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Investigation into equal channel angular extrusion process of billet with internal defects
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
journal homepage: www.elsevier.com/locate/jmatprotec
Investigation into equal channel angular extrusion process of billet with internal defects Dyi-Cheng Chen ∗ , Ching-Pin Chen Department of Industrial Education and Technology, National Changhua University of Education, Changhua 500, Taiwan, ROC
a r t i c l e
i n f o
a b s t r a c t
Article history:
The shear plastic deformation behavior of a material during equal channel angular (ECA)
Received 13 January 2006
extrusion is governed primarily by the die geometry, the material properties, and the process
Received in revised form
conditions. This study uses the commercial DEFORMTM 2D (two-dimensional) rigid-plastic
26 October 2007
finite element code to investigate the plastic deformation behavior of materials with inter-
Accepted 8 November 2007
nal defective voids during 1- and 2-turn ECA extrusion processing. The present simulations investigate the damage factor distributions, the total velocity distributions, the rotation angle distributions, the void dimension, and the stress–strain distributions around the
Keywords:
defective voids under various extrusion conditions. The mesh element increase of the bil-
Equal channel angular (ECA)
let mesh in the 2-turn ECA extrusion process is also investigated. The present numerical
extrusion
results provide valuable insights into the shear plastic deformation behavior of materials
Rigid-plastic finite element
containing defective voids in the ECA extrusion process.
Defective voids
1.
Introduction
Methods of severe plastic deformation such as rolling, extrusion and forging are those in which materials are subjected to a very high strains with the subsequent changes in physical and mechanical properties. It has long been known that there are significant benefits to be gained from deforming metallic alloys under very high plastic strains. The equal channel angular (ECA) extrusion or ECA pressing was first developed by Segal (1977) and Segal et al. (1981) as a process for introducing large plastic strains in a metal without a substantial change in the outer dimensions of the workpiece. Liu et al. (2000) presented the novel changing channel extrusion (CCE) method, which was designed to reduce the tensile stress and increase the hydrostatic pressure in the workpiece during extrusion. Rosochowski and Olejnik (2002) employed a finite element method to investigate the mechanisms involved in the 2-turn equal ECA extrusion process. In the ECA extrusion process, the workpiece is extruded through two or more inter-
∗
Corresponding author. Fax: +886 4 7211287. E-mail address: [email protected] (D.-C. Chen). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.066
© 2007 Elsevier B.V. All rights reserved.
connecting channels, which are typically orientated at angles of between 90◦ and 135◦ to one another. Iwahashi et al. (1996) reported that ECA pressing is a simple and attractive procedure for producing materials with ultra-fine grain size. Wu and Baker (1997) found that the shear strain accumulation in the workpiece after three passes through a 90◦ round-corned jig is equivalent to that accumulated after seven passes through a 120◦ round-cornered jig. Prangnell et al. (1997) employed the DEFORMTM code to perform finite element simulations of the ECA extrusion process. The validity of the numerical results was demonstrated by comparing the FE modeling results with the shape changes observed in a commercial pure aluminum (99.75% Al) sample following partial passage through a steel die with an internal angle of 100◦ . Srinivasan (2001) established that the magnitude of the maximum strain in a single pass through a die is determined by the value of round-cornered. Suh et al. (2001) developed a simple two-dimensional plane strain model to investigate the material flow in ECA pressing. Segal (1999) investigated
420
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Table 1 – The stress–strain relationship of the aluminum A1100 flow stress = f (temperature 550 ◦ C, strain rate 4, strain) (MPa)
Nomenclature k m Sw f Vw
the local flow stress in shear the friction factor the tractional boundary surface of the workpiece the volume of the workpiece
Greek symbols ˛ the work-hardening effect constant the magnitude of the shear strain ε the effective strain per pass the internal angle between the two die channels
the stress, strain, and shear developed in multi-pass ECA extrusion processing and analyzed the steady and localized material flows. Bowen et al. (2000) reported that the strain induced in the workpiece is related to the die angle, the friction conditions, and the application of a back pressure. These factors are all known to have a significant effect on the microstructure and strain inhomogeneity within the processed billet. Kim et al. (2000) and Kim (2001) performed finite element analysis using DEFORMTM 2D to investigate the corner gap formation between the die and the workpiece during the plane strain ECA pressing process. The present study also uses the commercial DEFORMTM 2D software, and analyzes the plastic deformation behavior of materials with internal defective voids during 1- and 2-turn ECA extrusion.
Strain
Strain rate 4
0.105 0.223 0.338 0.512 0.695
18.169 19.82 20.963 20.548 20.519
of the literature suggests that a finite element analysis of the passage of a sample through an ECA extrusion die has yet to be reported. According to Segal (1999), the deformation behavior in ECA extrusion is characterized by homogeneous plane shear throughout the majority of the sample. Hence, the effective strain per pass, ε, is given by 2 ε = √ cot 3
(1)
2
where is the internal angle between the two die channels (see Fig. 1). Under these conditions, the magnitude of the shear strain, , is calculated as = 2 cot
(2)
2
According to Kim and Yang (1985), the finite element formulation for rigid-plastic deformation in a material subject to a work-hardening effect is given by
2.
Analytical method
Although the deformation process in ECA extrusion has been treated analytically (Iwahashi et al., 1996; Segal, 1999), a review
(+˛t ¯ ε¯˙ H )ıε¯˙ dV+K
Vw
where ¯ =
ε˙ v ı˙εv dV − Sw
Vw
(3/2)ij ij , ε¯˙ =
f
(f + ˛fi )ıvi dS=0 (3)
(2/3)˙εij ε˙ ij , and ε˙ v = ε˙ ii . Further-
more, K, ij , H
and ˛ are the penalty constant, deviatoric stress, strain-hardening rate and the work-hardening effect constant (0 ˛ 1), respectively. Finally, Vw and Sw are the volume and f tractional boundary surface of the workpiece, respectively. The frictional boundary condition is given by Yoon and Yang (1988) and Chen and Kobayashi (1978): 2 f = − mk tan−1
Fig. 1 – Schematic view of ECA extrusion process.
|V | s
u0
t
(4)
where m is the friction factor, k is the local flow stress in shear and u0 is a positive number whose value is very small compared to |Vs |. Vs is the velocity vector of the workpiece relative to the die and t is the unit vector in the direction of Vs . An initial velocity field can be generated by assuming the billet to be a linear viscous material. The velocity boundary conditions and the frictional boundary conditions on an arbitrarily curved surface are imposed via the successive application of a skew boundary condition (Yoon and Yang, 1988; Yang et al., 1989). This study applies the commercial finite element code DEFORMTM 2D to simulate the plastic deformation behavior during the ECA extrusion processing of a material with internal defective voids. The finite element code is based on the
421
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Table 2 – ECA extrusion conditions for defective void simulations No. Void diameter do (mm) Friction factor m The internal angle between the two die channels (◦ ) Temperature (◦ C) Billet dimension
Fig. 2 – Load prediction history in 1-turn ECA extrusion (˚ = 150◦ ).
flow formulation approach using an updated Lagrangian procedure. A direct iteration method and the Newton–Raphson method are employed to solve the nonlinear equations in the finite element software. The direct iteration method is used to generate a suitable initial estimate for the Newton–Raphson method. The Newton–Raphson method is then employed to obtain a rapid final convergence. The convergence criteria for the iteration procedure are defined as the velocity error norm v/v 0.001 and the force error norm F/F 0.01, where v is (vT v)1/2 . The modeling formulations of various ductility damage values are available in Klocke et al. (2002). The present study considers the normalized C&L criterion damage values presented below:
normalized C&L criterion : 0
ε¯ f
max d¯ε = C ¯
(5)
where max is the maximum ductility stress, ¯ is the effective stress, ε¯ is the effective strain, ε¯ f is the effective strain of fracture, and C is the damage value of the material. The Eq. (5) was integrated with ε¯ calculated by simulation instead of ε¯ f . The C value must be experimented on various ECA extrusion with internal defects in the future work.
Case 1–2 0.1–0.25 120–150
550 18 mm × 18 mm × 100 mm
stress–strain relationship of the aluminum A1100 is presented in Table 1. Fig. 2 plots the variation of the extrusion force during the 1-turn ECA extrusion processing of an aluminum A1100 billet with an internal void. Initially, the extrusion force increases monotonously until the die is completely filled by the billet. Following a period during which the extrusion force remains relatively stable, plastic strain and strain-hardening effects cause the extrusion force to increase to a maximum value of approximately 65 N. As the internal void flows into the angled region between the two flow channels (˚ = 150◦ in this case), the extrusion force reduces. The maximum reduction of the extrusion force is approximately 30% of the maximum extrusion force.
4.
Results and discussion
The ECA extrusion conditions used in the current numerical simulations are presented in Table 2. Fig. 3 shows the damage distribution within an aluminum A1100 billet containing an internal void defect during the 1-turn ECA extrusion process (˚ = 135◦ ) for normalized C&L criterion judgement norms. The simulated extrusion conditions are as follows: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion damage distribution is clearly greater in the void region of the billet. Fig. 4(a) and (b) shows the effective stress distribution within the aluminum A1100 billet for different increase step
3. Mesh configuration of ECA extrusion material The current study makes the following assumptions: (1) the container and the die are rigid bodies; (2) the extrusion billet is a rigid-plastic material; and (3) the friction factors between the extrusion billet and the ram, container, and die are constant. Fig. 1 presents a schematic illustration of the ECA extrusion processing of a material with an internal semicircular defective void, where ˚ indicates the internal angle between the two flow channels. The defective void is internal semi-circular in the ECA extrusion billet. The present simulations assumed the billet to be aluminum A1100. The
Fig. 3 – Damage distribution in 1-turn ECA extrusion (˚ = 135◦ ).
422
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Fig. 4 – Effective stress distribution within billet for different increase step of inner and outer of channel (˚ = 150◦ ).
of the inner and outer of the channel. In both cases, the simulations consider the 1-turn ECA extrusion process and apply the following extrusion conditions: void diameter d0 = 2 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion effective stress distribution is clearly greater in the void region of the billet in the inner and outer of the channel. It can be seen that the effective stress is slightly larger in the inner void region. Fig. 5(a) and (b) shows the mesh distributions within the aluminum A1100 billet for dies with different internal angles. In both cases, the simulations consider the 2-turn ECA extrusion process and assume the following extrusion conditions: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion mesh distribution is clearly much finer in the 2-turn ECA extrusion process than in the 1turn ECA extrusion process. Furthermore, it can be seen that the mesh element increase of the billet is refined as it passes around the second turn of the channel. Fig. 6 shows the rotation angle distribution within the aluminum A1100 billet during the 2-turn ECA extrusion process. In this case, the extrusion conditions are as follows: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C.
Fig. 5 – FEM mesh distribution within billet for different internal angle.
The average rotation angle is found to be 40.8◦ after the first turn. However, the average rotation angle is −5.3◦ after the second turn. Consequently, a mesh element increasing is generated in metallic alloys extruded using the ECA extrusion
Fig. 6 – Distribution of rotation angle in 2-turn ECA extrusion (˚ = 120◦ ).
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
423
Fig. 7 – Void dimension within billet for different internal angle.
process because of the very high plastic strains involved and the rotation angles induced in the billet. Fig. 7 shows the void dimension within billet for different internal angle. In this case, the extrusion conditions are as follows: void diameter d0 = 2 mm, friction factor m = 0.25, billet A1100 and temperature 550 ◦ C. The ECA extrusion void dimension is clearly much smaller in the ˚ = 120◦ ECA extrusion process than in the ˚ = 135◦ and 150◦ ECA extrusion process.
Furthermore, it can be seen that the void size of the billet is closed as it passes around less than ˚ = 120◦ of the channel.
5.
Conclusions
This study has utilized DEFORMTM 2D finite element code to examine the plastic deformation behavior of an aluminum
424
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
alloy containing internal defects during equal channel angular (ECA) extrusion. The numerical results have shown that: (1) the maximum reduction in the extrusion force is approximately 30% of the maximum extrusion force; (2) the effective stress distribution is clearly greater in the void region of the billet in the inner and outer of the channel; (3) the mesh element distribution is significantly increasing in the 2-turn ECA extrusion process than in the 1-turn ECA extrusion process; and (4) the void dimension is clearly much smaller in the ˚ = 120◦ ECA extrusion process than in the ˚ = 135◦ and 150◦ ECA extrusion process. The present numerical results provide valuable insights into the shear plastic deformation behavior of materials containing defective voids in the ECA extrusion process.
references
Bowen, J.R., Gholinia, A., Roberts, S.M., Prangnell, P.B., 2000. Mater. Sci. Eng. A 287, 87–99. Chen, C.C., Kobayashi, S., 1978. ASME, AMD 28, 163.
Iwahashi, Y., Wang, J., Horita, Z., Nemoto, M., Langdon, T.G., 1996. Scripta Mater. 35 (2), 143–146. Kim, H.S., 2001. Mater. Sci. Eng. A 315, 122–128. Kim, Y.J., Yang, D.Y., 1985. Int. J. Mech. Sci. 27, 487. Kim, H.S., Seo, M.H., Hong, S.I., 2000. Mater. Sci. Eng. A 291, 86–90. Klocke, F., Breuer, D., Raedt, H., 2002. Proceedings of the 7th ICTP, Advanced Technology of Plasticity, vol. 1, Yokohama, Japan, p. 721. Liu, Z.Y., Liu, G., Wang, Z.R., 2000. J. Mater. Process. Technol. 102, 30–32. Prangnell, P.B., Harris, C., Roberts, S.M., 1997. Scripta Mater. 37 (7), 983–989. Rosochowski, A., Olejnik, L., 2002. J. Mater. Process. Technol. 125–126, 309–316. Segal, V.M., 1997. USSR Patent 575892. Segal, V.M., 1999. Mater. Sci. Eng. A 271, 322–333. Segal, V.M., Reznikov, V.I., Drobyshevskiy, A.E., Kopylov, V.I., 1981. Russ. Metall. 1 (99). Srinivasan, R., 2001. Scripta Mater. 44, 91–96. Suh, J.Y., Kim, H.S., Park, J.W., Chang, J.Y., 2001. Scripta Mater. 44, 677–681. Wu, Y., Baker, I., 1997. Scripta Mater. 37 (4), 437–442. Yang, D.Y., Lee, C.M., Yoon, J.H., 1989. Int. J. Mech. Sci. 31, 145. Yoon, J.H., Yang, D.Y., 1988. Int. J. Mech. Sci. 30, 997.
journal homepage: www.elsevier.com/locate/jmatprotec
Investigation into equal channel angular extrusion process of billet with internal defects Dyi-Cheng Chen ∗ , Ching-Pin Chen Department of Industrial Education and Technology, National Changhua University of Education, Changhua 500, Taiwan, ROC
a r t i c l e
i n f o
a b s t r a c t
Article history:
The shear plastic deformation behavior of a material during equal channel angular (ECA)
Received 13 January 2006
extrusion is governed primarily by the die geometry, the material properties, and the process
Received in revised form
conditions. This study uses the commercial DEFORMTM 2D (two-dimensional) rigid-plastic
26 October 2007
finite element code to investigate the plastic deformation behavior of materials with inter-
Accepted 8 November 2007
nal defective voids during 1- and 2-turn ECA extrusion processing. The present simulations investigate the damage factor distributions, the total velocity distributions, the rotation angle distributions, the void dimension, and the stress–strain distributions around the
Keywords:
defective voids under various extrusion conditions. The mesh element increase of the bil-
Equal channel angular (ECA)
let mesh in the 2-turn ECA extrusion process is also investigated. The present numerical
extrusion
results provide valuable insights into the shear plastic deformation behavior of materials
Rigid-plastic finite element
containing defective voids in the ECA extrusion process.
Defective voids
1.
Introduction
Methods of severe plastic deformation such as rolling, extrusion and forging are those in which materials are subjected to a very high strains with the subsequent changes in physical and mechanical properties. It has long been known that there are significant benefits to be gained from deforming metallic alloys under very high plastic strains. The equal channel angular (ECA) extrusion or ECA pressing was first developed by Segal (1977) and Segal et al. (1981) as a process for introducing large plastic strains in a metal without a substantial change in the outer dimensions of the workpiece. Liu et al. (2000) presented the novel changing channel extrusion (CCE) method, which was designed to reduce the tensile stress and increase the hydrostatic pressure in the workpiece during extrusion. Rosochowski and Olejnik (2002) employed a finite element method to investigate the mechanisms involved in the 2-turn equal ECA extrusion process. In the ECA extrusion process, the workpiece is extruded through two or more inter-
∗
Corresponding author. Fax: +886 4 7211287. E-mail address: [email protected] (D.-C. Chen). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.066
© 2007 Elsevier B.V. All rights reserved.
connecting channels, which are typically orientated at angles of between 90◦ and 135◦ to one another. Iwahashi et al. (1996) reported that ECA pressing is a simple and attractive procedure for producing materials with ultra-fine grain size. Wu and Baker (1997) found that the shear strain accumulation in the workpiece after three passes through a 90◦ round-corned jig is equivalent to that accumulated after seven passes through a 120◦ round-cornered jig. Prangnell et al. (1997) employed the DEFORMTM code to perform finite element simulations of the ECA extrusion process. The validity of the numerical results was demonstrated by comparing the FE modeling results with the shape changes observed in a commercial pure aluminum (99.75% Al) sample following partial passage through a steel die with an internal angle of 100◦ . Srinivasan (2001) established that the magnitude of the maximum strain in a single pass through a die is determined by the value of round-cornered. Suh et al. (2001) developed a simple two-dimensional plane strain model to investigate the material flow in ECA pressing. Segal (1999) investigated
420
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Table 1 – The stress–strain relationship of the aluminum A1100 flow stress = f (temperature 550 ◦ C, strain rate 4, strain) (MPa)
Nomenclature k m Sw f Vw
the local flow stress in shear the friction factor the tractional boundary surface of the workpiece the volume of the workpiece
Greek symbols ˛ the work-hardening effect constant the magnitude of the shear strain ε the effective strain per pass the internal angle between the two die channels
the stress, strain, and shear developed in multi-pass ECA extrusion processing and analyzed the steady and localized material flows. Bowen et al. (2000) reported that the strain induced in the workpiece is related to the die angle, the friction conditions, and the application of a back pressure. These factors are all known to have a significant effect on the microstructure and strain inhomogeneity within the processed billet. Kim et al. (2000) and Kim (2001) performed finite element analysis using DEFORMTM 2D to investigate the corner gap formation between the die and the workpiece during the plane strain ECA pressing process. The present study also uses the commercial DEFORMTM 2D software, and analyzes the plastic deformation behavior of materials with internal defective voids during 1- and 2-turn ECA extrusion.
Strain
Strain rate 4
0.105 0.223 0.338 0.512 0.695
18.169 19.82 20.963 20.548 20.519
of the literature suggests that a finite element analysis of the passage of a sample through an ECA extrusion die has yet to be reported. According to Segal (1999), the deformation behavior in ECA extrusion is characterized by homogeneous plane shear throughout the majority of the sample. Hence, the effective strain per pass, ε, is given by 2 ε = √ cot 3
(1)
2
where is the internal angle between the two die channels (see Fig. 1). Under these conditions, the magnitude of the shear strain, , is calculated as = 2 cot
(2)
2
According to Kim and Yang (1985), the finite element formulation for rigid-plastic deformation in a material subject to a work-hardening effect is given by
2.
Analytical method
Although the deformation process in ECA extrusion has been treated analytically (Iwahashi et al., 1996; Segal, 1999), a review
(+˛t ¯ ε¯˙ H )ıε¯˙ dV+K
Vw
where ¯ =
ε˙ v ı˙εv dV − Sw
Vw
(3/2)ij ij , ε¯˙ =
f
(f + ˛fi )ıvi dS=0 (3)
(2/3)˙εij ε˙ ij , and ε˙ v = ε˙ ii . Further-
more, K, ij , H
and ˛ are the penalty constant, deviatoric stress, strain-hardening rate and the work-hardening effect constant (0 ˛ 1), respectively. Finally, Vw and Sw are the volume and f tractional boundary surface of the workpiece, respectively. The frictional boundary condition is given by Yoon and Yang (1988) and Chen and Kobayashi (1978): 2 f = − mk tan−1
Fig. 1 – Schematic view of ECA extrusion process.
|V | s
u0
t
(4)
where m is the friction factor, k is the local flow stress in shear and u0 is a positive number whose value is very small compared to |Vs |. Vs is the velocity vector of the workpiece relative to the die and t is the unit vector in the direction of Vs . An initial velocity field can be generated by assuming the billet to be a linear viscous material. The velocity boundary conditions and the frictional boundary conditions on an arbitrarily curved surface are imposed via the successive application of a skew boundary condition (Yoon and Yang, 1988; Yang et al., 1989). This study applies the commercial finite element code DEFORMTM 2D to simulate the plastic deformation behavior during the ECA extrusion processing of a material with internal defective voids. The finite element code is based on the
421
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Table 2 – ECA extrusion conditions for defective void simulations No. Void diameter do (mm) Friction factor m The internal angle between the two die channels (◦ ) Temperature (◦ C) Billet dimension
Fig. 2 – Load prediction history in 1-turn ECA extrusion (˚ = 150◦ ).
flow formulation approach using an updated Lagrangian procedure. A direct iteration method and the Newton–Raphson method are employed to solve the nonlinear equations in the finite element software. The direct iteration method is used to generate a suitable initial estimate for the Newton–Raphson method. The Newton–Raphson method is then employed to obtain a rapid final convergence. The convergence criteria for the iteration procedure are defined as the velocity error norm v/v 0.001 and the force error norm F/F 0.01, where v is (vT v)1/2 . The modeling formulations of various ductility damage values are available in Klocke et al. (2002). The present study considers the normalized C&L criterion damage values presented below:
normalized C&L criterion : 0
ε¯ f
max d¯ε = C ¯
(5)
where max is the maximum ductility stress, ¯ is the effective stress, ε¯ is the effective strain, ε¯ f is the effective strain of fracture, and C is the damage value of the material. The Eq. (5) was integrated with ε¯ calculated by simulation instead of ε¯ f . The C value must be experimented on various ECA extrusion with internal defects in the future work.
Case 1–2 0.1–0.25 120–150
550 18 mm × 18 mm × 100 mm
stress–strain relationship of the aluminum A1100 is presented in Table 1. Fig. 2 plots the variation of the extrusion force during the 1-turn ECA extrusion processing of an aluminum A1100 billet with an internal void. Initially, the extrusion force increases monotonously until the die is completely filled by the billet. Following a period during which the extrusion force remains relatively stable, plastic strain and strain-hardening effects cause the extrusion force to increase to a maximum value of approximately 65 N. As the internal void flows into the angled region between the two flow channels (˚ = 150◦ in this case), the extrusion force reduces. The maximum reduction of the extrusion force is approximately 30% of the maximum extrusion force.
4.
Results and discussion
The ECA extrusion conditions used in the current numerical simulations are presented in Table 2. Fig. 3 shows the damage distribution within an aluminum A1100 billet containing an internal void defect during the 1-turn ECA extrusion process (˚ = 135◦ ) for normalized C&L criterion judgement norms. The simulated extrusion conditions are as follows: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion damage distribution is clearly greater in the void region of the billet. Fig. 4(a) and (b) shows the effective stress distribution within the aluminum A1100 billet for different increase step
3. Mesh configuration of ECA extrusion material The current study makes the following assumptions: (1) the container and the die are rigid bodies; (2) the extrusion billet is a rigid-plastic material; and (3) the friction factors between the extrusion billet and the ram, container, and die are constant. Fig. 1 presents a schematic illustration of the ECA extrusion processing of a material with an internal semicircular defective void, where ˚ indicates the internal angle between the two flow channels. The defective void is internal semi-circular in the ECA extrusion billet. The present simulations assumed the billet to be aluminum A1100. The
Fig. 3 – Damage distribution in 1-turn ECA extrusion (˚ = 135◦ ).
422
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
Fig. 4 – Effective stress distribution within billet for different increase step of inner and outer of channel (˚ = 150◦ ).
of the inner and outer of the channel. In both cases, the simulations consider the 1-turn ECA extrusion process and apply the following extrusion conditions: void diameter d0 = 2 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion effective stress distribution is clearly greater in the void region of the billet in the inner and outer of the channel. It can be seen that the effective stress is slightly larger in the inner void region. Fig. 5(a) and (b) shows the mesh distributions within the aluminum A1100 billet for dies with different internal angles. In both cases, the simulations consider the 2-turn ECA extrusion process and assume the following extrusion conditions: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C. The ECA extrusion mesh distribution is clearly much finer in the 2-turn ECA extrusion process than in the 1turn ECA extrusion process. Furthermore, it can be seen that the mesh element increase of the billet is refined as it passes around the second turn of the channel. Fig. 6 shows the rotation angle distribution within the aluminum A1100 billet during the 2-turn ECA extrusion process. In this case, the extrusion conditions are as follows: void diameter d0 = 1 mm, friction factor m = 0.1, and temperature 550 ◦ C.
Fig. 5 – FEM mesh distribution within billet for different internal angle.
The average rotation angle is found to be 40.8◦ after the first turn. However, the average rotation angle is −5.3◦ after the second turn. Consequently, a mesh element increasing is generated in metallic alloys extruded using the ECA extrusion
Fig. 6 – Distribution of rotation angle in 2-turn ECA extrusion (˚ = 120◦ ).
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
423
Fig. 7 – Void dimension within billet for different internal angle.
process because of the very high plastic strains involved and the rotation angles induced in the billet. Fig. 7 shows the void dimension within billet for different internal angle. In this case, the extrusion conditions are as follows: void diameter d0 = 2 mm, friction factor m = 0.25, billet A1100 and temperature 550 ◦ C. The ECA extrusion void dimension is clearly much smaller in the ˚ = 120◦ ECA extrusion process than in the ˚ = 135◦ and 150◦ ECA extrusion process.
Furthermore, it can be seen that the void size of the billet is closed as it passes around less than ˚ = 120◦ of the channel.
5.
Conclusions
This study has utilized DEFORMTM 2D finite element code to examine the plastic deformation behavior of an aluminum
424
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 4 ( 2 0 0 8 ) 419–424
alloy containing internal defects during equal channel angular (ECA) extrusion. The numerical results have shown that: (1) the maximum reduction in the extrusion force is approximately 30% of the maximum extrusion force; (2) the effective stress distribution is clearly greater in the void region of the billet in the inner and outer of the channel; (3) the mesh element distribution is significantly increasing in the 2-turn ECA extrusion process than in the 1-turn ECA extrusion process; and (4) the void dimension is clearly much smaller in the ˚ = 120◦ ECA extrusion process than in the ˚ = 135◦ and 150◦ ECA extrusion process. The present numerical results provide valuable insights into the shear plastic deformation behavior of materials containing defective voids in the ECA extrusion process.
references
Bowen, J.R., Gholinia, A., Roberts, S.M., Prangnell, P.B., 2000. Mater. Sci. Eng. A 287, 87–99. Chen, C.C., Kobayashi, S., 1978. ASME, AMD 28, 163.
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