**3.2.1 Modeling of texture evolution**

446 Recent Trends in Processing and Degradation of Aluminium Alloys

second phase particles contributes to the transformation from low angle subgrain boundaries to high angle grain boundaries by increasing the misorientation between two adjacent subgrains and removes the unrefined bands from the microstructure. For a better understanding of the texture evolution, the main FCC fibers were calculated and plotted in Fig. 17. Generally, with increasing the number of cycles, the intensity of the α fiber decreased while the intensities of the β and τ fibers increased. The α fiber, running from Goss to brass in Fig. 17a, indicates how the brass component decreased during the ARB process. It is seen that during all ARB cycles the intensity of Goss component is negligible.

Fig. 17. Intensity of the FCC fibers in the ARB processed aluminum sheets: (a) β-fiber, (b) τ-

Fig. 17b shows the intensity of the β fibers.

fiber, and (c) α-fiber

In order to interpret the texture change involved in the ARB process, the texture development was simulated with the Alamel model (Van Houtte et al., 2005, 2006). The deformation during ARB processing is approximated by a two-dimensional velocity gradient tensor which is composed of a compressive strain (εzz, εyy = 0 and εzz =−εxx) added with a simple shear strain (εxz). The texture simulations have been performed on the initial texture of Fig. 14 for different strain modes with various ratios of the simple shear component (εxz) to the plane strain compression components. The imposed shear during the ARB process is characterized by the shear coefficient K (K= εxz/εzz).

The texture simulation for the subsurface region has been performed with a large value of the shear coefficient (K= 2.4) due to localization of shear deformation in this region. The texture prediction for the mid-thickness part has been performed under the deformation condition with K= 0.1. It is assumed here that even in the middle layers of the sheet there will still be a small amount of frictional shear as the ARB experiment was carried out in totally dry conditions (i.e. without lubrication). Due to the specific stack-and-roll geometry of the ARB process, the subsurface texture after the first ARB pass appears in the central layer of the composite sample in the second ARB pass. Hence, in order to simulate the texture evolution in the middle layer in the ARB pass ni the Alamel model was applied on the subsurface from previous pass n(i−1) with a deformation mode that was characterized by K= 0.1. Fig. 18 presents results of the texture predictions for second, fourth, sixth and eighth ARB cycles. The calculated textures are in very good qualitative and quantitative agreement with the experimentally measured ODFs (Figs. 16 and 18).

The model calculation has produced the textures which exhibit a strong rolling β-fiber. It is important to notice, though, that the Dillamore and S components are far more important than the brass orientation, which corresponds very well to the experimentally observed texture, cf. Fig. 16. Furthermore, intensities of both S and brass orientations increase insignificantly whereas a considerable strengthening of the Dillamore orientation is observed during ARB process. Hence, it is shown here, on the basis of crystal plasticity modeling, that the sequence of rolling, cutting and stacking, which is characteristic for the ARB process eventually triggers a mechanism which leads to strengthening of the Dillamore component in the middle layers of the ARB sample.

Rotation of different texture components during ARB cycles, i.e. shear to copper and Dillamore components in the midsection under the plane strain compression mode and copper, S and brass to the shear component in the surface layer due to the shear deformation, is the unique feature of ARBed aluminum sheets (Heason & Prangnell, 2002a; Kim et al., 2005). This can be considered as the result of introduction of surface layer to the midsection during the next cycle and it is also associated with the increase in the number of interfaces. In fact, these interfaces induce additional strain during rolling and are responsible for the unique property.

Nanostructure, Texture Evolution and Mechanical Properties of

established.

of elongated grains.

ARB process

Aluminum Alloys Processed by Severe Plastic Deformation 449

phenomenon, Fig. 19. The hardness curve in this figure corresponds well with the microstructural changes mentioned above. Initial work hardening caused by the reduction of grain size and the growth of dislocation density inside the crystalline lattice leads to a rapid increase in microhardness at the first ARB cycle (εvM = 0.8). During the following cycles, static or dynamic recovery caused by the interpass annealing treatment, the heat of deformation and the accumulation of dislocations in the vicinity of the second phase particles, prevents a further increase of the hardness and a plateau around 80 HV is

An interesting feature of this figure is the significant increase of the hardness value (close to two times of the initial value) after the eighth cycle, while the sample exhibits a fully recovered microstructure and probably still provides an acceptable ductility. According to the results presented here, different mechanisms of grain refinement can be attributed to the different levels of strain. During the first two cycles of ARB (ε < 1.6) grain subdivision is the dominant mechanism. This mechanism promotes the formation of a fibrous microstructure

Fig. 19. Variation of Vickers microhardness of AA3003 alloy with increasing strain during

The results of the mechanical properties clarified that the strength of the ARBed aluminum sheets increases with increasing the number of cycles, Fig. 20. In order to study the relation between the mechanical properties and the microstructural changes, the tensile strength and the 0.2% yield strength were plotted as a function of minus square root of grain size in Fig. 21. The strength of the ARBed aluminum sheets is in a good conformity with Hall–Petch relationship, even for submicron grain structures. It was shown (Pirgazi et al., 2008b) shows that the amount of work hardening after yielding is rather small and necking occurs suddenly and causes the limited uniform elongation. It should be noted that the described microstructural evolution corresponds to the changes in mechanical properties very well. This suggests that the strength of the ARB samples is mainly attributed to grain boundary

Fig. 18. Simulation of the texture development in the center region during different ARB cycles

### **3.3 Mechanical properties 3.3.1 ARB samples**

Second phase particles in AA3003 alloy can also accelerate the rate of dynamic recovery which is very likely to occur in warm rolled aluminum sheets. Accumulation of dislocations in the vicinity of these particles leads to rapid transformation of low angle sub-grain boundaries to high angle grain boundaries and decreases the dislocation density inside the grains. Static recovery during pre-heating may also contribute to the reduction of dislocation density and promote the softening behavior. The variation of the microhardness with increasing strain during the ARB process confirms the occurrence of recovery in this

Fig. 18. Simulation of the texture development in the center region during different ARB

Second phase particles in AA3003 alloy can also accelerate the rate of dynamic recovery which is very likely to occur in warm rolled aluminum sheets. Accumulation of dislocations in the vicinity of these particles leads to rapid transformation of low angle sub-grain boundaries to high angle grain boundaries and decreases the dislocation density inside the grains. Static recovery during pre-heating may also contribute to the reduction of dislocation density and promote the softening behavior. The variation of the microhardness with increasing strain during the ARB process confirms the occurrence of recovery in this

cycles

**3.3 Mechanical properties 3.3.1 ARB samples** 

phenomenon, Fig. 19. The hardness curve in this figure corresponds well with the microstructural changes mentioned above. Initial work hardening caused by the reduction of grain size and the growth of dislocation density inside the crystalline lattice leads to a rapid increase in microhardness at the first ARB cycle (εvM = 0.8). During the following cycles, static or dynamic recovery caused by the interpass annealing treatment, the heat of deformation and the accumulation of dislocations in the vicinity of the second phase particles, prevents a further increase of the hardness and a plateau around 80 HV is established.

An interesting feature of this figure is the significant increase of the hardness value (close to two times of the initial value) after the eighth cycle, while the sample exhibits a fully recovered microstructure and probably still provides an acceptable ductility. According to the results presented here, different mechanisms of grain refinement can be attributed to the different levels of strain. During the first two cycles of ARB (ε < 1.6) grain subdivision is the dominant mechanism. This mechanism promotes the formation of a fibrous microstructure of elongated grains.

Fig. 19. Variation of Vickers microhardness of AA3003 alloy with increasing strain during ARB process

The results of the mechanical properties clarified that the strength of the ARBed aluminum sheets increases with increasing the number of cycles, Fig. 20. In order to study the relation between the mechanical properties and the microstructural changes, the tensile strength and the 0.2% yield strength were plotted as a function of minus square root of grain size in Fig. 21. The strength of the ARBed aluminum sheets is in a good conformity with Hall–Petch relationship, even for submicron grain structures. It was shown (Pirgazi et al., 2008b) shows that the amount of work hardening after yielding is rather small and necking occurs suddenly and causes the limited uniform elongation. It should be noted that the described microstructural evolution corresponds to the changes in mechanical properties very well. This suggests that the strength of the ARB samples is mainly attributed to grain boundary

Nanostructure, Texture Evolution and Mechanical Properties of

by the development of ultra-fine grained structures.

Aluminum Alloys Processed by Severe Plastic Deformation 451

During the following cycles, in which the incremental increase of the strength becomes smaller, the dislocation density is almost constant (Parh et al., 2001; Costa et al., 2005). The low density of dislocations at relatively high strains is due to the dynamic recovery (Costa et al., 2005), or absorption of dislocations into the grain boundaries (Prangnell et al., 2001). In any way, the increase of the volume fraction of ultra-fine elongated grains due to increase in the fraction of HAGBs can be contributed to the strengthening in the medium levels of strain (1.6 < ε < 4.8). Finally, the large strength at relatively high strains (ε > 4.8) can be explained

Fig. 21. Strength of ARBed AA1100 aluminum sheets versus the grain size. The grain sizes reported in this figure are the size of grains bounded by high angle grain boundaries

Fig. 22. Distribution of microhardness across the thickness of ASBed specimens

strengthening, though the details of the strengthening mechanism in the SPD materials should be discussed more. As has been already known, the ARB processed specimens have the dislocation substructures inside the UFGs as well as the elongated grain morphology. This means that the strength of these specimens might be affected not only by grain refinement strengthening but also by strain hardening. It has been proposed that when a deformation structure consists of a mixture of low and high angle grain boundaries, the strength can be considered as the sum of dislocation strengthening from LAGBs and grain size strengthening from HAGBs (Hansen, 2004). However, the detailed discussion about the Hall–Petch relationship and strengthening mechanisms should be done in the future works. In a similar study by Park et al. (2001) on AA6061 alloy processed by the ARB at 250 °C it has been reported that the rapid increase in strength at relatively low strains is mainly due to the work hardening caused by an increase in dislocation density and formation of the sub-grains.

Fig. 20. (a) Engineering stress–strain curves and (b) the corresponding tensile properties of AA1100 aluminum sheets processed at different ARB cycles

strengthening, though the details of the strengthening mechanism in the SPD materials should be discussed more. As has been already known, the ARB processed specimens have the dislocation substructures inside the UFGs as well as the elongated grain morphology. This means that the strength of these specimens might be affected not only by grain refinement strengthening but also by strain hardening. It has been proposed that when a deformation structure consists of a mixture of low and high angle grain boundaries, the strength can be considered as the sum of dislocation strengthening from LAGBs and grain size strengthening from HAGBs (Hansen, 2004). However, the detailed discussion about the Hall–Petch relationship and strengthening mechanisms should be done in the future works. In a similar study by Park et al. (2001) on AA6061 alloy processed by the ARB at 250 °C it has been reported that the rapid increase in strength at relatively low strains is mainly due to the work hardening caused by an increase in dislocation density and formation of the

Fig. 20. (a) Engineering stress–strain curves and (b) the corresponding tensile properties of

AA1100 aluminum sheets processed at different ARB cycles

sub-grains.

During the following cycles, in which the incremental increase of the strength becomes smaller, the dislocation density is almost constant (Parh et al., 2001; Costa et al., 2005). The low density of dislocations at relatively high strains is due to the dynamic recovery (Costa et al., 2005), or absorption of dislocations into the grain boundaries (Prangnell et al., 2001). In any way, the increase of the volume fraction of ultra-fine elongated grains due to increase in the fraction of HAGBs can be contributed to the strengthening in the medium levels of strain (1.6 < ε < 4.8). Finally, the large strength at relatively high strains (ε > 4.8) can be explained by the development of ultra-fine grained structures.

Fig. 21. Strength of ARBed AA1100 aluminum sheets versus the grain size. The grain sizes reported in this figure are the size of grains bounded by high angle grain boundaries

Fig. 22. Distribution of microhardness across the thickness of ASBed specimens

Nanostructure, Texture Evolution and Mechanical Properties of

mostly related to the hardness homogenization.

Aluminum Alloys Processed by Severe Plastic Deformation 453

of the inner materials, the overall flow strength of the specimen is increased during tension. That is why there is a high difference between the yield strength and the tensile strength in this work in comparison to that of ARB (Pirgazi et al., 2008b). By this explanation, more hardness inhomogeneity causes higher ratio of tensile to yield strength. Therefore, decrease of the difference between the yield and tensile strengths by the ASB cycles in Fig. 24, is

Fig. 23. Tensile stress–strain curves of the tubes processed by various ASB cycles

Fig. 24. Development of the tensile properties of tubes processed by various ASB cycles
