Topological aspects in the microstructural evolution of AA6082 during hot plastic deformation

Abstract During thermomechanical processing of AA6082, the continuous dynamic recrystallization phenomenon is the restoration mechanism following dynamic recovery at high temperatures. This work proposes a microstructure model to describe the evolution of dislocation densities, misorientation distributions, fractions of high and low angle grain boundaries, and grain and subgrain sizes during hot deformation. The microstructure evolution is coupled with constitutive equations to predict the flow stresses depending on the strain, strain rate, and temperature. The flow curves, obtained by compression tests and the microstructure characterization done with SEM-EBSD analysis of non-deformed and deformed samples, are used to refine and validate the physical-based model. The topology of the grains before deformation is considered by assuming a mean ellipsoidal shape of the grains. Therefore, the influence of the deformation direction for an initially elongated grain structure can be predicted. The deformation in the normal direction leads to faster evolution of the microstructure than in the rolling direction. The hot compression changes the initial fibre texture to Brass and Goss type for compression in normal and rolling directions, respectively. Due to progressive crystal rotation, the changes in texture and the progressive formation of new low-angle grain boundaries evidence continuous dynamic recrystallization.


Introduction
Metallic parts that undergo hot deformation restore their microstructure.Whether the dynamic recrystallization (DRX) restoration mechanism takes place is a matter of the deformation process and the nature of the material (Huang & Logé, 2016).Discontinuous dynamic recrystallization (DDRX) occurs in moderate and low stacking fault energy (SFE) (Humphreys & Hatherly, 2004;Sakai, Belyakov, Kaibyshev, Miura, & Jonas, 2014) materials by nucleation followed by grain growth.Two different mechanisms have been proposed in the literature to explain the modification of the microstructure for high SFE materials: (i) continuous dynamic recrystallization (CDRX) correlated with a lattice rotation and increment of HAGB fraction (Canelo-Yubero et al., 2020;Gourdet & Montheillet, 2000, 2002), and (ii) geometric dynamic recrystallization (GDRX) where texture remains unaltered (Blum, Zhu, Merkel, & McQueen, 1996;Martorano & Padilha, 2008).The CDRX is described as the microstructural change by a progressive formation and rotation of subgrains resulting in a total misorientation increment.Thus, during plastic deformation, the low angle grain boundaries (LAGB) are progressively converted into high angle grain boundaries (HAGB).In GDRX, subgrains are formed, followed by migration and pinching off original HAGBs (Gholinia, Prangnell, & Markushev, 2000).The GDRX and CDRX were discussed extensively since the beginning of their conceptualization (McQueen & Kassner, 2004).
In previous works, physically-based models were developed to describe the evolution of the microstructure and the stresses of AA6082 under hot deformation, assuming that DRV (Poletti et al., 2018) and CDRX (Poletti et al., 2019) are the main restoration mechanisms.Approaches to model GDRX are primarily based on geometrical considerations, whose geometrical change occurs due to the applied strain, the evolution of the grain morphology, the HAGB migration, and the formation of new HAGBs (Huang & Logé, 2016).Goetz and Semiatin (2001) developed a model of pure geometrical nature.The grains are modelled as truncated octahedron shapes with missing consideration of HAGB migration.Khan and Liang (1999) attempted to predict HAGB migration after boundary serration without considering the geometric shape changes due to the deformation.Pettersen and Nes (2003) assessed the geometric shape change due to their model's imposed strain and grain size evolution.GDRX and CDRX mechanisms can take place simultaneously.Whether the formation of HAGBs is a consequence of the transformation from LAGB or only a result of the migration of HAGB depends on the initial microstructure, the force direction, and the deformation parameters of temperature, strain, and strain rate.
This work aims to characterize and model the microstructure evolution of aluminium alloys under different deformation conditions considering different starting microstructures to determine the microstructural changes as a function of the deformation conditions.Samples of a wrought AA6082 alloy were deformed and characterized using SEM and EBSD.A dislocation-based model that describes the topological evolution of the original grains and their influence on the other microstructural features is developed.Finally, the simulation results are compared with the measured microstructure.

Experimental setup
The wrought AA6082 aluminium alloy with an fcc lattice structure and high SFE has the measured chemical composition given in Table 1.AMAG Austria Metall AG provided the material in a hot rolled condition, where the aluminium plate was air-cooled after deformation and natural aged.
The as-received material was cut in different directions to produce the compression samples, as shown in Figure 1.Compression tests were performed to obtain a wide range of strain rates, strains, and temperatures with different compression directions.As an example, two compressed samples are also inserted in Figure 1.The hot compression tests were carried out on samples of 15 mm in length and 10 mm in diameter using a Gleeble® 3800 system.A test matrix for both normal direction (ND) and rolling direction (RD) samples consisted of four temperatures, namely 350, 400, 450 and 500 °C, and four different strain rates of 0.01, 0.1, 1 and 10 s −1 .The compression tests were carried out up to a true strain of 0.8.Ni-paste and graphite foil was used as a lubricant to minimize the friction between sample and anvil.K-type thermocouples were welded at the sample's surface to measure and control the temperature.The sample was ohmically heated with a heating rate of 5°Cs −1 and held at the temperature during the 30 s before deformation.After deformation, the samples were in-situ water quenched with water jets.As done in other works (Goetz & Semiatin, 2001;Khan & Liang, 1999), the flow curves were corrected due to adiabatic heating.The effects of friction were minimal as the barreling was considerably small.Thus, the flow curves were only corrected considering the adiabatic heating effects.
Scanning electron microscopy (SEM) was conducted using a Tescan Mira3 SEM equipped with a Hikari Electron Backscattered Electron Diffraction (EBSD) camera.EBSD measurements were performed for an area of 500 × 500 µm and 100 × 100 µm using a step size of 0.5 µm and 0.1 µm, respectively.The data treatment was performed using the OIM Analysis® 8.6 software.A confidence index standardization was performed considering a grain with a minimum size of 10 points and a tolerance angle of 10°.Finally, the neighbour confidence index correlation was used to clean the data points with a confidence index lower than 0.2.A subgrain was defined as a region within grains where at least 10 points share a similar orientation with a boundary misorientation less than 10° and greater than 2°.Thus, 10° was considered the transition angle between LAGB and HAGB.The grain orientation spread (GOS) was calculated assuming a grain as a region with at least 10 points and a boundary misorientation higher than 10°.The fractions of LAGBs and HAGBs were also calculated from the EBSD measurements.The crystallographic texture was calculated using the harmonic series expansion method for a series rank of 16 with a Gaussian half-width of 5°.The sample symmetry was considered triclinic for the crystallographic texture calculations.Pole figures were calculated for the (001), (111), and (110) planes for a resolution of 5°.

Modelling strategy
The structure of the model consists of the microstructure description and its initialization, the constitutive equation, and the dislocation rate equations.A more detailed description can be found in the published manuscripts (Buzolin, Ferraz, Lasnik, Krumphals, & Poletti, 2020;Buzolin, Lasnik, Krumphals, & Poletti, 2021a;Buzolin, Lasnik, Krumphals, & Poletti, 2021b).The hot deformation leads to several microstructural changes, and the model described here is based on continuous dynamic recrystallization (CDRX).The model parameters are listed in the Appendix.

Microstructure description
The microstructure is represented by mean values of internal variables, such as subgrain and grain sizes, dislocation densities, and boundary misorientation distribution.The present model does not consider the effects of the precipitates and intermetallic compounds on pinning dislocations and grain boundaries.The dislocation densities are separated into mobile dislocation density (Shanthraj & Zikry, 2011) (ρ m ), immobile dislocations (Hansen, Beyerlein, Bronkhorst, Cerreta, & Dennis-Koller, 2013;Ma, Roters, & Raabe, 2006) (ρ i ), and wall dislocation density (ρ w ) (Aoyagi, Kobayashi, Kaji, & Shizawa, 2013;Castelluccio & McDowell, 2017;Yan, Shen, Li, Li, & Yan, 2010).The boundary misorientation distribution is modelled as a sum of Rayleigh and Mackenzie distributions (Buzolin et al., 2021b).The boundary misorientation distribution of the LAGBs formed during plastic deformation is assumed to obey a Rayleigh distribution, and its mean misorientation value increases due to CDRX.The Mackenzie distribution considers a fully recrystallized material with random texture (Mason & Schuh, 2009).A detailed description of the calculation of the boundary misorientation distribution is given elsewhere (Buzolin et al., 2021b).

Microstructure initialization
The initial microstructure is defined by its initial subgrain (SG s 0 ) and grain (G s 0 ) sizes, and the average boundary misorientation angle and dislocation densities.The prior grain before deformation is modelled to have an ellipsoidal shape with the axis l 1 , l 2 and l 3 .The maximum boundary surface density (S v ) is given by the total surface of boundaries (HAGB + LAGB) over the total volume.The description allows considering the evolution of boundaries formed during deformation as in (Mason & Schuh, 2009) and predicting a steady-state recrystallized boundary misorientation distribution, enabling the simulation of any starting microstructure.Finally, the ρ w is considered as n sets of aligned dislocation walls forming a LAGB with an average misorientation (θ LAGB ) and are calculated according to Equation 1 (Gourdet & Montheillet, 2003).The fraction of LAGBs f LAGB is calculated according to Equation 2. θ c is the transition angle between LAGB and HAGB and considered 10° in this work.

Constitutive equation
Constitutive equations couple the microstructure with the flow stress.The flow stress is considered a sum of the thermal (σ th ), and athermal (σ ath ) stresses, V V V ath t h .The athermal stress is expressed according to Equation 3, and the thermal stress is explained in section 3.5.
α is the Taylor constant, M is the Taylor factor, G is the shear mod- ulus at the deformation temperature, and an empirical factor F w is used to reduce the influence of the lattice strain caused by the wall dislocations on the athermal stresses, as explained in (Buzolin et al., 2020(Buzolin et al., , 2021a(Buzolin et al., , 2021b)).

Rate equations
The plastic strain rate is considered equal to the applied strain rate.Using Orowan's relationship (Equation 4), the glide velocity Equation 5 describes the rate for mobile dislocation density.Equation 6 describes the rate equations for immobile dislocation density.
The production of mobile dislocations due to Frank-Read's source and at subgrain boundaries correspond to the first and second terms in Equation 5, respectively (Buzolin et al., 2021a).The third, fourth and fifth terms in Equation 5 correspond to the immobilization of mobile dislocations at subgrain boundaries, the static recovery due to climb, and the dynamic recovery, respectively.The last term describes the annihilation of mobile dislocations due to the movement of HAGBs.λ is the inter-dislocation distance, and δ DRV is the critical distance of dislocation annihilation via DRV (Buzolin et al., 2021a).δ SG a constant to produce dislocations at grain boundaries.v HAGB is the HAGB velocity and S v is the boundary density.Immobile dislocations are produced by immobilising mobile dislocations (first term in Equation 6).In contrast, SRV and DRV are responsible for annihilating immobile dislocations (second and third terms in Equation 6, respectively) (Buzolin et al., 2021a).
The SRV of mobile and immobile dislocations is modelled as a process of formation and annihilation of dislocation dipoles by climbing (Ghoniem, Matthews, & Amodeo, 1990).The climb dislocation velocity ( V c ) is calculated using Equation 7 (Ghoniem et al., 1990).The climb stress (σ climb ) is calculated according to Equation 8 (Ghoniem et al., 1990).ν is the Poisson ratio.D s is the self-diffusion coefficient, η is a fitting parameter for the transfer of defect into jogs on the dislocation, and L CLIMB α is the length governing the elastic interaction between the dislocation and the defects (Equation 9 (Ghoniem et al., 1990)

Thermal stress and yield stress
The thermal stress is assumed to be related to the strain rate and temperature of deformation.Simplifying, the thermal stress is considered dependent on the yield stress, σ YS , as expressed in Equation 10.
σ ath 0 is calculated considering initial dislocation densities.Therefore, the thermal stress is constant for a given strain rate and temperature.The definition of the initial microstructure is the major limitation of this approach because it affects the calculation of the initial athermal stress (Buzolin et al., 2021b).The yield stress is considered to obey a simple Arrhenius-type relationship to the temperature and the Zener-Hollomon parameter.Despite limitations, this approach can describe in a simplified way the influence of strain rate and temperature on the yield stress, Equation 11.The expression is deduced in the work of Souza, Beladi, Singh, Hodgson, and Rolfe (2018), considering that the Zener-Hollomon parameter relates to the strain rate and temperature (  H exp / Q RT
The strain rate is related to the hyperbolic sine of the stress (Souza et al., 2018).
 ε is the strain rate.The activation energy (Q YS YS σ ), and the values of α YS , A YS , and n YS define the yield stress.A detailed procedure for the parameter calculation was published elsewhere (Souza et al., 2018).

Continuous dynamic recrystallization: boundary density and misorientation distribution evolutions
The proposed model considers the formation of a sharp LAGB.The dislocations that contribute to CDRX are a fraction of the mobile and immobile dislocations that are dynamically recovered and form new LAGBs or promote the increment in lattice misorientation (Buzolin et al., 2021b;Gourdet & Montheillet, 2003).A fraction α CDRX for the formation of new LAGB of an average misorientation (θ 0 ) is considered.The complementary fraction ( ) 1D CDRX accounts for the increase in the average misorientation of existing LAGB.The overall surface fraction rate is given according to Equation 12 (Gourdet & Montheillet, 2003).
Equation 13 yields the evolution of the mean Rayleigh boundary misorientation angle (Gourdet & Montheillet, 2003), considering that the boundary density S v formed by n aligned dislocations with a Burges vector magnitude b and with an average misorientation angle θ R increases its mean boundary misorientation angle due to the fraction (1D CDRX ) of dynamically recovered dislocations 'U CDRX that are incorporated into the existing boundaries.The Mackenzie distribution is constant, assuming a random texture material (Mason & Schuh, 2009).The evolution due to CDRX of the fractions of the Rayleigh and Mackenzie in the overall boundary misorientation distribution is shown in detail elsewhere (Buzolin et al., 2021b).

Wall dislocation density, grain and subgrain size evolutions
The evolution of the prior grain boundaries associated with an equivalent ellipsoidal grain due to the plastic deformation is expressed by Equation 14(modified from (Maire et al., 2018)).Each grain is defined by three semi-axis (l 1 , l 2 , and l 3 ).The macroscopic strain tensor applied to the material is considered the local strain tensor for the mean semi-axis evolutions.However, only the diagonal terms of the strain tensor (ε yy , y = 1 2 3 , , , ε yy is the local strain argument for the axis 'y') are considered to preserve the ellipsoidal grains.Consequently, the grain shape does not change in this approach if only shear components are applied.In addition, Equation 14 also considers the role of the formed boundaries during deformation that limits the evolution of the initial grain semi-axis.The maximum variation of the grain axis corresponds to dl dt l y y yy y p H H  1 2 3 , , (Maire et al., 2018).This evolution is reduced by multiplying by the fraction f 3 , obtained by integrating the Rayleigh boundary misorientation distribution () T R ) considering the bonds as the interval of misorien- tation of the Mackenzie distribution [0, θ max ], f 3 0 . Thus, if the material reaches the steady-state, f 3 = 0, and there is no further evolution of the initial grain semi-axis.The f HAGB CDRX represents the fraction of HAGB of the boundaries non-associated with the prior grain HAGBs and also limits the evolution of the initial grain semi-axis.If the material starts deforming from a fully statically recrystallized condition, f HAGB CDRX is initially zero.With increase in strain, HAGBs are formed due to CDRX.Consequently, the f HAGB CDRX increases, decreasing dl dt / .Finally, the subgrain size also limits the initial grain semi-axis evolution and it is described by the term l SG l If the grain semi-axis is notably large compared to the subgrain size, this term tends to be one.During deformation, the value of a given grain semi-axis will decrease, and it will eventually reach the subgrain size, yielding that this term tends to zero.
An equivalent grain size (G s ) and a mean subgrain size (SG s ) are calculated according to Equation 15 and Equation 16 (Gourdet & Montheillet, 2003), respectively.
Finally, the wall dislocation density (ρ w ) is updated according to Equation 1 at each iteration.

As-received material
In the as-received state, the wrought AA6082 has flat and elongated grains in the rolling direction, with many intermetallic phases, as shown in Figure 2. Some broken intermetallic Al(Mn,Fe)Si phases formed in the casting process were transformed, broken and oriented in the rolling direction, as shown in Figure 2. Mg 2 Si type particles precipitated within grains during cooling.Figure 3 shows the EBSD results for the as-received AA6082.Figure 3(a) shows the elongated grain structure densely populated with LAGB.The deformed microstructure with a low level of static recrystallization is shown in Figure 3(b).A typical aluminium rolling texture (Dirras, Duval, & Swiatnicki, 1999;Li, Zhao, Liu, & Li, 2018;Pérocheau & Driver, 2000) is shown in Figure 3(c-e).Figure 3(f) shows the ideal orientations for the texture components.

Flow curves
The measured (M) and simulated (S) flow curves are shown in Figure 4 for the RD deformed samples.The flow stress model could not reproduce the shape of the flow curves in the early stages of the deformation.The increase in flow stress is faster in the simulation than in the measurements.The model initially predicts a sharp increment of mobile dislocation, responsible for the quick increment in flow stress.The influence of temperature, strain rate, and the initial work hardening trend are well-predicted.The model predicts saturation of the flow stress, where the production of dislocations, mainly mobile dislocations, is counterbalanced by dynamic recovery.Consequently, the model predicts a nearly constant mobile dislocation density for a constant strain rate and temperature.Since the wall dislocation density contribution is diminished (Equation 3), the predicted flow stress reaches a systematical saturation for the tested conditions.
A difference in the flow stress values for ND-samples compared to RD-samples could not be observed significantly.Figure 5 shows the measured and simulated flow curves at 350 °C and 0.1 s −1 .The Taylor parameter is considered constant, and there is no parameter in the model to describe the influence of texture on the yield stress.Thus, the only difference between compression in ND and RD is related to the microstructure evolution.

Microstructure experimental and simulated
Figure 6 shows the inverse pole figure (IPF) maps for samples deformed at strain rates of 0.1 s −1 and temperatures between 350 °C to 500 °C.The elongated grains were compressed along their long axis for the samples deformed in the RD direction (Figure 6(a-d)), i.e. they became shorter and thicker.In contrast, the grains in the ND samples (Figure 6(a-d)) were compressed along their short axis, which means they got even thinner during hot compression.
The local crystallographic texture after hot compression in the ND direction is shown in Figure 7 for the strain rate of 0.1 s −1 .There is no evident temperature influence on the overall texture modification.From a fibre-like texture of the as-received AA6082 (Figure 3(c-f)), a more pronounced Brass texture evolves after hot compression in the ND direction.
The temperature has a more noticeable effect on the crystallographic texture formation for the wrought AA6082 deformed in the RD direction, Figure 8. Starting with a fibre texture represented in Figure 3(c-e), a Goss texture is formed after hot compression in the RD direction.It is visible at 350 °C and 400 °C, Figure 8(a-c) and Figure 8(d-f), respectively.The poles are less defined at 450 °C, Figure 8(g-i) and even less clear at 500 °C (Figure 8(j-l)).In addition, the hot compression at 500 °C in the RD leads to the weakest texture among all tested conditions.For the hot compression at RD, there is a clear tendency to decrease texture intensity with increased temperature.
The initial microstructure shown in Figure 3 is modified after hot compression to the ones shown in Figure 6.The deformation in RD or ND directions for the initial elongated grain structure leads to different topological evolutions.Figure 9(a,b) shows the minimum and maximum grain Feret dimensions after hot compression at 0.1 s −1 for the ND and RD, respectively, for different temperatures.The initial elongated grains are fragmented due to the new HAGB formed during hot compression, decreasing minimum and maximum Feret.This effect seems to be less   temperature-dependent the deformation in ND, although there is a slight tendency of larger minimum Feret for higher temperatures.The deformation in RD results in an increment in the minimum Feret at  350 °C.Higher deformation temperatures lead to a decrease of both minimum and maximum Feret.It is also visible that the values of minimum Feret are larger at RD than ND since the initial grains are compressed perpendicular and along their minimum axis, respectively.
The influence of the strain rate on the topological evolution of the initial elongated grain structure is shown in Figure 9(c).Apart from the Figure 10.Evolution of microstructural features of the wrought aa6082: a) grain and subgrain equivalent mean diameter for deformation in rD at 400 °C and 0.1 s −1 ; b) grain and subgrain sizes for deformation in rD at 400 °C and 10 s −1 ; c) grain and subgrain sizes for deformation in nD at 350 °C and 0.1 s −1 ; d) grain and subgrain sizes for deformation in nD at 450 °C and 10 s −1 ; e) grain and subgrain sizes as well as prior grain ellipsoid axis for deformation in rD at 400 °C; f ) grain and subgrain sizes as well as prior grain ellipsoid axis for deformation in nD at 400 °C.
decrease of maximum Feret associated with new HAGB formed during hot compression, there is no clear tendency concerning the strain rate influence.The different behaviour shown by the sample deformed at 1 s −1 can be correlated with the experimental hardening in the flow curves.
Here it is suggested that a pinning effect by intermetallic phases at the HAGB is probably the reason for this singular behaviour.
Figure 10 shows the evolution of some modelled and experimental microstructural features.Figure 10(a,b) shows the grain and subgrain size evolutions for the RD samples deformed at 400 °C and 0.1 s −1 , and 10 s −1 , respectively.The simulations are extended to larger strains beyond the validated data.The slight initial increment in mean grain size is related to the change in the prior grain shape.The deformation in RD leads to a decrement in grain axis 1 in Figure 10(e).Grain axis 2 and 3 consequently increase (Figure 10(e)).Therefore, the overall grain size increases.The fast production of new LAGBs and the evolution of the already present substructure result in the refinement of both grains and subgrains with increasing strain (Figure 10(a,b)).The deformation in ND leads to a further elongation of the already present grain structure (Figure 10(f)).Grain axis 2 and 3, representing the smaller axis of the grain ellipsoid, decrease with deformation in ND, and their sizes converge to the value of the formed subgrain size (Figure 10(f)).Thus, the mean grain size decreases faster in ND (Figure 10(c,d)) than in RD (Figure 10(a,b)).At very large strains, it is predicted that the subgrain and the grain have the same size, meaning that the material is recrystallized continuously.It seems to occur at smaller strains in the ND sample.

Discussion
The initial fibre texture (Figure 3(c-e)) was changed into Brass and Goss texture for the hot compression in the ND and RD directions, respectively.The change in texture shows that the crystals rotated during the hot compression up to the reached strain.The velocity of HAGB, the role of DRV, and the dissolution of the intermetallic phases and precipitates depend on the temperature and strain rate.The initial and final textures differ for the deformation in RD and ND.The same texture remains for hot compression in ND since the compression is in the same rolling direction.The Taylor factor, and therefore accommodation of the lattice and the formation of new texture, leads to different behaviour in the case of RD.In addition, the grains buckle in the case of RD (Figure 10(e)), by shortening the longer axis during deformation.The contrary occurs during deformation in ND, where the grains become increasingly elongated.
The roles of CDRX and GDRX as restoration mechanisms are indistinguishable in such a case.DRV forms new LAGBs, and CDRX can be correlated with a progressive lattice rotation that leads to texture changes and progressive transformation of LAGB into HAGB (Canelo-Yubero et al., 2020;Gourdet & Montheillet, 2000, 2002).Grain boundary serration and grain boundary impingement by another HAGB are the mechanisms of GDRX (Blum et al., 1996;Martorano & Padilha, 2008) and can be associated with forming new grain boundaries during deformation in ND.
The developed dislocation-based model considers the initial grain structure's topology by introducing the grains' mechanical evolution according to the deformation matrix and the deformation rate, Equation 14.Although there is no directed correlation to the GDRX mechanisms, the mechanical movement of the prior HAGB is also a function of the fraction of HAGB and the subgrain size.Thus, CDRX is connected to the topological movement of the original HAGBs, evidenced by the change in texture and subgrain formation.
This hybrid model predicts the influence of any initial microstructure on the microstructure evolution and flow stress, including the influence of the initial grain shape.As an example, Figure 11 shows the influence of the temperature and deformation direction on the evolution of the fraction of HAGB.The hot compression in ND leads to faster microstructure evolution than the RD, as shown in Figure 10.

Summary and conclusions
The hot compression behaviour of a wrought AA6082 was investigated using the Gleeble® 3800 and scanning electron microscopy.The

Figure 1 .
Figure 1.3D microstructure and schematic drawing of the direction of the specimen cut for compression tests.the green arrows refer to the compression direction during the compression tests.the samples are called rD and nD. the elliptical form of all rD samples after deformation is the result of the rolling texture, as shown in the images to the right.

Figure 2 .
Figure 2. Backscattered electron (BsE) micrograph of the as-received aa6082 with the main classes of intermetallic and precipitates indicated by the yellow arrows.

Figure 4 .
Figure 4. Measured (M) and simulated (s) flow curves of the wrought aa6082 deformed in the rD direction.

Figure 5 .
Figure 5. Measured (M) and simulated (s) flow curves of the wrought aa6082 deformed in the nD and rD directions at 350 °C and 0.1 s −1 .

Figure 6 .
Figure 6.EBsD inverse pole figure (ipf) maps of samples deformed at different temperatures and 0.1 s −1 of strain rate.the red arrows indicate the direction of deformation.

Figure 9 .
Figure 9. Minimum (Min) and maximum (Max) feret for different hot compression conditions: a) at the nD direction and 0.1 s −1 ; b) at rD direction and 0.1 s −1 ; c) at rD direction and 400 °C.

Figure 11 .
Figure 11.Measured values of fraction of HaGB at a strain of 0.85 and evolution of the fraction of HaGB for the hot compression at 350 °C at 0.1 s −1 in the rD and nD directions.

Table 1 .
nominal chemical composition in weight% of a typical aluminium alloy 6082.