Fig. 1. Heat-treatment conditions for the three different alloys.

Fig. 2. Bright-field TEM images and schematic morphologies of the second phases. The 2024 Al alloy was aged at 180 °C for (a) 2 h (UA) and (b, c) 120 h (OA); the 6A01 Al alloy was aged at 175 °C for (d) 50 min (UA) and (e, f) 168 h (OA); the 7075 Al alloy was aged at 140 °C for (g) 2 h (UA) and (h, i) 264 h (OA). The electron beam is close to $$.

Fig. 3. (a-c) Engineering stress-strain curves and (d-f) evolution of UTS and UE with aging times for the three different Al alloys. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 4. Tensile strength and elongation for various grades of wrought Al alloys with different aging states. (a) 2xxx series [13⇓⇓-16], [19]; (b) 6xxx series [20⇓⇓-23,26⇓-28]; (c) 6082 in different aging heat-treating regime [29]; (d) 7xxx series [30], [31], [32], [33], [34].

Fig. 5. Dislocation morphologies under different aging states. (a) and (d) 2024 Al alloy subjected to a strain of ε = 6%; (b) and (e) 6A01 Al alloy subjected to an ε = 5.5% deformation; (c) and (f) 7075 Al alloy subjected to a strain of ε = 8%. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 6. Tensile true stress-strain curves and corresponding work-hardening rate Θ vs flow stress, where the UA and OA states have similar yield strength. (a) and (d) 2024; (b) and (e) 6A01; and (c) and (f) 7075 alloys.

Fig. 7. Compressive true stress-strain curves and corresponding work-hardening rate Θ vs flow stress: (a) 2024; (b) 6A01; and (c) 7075 alloys.

Fig. 8. Bright-field TEM micrographs of the compressive specimen after 40% true strain. (a), (d) 2024; (b), (e) 6A01; (c), (f) 7075 alloys. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 9. (a) The calculation result of the generalized stacking fault energy (GSFE) curves; (b) the calculated values of the unstable stacking fault (USF) and the stacking fault (SF).

Fig. 10. Change of hardening exponent n with aging time for the three Al alloys, which shows that the slip mode of dislocations is closely related to the evolution of the second phases rather than to the matrix from three separate aspects corresponding to the initial n0, saturated ns, and the change of n during aging.

Fig. 11. True stress-strain curves, microstructures, and exponential fitted values of n for pure Al. The value n of pure Al (～7-8) is close to that of the SSS state (n = 9) which proves that the alloying elements have little effect on the value of n.

Fig. 12. Schematic illustration of a simplified 3D annihilation model of Al alloys with two typical second phases.

Fig. 13. The variation trend of the hardening exponent n with the annihilation coefficient k, the volume fraction fsp, the aspect ratio ω, and the size l for the rod-shaped second phase.

Fig. 14. Effects of the four parameters, (a) k, (b) fsp, (c) ω, and (d) l (or d) on the hardening exponent n for the two typical shaped second phases, which indicates some methods to reduce the n value of the Al alloys containing by-passable second phases: (i) select the second phase with the smaller influence range, (ii) reduce the density of the second phases, (iii) increase the size of the second phases, and (iv) control the shape of the second phases to be equiaxial or spherical.

Fig. 15. The evolution of second phase morphologies with the aging time: (a) 2024; (b) 6A01; and (c) 7075 alloys; horizontal and vertical comparisons of the microstructures show that the value of n increases with the density and aspect ratio of the second phase where this is consistent with the trend reflected by Eq. (11) and Fig. 14.

Fig. 16. Variation trend of k values with aging time for the three different Al alloys (the respective typical dislocation configurations are also displayed). These plots show that the value of k is determined mainly by the characteristics of the second phases and it is little affected by the geometric features or volume fractions of the second phases.

Fig. 17. Illustration of the general relationship between the strength and plasticity and the common mechanism defining the wrought Al alloys: the strength-plasticity curve behaves in a “barb” shape with changing aging time, where this is owing to the increasing cross-slip tendency with aging time.