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A finite element study of the temperature rise during equal channel angular pressing
Scripta Materialia 49 (2003) 303–308 www.actamat-journals.com
A finite element study of the temperature rise during equal channel angular pressing Q.X. Pei
a,*
, B.H. Hu b, C. Lu a, Y.Y. Wang
a
a
b
Institute of High Performance Computing, 1 Science Park Road, Singapore 117528, Singapore Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075, Singapore Received 15 January 2003; received in revised form 8 May 2003; accepted 9 May 2003
Abstract The temperature rise and temperature distribution in the workpiece during equal channel angular pressing were investigated by using the finite element method for Al–1%Mg and Al–3%Mg at different pressing speeds. The simulated temperature rise was compared with published experimental and analytical results. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Equal channel angular pressing; Finite element method; Temperature rise; Deformation heating
1. Introduction Equal channel angular pressing (ECAP) is an attractive grain-refining method to obtain bulk nanostructured materials in which grain sizes are up to about 100 nm [1,2]. During ECAP, the workpiece undergoes severe plastic deformation as it passes through the intersection of the two channels of equal cross-sectional area with a predetermined angle. Since there is no change in area, this process can be repeated to impose large cumulative strains in the materials. To analyze the deformation behavior and the related strain and strain rate distributions in the workpiece, the finite element method (FEM) has been used by some researchers [3–5]. However, the
* Corresponding author. Tel.: +65-64191225; fax: +6564191280. E-mail address: [email protected] (Q.X. Pei).
isothermal condition was assumed in those studies. Although DeLo and Semiatin [6] made nonisothermal simulations, the temperature rise in the workpiece due to deformation heating was not analyzed in their work. At a very low pressing speed, the temperature rise resulting from deformation heating is minor and thus can be ignored. However, a temperature rise of 73 K was recorded in experiment [7] with a high pressing speed of 18 mm/s. Much higher temperature rise than this one can be expected when a multi-channel or multi-pass ECAP process is employed. The temperature rise in the workpiece will change the recrystallization temperature and thus affect the grain size formed [8,9]. It is therefore necessary to analyze the deformation heating and the temperature rise during ECAP for precise control of the recrystallization temperature, and hence of the grain size. Some analytical models [9,10] based on lumped heat transfer have been proposed to quantify the temperature rise during
1359-6462/03/$ - see front matter 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6462(03)00284-7
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Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308
ECAP, however those models can only give out an average temperature rise of the workpiece and cannot give out the transient temperature change and the temperature distribution in the workpiece. Until now, no report on using FEM to study the temperature rise during ECAP has been found. In this study, the ECAP process was analyzed by FEM with the focus on the temperature rise due to deformation heating. The effects of two different aluminum alloys and various pressing speeds on the temperature rise and distribution in the workpiece during ECAP were investigated. The simulated temperature rise was compared with the experimental [7] and analytical [9] results.
2. Finite element models The simulations were carried out using the commercial FEM code ABAQUS. For simplicity, two-dimensional plane strain and heat transfer models were used. The workpiece dimensions and the ECAP die geometry are show in Fig. 1, which are same as those used in the experiments of Yamaguchi et al. [7], so that the simulated temperatures can be compared with their measured temperatures. In the earlier work, thermocouples were put at the center of the 60-mm-length work-
piece to measure the temperature rise during ECAP. The pressing speeds used in the simulations were 18.0, 1.8, and 0.18 mm/s. The initial temperatures of the die and the workpiece were 286 K. The heat generation rate due to plastic deformation, qp , is calculated by the following equation qp ¼ gp re_
ð1Þ
where e_ is the plastic strain rate; r is the flow stress; gp is the fraction of plastic deformation energy transformed into heat, which is taken to be 0.9 [11]. Two aluminum alloys of Al–1%Mg and Al– 3%Mg were used as the workpiece materials. For ECAP with high strain rate and big temperature rise, the correct material constitutive model used in the simulation is crucial to obtain accurate simulation results. The material model must be able to consider the multiplication effects of strain, strain rate, and temperature on the flow stress. Therefore, the Johnson–Cook (JC) model [12] was used in the simulations. In the JC model, the flow stress is expressed as " !# m T Tr e_ n r ¼ ðA þ Be Þ 1 þ C ln 1 Tm Tr e_0 ð2Þ where e is the equivalent plastic strain; e_ is the strain rate; e_0 is a reference strain rate; Tr is a reference temperature; Tm is the melting temperature of the material; A, B, C, n, and m are material constants. In the simulations, Tr was taken to be 286 K and Tm was 893 K. e_0 was taken to be 3.3 · 104 s1 [13]. The values of the material constants A, B, C, n, and m for both Al–1%Mg and Al–3%Mg are listed in Table 1, which are determined from the experimental data in Refs. [13–16]. The heat generation rate due to the friction between the workpiece and the ECAP die, qf , is calculated as qf ¼ gf lrn c_
Fig. 1. Schematic of the workpiece and the ECAP die.
ð3Þ
where c_ is the slip rate; rn is the normal stress at the interface between the workpiece and die; l is the friction coefficient; gf is the fraction of dissi-
Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308 Table 1 The material constants in Johnson–Cook model used in the simulations Alloy
A (MPa)
B (MPa)
C
n
m
Al– 1%Mg Al– 3%Mg
53.68
116.32
0.0234
0.266
0.78
82.54
177.46
0.0421
0.236
0.65
pation energy converted into heat, which is taken to be 0.9. The friction coefficient, l, is on the order of 0.03–0.08 in cold extrusion [17]. In the simulations, l was taken to be 0.05, considering that a lubricant was used in the YamaguchiÕs experiments. The frictional heat, qf , is assumed to be evenly distributed between the workpiece and the die, thus, half of the frictional heat is taken to be transferred to the workpiece [11]. The workpiece is modeled with the coupled thermal-structure elements, while the die and the punch are modeled with the heat capacitance elements [18]. The thermophysical properties of the Al-alloys for the workpiece and the steel for the die and the punch are listed in Table 2. The heat transfer coefficient at the interface of the workpiece and the die is dependent on the interface pressure and is taken from the experimental data [19] as shown in Table 3.
Table 2 The thermophysical properties used in the simulations Alloy
Density (kg/m3 )
Specific heat (J/kg K)
Thermal conductivity (W/m K)
Al–1%Mg Al–3%Mg Die steel
2700 2670 7750
890 890 460
200 130 –
Table 3 Heat transfer coefficient between workpiece and die Interface pressure (MPa)
Heat transfer coefficient (kW/m2 K)
0.0 0.03 0.85 14.0 85.0
0.5 0.9 4.0 6.5 7.5
305
3. Results and discussion Fig. 2 shows the simulated transient temperature distribution in the Al–1%Mg workpiece at the pressing speed of 18 mm/s. It can be seen in Fig. 2a that at a time in the initial deformation stage, the temperature in the front part of the workpiece increases to about 299 K due to the deformation heating, while most of the undeformed part remains the initial temperature of 286 K. At a time during the steady-state deformation stage, see Fig. 2b, the temperature in the deformation region reaches about 329 K. As aluminum alloy is a good thermal conductor, heat transfers from the high temperature deformation region to low temperature regions. Therefore, it can be seen that the temperature in the front part increases to about 310 K, and the temperature in the undeformed part also becomes higher. At the final stage of the ECAP process, see Fig. 2c, the temperature in the deformation region increases to about 338 K, while the temperature in the front part drops to about 307 K due to the cooling effect of the cold die. Fig. 3 shows the simulated temperature change during ECAP process at five locations in the workpiece (points 1–5 in Fig. 1) for Al–1%Mg at 18 mm/s pressing speed. It can be seen that the temperatures increase to a peak value and then drop down. The peak temperature rises at the five points are in the range of 28.4–48.7 K with the rise at point 5 being the highest. The peak temperature rise at point 1 is only about 60% of the peak temperature rise at point 5, which shows that the temperature rises at different locations of the workpiece can be very different. One reason for the different temperature rise is that heat transfers from the deformed part to the undeformed part of the workpiece, which makes the later deform at a higher temperature and thus have a higher temperature rise. Another reason is that the die is heated by the deformed part, and then the undeformed part deforms in a pre-heated die, which results in less heat loss and higher temperature rise. Fig. 4 shows the temperature change at point 3 (the central point of the workpiece) during ECAP for Al–1%Mg at three different pressing speeds: 0.18, 1.8, and 18 mm/s. As the time taken to finish the ECAP process is much longer at the pressing
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Fig. 3. The simulated temperature change at five points in the workpiece during ECAP process for Al–1%Mg at 18 mm/s pressing speed.
Fig. 4. The simulated temperature change at the central point of Al–1%Mg workpiece during ECAP process at different pressing speeds.
Fig. 2. Temperature distributions at different times during ECAP process for Al–1%Mg at the pressing speed of 18 mm/s. (a) t ¼ 0:66 s; (b) t ¼ 1:98 s; (c) t ¼ 3:30 s.
speed of 0.18 mm/s than that at 18 mm/s, the time axis of the temperature–time curves is scaled logarithmically to have a better view of the curves. It
can be seen from the curves that the pressing speed has great influence on the temperature rise. When the pressing speed is 18 mm/s, the peak temperature rise is about 44.3 K. However, when the pressing speed is 0.18 mm/s, the peak temperature rise is only about 1.0 K, which is due to lower deformation heating and more time for heat transferring from the workpiece to the die. The simulated peak temperature rise at the central point of the workpiece is compared with the measured one [7], which is listed in Table 4. In addition, the calculated peak temperature rise in Ref. [9] with the analytical model is also listed in Table 4. It can be seen that the simulated DT values are in good agreement with the measured ones for the two
Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308
307
Table 4 The peak temperature rise ðDT Þ at the center of workpiece during ECAP Alloy
Pressing speed (mm/s)
FEM simulated DT (K)
Measured [7] DT (K)
Calculated [9] DT (K)
Al–1%Mg Al–3%Mg
18.0 18.0
44.3 75.1
40.6 73.0
38.7 67.6
aluminum alloys at the pressing speed of 18 mm/s. Besides, it can be seen that the calculated DT values with the analytical model also show a good agreement with the measurements. However, the analytical model can only give out the peak temperature rise, which is assumed to be uniformly distributed in the workpiece. Compared to the analytical model, the FEM simulation can give out the transient temperature distribution and the temperature–time profiles at different locations in the workpiece. A comparison between the simulated temperature–time curve at the central point and the measured one in YamaguchiÕs experiments [7] is made in Fig. 5 for Al–3%Mg at 18 mm/s pressing speed. In YamaguchiÕs experiments, three similar temperature–time curves with a little different peak temperature rise were obtained for three Al–3%Mg specimen at 18 mm/s pressing speed. This small variation in the peak temperature rise may be due to the fact that it is very difficult to accurately control the pressing speed in the experiments, which resulted in the pressing speed a little higher or lower than 18 mm/s. To be consistent with the earlier analyses in Refs. [7,9], the average value of the three measured peak temperature rises has also
Fig. 5. Comparison of the simulated and the measured temperature–time curves for Al–3%Mg at 18 mm/s pressing speed.
been used in our comparison in Table 4. Therefore, the measured curve with the peak temperature rise being closest to the average value is chosen for the comparison in Fig. 5. In Fig. 5 the simulated temperature curve has been shifted about 2 s right to make the simulated and the measured peak temperature rises at the same time point in the graph, which gives a better view to compare the two curves. It can be seen that although there is some small difference between the two curves, a good match between them is obtained with regard to both the peak temperature rise and the curve shape. In the two curves, the temperatures increase rapidly from the initial level of 286 K to a peak value of about 360 K upon ECAP. Then the temperatures decrease to less than 293 K in about 10 s. The small difference between the two curves can be attributed to the difference between the pressing speeds in the experiment and simulation. In the simulation, a constant pressing speed of 18 mm/s was applied. However, in the experiment, the workpiece was accelerated from 0 to 18 mm/s at the start of the pressing, and the workpiece speed dropped from 18 to 0 mm/s at the end of the pressing. Therefore, it is not surprising to find that the measured temperature rise starts a little earlier than the simulated one in Fig. 5, and the measured temperature drops faster than the simulated one at the later stage of ECAP. Fig. 6 shows a comparison of the simulated and calculated [9] peak temperature rise along the central line of the workpiece at the pressing speed of 18 mm/s. It can be seen that the analytical model predicts the same temperature rise at different locations along the workpiece, because the lumped heat transfer analysis is used in the model. However, the space inhomogeneity of the temperature rise is observed with the FEM simulations. From the simulation results it can be seen that beside the much lower temperature rise at the both ends of the workpiece due to end effect, the
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Acknowledgement This work was supported by the Agency for Science, Technology and Research (A*Star), Singapore.
References
Fig. 6. Comparison of the simulated and calculated temperature rise DT along the central line of the workpiece at the pressing speed of 18 mm/s.
temperature rise at different locations in the middle of the workpiece is also different. Therefore, when using an analytical model to predict the temperature rise during ECAP, one must keep in mind that the temperature rise may be very inhomogeneous in the workpiece.
4. Conclusions 1. Finite element method has been used to study the temperature rise and temperature distribution in the workpiece during ECAP process. A good agreement between the simulated and measured temperature rise is obtained. 2. The simulation results show that the temperature rise at different locations can be very different. Therefore, the FEM simulation, instead of the lumped heat transfer analysis model, has to be used to accurately predict the temperature rise during ECAP. 3. From the simulation results it is found that both the workpiece material and the pressing speed have great influence on the temperature rise during ECAP.
[1] Suryanarayana C. Int Mater Rev 1995;40:41. [2] Valiev RZ, Islamgaliev RK, Alexandrov IV. Prog Mater Sci 2000;45:103. [3] Srinivasan R. Scripta Mater 2001;44:91. [4] Suh JY, Kim HS, Park JW, Chang JY. Scripta Mater 2001;44:677. [5] Kim HS. Mater Sci Eng A 2002;328:317. [6] DeLo DP, Semiatin SL. Metall Mater Trans A 1999;30:1391. [7] Yamaguchi D, Horita Z, Nemoto M, Langdon TG. Scripta Mater 1999;41:791. [8] Yamashita A, Yamaguchi D, Horita Z, Langdon TG. Mater Sci Eng A 2000;287:100. [9] Semiatin SL, Berbon PB, Langdon TG. Scripta Mater 2001;44:135. [10] Nishida Y, Ando T, Nagase M, Lim SW, Shigematsu I, Watazu A. Scripta Mater 2002;46:211. [11] Kobayashi S, Oh SI, Altan T. Metal forming and the finiteelement method. Oxford: Oxford University Press; 1989. p. 225-8. [12] Liang R, Khan AS. Int J Plasticity 1999;15:963. [13] Iwahashi Y, Norita Z, Nemoto M, Langdon TG. Metall Mater Trans A 1998;29:2503. [14] Ryen Ø, Holmedal B, Nes E. Mater Sci Forum 2002;396:1145. [15] Baxter GJ, Furu T, Whiteman JA, Sellars CM. Mater Sci Forum 1996;217:459. [16] Altan T, Oh SI, Gegel HL. Metal forming: fundamentals and applications. ASM, OH: Carnes Publication Services; 1992. p. 66. [17] Altan T, Oh SI, Gegel HL. Metal forming: fundamentals and applications. ASM, OH: Carnes Publication Services; 1992. p. 237. [18] ABAQUS/Explicit UserÕs Manual, Version 6.2. Hibbitt, Karlsson & Sorensen, Inc. USA, 2001. [19] Im YT, Altan T. Thermal aspects in manufacturing. In: Proceedings of the winter annual meeting of ASME, Chicago, 1988. p. 77.
A finite element study of the temperature rise during equal channel angular pressing Q.X. Pei
a,*
, B.H. Hu b, C. Lu a, Y.Y. Wang
a
a
b
Institute of High Performance Computing, 1 Science Park Road, Singapore 117528, Singapore Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075, Singapore Received 15 January 2003; received in revised form 8 May 2003; accepted 9 May 2003
Abstract The temperature rise and temperature distribution in the workpiece during equal channel angular pressing were investigated by using the finite element method for Al–1%Mg and Al–3%Mg at different pressing speeds. The simulated temperature rise was compared with published experimental and analytical results. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Equal channel angular pressing; Finite element method; Temperature rise; Deformation heating
1. Introduction Equal channel angular pressing (ECAP) is an attractive grain-refining method to obtain bulk nanostructured materials in which grain sizes are up to about 100 nm [1,2]. During ECAP, the workpiece undergoes severe plastic deformation as it passes through the intersection of the two channels of equal cross-sectional area with a predetermined angle. Since there is no change in area, this process can be repeated to impose large cumulative strains in the materials. To analyze the deformation behavior and the related strain and strain rate distributions in the workpiece, the finite element method (FEM) has been used by some researchers [3–5]. However, the
* Corresponding author. Tel.: +65-64191225; fax: +6564191280. E-mail address: [email protected] (Q.X. Pei).
isothermal condition was assumed in those studies. Although DeLo and Semiatin [6] made nonisothermal simulations, the temperature rise in the workpiece due to deformation heating was not analyzed in their work. At a very low pressing speed, the temperature rise resulting from deformation heating is minor and thus can be ignored. However, a temperature rise of 73 K was recorded in experiment [7] with a high pressing speed of 18 mm/s. Much higher temperature rise than this one can be expected when a multi-channel or multi-pass ECAP process is employed. The temperature rise in the workpiece will change the recrystallization temperature and thus affect the grain size formed [8,9]. It is therefore necessary to analyze the deformation heating and the temperature rise during ECAP for precise control of the recrystallization temperature, and hence of the grain size. Some analytical models [9,10] based on lumped heat transfer have been proposed to quantify the temperature rise during
1359-6462/03/$ - see front matter 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6462(03)00284-7
304
Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308
ECAP, however those models can only give out an average temperature rise of the workpiece and cannot give out the transient temperature change and the temperature distribution in the workpiece. Until now, no report on using FEM to study the temperature rise during ECAP has been found. In this study, the ECAP process was analyzed by FEM with the focus on the temperature rise due to deformation heating. The effects of two different aluminum alloys and various pressing speeds on the temperature rise and distribution in the workpiece during ECAP were investigated. The simulated temperature rise was compared with the experimental [7] and analytical [9] results.
2. Finite element models The simulations were carried out using the commercial FEM code ABAQUS. For simplicity, two-dimensional plane strain and heat transfer models were used. The workpiece dimensions and the ECAP die geometry are show in Fig. 1, which are same as those used in the experiments of Yamaguchi et al. [7], so that the simulated temperatures can be compared with their measured temperatures. In the earlier work, thermocouples were put at the center of the 60-mm-length work-
piece to measure the temperature rise during ECAP. The pressing speeds used in the simulations were 18.0, 1.8, and 0.18 mm/s. The initial temperatures of the die and the workpiece were 286 K. The heat generation rate due to plastic deformation, qp , is calculated by the following equation qp ¼ gp re_
ð1Þ
where e_ is the plastic strain rate; r is the flow stress; gp is the fraction of plastic deformation energy transformed into heat, which is taken to be 0.9 [11]. Two aluminum alloys of Al–1%Mg and Al– 3%Mg were used as the workpiece materials. For ECAP with high strain rate and big temperature rise, the correct material constitutive model used in the simulation is crucial to obtain accurate simulation results. The material model must be able to consider the multiplication effects of strain, strain rate, and temperature on the flow stress. Therefore, the Johnson–Cook (JC) model [12] was used in the simulations. In the JC model, the flow stress is expressed as " !# m T Tr e_ n r ¼ ðA þ Be Þ 1 þ C ln 1 Tm Tr e_0 ð2Þ where e is the equivalent plastic strain; e_ is the strain rate; e_0 is a reference strain rate; Tr is a reference temperature; Tm is the melting temperature of the material; A, B, C, n, and m are material constants. In the simulations, Tr was taken to be 286 K and Tm was 893 K. e_0 was taken to be 3.3 · 104 s1 [13]. The values of the material constants A, B, C, n, and m for both Al–1%Mg and Al–3%Mg are listed in Table 1, which are determined from the experimental data in Refs. [13–16]. The heat generation rate due to the friction between the workpiece and the ECAP die, qf , is calculated as qf ¼ gf lrn c_
Fig. 1. Schematic of the workpiece and the ECAP die.
ð3Þ
where c_ is the slip rate; rn is the normal stress at the interface between the workpiece and die; l is the friction coefficient; gf is the fraction of dissi-
Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308 Table 1 The material constants in Johnson–Cook model used in the simulations Alloy
A (MPa)
B (MPa)
C
n
m
Al– 1%Mg Al– 3%Mg
53.68
116.32
0.0234
0.266
0.78
82.54
177.46
0.0421
0.236
0.65
pation energy converted into heat, which is taken to be 0.9. The friction coefficient, l, is on the order of 0.03–0.08 in cold extrusion [17]. In the simulations, l was taken to be 0.05, considering that a lubricant was used in the YamaguchiÕs experiments. The frictional heat, qf , is assumed to be evenly distributed between the workpiece and the die, thus, half of the frictional heat is taken to be transferred to the workpiece [11]. The workpiece is modeled with the coupled thermal-structure elements, while the die and the punch are modeled with the heat capacitance elements [18]. The thermophysical properties of the Al-alloys for the workpiece and the steel for the die and the punch are listed in Table 2. The heat transfer coefficient at the interface of the workpiece and the die is dependent on the interface pressure and is taken from the experimental data [19] as shown in Table 3.
Table 2 The thermophysical properties used in the simulations Alloy
Density (kg/m3 )
Specific heat (J/kg K)
Thermal conductivity (W/m K)
Al–1%Mg Al–3%Mg Die steel
2700 2670 7750
890 890 460
200 130 –
Table 3 Heat transfer coefficient between workpiece and die Interface pressure (MPa)
Heat transfer coefficient (kW/m2 K)
0.0 0.03 0.85 14.0 85.0
0.5 0.9 4.0 6.5 7.5
305
3. Results and discussion Fig. 2 shows the simulated transient temperature distribution in the Al–1%Mg workpiece at the pressing speed of 18 mm/s. It can be seen in Fig. 2a that at a time in the initial deformation stage, the temperature in the front part of the workpiece increases to about 299 K due to the deformation heating, while most of the undeformed part remains the initial temperature of 286 K. At a time during the steady-state deformation stage, see Fig. 2b, the temperature in the deformation region reaches about 329 K. As aluminum alloy is a good thermal conductor, heat transfers from the high temperature deformation region to low temperature regions. Therefore, it can be seen that the temperature in the front part increases to about 310 K, and the temperature in the undeformed part also becomes higher. At the final stage of the ECAP process, see Fig. 2c, the temperature in the deformation region increases to about 338 K, while the temperature in the front part drops to about 307 K due to the cooling effect of the cold die. Fig. 3 shows the simulated temperature change during ECAP process at five locations in the workpiece (points 1–5 in Fig. 1) for Al–1%Mg at 18 mm/s pressing speed. It can be seen that the temperatures increase to a peak value and then drop down. The peak temperature rises at the five points are in the range of 28.4–48.7 K with the rise at point 5 being the highest. The peak temperature rise at point 1 is only about 60% of the peak temperature rise at point 5, which shows that the temperature rises at different locations of the workpiece can be very different. One reason for the different temperature rise is that heat transfers from the deformed part to the undeformed part of the workpiece, which makes the later deform at a higher temperature and thus have a higher temperature rise. Another reason is that the die is heated by the deformed part, and then the undeformed part deforms in a pre-heated die, which results in less heat loss and higher temperature rise. Fig. 4 shows the temperature change at point 3 (the central point of the workpiece) during ECAP for Al–1%Mg at three different pressing speeds: 0.18, 1.8, and 18 mm/s. As the time taken to finish the ECAP process is much longer at the pressing
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Fig. 3. The simulated temperature change at five points in the workpiece during ECAP process for Al–1%Mg at 18 mm/s pressing speed.
Fig. 4. The simulated temperature change at the central point of Al–1%Mg workpiece during ECAP process at different pressing speeds.
Fig. 2. Temperature distributions at different times during ECAP process for Al–1%Mg at the pressing speed of 18 mm/s. (a) t ¼ 0:66 s; (b) t ¼ 1:98 s; (c) t ¼ 3:30 s.
speed of 0.18 mm/s than that at 18 mm/s, the time axis of the temperature–time curves is scaled logarithmically to have a better view of the curves. It
can be seen from the curves that the pressing speed has great influence on the temperature rise. When the pressing speed is 18 mm/s, the peak temperature rise is about 44.3 K. However, when the pressing speed is 0.18 mm/s, the peak temperature rise is only about 1.0 K, which is due to lower deformation heating and more time for heat transferring from the workpiece to the die. The simulated peak temperature rise at the central point of the workpiece is compared with the measured one [7], which is listed in Table 4. In addition, the calculated peak temperature rise in Ref. [9] with the analytical model is also listed in Table 4. It can be seen that the simulated DT values are in good agreement with the measured ones for the two
Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308
307
Table 4 The peak temperature rise ðDT Þ at the center of workpiece during ECAP Alloy
Pressing speed (mm/s)
FEM simulated DT (K)
Measured [7] DT (K)
Calculated [9] DT (K)
Al–1%Mg Al–3%Mg
18.0 18.0
44.3 75.1
40.6 73.0
38.7 67.6
aluminum alloys at the pressing speed of 18 mm/s. Besides, it can be seen that the calculated DT values with the analytical model also show a good agreement with the measurements. However, the analytical model can only give out the peak temperature rise, which is assumed to be uniformly distributed in the workpiece. Compared to the analytical model, the FEM simulation can give out the transient temperature distribution and the temperature–time profiles at different locations in the workpiece. A comparison between the simulated temperature–time curve at the central point and the measured one in YamaguchiÕs experiments [7] is made in Fig. 5 for Al–3%Mg at 18 mm/s pressing speed. In YamaguchiÕs experiments, three similar temperature–time curves with a little different peak temperature rise were obtained for three Al–3%Mg specimen at 18 mm/s pressing speed. This small variation in the peak temperature rise may be due to the fact that it is very difficult to accurately control the pressing speed in the experiments, which resulted in the pressing speed a little higher or lower than 18 mm/s. To be consistent with the earlier analyses in Refs. [7,9], the average value of the three measured peak temperature rises has also
Fig. 5. Comparison of the simulated and the measured temperature–time curves for Al–3%Mg at 18 mm/s pressing speed.
been used in our comparison in Table 4. Therefore, the measured curve with the peak temperature rise being closest to the average value is chosen for the comparison in Fig. 5. In Fig. 5 the simulated temperature curve has been shifted about 2 s right to make the simulated and the measured peak temperature rises at the same time point in the graph, which gives a better view to compare the two curves. It can be seen that although there is some small difference between the two curves, a good match between them is obtained with regard to both the peak temperature rise and the curve shape. In the two curves, the temperatures increase rapidly from the initial level of 286 K to a peak value of about 360 K upon ECAP. Then the temperatures decrease to less than 293 K in about 10 s. The small difference between the two curves can be attributed to the difference between the pressing speeds in the experiment and simulation. In the simulation, a constant pressing speed of 18 mm/s was applied. However, in the experiment, the workpiece was accelerated from 0 to 18 mm/s at the start of the pressing, and the workpiece speed dropped from 18 to 0 mm/s at the end of the pressing. Therefore, it is not surprising to find that the measured temperature rise starts a little earlier than the simulated one in Fig. 5, and the measured temperature drops faster than the simulated one at the later stage of ECAP. Fig. 6 shows a comparison of the simulated and calculated [9] peak temperature rise along the central line of the workpiece at the pressing speed of 18 mm/s. It can be seen that the analytical model predicts the same temperature rise at different locations along the workpiece, because the lumped heat transfer analysis is used in the model. However, the space inhomogeneity of the temperature rise is observed with the FEM simulations. From the simulation results it can be seen that beside the much lower temperature rise at the both ends of the workpiece due to end effect, the
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Q.X. Pei et al. / Scripta Materialia 49 (2003) 303–308
Acknowledgement This work was supported by the Agency for Science, Technology and Research (A*Star), Singapore.
References
Fig. 6. Comparison of the simulated and calculated temperature rise DT along the central line of the workpiece at the pressing speed of 18 mm/s.
temperature rise at different locations in the middle of the workpiece is also different. Therefore, when using an analytical model to predict the temperature rise during ECAP, one must keep in mind that the temperature rise may be very inhomogeneous in the workpiece.
4. Conclusions 1. Finite element method has been used to study the temperature rise and temperature distribution in the workpiece during ECAP process. A good agreement between the simulated and measured temperature rise is obtained. 2. The simulation results show that the temperature rise at different locations can be very different. Therefore, the FEM simulation, instead of the lumped heat transfer analysis model, has to be used to accurately predict the temperature rise during ECAP. 3. From the simulation results it is found that both the workpiece material and the pressing speed have great influence on the temperature rise during ECAP.
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