**3.3.2 ASB samples**

Distributions of microhardness across the thickness of specimens are compared in Fig. 22. The hardness of annealed specimen before ASB is shown by a dash line. It can be seen in this figure that the hardness is increased from the inner layers to the outer ones. Two trends in the hardness evolutions during the ASB cycles can be derived from this figure. First, the degree of hardness is increased, and second, the hardness distribution across the thickness of the tubes is homogenized. Fig. 23 shows the tensile stress–strain curves of the ASBed tubes.

Tensile properties derived from these curves are summarized in Fig. 24. The yield strength (at 0.2% offset strain) and the tensile strength are increased by the ASB cycles, although the growth rate is diminished. So that, the yield strength is increased up to 194 MPa after four cycles of ASB, which is about five times higher comparing to the initial material (40 MPa). Fig. 24 also shows that the difference between the yield and the tensile strengths is slightly decreased during the ASB cycles. Regarding the rupture elongation, a sharp drop is observed after the first cycle from 38% to 9%. Decrease of the elongation at subsequent cycles is quite low as compared to that of the first cycle. Hardness distribution across the thickness of the tubes confirms that materials below the outer surface undergo heavier plastic strain in comparison to the internal ones. This is due to not only higher thickness reduction but also higher redundant strains at the outer regions (Mohebbi & Akbarzadeh, 2010c).

Although this inhomogeneous hardness distribution is observed at all specimens, its intensity is decreased by increasing the number of ASB cycles. Two reasons can be mentioned for this scheme of hardness evolution. First, at each cycle of ASB, a tube is used as internal tube and so, its severely strained external layer is located within the interior regions. By this periodical entrance of the highly deformed outer materials within the thickness, the hardness distribution becomes more homogeneous by increasing the number of ASB cycles. Second, due to saturation of dislocation density and microstructural evolutions, the hardness and strength are always saturated at large strains (Valiev et al., 2000). Therefore, despite of inhomogeneous deformation, hardness becomes homogenized at large strains.

As it can be seen in Figs. 23 and 24, the yield strength and the tensile strength of the specimens are increased by increasing the ASB cycles, although its rate is gradually diminished. Grain refinement by mentioned mechanism, i.e. increase of dislocation density and formation of subgrains at early stages as well as increase of the misorientations at next stages are responsible for this strengthening (Pirgazi et al., 2008b; Sevillano et al., 1981). While based on this mechanism a steady state plateau is expected for strength of material, Fig. 24 shows that yield and tensile strengths are continuously increased. One may conclude that the strain induced by four cycles is not enough for strength saturation, especially at high value of Z in this work. However, it is shown that this continuous increase of the strength can be attributed to the through thickness inhomogeneity of hardness. Considering the mentioned hardness evolutions, it can be said that outer materials are severely work hardened after the two first cycles in comparison to inner ones. Therefore, in spite of strength saturation of the outer material, inner material has the possibility of work hardening at following cycles. This work hardening has two effects on the tensile properties. The first effect is continuous increase of the strength. By increasing the ASB cycles, inner materials are work hardened and therefore, the strength is increased. The second effect is related to the ratio of tensile to yield strength in tensile tests. As a result of work hardening

Distributions of microhardness across the thickness of specimens are compared in Fig. 22. The hardness of annealed specimen before ASB is shown by a dash line. It can be seen in this figure that the hardness is increased from the inner layers to the outer ones. Two trends in the hardness evolutions during the ASB cycles can be derived from this figure. First, the degree of hardness is increased, and second, the hardness distribution across the thickness of the tubes is homogenized. Fig. 23 shows the tensile stress–strain curves of the ASBed

Tensile properties derived from these curves are summarized in Fig. 24. The yield strength (at 0.2% offset strain) and the tensile strength are increased by the ASB cycles, although the growth rate is diminished. So that, the yield strength is increased up to 194 MPa after four cycles of ASB, which is about five times higher comparing to the initial material (40 MPa). Fig. 24 also shows that the difference between the yield and the tensile strengths is slightly decreased during the ASB cycles. Regarding the rupture elongation, a sharp drop is observed after the first cycle from 38% to 9%. Decrease of the elongation at subsequent cycles is quite low as compared to that of the first cycle. Hardness distribution across the thickness of the tubes confirms that materials below the outer surface undergo heavier plastic strain in comparison to the internal ones. This is due to not only higher thickness reduction but also higher redundant strains at the outer regions (Mohebbi & Akbarzadeh,

Although this inhomogeneous hardness distribution is observed at all specimens, its intensity is decreased by increasing the number of ASB cycles. Two reasons can be mentioned for this scheme of hardness evolution. First, at each cycle of ASB, a tube is used as internal tube and so, its severely strained external layer is located within the interior regions. By this periodical entrance of the highly deformed outer materials within the thickness, the hardness distribution becomes more homogeneous by increasing the number of ASB cycles. Second, due to saturation of dislocation density and microstructural evolutions, the hardness and strength are always saturated at large strains (Valiev et al., 2000). Therefore, despite of inhomogeneous deformation, hardness becomes homogenized

As it can be seen in Figs. 23 and 24, the yield strength and the tensile strength of the specimens are increased by increasing the ASB cycles, although its rate is gradually diminished. Grain refinement by mentioned mechanism, i.e. increase of dislocation density and formation of subgrains at early stages as well as increase of the misorientations at next stages are responsible for this strengthening (Pirgazi et al., 2008b; Sevillano et al., 1981). While based on this mechanism a steady state plateau is expected for strength of material, Fig. 24 shows that yield and tensile strengths are continuously increased. One may conclude that the strain induced by four cycles is not enough for strength saturation, especially at high value of Z in this work. However, it is shown that this continuous increase of the strength can be attributed to the through thickness inhomogeneity of hardness. Considering the mentioned hardness evolutions, it can be said that outer materials are severely work hardened after the two first cycles in comparison to inner ones. Therefore, in spite of strength saturation of the outer material, inner material has the possibility of work hardening at following cycles. This work hardening has two effects on the tensile properties. The first effect is continuous increase of the strength. By increasing the ASB cycles, inner materials are work hardened and therefore, the strength is increased. The second effect is related to the ratio of tensile to yield strength in tensile tests. As a result of work hardening

**3.3.2 ASB samples** 

tubes.

2010c).

at large strains.

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 mostly related to the hardness homogenization.

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

Nanostructure, Texture Evolution and Mechanical Properties of

boundaries at the next stages.

**5. Acknowledgments** 

**6. References** 

University of technology is also acknowledged.

*Technology*, Vol. 137, pp. 10–16

*Engineering A*, Vol. 428, pp. 351–357

*Engineering A*, Vol. 406, pp. 279–285

54, pp. 1691–1696

*Processing Technology*, Vol. 177, pp. 582–586

Aluminum Alloys Processed by Severe Plastic Deformation 455

almost homogeneous, but with increasing the number of cycles the intensity of the copper

It is demonstrated that due to incremental deformation in ASB process, high value of strain rate without considerable temperature rise is applied, leading to a high degree of Zener– Hollomon parameter, as a characteristic of this SPD process. The grain structure of commercially pure aluminum is refined by this process and an average grain thickness and length of 186 and 419 nm are developed after the four cycles of ASB, respectively. TEM micrographs and SAD patterns as well as the EBSD analysis indicate that this grain refinement occurred by formation of subgrains at early stages of severe deformation followed by increase of the misorientations by transition of low angle to high angle grain

The characterization of mechanical properties revealed that the strength of the aluminum sheets considerably increased by the first two ARB cycles which is attributed to work hardening caused by increase in dislocation density and formation of subgrains. It was also included that the strength of ARBed aluminum sheets obeys the Hall–Petch relationship and corresponds well with microstructural variations. Microhardness distributions across the thickness of the tubes illustrate that because of high equivalent strain at outer regions, the hardness is increased from the inner regions to the outer ones. Due to periodical entrance of the external layer within the thickness and the consequent hardness saturation, the hardness and its homogeneity is increased with increase of the ASB cycles. The yield and tensile strengths of the material are significantly increased up to the values of 194 and 235 MPa, respectively. The scheme of hardness development leads to decrease of the ratio of tensile

strength to yield strength and consequently to decrease of the uniform elongation.

Professors Leo Kestens and Roumen Petrov's permission for access to EBSD analysis and their help in the EBSD mapping and discussion about the texture analysis, at Ghent University in Belgium, are gratefully acknowledged. The author would like to express his sincere gratitude to Mr. Hadi Pirgazi and Mr. M.S. Mohebbi for their excellent research works at Sharif University led to this manuscript. The support of research office of Sharif

Berski, S., Dyja, H., Maranda, A., Nowaczewski, J. & Banaszek, G. (2006). *Journal of Materials* 

Chen, Z., Ikeda, K., Murakami, T, Takeda, T., Xie, J.X. (2003). *Journal of Materials Processing* 

Chowdhury, S.G., Srivastava, V.C., Ravikumar, B. & Soren, S. (2006a). *Scripta Materialia*, Vol.

Chowdhury, S.G., Dutta, A., Ravikumar, B. & Kumar, A. (2006b). *Materials Science and* 

Costa, A.L.M., Reis, A.C.C., Kestens, L. & Andrade, M.S. (2005). *Materials Science and* 

component gradually grows at the expense of the brass and S components.

Fig. 24 demonstrates a severe drop in elongation after the first cycle of ASB while its rate of reduction is very low at next cycles. This result is similar to the reported ones for ARB (Lee et al., 2002; Pirgazi et al., 2008b). Uniform elongation, which is reduced by increasing the ASB cycles, is related to onset of the plastic instability or necking. Plastic instability, on the other hand, is a function of work hardening and consequently, of the ratio of tensile to yield strength (Semiatin & Jonas, 1984). Therefore, it can be said that since this ratio is decreased by increasing the ASB cycles, the uniform elongation is decreased. In other words, inner materials of specimens after the early cycles of ASB, whose work hardening is not saturated, are work hardened during the tensile test, leading to delay in necking. At next cycles, due to saturation of work hardening across the entire thickness, plastic instability starts earlier and causes a less uniform elongation.

It is seen in Fig. 23 that post-uniform elongation includes a considerable portion of the total elongation. Previous studies on SPD have demonstrated that strain rate sensitivity of fcc metals increases by decreasing the grain size (Wang & Ma, 2004; Wei et al., 2004). High strain rate sensitivity, on the other hand, causes the increase of both uniform and post uniform elongations (Semiatin & Jonas, 1984). Takata et al. (2008) have illustrated that uniform elongation of commercially pure aluminum increases with increasing the strain rate in the specimens with a grain size larger than 1 μm, while post-uniform elongation increases with increasing the strain rate in the sub-micrometer grain size specimens. Therefore, it can be concluded that high strain rate sensitivity is effective on post-uniform elongation of aluminum with sub-micron grains. In fact, the high magnitude of post-uniform elongation in Fig. 23 can be mostly related to the high strain rate sensitivity.
