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Deformation behavior in Simple Shear Extrusion (SSE) as a new severe plastic deformation technique
Materials Science and Engineering A 527 (2009) 355–360
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation behavior in Simple Shear Extrusion (SSE) as a new severe plastic deformation technique N. Pardis, R. Ebrahimi ∗ Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 3 May 2009 Received in revised form 3 August 2009 Accepted 25 August 2009
Keywords: Simple Shear Extrusion Severe plastic deformation Finite element analysis Shear strain Equivalent strain Back-pressure
a b s t r a c t A new method for severe plastic deformation is proposed herein, entitled as Simple Shear Extrusion (SSE) due to the manner in which specimen’s cross-section shape changes. This method is based on pressing material through a specially designed direct extrusion die. The process was investigated experimentally on commercially pure aluminum. Additionally, simulation of the process was also carried out, using the commercial finite element code ABAQUS/Explicit. Moreover, effect of back-pressure on the results was studied. Results show that SSE method is capable of imposing high strain values via strain accumulation during repeating the process, which is of great importance in producing ultrafine-grained or nanostructured materials. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ultrafine-grained (UFG) materials are considered as the subject of many scientific studies due to their unique physical and mechanical properties. Among different approaches in processing these materials, severe plastic deformation (SPD) methods are of more interest since they provide bulk nanostructured materials with no contamination or porosity [1–3]. Different SPD techniques have been proposed such as equal-channel angular pressing (ECAP) [2], high pressure torsion (HPT) [3], multi-axial compressions/forging (MAC/F) [4] and twist extrusion (TE) [5] for processing bulk materials, and constrained groove pressing (CGP) [6] and accumulative roll bonding (ARB) [7] for processing sheet materials. These are all based on different methods of imposing strain on a specimen without changing its dimensions. This provides the capability to repeat the process for more cycles, attaining high strain values in order to introduce a high density of dislocations and eventually resulting in UFG structures [2]. Among these methods, many researches have been conducted on ECAP and HPT [2], which might be due to their simplicity or capability to produce exceptional grain refinement to at least the submicron level [3]. This fact has reduced interests for carrying out detailed investigation of alternative methods, or efforts to present novel methods which might be more efficient. In this paper, a new SPD technique is introduced for the first time,
∗ Corresponding author. Tel.: +98 711 2307293; fax: +98 711 2307293. E-mail address: [email protected] (R. Ebrahimi). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.08.051
which is called Simple Shear Extrusion (SSE). There are some similarities between this technique and twist extrusion method, as both are based on direct extrusion and they can be easily installed on any standard extrusion equipment or set in industrial production lines [8]. Furthermore, the amount of waste material at the front and rear of samples is significantly reduced in comparison to ECAP processed samples [8]. However, SSE and TE are basically different in the way the specimen deforms through extrusion channel. Moreover, there is a symmetrical distribution of strain across the specimen and normal to direction of extrusion in SSE samples, with the higher strain values at the center of specimen and reducing to lower values towards the periphery. This is quite different from what is reported for TE samples in which higher values of strain appear to be at the periphery and decreasing towards the central point [9,10]. In this paper, deformation behavior of material during SSE is studied and the above statements and the effect of back-pressure on the results are investigated. 2. Principles of Simple Shear Extrusion method SSE is based on pressing the specimen through a direct channel with a specific shape. As the specimen passes through the channel it deforms gradually while its cross-section area remains constant. This allows repeating the process successively which is one of the main requirements of SPD processes. A scheme of SSE processing is illustrated in Fig. 1. In this process, samples are chosen with square cross section. By passing through the extrusion channel, the material undergoes
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According to Mises criterion the strain value can be calculated as well: εeff. = √ = 1.15 3
(2)
These values are equal to those obtained from ECAP in which ˚ = /2 and = 0 where ˚ and represent the channel angle and the angle associated with the arc of curvature respectively [11]. In practice, the theoretical value of strain in SSE is expected to be obtained by imposing proper amount of back-pressure which facilitates the process of grain refinement as well. It also makes it possible to deform materials with low workability to higher values of strain [2,12]. Based on Eqs. (1) and (2), it is possible to attain different equivalent strain values per pass by changing the maximum distortion angle (˛), which is considered as /4 in this paper.
3. Experimental procedures
Fig. 1. Schematic presentation of Simple Shear Extrusion processing and geometry of extrusion channel in a die.
Fig. 2. Gradual change in specimen’s cross section while passing through the deformation channel.
shear deformation from square cross-section shape at the channel inlet to a parallelogram shape with maximum distortion angle (˛) in middle of the channel, and back to square at the outlet (Fig. 1). In this study, maximum distortion angle ˛ is considered as /4. The gradual change in the cross-sectional shape of the sample is illustrated in Fig. 2. Since there is no change in the cross-sectional area throughout the channel, there is no tendency for elongation, and thus the final shape and dimensions remain unchanged. Therefore, by repeating the process successively, it is possible to reach a high degree of strain. In order to calculate the strain in this process, the initially square planar section normal to direction of extrusion is studied. This element deforms under shear while passing through the first half of the channel. The same shear strain is accumulated as the element deforms back to its initial configuration, while passing through the second half of the channel (Fig. 3). Therefore, for SSE process with ˛ = /4 the shear strain, , is given by: = 2 tan(˛) = 2 tan
4
=2
Billets of 10 mm × 10 mm cross section by 30 mm long were machined out of commercially pure aluminum (AA1050) and then annealed at 600 ◦ C for 2 h and furnace cooled at a rate of 25 ◦ C/h. Aluminum samples were then wrapped with Teflon tape and also silicon sprayed to reduce friction. SSE processing was carried out using a screw press with ram speed of 0.2 mm/s at room temperature. In the die used, the length of deformation zone was considered as 60 mm, which can be filled by inserting either a 60 mm long or two 30 mm long samples. Accordingly, a 60 mm length aluminum sample was extruded and stopped during the process to show the in situ geometry of the workpiece, as illustrated in Fig. 4. Microhardness measurements were taken on a plane normal to the extrusion direction for first pass SSE and annealed specimens in which a load of 25 g was applied with rate of 0.2 g s−1 and 15 s dwell time. The Vickers microhardness, Hv , was recorded along horizontal and vertical lines AB and CD respectively (Fig. 5) with an incremental step of 0.5 mm. In addition, double compression test [13] was performed in which compression specimens with the same geometry were machined out two specimens, one being annealed and the other pre-strained, both compressed simultaneously. This test is originally presented as a method for determination of material’s strain-hardening exponent by considering the amount of pre-strain and difference in height of specimens after the test. However, SSE specimens can be considered as being pre-strained in double compression test. Therefore, by performing this test on annealed and first pass SSE samples, and knowing material strain-hardening exponent, the average strain value for first pass specimen was determined experimentally.
(1)
Fig. 3. Illustration of a planar section of specimen normal to extrusion direction.
Fig. 4. Specimens before and during Simple Shear Extrusion process.
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test, were considered in the simulation. The lubrication condition used in experimental procedure, led to friction factor m = 0.1 at the die-sample interface which was determined by barrel compression test [14]. Therefore, in order to apply this value in simulation, it was converted to friction coefficient = 0.02 by using the following relation [15]: =
m
27(1 − m2 )
(3)
8-node linear brick elements (C3D8R) were used to mesh the billet, and 4-node 3-D bilinear rigid quadrilateral elements (R3D4) for die rigid parts [16]. In addition, a 0.5 mm radius fillet was assigned to the longitudinal edges of the billet to avoid distortion of elements adjacent to this region. Initial cross section of a meshed sample is illustrated in Fig. 5. 5. Results and discussion
Fig. 5. Initial cross section of a meshed sample normal to extrusion direction.
Fig. 6. Comparison of load-displacement curves obtained by experiment and simulation.
4. Finite element analysis procedure The commercial finite element code, ABAQUS, was used to simulate and investigate characteristics of deformation in this new process. Simulation was performed using 3-D models in which the geometrical dimensions and mechanical properties of specimens in the simulation were the same as those of the experiment, making it possible to compare the simulation results with those obtained experimentally. Therefore, billets with dimensions of 10 mm × 10 mm × 30 mm and stress–strain relationship as = 106ε0.347 (MPa), experimentally obtained from compression
The experimental processing load is compared with that predicted by simulation to verify the validity of simulation as illustrated in Fig. 6. This curve can be divided into three regions, the first of which represents the load required for the first specimen as it fills the first half of the deformation channel. As the second specimen pushes the first one to the second half of the channel, the load increases which is observed in the second region of the diagram. By pressing the third sample to the channel, the first one exits from the other side of the die. Since the die is completely filled with samples, the load reaches the steady state condition. It is observed that there is an acceptable compatibility between simulation and experimental load curves. In addition, the final shape of the billet obtained by experiment, is compared with simulation results as illustrated in Fig. 7. There is a good consistence between the final shape of the experimented billet and the geometry of FEM simulation result. The final shape of a specimen processed by ECAP with ˚ = /2 and = 0 as predicted by simulation was compared with those of SSE specimens. The geometrical dimension and mechanical properties of the samples were the same in simulation of both processes. Moreover, the processing conditions such as friction coefficient, ram speed, etc. were held constant to make the comparison possible. Referring to Fig. 8, it is observed that the amount of waste material is considerably lower for samples processed by SSE than ECAP. Fig. 9 illustrates the experimental cross section of a sample before and after processing by SSE method without back-pressure. As seen in this figure, the material has not completely filled the channel and complete deformation has not occurred. A similar case is also reported for processing materials by TE with application of no back-pressure [17]. Therefore, the effect of different values of backpressure on strain distribution and the final shape of specimen’s cross section was studied.
Fig. 7. Comparison between finial shape of samples obtained experimentally (right) and predicted by simulation (left).
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Fig. 10. Variation of shear strain at the center of specimen’s cross section along extrusion channel.
Fig. 8. Comparison between finial shape of ECAP and SSE samples and assessment of waste material. (a) SSE experimental result, (b) SSE simulation result, (c) ECAP simulation result.
Fig. 10 illustrates the variation of shear strain at the center of cross section from the beginning to the end of deformation channel (M-N) obtained by finite element simulation. The effect of different values of back-pressure is illustrated in this figure and compared with the theoretical curve which is obtained by = tan(˛) with consideration of angle (˛) at every section of the die. As can be seen, the theoretical shear strain reaches to = 1 at the midway of the channel where the die angle (˛) is /4 and decreases to zero in the
second half of the channel as the specimen deforms by the same amount of shear strain in the reverse direction. In case of deforming a specimen with no back-pressure the shear strain reaches the average value of = 0.7, which is lower than theoretically expected ( = 1), and continues to decrease but not to zero as expected theoretically. By increasing back-pressure, the maximum value of the shear strain increases to higher values and the curve approaches the theoretical one. This implies that application of back-pressure increases the tendency for deformation in reverse manner at the second half of the die to fill the channel completely. Distribution of equivalent strain in the specimen’s cross section along horizontal line AB and vertical line CD (Fig. 5) are presented in Figs. 11 and 12 respectively. From these figures which are obtained by simulation, it is observed that the equivalent strain distribution is symmetrical and higher at center of the specimen and slightly decreases to the periphery. The geometrical nature of this process imposes such distribution of strain in the specimen’s cross section. At the first half of the deformation channel, the die geometry forces the sample to move laterally in simple shear manner. This results in development of strain along a diagonal line from upper right corner to the lower left corner (Fig. 5). At the second half of the channel, this phenomenon occurs in reverse manner, in which strain
Fig. 9. Cross section of samples normal to extrusion direction before (left) and after (right) processing by SSE without back-pressure.
N. Pardis, R. Ebrahimi / Materials Science and Engineering A 527 (2009) 355–360
Fig. 11. Distribution of equivalent strain in the cross section of sample along line AB.
Fig. 12. Distribution of equivalent strain in the cross section of sample along line CD.
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contours propagate along the other diagonal line from upper left corner to the lower right corner. As a result, the value of strain at the center of specimen’s cross section is higher and decreases towards periphery in a symmetrical manner. In addition, application of back-pressure has generally increased the average value of strain. However, increasing the amount of back-pressure has no significant effect on the strain values at locations near upper and lower die walls (points C and D). This might be due to the effect of friction at the upper and lower die walls which prevents the material from deforming in simple shear manner. Therefore, there is no tendency for elongation of materials at these positions (C and D) and application of back-pressure has no significant effect on strain values near these regions. But, these regions are very small and ignorable when compared with the whole area of cross section as shown in Fig. 13. This figure illustrates the distribution of strain in the cross section of specimen normal to extrusion direction for sample processed by SSE with 100 MPa back-pressure. The uniform and symmetrical distribution of equivalent strain, together with higher values of strain at the center of specimen can be considered as major advantage of this method especially as compared with TE. Effect of back-pressure on material flow and sample’s crosssectional shape in the middle and end of process is shown in Fig. 14. Increasing back-pressure to 150 MPa can fill the gap in the die which was shown previously to be effective on shear and equivalent strain values as well. Moreover, it is observed that the major mode of deformation in this method is simple shear, which is considered as the optimal deformation mode in SPD techniques [18]. Knowing material’s strain-hardening exponent (n = 0.347), double compression test [13] was performed on annealed and first pass SSE specimens which revealed the average strain value per pass as ε¯ ave. = 0.83. Referring to Figs. 11 and 12 it is concluded that such value is nearly close to the average strain values obtainable by
Fig. 13. Strain distribution in the cross section of a sample processed with 100 MPa back-pressure.
Fig. 14. Effect of back-pressure on cross-sectional shape of samples in the middle and end of process.
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Fig. 15. Hardness profiles in the cross section of annealed and single pass SSE samples along lines AB and CD (Fig. 5).
tion. Results show that this method is capable of imposing strain to the material without any significant change in specimen’s shape and geometrical dimensions, depending on application of proper amount of back-pressure. The latter, enhances the average value of strain and can facilitate approaching the theoretical strain values. Comparison of the final shape of samples processed by ECAP and SSE revealed that SSE is more beneficial as the amount of waste material is negligible compared to those of ECAP. In addition, the symmetric manner of deformation, results in a symmetrical distribution of strain in specimen’s cross section which is a great advantage of this method compared to other SPD techniques. On the whole, further experiments are needed for better understanding of the process, the effect of repeating cycles of SSE and also the effect of applying different processing routes on microstructural and mechanical properties, which are the subject of authors undergoing studies. References
imposing back-pressure values of 30–50 MPa. Although no backpressure system was applied in this experiment, some amount of back-pressure practically exists due to the fact that each sample forces the previous one through the deformation channel. Fig. 15 shows values of the Vickers microhardness on the crosssectional plane after processing by SSE through first pass, which were recorded along lines AB and CD (Fig. 5). The lower dashed line indicates a microhardness of Hv ≈ 30 recorded for the material in the initial annealed condition. In this figure the hardness variation is symmetrical and highest at the center of specimen (Hv ≈ 50). This distribution of hardness provides good compatibility with strain distribution along lines AB and CD (Figs. 11 and 12). In addition, the increase in hardness values after first pass SSE is comparable with those reported for materials processed by ECAP [19,20], HPT [21] and TE [17]. 6. Conclusion In conclusion, SSE is introduced as a new SPD process in this paper which is suitable for deforming bulk materials to extremely large strains. Simulation of the process was carried out using ABAQUS/explicit to investigate deformation behavior of material. In addition, aluminum samples were processed by this method and experimental results were used to verify the validity of simula-
[1] R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov, Prog. Mater. Sci. 45 (2000) 103–189. [2] R.Z. Valiev, T.G. Langdon, Prog. Mater. Sci. 51 (2006) 881–981. [3] A.P. Zhilyaev, T.G. Langdon, Prog. Mater. Sci. 53 (2008) 893–979. [4] A.K. Gosh, U.S. Patent 4,721,537, January 26, 1988. [5] Y. Beygelzimer, V. Varyukhin, S. Synkov, D. Orlov, Mater. Sci. Eng. A 503 (2009) 14–17. [6] D.H. Shin, J.J. Park, Y.S. Kim, K.T. Park, Mater. Sci. Eng. A. 328 (2002) 98–103. [7] Y. Saito, N. Tsuji, H. Utsunomiya, T. Sakai, R.G. Hong, Scr. Mater. 39 (1998) 1221–1227. [8] Y. Beygelzimer, D. Orlov1, A. Korshunov, S. Synkov, V. Varyukhin, I. Vedernikova, A. Reshetov, A. Synkov, L. Polyakov, I. Korotchenkova, Solid State Phenomena 114 (2006) 69–78. [9] D. Orlov, Y. Beygelzimer, S. Synkov, V. Varyukhin, Z. Horita, Mater. Trans. 49 (2008) 2–6. [10] Y. Beygelzimer, A. Reshetov, S. Synkov, O. Prokof’eva, R. Kulagin, J. Mater. Process. Technol. 209 (2009) 3650–3656. [11] Y. Iwahashi, J. Wang, Z. Horita, M. Nemoto, T.G. Langdon, Scr. Mater. 35 (1996) 143–146. [12] R.Y. Lapovok, J. Mater. Sci. 40 (2005) 341–346. [13] R. Ebrahimi, N. Pardis, Mater. Sci. Eng. A 518 (2009) 56–60. [14] R. Ebrahimi, A. Najafizadeh, J. Mater. Process. Technol. 152 (2004) 136–143. [15] N. Bay, J. Mech. Work. Technol. 14 (1987) 203–223. [16] Abaqus/Explicit User’s Manual, Version 6.3, Hibbitt, Karlsson & Sorensen, Inc., USA, 2002. [17] D. Orlov, Y. Beygelzimer, S. Synkov, V. Varyukhin, N. Tsuji, Z. Horita, Mater. Sci. Eng. A 519 (2009) 105–111. [18] V.M. Segal, Mater. Sci. Eng. A 338 (2002) 331–344. [19] X.G. Qiao, M.J. Starink, N. Gao, Mater. Sci. Eng. A 513–514 (2009) 52–58. [20] C. Xu, T.G. Langdon, J. Mater. Sci. 42 (2007) 1542–1550. [21] C. Xu, Z. Horita, T.G. Langdon, Acta Mater. 55 (2007) 203–212.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation behavior in Simple Shear Extrusion (SSE) as a new severe plastic deformation technique N. Pardis, R. Ebrahimi ∗ Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 3 May 2009 Received in revised form 3 August 2009 Accepted 25 August 2009
Keywords: Simple Shear Extrusion Severe plastic deformation Finite element analysis Shear strain Equivalent strain Back-pressure
a b s t r a c t A new method for severe plastic deformation is proposed herein, entitled as Simple Shear Extrusion (SSE) due to the manner in which specimen’s cross-section shape changes. This method is based on pressing material through a specially designed direct extrusion die. The process was investigated experimentally on commercially pure aluminum. Additionally, simulation of the process was also carried out, using the commercial finite element code ABAQUS/Explicit. Moreover, effect of back-pressure on the results was studied. Results show that SSE method is capable of imposing high strain values via strain accumulation during repeating the process, which is of great importance in producing ultrafine-grained or nanostructured materials. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ultrafine-grained (UFG) materials are considered as the subject of many scientific studies due to their unique physical and mechanical properties. Among different approaches in processing these materials, severe plastic deformation (SPD) methods are of more interest since they provide bulk nanostructured materials with no contamination or porosity [1–3]. Different SPD techniques have been proposed such as equal-channel angular pressing (ECAP) [2], high pressure torsion (HPT) [3], multi-axial compressions/forging (MAC/F) [4] and twist extrusion (TE) [5] for processing bulk materials, and constrained groove pressing (CGP) [6] and accumulative roll bonding (ARB) [7] for processing sheet materials. These are all based on different methods of imposing strain on a specimen without changing its dimensions. This provides the capability to repeat the process for more cycles, attaining high strain values in order to introduce a high density of dislocations and eventually resulting in UFG structures [2]. Among these methods, many researches have been conducted on ECAP and HPT [2], which might be due to their simplicity or capability to produce exceptional grain refinement to at least the submicron level [3]. This fact has reduced interests for carrying out detailed investigation of alternative methods, or efforts to present novel methods which might be more efficient. In this paper, a new SPD technique is introduced for the first time,
∗ Corresponding author. Tel.: +98 711 2307293; fax: +98 711 2307293. E-mail address: [email protected] (R. Ebrahimi). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.08.051
which is called Simple Shear Extrusion (SSE). There are some similarities between this technique and twist extrusion method, as both are based on direct extrusion and they can be easily installed on any standard extrusion equipment or set in industrial production lines [8]. Furthermore, the amount of waste material at the front and rear of samples is significantly reduced in comparison to ECAP processed samples [8]. However, SSE and TE are basically different in the way the specimen deforms through extrusion channel. Moreover, there is a symmetrical distribution of strain across the specimen and normal to direction of extrusion in SSE samples, with the higher strain values at the center of specimen and reducing to lower values towards the periphery. This is quite different from what is reported for TE samples in which higher values of strain appear to be at the periphery and decreasing towards the central point [9,10]. In this paper, deformation behavior of material during SSE is studied and the above statements and the effect of back-pressure on the results are investigated. 2. Principles of Simple Shear Extrusion method SSE is based on pressing the specimen through a direct channel with a specific shape. As the specimen passes through the channel it deforms gradually while its cross-section area remains constant. This allows repeating the process successively which is one of the main requirements of SPD processes. A scheme of SSE processing is illustrated in Fig. 1. In this process, samples are chosen with square cross section. By passing through the extrusion channel, the material undergoes
356
N. Pardis, R. Ebrahimi / Materials Science and Engineering A 527 (2009) 355–360
According to Mises criterion the strain value can be calculated as well: εeff. = √ = 1.15 3
(2)
These values are equal to those obtained from ECAP in which ˚ = /2 and = 0 where ˚ and represent the channel angle and the angle associated with the arc of curvature respectively [11]. In practice, the theoretical value of strain in SSE is expected to be obtained by imposing proper amount of back-pressure which facilitates the process of grain refinement as well. It also makes it possible to deform materials with low workability to higher values of strain [2,12]. Based on Eqs. (1) and (2), it is possible to attain different equivalent strain values per pass by changing the maximum distortion angle (˛), which is considered as /4 in this paper.
3. Experimental procedures
Fig. 1. Schematic presentation of Simple Shear Extrusion processing and geometry of extrusion channel in a die.
Fig. 2. Gradual change in specimen’s cross section while passing through the deformation channel.
shear deformation from square cross-section shape at the channel inlet to a parallelogram shape with maximum distortion angle (˛) in middle of the channel, and back to square at the outlet (Fig. 1). In this study, maximum distortion angle ˛ is considered as /4. The gradual change in the cross-sectional shape of the sample is illustrated in Fig. 2. Since there is no change in the cross-sectional area throughout the channel, there is no tendency for elongation, and thus the final shape and dimensions remain unchanged. Therefore, by repeating the process successively, it is possible to reach a high degree of strain. In order to calculate the strain in this process, the initially square planar section normal to direction of extrusion is studied. This element deforms under shear while passing through the first half of the channel. The same shear strain is accumulated as the element deforms back to its initial configuration, while passing through the second half of the channel (Fig. 3). Therefore, for SSE process with ˛ = /4 the shear strain, , is given by: = 2 tan(˛) = 2 tan
4
=2
Billets of 10 mm × 10 mm cross section by 30 mm long were machined out of commercially pure aluminum (AA1050) and then annealed at 600 ◦ C for 2 h and furnace cooled at a rate of 25 ◦ C/h. Aluminum samples were then wrapped with Teflon tape and also silicon sprayed to reduce friction. SSE processing was carried out using a screw press with ram speed of 0.2 mm/s at room temperature. In the die used, the length of deformation zone was considered as 60 mm, which can be filled by inserting either a 60 mm long or two 30 mm long samples. Accordingly, a 60 mm length aluminum sample was extruded and stopped during the process to show the in situ geometry of the workpiece, as illustrated in Fig. 4. Microhardness measurements were taken on a plane normal to the extrusion direction for first pass SSE and annealed specimens in which a load of 25 g was applied with rate of 0.2 g s−1 and 15 s dwell time. The Vickers microhardness, Hv , was recorded along horizontal and vertical lines AB and CD respectively (Fig. 5) with an incremental step of 0.5 mm. In addition, double compression test [13] was performed in which compression specimens with the same geometry were machined out two specimens, one being annealed and the other pre-strained, both compressed simultaneously. This test is originally presented as a method for determination of material’s strain-hardening exponent by considering the amount of pre-strain and difference in height of specimens after the test. However, SSE specimens can be considered as being pre-strained in double compression test. Therefore, by performing this test on annealed and first pass SSE samples, and knowing material strain-hardening exponent, the average strain value for first pass specimen was determined experimentally.
(1)
Fig. 3. Illustration of a planar section of specimen normal to extrusion direction.
Fig. 4. Specimens before and during Simple Shear Extrusion process.
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test, were considered in the simulation. The lubrication condition used in experimental procedure, led to friction factor m = 0.1 at the die-sample interface which was determined by barrel compression test [14]. Therefore, in order to apply this value in simulation, it was converted to friction coefficient = 0.02 by using the following relation [15]: =
m
27(1 − m2 )
(3)
8-node linear brick elements (C3D8R) were used to mesh the billet, and 4-node 3-D bilinear rigid quadrilateral elements (R3D4) for die rigid parts [16]. In addition, a 0.5 mm radius fillet was assigned to the longitudinal edges of the billet to avoid distortion of elements adjacent to this region. Initial cross section of a meshed sample is illustrated in Fig. 5. 5. Results and discussion
Fig. 5. Initial cross section of a meshed sample normal to extrusion direction.
Fig. 6. Comparison of load-displacement curves obtained by experiment and simulation.
4. Finite element analysis procedure The commercial finite element code, ABAQUS, was used to simulate and investigate characteristics of deformation in this new process. Simulation was performed using 3-D models in which the geometrical dimensions and mechanical properties of specimens in the simulation were the same as those of the experiment, making it possible to compare the simulation results with those obtained experimentally. Therefore, billets with dimensions of 10 mm × 10 mm × 30 mm and stress–strain relationship as = 106ε0.347 (MPa), experimentally obtained from compression
The experimental processing load is compared with that predicted by simulation to verify the validity of simulation as illustrated in Fig. 6. This curve can be divided into three regions, the first of which represents the load required for the first specimen as it fills the first half of the deformation channel. As the second specimen pushes the first one to the second half of the channel, the load increases which is observed in the second region of the diagram. By pressing the third sample to the channel, the first one exits from the other side of the die. Since the die is completely filled with samples, the load reaches the steady state condition. It is observed that there is an acceptable compatibility between simulation and experimental load curves. In addition, the final shape of the billet obtained by experiment, is compared with simulation results as illustrated in Fig. 7. There is a good consistence between the final shape of the experimented billet and the geometry of FEM simulation result. The final shape of a specimen processed by ECAP with ˚ = /2 and = 0 as predicted by simulation was compared with those of SSE specimens. The geometrical dimension and mechanical properties of the samples were the same in simulation of both processes. Moreover, the processing conditions such as friction coefficient, ram speed, etc. were held constant to make the comparison possible. Referring to Fig. 8, it is observed that the amount of waste material is considerably lower for samples processed by SSE than ECAP. Fig. 9 illustrates the experimental cross section of a sample before and after processing by SSE method without back-pressure. As seen in this figure, the material has not completely filled the channel and complete deformation has not occurred. A similar case is also reported for processing materials by TE with application of no back-pressure [17]. Therefore, the effect of different values of backpressure on strain distribution and the final shape of specimen’s cross section was studied.
Fig. 7. Comparison between finial shape of samples obtained experimentally (right) and predicted by simulation (left).
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Fig. 10. Variation of shear strain at the center of specimen’s cross section along extrusion channel.
Fig. 8. Comparison between finial shape of ECAP and SSE samples and assessment of waste material. (a) SSE experimental result, (b) SSE simulation result, (c) ECAP simulation result.
Fig. 10 illustrates the variation of shear strain at the center of cross section from the beginning to the end of deformation channel (M-N) obtained by finite element simulation. The effect of different values of back-pressure is illustrated in this figure and compared with the theoretical curve which is obtained by = tan(˛) with consideration of angle (˛) at every section of the die. As can be seen, the theoretical shear strain reaches to = 1 at the midway of the channel where the die angle (˛) is /4 and decreases to zero in the
second half of the channel as the specimen deforms by the same amount of shear strain in the reverse direction. In case of deforming a specimen with no back-pressure the shear strain reaches the average value of = 0.7, which is lower than theoretically expected ( = 1), and continues to decrease but not to zero as expected theoretically. By increasing back-pressure, the maximum value of the shear strain increases to higher values and the curve approaches the theoretical one. This implies that application of back-pressure increases the tendency for deformation in reverse manner at the second half of the die to fill the channel completely. Distribution of equivalent strain in the specimen’s cross section along horizontal line AB and vertical line CD (Fig. 5) are presented in Figs. 11 and 12 respectively. From these figures which are obtained by simulation, it is observed that the equivalent strain distribution is symmetrical and higher at center of the specimen and slightly decreases to the periphery. The geometrical nature of this process imposes such distribution of strain in the specimen’s cross section. At the first half of the deformation channel, the die geometry forces the sample to move laterally in simple shear manner. This results in development of strain along a diagonal line from upper right corner to the lower left corner (Fig. 5). At the second half of the channel, this phenomenon occurs in reverse manner, in which strain
Fig. 9. Cross section of samples normal to extrusion direction before (left) and after (right) processing by SSE without back-pressure.
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Fig. 11. Distribution of equivalent strain in the cross section of sample along line AB.
Fig. 12. Distribution of equivalent strain in the cross section of sample along line CD.
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contours propagate along the other diagonal line from upper left corner to the lower right corner. As a result, the value of strain at the center of specimen’s cross section is higher and decreases towards periphery in a symmetrical manner. In addition, application of back-pressure has generally increased the average value of strain. However, increasing the amount of back-pressure has no significant effect on the strain values at locations near upper and lower die walls (points C and D). This might be due to the effect of friction at the upper and lower die walls which prevents the material from deforming in simple shear manner. Therefore, there is no tendency for elongation of materials at these positions (C and D) and application of back-pressure has no significant effect on strain values near these regions. But, these regions are very small and ignorable when compared with the whole area of cross section as shown in Fig. 13. This figure illustrates the distribution of strain in the cross section of specimen normal to extrusion direction for sample processed by SSE with 100 MPa back-pressure. The uniform and symmetrical distribution of equivalent strain, together with higher values of strain at the center of specimen can be considered as major advantage of this method especially as compared with TE. Effect of back-pressure on material flow and sample’s crosssectional shape in the middle and end of process is shown in Fig. 14. Increasing back-pressure to 150 MPa can fill the gap in the die which was shown previously to be effective on shear and equivalent strain values as well. Moreover, it is observed that the major mode of deformation in this method is simple shear, which is considered as the optimal deformation mode in SPD techniques [18]. Knowing material’s strain-hardening exponent (n = 0.347), double compression test [13] was performed on annealed and first pass SSE specimens which revealed the average strain value per pass as ε¯ ave. = 0.83. Referring to Figs. 11 and 12 it is concluded that such value is nearly close to the average strain values obtainable by
Fig. 13. Strain distribution in the cross section of a sample processed with 100 MPa back-pressure.
Fig. 14. Effect of back-pressure on cross-sectional shape of samples in the middle and end of process.
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Fig. 15. Hardness profiles in the cross section of annealed and single pass SSE samples along lines AB and CD (Fig. 5).
tion. Results show that this method is capable of imposing strain to the material without any significant change in specimen’s shape and geometrical dimensions, depending on application of proper amount of back-pressure. The latter, enhances the average value of strain and can facilitate approaching the theoretical strain values. Comparison of the final shape of samples processed by ECAP and SSE revealed that SSE is more beneficial as the amount of waste material is negligible compared to those of ECAP. In addition, the symmetric manner of deformation, results in a symmetrical distribution of strain in specimen’s cross section which is a great advantage of this method compared to other SPD techniques. On the whole, further experiments are needed for better understanding of the process, the effect of repeating cycles of SSE and also the effect of applying different processing routes on microstructural and mechanical properties, which are the subject of authors undergoing studies. References
imposing back-pressure values of 30–50 MPa. Although no backpressure system was applied in this experiment, some amount of back-pressure practically exists due to the fact that each sample forces the previous one through the deformation channel. Fig. 15 shows values of the Vickers microhardness on the crosssectional plane after processing by SSE through first pass, which were recorded along lines AB and CD (Fig. 5). The lower dashed line indicates a microhardness of Hv ≈ 30 recorded for the material in the initial annealed condition. In this figure the hardness variation is symmetrical and highest at the center of specimen (Hv ≈ 50). This distribution of hardness provides good compatibility with strain distribution along lines AB and CD (Figs. 11 and 12). In addition, the increase in hardness values after first pass SSE is comparable with those reported for materials processed by ECAP [19,20], HPT [21] and TE [17]. 6. Conclusion In conclusion, SSE is introduced as a new SPD process in this paper which is suitable for deforming bulk materials to extremely large strains. Simulation of the process was carried out using ABAQUS/explicit to investigate deformation behavior of material. In addition, aluminum samples were processed by this method and experimental results were used to verify the validity of simula-
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