [17] where it was observed that recovery continued obeying classic Bailey-Orowan recovery kinetics. These results would be in line with the view presented in the case of Al-Mg-Sc alloys where a stasis in the recovery was observed owing to dislocation/precipitate interactions [7].

Figure 9 shows the predicted evolution of $\sigma_{ppt}$ with aging time and temperature for these samples. Also shown here are results from the same alloy aged at 200^∘C from the solution treated state [6]. Coinciding with the results in Figure 2 we see that, except for short aging times at 160^∘C, the aging response follows the same trend regardless of aging temperature. This also mirrors the aging response that was reported for the as-solution treated samples [6]. What is notable here, however, is the fact that the precipitation contribution to the flow stress is lower, compared at equal aging time, for the samples that had been pre-deformed compared to those that were aged starting from the as-solutionized state. This would suggest that pre-deformation leads to less efficient precipitation hardening.

While the results in Figures 5 and 6 indicate a very good ability of the model to reproduce the experimental stress-strain response, this was not true for all cases. In particular the sample aged for the longest time (420 min) at 200^∘C could not be satisfactorily fit by the model. Figure 9 shows the experimental results for this condition. It is notable here that the yield stress of the pre-deformed and aged sample is slightly higher than the flow stress of the material at the end of pre-deformation. Given that recovery has happened, this suggests significant precipitation hardening. However, if one looks at the flow-stress, work hardening plot (Figure 10b) one sees that the slope of the work hardening rate of the aged sample at high flow stress does not approach parallel with that of the solution treated sample. Indeed, the two curves appear to cross close to the point of necking. Given the arguments made above regarding the effect of $\sigma_{ppt}$ this would seem inconsistent.

This observation is a likely consequence of a majority of precipitates no longer being shearable. Indeed, in our detailed work on the precipitation hardening in the absence of pre-deformation [6] it was found that a significant portion of the observed precipitates were above the estimated shearable/non-shearable transition after aging for 160 minutes at 200^∘C. With further over-aging of the sample, the precipitates will influence not only the yield strength but also the work hardening rate of the material, these effects not being properly accounted for in the model used here.

The work detailed above shows that the evolution of the yield strength with aging is dominated by precipitation hardening in the case of pre-deformed samples. Recovery occurs rapidly at short times but then stagnates once significant solute segregation or precipitation on dislocations occurs. In this case, the ability of small Cu additions to reduce the strength loss on aging would appear to be a combined effect arising both from precipitation strengthening and the cessation of dislocation loss via slowed recovery. The last question to examine is why the precipitation hardening appears to be slower in the case of pre-deformed samples.

It is believed that vacancies play a vital role in determining the formation of solute clusters in the early stages of aging in Al-Cu-Mg and Al-Mg-Cu alloys (see e.g. [20, 21, 22, 23]). In the as-quenched state the microstructure can be described as being composed of a random solid solution with a low density dislocations. Quenched in excess vacancies from solution treatment will allow for accelerated formation of clusters due to accelerated diffusion of solute [24, 25, 26], with some vacancies becoming incorporated into the clusters/GPB zones, possibly to thermodynamically stabilize small clusters [27, 28, 20]. Those excess vacancies not captured within clusters/GPB zones may annihilate at other defects (dislocations and/or grain boundaries) or they may cluster to form dislocation loops [29]. STEM observation on solution treated and aged samples revealed classical helical dislocations and small dislocations loops in the alloys studied here, similar to observations made in commercial Al-Cu-Mg alloys [30, 31]. The loss of these excess vacancies would be expected to i) slow the formation/growth of clusters/GPB zones due to reduced diffusivity and ii) lower the rate of cluster/GPB-zone nucleation. Such an explanation would account for the ‘rapid hardening effect’ observed for the present alloy, aged from the undeformed state [6].

If the solution treated material is pre-deformed (here at 77 K) then one can have the further generation of deformation induced vacancies [32]. Taking parameters typical of Al-Mg alloys and considering the relatively small levels of pre-deformation used here, we expect only a small change in the concentration of vacancies due to our pre-deformation [33]. Upon aging, the presence of dislocations can have a significant effect on reducing the vacancy concentration. Dislocations act as sinks for vacancies and the much higher density of dislocations in the pre-deformed sample compared to the as-solutionized sample leads to a potential competition between vacancy annihilation and vacancy incorporation into clusters/GPB-zones. The recent work of Fischer et al. [34] has shown the importance of dislocation density on the rate of vacancy annihilation. We find, using the Fischer model parameterized for Al-Mg alloys [33], that samples containing a low dislocation density ($\rho\approx 10^{10}-10^{11}$ m^-2, consistent with a solution treated sample) will retain a large fraction of their excess vacancy concentration over aging times of minutes. In contrast, samples containing $\rho\approx 10^{13}-10^{14}$ m^-2 (consistent with the dislocation densities in the pre-deformed samples studied here) would lose their excess vacancies within seconds, potentially even during the process of heating to the aging temperature. Thus, it is proposed here that the origins of the reduced precipitation hardening for pre-deformed samples arises from the rapid loss of excess vacancies due to the higher density of sinks.

Finally, reflecting back on the original aim to distinguish between precipitation hardening and recovery induced softening on the yield strength evolution in these alloys, one may ask the question of whether the results presented here are representative of conditions more typical to those found in the automotive paint bake cycle. Here, for example, deformation was performed at 77 K so as to explicitly avoid the challenges associated with dynamic strain aging at room temperature. We can, however, compare the results obtained here to those reported by Court and Lloyd [4] who studied very similar alloys (containing 3wt.%Mg and 0.2 and 0.6wt.%Cu) pre-strained in room temperature tensile tests to 10% plastic strain (very similar to the pre-deformation to $\Delta\sigma=$ 176 MPa used here). Comparing first the yield strength data from their study (Figure 11a) we see that the yield strength of the sample containing 0.6wt.%Cu is higher than that of the sample containing 0.2wt.%Cu. This, however, is complicated by the fact that the yield strength following pre-deformation was slightly higher than the latter. When these are compared with the 0.5wt.%Cu alloy studied here, we see that rather than lying between these two, the 0.5wt.%Cu alloy is situated at much higher stresses. This, however, arises from the much higher flow stress obtained, despite the similar level of pre-deformation, due to the much lower temperature of deformation (77 K vs. room temperature).

To approximately remove this difference, the data has been re-plotted as the difference between the time evolving yield stress and the yield stress of the as-pre-deformed sample (before aging) in Figure 11b. This clearly collapses the data more closely together. Reflecting on eqn. 1, we see that the data in Figure 11b is given by,

In the case of all three samples, $\sigma_{ss}$ is nearly the same since it is dominated by the Mg content of the alloy. If we take the term relating to recovery, $\left(\sigma_{\rho_{f}}-\sigma_{\rho_{f,0}}\right)$ to be a constant (cf. Figure 8) then the only time evolution should arise from the time evolution of $\sigma_{ppt}$. In the case of the samples from [4], we can assume that amount of recovery is very similar thus, the slightly higher stress for the samples containing 0.6wt.%Cu likely reflects a slightly higher level of precipitation hardening. In the case of the sample containing 0.5wt.%Cu such an increase is not seen but this is likely due to the fact that one cannot assume the same amount of recovery. Owing to the higher flow stress (and thus dislocation density) in the pre-deformed state one would expect a faster rate of initial recovery.

Despite the points made above, the three samples in Figure 11 show remarkably similar results despite quite different chemistries, loading conditions and aging temperature. Indeed, the lines shown in each case use the trend line for $\sigma_{ppt}$ shown in Figure 9 to predict the evolution of the yield strength. Overall, this points to the fact that variations in chemistry between 0.2-0.6wt.%Cu and aging temperatures between 160 and 200^∘C will have little effect on the overall rate of strengthening during the paint baking of these alloys and that this evolution is ultimately predictable with limited experimental validation as long as all of the contributions to the strength are properly accounted for.