3.1. True Stress–Strain Curve
Figure 1 shows the stress–strain curves of the 6082 Al alloy at strain rates of 0.01 to 5 s
−1 and deformation temperatures of 623 to 773 K. The flow stress was affected by the deformation temperature and strain rate: with increasing deformation temperature or a reduction in the strain rate, the corresponding peak stress decreased. By comparing true stress–strain curves at different strain rates, it can be seen that at low strain rates (
Figure 1a,b), the Al alloy entered a steady-state flow stage with little strain (about 0.1), and the flow stress decreased thereafter: this indicated that, with a constant increase in strain, the dynamic softening effect of materials was constantly strengthened at a low strain rate, which was more significant than the work-hardening effect. At a high strain rate (
Figure 1c,d), the Al alloy started to enter the steady-state flow stage after the strain exceeded 0.3. In this case, the stress remained constant, which implied that there was a certain equilibrium between the dynamic softening and work-hardening effects. Above all, with increasing temperature or a decreasing strain rate, the flow stress of the 6082 Al alloy decreased until the Al alloy entered a steady-state flow stage. In this process, the effect of strain hardening decreased while the dynamic softening effect was enhanced. Moreover, dynamic recrystallization probably occurred. The occurrence of peak stress in the true stress–strain curve shows that dynamic recrystallization occurred during thermoplastic forming; however, it was hard to judge the extent of the material deformation based on peak stress from the flow curves alone.
Sellars and Mctegart [
15] have proposed a hyperbolic sine model containing activation energy
Q for dynamic recrystallization and deformation temperature
T. The model is used to describe the quantitative relationship between various thermodynamic parameters (e.g., the flow stress, deformation temperature, and strain rate) during high-temperature plastic deformation. To consider the effects of the strain rate and deformation temperature on dynamic recrystallization, the Zener–Hollomon factor (parameter
Z) is introduced:
where,
Z,
,
Q,
R,
, and
T refer to the Zener–Hollomon parameter, strain rate (s
−1), activation energy (kJ/mol) for thermal deformation, molar gas constant (8.3145 J/(mol·K)), flow stress (MPa), and deformation temperature (K), respectively;
A1,
A2,
A,
n1,
n,
α, and
β denote material constants; and
.
Taking the logarithm of each side in Equations (2) and (3):
Origin software was used to obtain a best fit for the stress peak data obtained through thermal compression testing of the 6082 Al alloy, and the
and
curves can be separately obtained, as shown in
Figure 2. The average slope of the curves is
n1 = 8.6877 and
β = 0.2036, and thus
.
Accordingly, Equation (4) gives
Here, the
and
curves are plotted in
Figure 3: the double-logarithm relationship between the hyperbolic sine of flow stress and the strain rate, as well as the relationship between the logarithm of the hyperbolic sine of flow stress and the reciprocal temperature, are quasi-linear. It is thought that the stress and strain rate during high-temperature deformation of the 6082 Al alloy satisfies the hyperbolic sine relationship in the form of an Arrhenius equation; therefore, an Arrhenius relationship in the form of a hyperbolic sine containing the activation energy
Q for deformation can be applied to describe the flow stress on materials during high-temperature deformation, as shown in Equation (4) [
16]. The partial differentiation of both sides (Equation (7)) is
By substituting the average slopes of the curves in
Figure 3a,b into Equation (8), it can be seen that
Q = 163.5337 kJ/mol. According to Equation (8), it can be seen that the average slope of the curve in
Figure 3a gives
n = 6.4741, with the intercept of
at −2.4527. By substituting
Q, R, and
T into Equation (8),
A = 11.9605 can be calculated. By substituting the above parameters into Equation (4), the equation for flow stress on the 6082 Al alloy at a high temperature was obtained:
3.2. Modeling of Dynamic Recrystallization
As mentioned above, during high-temperature plastic deformation of the Al alloy, it is hard to observe fine subgrain structures in the metallographs; moreover, the true stress–strain curve of the Al alloy also does not show significant peak stress. Therefore, the critical point of dynamic recrystallization cannot be clearly determined from the flow curve alone. Thus, some methods for determining the critical conditions of dynamic recrystallization have been proposed: Poliak and Jonas [
17] have proposed the use of the work-hardening rate (
) of materials as a variable for characterizing the rate of change of flow stress with strain, which can reflect the microstructural changes in a material. Using this method, they attained accurate critical conditions for dynamic recrystallization.
Utilizing Origin software, the corresponding true stress–strain curves under different deformation conditions (
Figure 1) were fitted to acquire the corresponding work-hardening rate
; moreover, the
relationship was plotted (
Figure 4) for a strain rate of 0.1 s
−1. It can be seen that the relationship curves at different temperatures all showed a minimum point, and the corresponding strain was the critical strain causing dynamic recrystallization.
Using the above methods, the critical strains under different deformation conditions could be calculated (
Table 1): the critical strain increased with an increasing strain rate or decreasing temperature. The reason for this is that, at a given deformation temperature, the greater the strain rate, the shorter the deformation time. As a result, there is no mutual timeous offset, and the dislocation density during deformation increases, with significant work-hardening tendencies exhibited. The critical strain causing dynamic recrystallization also increases. At the same strain rate, with increasing temperature, the driving force for vacancy–atom diffusion, the slip of screw dislocations, and the climb of edge dislocations increase. In this context, dynamic recrystallization is more likely to occur, so the critical strain causing dynamic recrystallization decreases [
18].
Figure 5 shows the
curve: the critical strain increased with increasing
Z. The reason for this is that, when the deformation of the materials reaches critical strain, work hardening and recovery lead to the formation of dislocation substructures. Moreover, tangled dislocations, rather than clear two-dimensional (2D) grid structures, form the boundary of such substructures. The presence of high-energy-state tangled subgrain boundaries enables local zones to acquire sufficient storage energy so that the misalignment of subgrain boundaries continues to increase until an HAB is formed, leading to new dynamic recrystallization. Therefore, with an increasing strain rate and a reduction in the deformation temperature, the increasing critical strain increases the difference in storage energy across each side of the moving subgrain boundary. This guarantees that grain boundaries move rapidly to promote the coarsening of subgrains before the dislocation density at the moving boundaries reduces the initial driving force, thus realizing the growth of the nucleus during dynamic recrystallization [
19]. Utilizing Origin software, linear fitting was conducted on data pertaining to the critical strain
causing dynamic recrystallization and the parameter
Z:
The relationship between the volume fraction after dynamic recrystallization and the plastic strain and grain size after dynamic recrystallization can be separately described as follows:
where
XDRX denotes the volume fraction after dynamic recrystallization;
,
, and
separately represent the strain, critical strain, and peak strain during high-temperature deformation;
dDRX and
d0 separately refer to the grain size after dynamic recrystallization and the original grain size;
,
T,
Q, and
R denote the strain rate, deformation temperature, thermal activation energy, and molar gas constant, respectively; and
k,
m1,
a,
n2,
n3,
n4,
k, and
m2 all denote material constants.
Generally, the volume fraction and grain size after dynamic recrystallization can be determined by observing metallographic structures of frozen high-temperature microstructures subjected to thermal deformation; however, the volume fraction after dynamic recrystallization mainly depends on the rate of nucleation of recrystallized grains and their rate of growth. During high-temperature plastic deformation, grains subjected to dynamic recrystallization are likely to merge or grow; therefore, it is hard to observe fine grains subjected to dynamic recrystallization in microstructures even if the grain size after significant deformation is larger than that of the original grains that have not undergone deformation. As a result, it is difficult to distinguish grains subjected to dynamic recrystallization from original grains utilizing metallographic methods. By virtue of the advantages of EBSD in large-area quantitative analyses, some information on microstructures and crystallography, e.g., the size, misalignment, and distribution of recrystallized grains, can be found. The orientation mapping of the 6082 Al alloy at a deformation temperature of 723 K and a strain rate of 0.1 s
−1 (from EBSD) is displayed in
Figure 6. Different colors represent different grain orientations, and the misalignments of the subgrain boundaries and grain boundaries were generally set to 2° and 15°, respectively. The grain boundaries were characterized as very low-angle boundaries (VLABs) with a misorientation range of 2–5°, as low-angle boundaries (LABs) with a misorientation range of 5–15°, and as high-angle boundaries (HABs) with a misorientation greater than 15°. Utilizing the Recrystallized Fraction Component Function of Channel 5 software, the misalignments (
Figure 6b) and percentage contents (
Figure 6c) of the various grains could be attained. Correspondingly, ln
Z = 24.9014 and
XDRX = 38.60%. Using the same method, data (including the volume fraction, the grain size, and ln
Z after dynamic recrystallization) involving different conditions could be obtained (
Table 2).
By substituting the data in
Table 2 into Equations (11) and (12), the dynamic model for dynamic recrystallization of the 6082 Al alloy is expressed as follows:
Additionally, it could be found that, at a low ln Z (ln Z = 24.9014), the volume fraction after dynamic recrystallization was large (XDRX = 38.6%), indicating that at a low strain rate and a high deformation temperature (corresponding to a low value of Z), dynamic recrystallization of the 6082 Al alloy was more likely to occur.
3.3. Processing Map of the 6082 Al Alloy
A map describing the workability of materials is called a processing map. A dynamic materials model (DMM) is established using various fundamental principles, e.g., physical system simulation, continuous mechanics, and irreversible thermodynamics. A hot-working processing map based on this model is widely used in the characterization of the hot-workability of materials and the optimization of technological parameters pertinent to hot-working [
20]. In a DMM, the heating process is regarded as a system. During hot-forming, the total externally input power is expressed as
. The majority of the total power consumption is transformed into a visco-plastic heat induced by the plastic deformation of materials (the dissipation capacity
G). The heat dissipated by the changes (such as dynamic recovery and dynamic recrystallization) in the microstructures during material deformation (the associated dissipation
J) [
21] can be expressed as follows:
The proportions of the two energies are determined by the sensitivity index (
m) of the materials to the strain rate, that is,
The efficiency factor (
η) of power dissipation is introduced to characterize the dissipation of power when the microstructures of the materials change:
The contour map of the power dissipation factor is drawn on a 2D plane consisting of the strain rate and the deformation temperature . The map describes the power dissipation conditions during microstructural evolution under deformation. Using metallographic observation, the deformation mechanisms (such as dynamic recovery and dynamic recrystallization) of microstructures due to different deformation conditions can be analyzed.
When establishing a processing map based on DMM, the instability of materials is generally judged according to the dimensionless parameter
, which is defined in Equation (18) [
22]. The contour map of the instability criterion is drawn on a 2D surface and consists of the strain rate
and the deformation temperature
, thus forming a map showing material instability. The processing map can be obtained by overlapping the map of material instability onto that showing the power dissipation. Through the processing map, the high-temperature deformation mechanism of materials in different conditions can be analyzed, and the instability zone and safe zone of materials can be determined. This method provides a theoretical and actual basis for optimizing the technological parameters of the hot-working of materials and controlling their deformed microstructures. Equation (18) is
It can be seen from
Figure 2a that
was linearly correlated with
at different temperatures; therefore, it was feasible to calculate the hot-working processing map of the 6082 Al alloy using the DMM calculation method and to determine the zone of flow instability and the safe zone from the processing map.
Experimental data pertaining to
and
were fitted by applying a cubic spline function. Afterwards, using Equation (16), the sensitivity index (
m) of the strain rate was calculated, while the efficiency factor
η of power dissipation was computed using Equation (17). According to the instability criterion shown in Equation (18),
was obtained similarly through curve fitting by employing a cubic spline function. On the basis of DMM, the data calculated using the hot-working processing map of the 6082 Al alloy are presented in
Table 3.
On the basis of the data in
Table 3, maps about power dissipation and instability were separately drawn; afterwards, the map of material instability was superimposed onto the map showing power dissipation to acquire the hot-working processing map of the 6082 Al alloy (
Figure 7).
As is shown in the power dissipation map (
Figure 7a), three peak zones (the zones with maximum
η) were found: a zone at 713 to 753 K, a strain rate of 0.1 to 0.2 s
−1, and a power dissipation factor of about 0.23 (the temperature and strain rate corresponding to the peak were 723 K and 0.2 s
−1); a zone at 743 K to 773 K, a strain rate of 0.3 to 5 s
−1, and a power dissipation factor of about 0.23 to 0.33; and a zone at 743 K to 773 K, a strain rate of 0.01 to 0.03 s
−1, and a power dissipation factor of about 0.23 to 0.28. The material instability map (
Figure 7b) showed that the 6082 Al alloy exhibited three instability zones: a low-temperature zone with a high strain rate at 623 K to 653 K and a strain rate of 0.3 to 5 s
−1; a medium-temperature zone with a high strain rate at 703 K to 743 K and a strain rate of 0.3 to 5 s
−1; and a high-temperature zone with a low strain rate at 743 K to 773 K and a strain rate of 0.01 to 0.1 s
−1.
A power dissipation map also represents a trajectory chart of microstructures, reflecting the rate of change during hot-working and deformation. Zones with a high power dissipation factor are frequently used to define the zone of best workability; however, the failure of wedge-shaped cracks also generally occurs in zones with a high power dissipation factor. Therefore, it was necessary to validate this by applying the microstructures of corresponding samples to observe the changes in microstructures in different zones of the processing map and verify the reliability of the hot-working processing map [
23].
Figure 8 shows a 3D map of the efficiency of power dissipation of the 6082 Al alloy. The figure illustrates the change trends of the efficiency of power dissipation in three peak zones with different technological parameters. In two peak zones at high temperature, the efficiency of the power dissipation of the Al alloy changed significantly, indicating that the hot workability in these zones was unstable and that local flow instability probably occurred.
At high temperatures, the deformed microstructures in the Al alloy were relatively bulky with an increase in the strain rate. As the deformation temperature increased, the degree of recovery from deformation was higher, causing the storage energy after deformation to be reduced and recrystallization nucleation to thus become more unlikely to occur. At a high strain rate, there was not enough time for the growth of dynamic recrystallization, and therefore the level of dynamic recrystallization decreased. In this case, the deformed microstructures in the Al alloy were bulky. As shown in
Figure 9b, the bulky grain structures had a significant effect on the mechanical properties of the 6082 Al alloy. Thus, the 6082 Al alloy underwent negligible hot-working in the high-temperature zone at a high strain rate. In the high-temperature zone with a low strain rate, on the one hand, the deformation temperature was high, so grains grew rapidly; on the other hand, new recrystallized grains were found at the grain boundary, so the grain structures exhibited significant heterogeneity (
Figure 9a). As a result, the nonuniform deformation of the grain boundary was likely to have occurred in the deformation process, triggering flow instability. Contour lines were sparse in the peak zone of the efficiency of power dissipation at 703 K to 743 K and at strain rates of 0.1 to 0.2 s
−1. The contour lines in the peak zone are sparse, and the distribution of contour lines is uniform while maintaining a high efficiency factor of power dissipation, an shown in
Figure 7a. The TEM image of the samples at 723 K shows that at a strain rate of 0.01 s
−1, the grains in the Al alloy were bulky, and many tangled dislocations were found (
Figure 9c). A possible reason for this was that the degree of recovery was low at a low strain rate, so it was difficult to prevent increasing dislocation density and grain crushing in the deformation process through recovery. Under these conditions, dynamic recrystallization had not yet occurred, so the grains remained bulky. With an increasing strain rate, the number of tangled dislocations gradually decreased (
Figure 9d), and the substructures became clearer.
At a strain rate of 0.1 s
−1, an apparent subgrain boundary appeared, with significant recrystallization characteristics (
Figure 10). A chart showing the grain angles (
Figure 10a) revealed that the grain boundary represented by the blue lines was misaligned, and some fine new grains appeared (
Figure 10b). The corresponding TEM images (
Figure 10c) show that the dislocation in the grains disappeared, and therefore the dislocation density was significantly reduced, implying that dynamic recrystallization occurred. The microstructures presented in
Figure 10 indicate a higher fraction of VLABs than LABs for all deformation levels. VLABs can form either during deformation or annealing. The geometrically necessary dislocations generated during deformation can manifest in the form of VLABs to maintain strain compatibility. On the other hand, dislocation annihilation during recovery can also give rise to the formation of VLABs. In the case of deformation, increases in the fraction of VLABs should be associated with a concomitant increase in LABs. However, an analysis of the EBSD scans clearly revealed that increases in the fraction of LABs were not as significant as those of the VLABs. Therefore, it could be inferred that the large increase in VLABs was mostly associated with recovery. The microstructural features also indicated that there was a consistent increase in the fraction of HABs, which is a clear indication of the occurrence and progress of dynamic recrystallization.
During plastic deformation of Al alloys at high temperatures, the stacking fault energy in the Al alloy is high, so the extended dislocations are narrow and are likely to become bundled during deformation. As a result, the climbing of edge dislocations and the cross-slipping of screw dislocations are likely to be transferred between slip surfaces. In this context, unlike dislocations that are mutually offset and disappear, the distribution of dislocations is also changed and forms a closed cell wall to cut originally intact grains into many zones with a low dislocation density [
24]. As deformation continues, cell walls of dislocations are subjected to polygonization to form regular boundaries, thus generating an LAB (
Figure 10b, represented using red lines), with subgrain structures (
Figure 10d) forming after deformation. Additionally, the dislocation generated in subsequent deformation continues to move and converges at the LAB, thus causing increasing misalignment of the subgrain boundary. With sufficient deformation, the misalignment of the subgrain boundary reaches its critical value, and eventually subgrain boundaries evolve into an HAB, thus forming new recrystallized grains [
25]. The recrystallization process (without the participation of a nucleation–growth mechanism) is completed as deformation accumulates, indicating the evolution of microstructural features during continuous dynamic recrystallization of the alloy [
26].
Dynamic recrystallization can eliminate many of the dislocations generated in the forming process of materials (through grain refinement), and it also maintains a certain dynamic equilibrium. Additionally, the efficiency of power dissipation is high within the zone, and therefore microstructures of such materials are improved, thus guaranteeing their stress stability and favorable workability during hot-working. Therefore, A zone with dynamic recrystallization should be selected preferentially when determining technological parameters according to the hot-working processing map [
17,
18].
On the basis of the above analyses of the hot-working processing map and microstructural observations, three peak zones with a high efficiency of power dissipation should be selected preferentially when selecting the technological parameters for the hot-working of the 6082 Al alloy. Moreover, during a deformation process at high temperatures, recrystallized grains and original grains are likely to coarsen, thus impairing the material properties; therefore, during the formation of the 6082 Al alloy through hot-working, the temperature should be between 713 and 723 K, and the strain rate should be between 0.1 and 0.2 s−1.