Continuous dynamic recrystallization (CDRX) model for aluminum alloys

Abstract

The control of a microstructure, during and after hot forming, is crucial to tailor optimum mechanical properties for specific applications. Recrystallization is a key process which may contribute to a great extent to microstructure development. Dynamic recrystallization is becoming an attracting research area to investigate novel hot forming routes in order to maximize the performance of aluminum products while shortening the time required for manufacturing. A continuous dynamic recrystallization (CDRX) mathematical model was developed by Gourdet–Montheillet (GM) to predict the inherent phenomena of an AA1200 alloy. In the present work, the original GM model has been extended and applied to study CDRX in a 5052 aluminum alloy. The proposed model embodies a solid solution and second phase strengthening, through newly estimated kinetic factors and a kinetic constant, respectively, to discern the CDRX behavior of 5052 aluminum alloy compared to AA1200. The latter kinetic constant relies on the Kocks–Mecking–Estrin (KME) theory. The input law of the fraction of high angle boundaries (f _HAB), as a function of strain (ε) (but independent of temperature and strain rate), is defined as the best fitting function of the experimental data. The results are presented in terms of stress–strain curves, dislocation density, and (sub) grain size, as these are important design parameters from an industrial and engineering viewpoint. The model has been validated successfully, from both a qualitative and quantitative point of view, against various literature data sources and tests (e.g., hot compression, hot plane strain compression, and equal channel angular pressing) pertaining to the 5052 alloy and other similar Al–Mg alloys.

Appendix 1

The f _HAB computed by the GM model has been criticized as being unrealistic [19]. GM predicted that f _HAB decreased with increasing plastic strain, until it reached a plateau at approximately 0.2. Conversely, ECAP experiments have shown that the Al–Li–Mg–Sc alloy could achieve f _HAB > 0.9 for larger strains than 8 [10], as shown in Fig. 10. In order to resolve this inconsistency, we fitted f _HAB data from a hot compression test for AA5052 [14] using Eq. (9):

$$ f_{\text{HAB}} = K_{1} \exp \left\{ { K_{2} \varepsilon } \right\} + K_{3} \exp \left\{ { K_{4} \varepsilon } \right\} $$

(9)

As shown in Fig. 11, the f _HAB value in Eq. (9) can reach greater values than 1 for larger strains than 3.5, which is physically unacceptable. A more realistic relationship between f _HAB and ε for the A5052 alloy under study can be achieved by fitting ECAP experiment (ε > 8, 300 °C and 0.1 s⁻¹) and compression data (ε < 2, 333 °C and 0.01 s⁻¹) for the Al–Li-Mg–Sc [10] and A5052 [14] alloys, respectively, using the following piecewise-defined function:

$$ f_{\text{HAB}} = \left\{ {\begin{array}{*{20}l} {K_{1} \exp \left\{ { K_{2} \varepsilon } \right\} + K_{3} \exp \left\{ { K_{4} \varepsilon } \right\}, } \hfill & {\varepsilon < 1.9} \hfill \\ {1 - K_{5} \exp \left\{ { - K_{6} \varepsilon } \right\},} \hfill & {\varepsilon \ge 1.9} \hfill \\ \end{array} } \right. $$

(10a, b)

Figure 11

Best fitted f _HAB − ε law (Eq. 9) compared with HCT experiments for A5052 at 333 °C and 0.01 s⁻¹ [14]

As shown in [25], even very different aluminum alloys can exhibit qualitatively similar f _HAB − ε laws. This implies that considering the lack of more specific data on AA5052, the f _HAB − ε law (Eq. 10) of the latter could be approximated with that of Al–Li-Mg–Sc with the constants listed in Table 2. These model parameters are quite sensitive.

Table 2 Coefficients used in Eqs. (9) and (10)

Figure 10 shows the results of the best fitting. Initially, the fraction of HABs was close to 0.9, and it then dropped to 0.2 at ε = 0.5. For ε > 0.5, f _HAB increased with increasing strain and asymptotically approached f _HAB = 1. The use of empirical Eq. (10) was found to be effective in describing the overall f _HAB − ε law for both low strains (Eq. 10a for ε < 1.9) and high strains (Eq. 10b, for ε > 1.9), which are typical of hot rolling and severe plastic deformation, respectively. However, there was a lack of experimental data on the influence of the temperature and strain rate on f _HAB − ε law for the AA5052 even though it was possible to show that the influence of the temperatures and strain rates on f _HAB, predicted by means of the GM model [15], was negligible for AA1200 over the 277–460 °C and 0.01–1 s⁻¹ ranges. Moreover, certain experiments [25] have shown that f _HAB − ε data of a large set of Al–Mg alloys fit well with one single curve for different temperatures (over the 20–400 °C range) and for larger strains than ε = 1. Thus, it was reasonable to assume that Eq. (10) had to be independent of the temperature and strain rates.

Preliminary attempts were made with the aim of calculating f _HAB by applying GM model [15] to AA5052 by simply adjusting the model parameters. The result is shown in Fig. 10. As can be seen, the predicted f _HAB started from 1 and dropped to a plateau of 0.22, even after very small strains, unlike what was found in experiments [10, 14, 25].