Materials Transactions, Vol. 45, No. 7 (2004) pp. 2165 to 2171 Special Issue on Ultrafine Grained Structures #2004 The Japan Institute of Metals
Finite Element Investigation of Equal Channel Angular Extrusion Process Jeong-Ho Lee, Il-Heon Son and Yong-Taek Im* Computer Aided Materials Processing Laboratory, Department of Mechanical Engineering, ME3227, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Daejeon 305-701, Korea In this study, the effect of material properties on deformation pattern and strain distribution of the commercially-available pure titanium (CP-Ti) specimen during an equal channel angular extrusion (ECAE) was investigated. Finite element analyses were carried out for twodimensional plane strain condition at elevated temperatures. Material properties were assumed by hardening, softening, and no hardening behaviors based on the measured experiment data. The effects of friction conditions, die geometries, and processing routes were also examined under the same processing condition. Based on the value of average strain and standard deviation of the strain distribution, the magnitude and uniformity of deformation was determined depending on process conditions. In addition, damage parameters based on plastic work and Cockroft and Latham criteria were calculated to check the likeliness of surface cracking. Finally, non-isothermal analyses were carried out to explore the effect of processing temperature in the ECAE process. (Received November 25, 2003; Accepted April 28, 2004) Keywords: equal channel angular extrusion, finite element analysis
1.
Introduction
The ECAE process is a recently developed technique that induces severe plastic shear deformation without changing the cross-sectional shape of the workpiece.1) As this technique greatly refines the grain size, it is an effective method of obtaining materials with high strength and toughness. Also, it is desirable to make the deformation pattern and strain distribution as uniform as possible to obtain rather homogeneous mechanical properties of the final product. The main advantage of the ECAE process compared with other forming processes is that multi-pass operations can be carried out without changing the cross-sectional shape. Thus, the workpiece can undergo different processing routes as it is rotated between passes and the strain is accumulated. Thus, the processing route is a very important factor that directly influences the deformation pattern and strain distribution in the final deformed workpiece. Many studies of the ECAE process have been conducted experimentally so far, following the theoretical work by Segal.2) In this work, the required load and imposed strain were calculated by neglecting frictions at the die interface. Iwahashi et al.3) extended the work of Segal for general shaped die geometry and Furukawa et al.4) evaluated the shearing characteristics and patterns for the multi-pass ECAE process. Kamachi et al.5) compared the strain distribution and deformed geometry between theoretical and experimental results of the ECAE process. Also Stolyarov et al.6) carried out the experiments with CP-Ti and proposed optimal processing conditions to obtain better physical and mechanical properties. For better understanding of the deformation behavior numerically, Prangnell et al.7) presented a simplified finite element model neglecting the frictional effect and Bowen et al.8) studied deformation behavior of the billet under various conditions by both finite element analyses and experiments. Semiatin et al.9) investigated the effect of material properties *Corresponding
author, E-mail:
[email protected]
and die geometries on deformation pattern and surface cracking by numerical simulations. Delo and Semiatin10) have demonstrated the instability of deformation in the hot ECAE process due to softening behavior. Kim et al.11) also numerically investigated the plastic flow and deformation during the ECAE. Kamachi et al.12) and Horita et al.13) reported that the Vickers hardness distribution can be considered to be globally uniform in the specimen after the ECAE process. However, they reported some inhomogeneity in microstructure or wavy and ill-defined grain boundaries, respectively. On the other hand, Chung et al.14) found that the distribution of Vickers hardness was inhomogeneous and that it was qualitatively consistent with the strain distribution obtained from finite volume method simulation results. Thus, further investigation of the strain distribution which will affect both the distribution of hardness and microstructure is required. In this study, the effects of various ECAE process parameters were examined using finite element analyses. For verification of these simulations, the stress components obtained from numerical results were first compared to the reported results by Semiatin et al.9) from the literature. In addition, experimentally obtained values of the Vickers hardness in three cross-sections of a circular ECAE specimen were compared to the three-dimensional non-isothermal simulation results of strain distribution. For examination of the effects of various ECAE process parameters such as material properties, friction conditions, die geometries, and processing routes on deformation behavior and strain distribution, numerous two-dimensional finite element analyses under the plane-strain and isothermal conditions were carried out. However, in the actual ECAE process temperature of the workpiece rises due to heat generation by plastic and frictional work.15) Thus, the nonisothermal analysis was carried out to investigate the effect of processing temperature. For numerical investigations, the material property was determined by compression test using Thermecmaster at various temperatures and strain rates.16) Based on the measured data, the effect of material properties on deformation during the process was investigated by
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J.-H. Lee, I.-H. Son and Y.-T. Im 600
Processing routes: A route : no rotation
500
300°C
Stress, σ/MPa
C route : 180° rotation
Processing Temperature: 300°C, 450°C, 600°C
Φ=90°
z
Material properties: · σ = K ε nε
y
m
K : strength coefficient n : strain hardenability m : strain rate sensitivity
Shear friction factor (mf): 0°, 45°, 90°
τ = − mf k
450°C 300
500°C
550°C 600°C
200
0 0.0
τ : friction stress mf : shear friction factor k : shear strength
Fig. 1 The ECAE process parameters used in FE simulations.
400°C
400
100
x Die Corner angles (Ψ):
350°C
·
ε = 1s–1 0.1
0.2
0.3
0.4
0.5
0.6
800 Experimental
Stress, σ/MPa
Hypothetical properties Strain Softening No Hardening Strain Hardening
300 °C 450 °C 600 °C
700 600 500 400 300 200 100
FE Models
Both isothermal and non-isothermal two-dimensional simulations were carried out using CAMPform-2D,19) an inhouse metal forming simulator developed based on rigid thermo-viscoplastic formulation and constant shear friction model, to investigate the effect of various ECAE process parameters. Since the details of mathematical formulation are available in the literature,20) it is omitted here. Figure 1 displays the ECAE process parameters investigated in the current study. The die channel geometry used in simulations was 10 10 70 mm3 and ¼ 90 . In simulations, 700 quadrilateral elements were used for the workpiece. All the simulations were carried out with a constant plunger speed of 8 mm/s. The material properties of the CP-Ti specimen used in simulations were obtained from hot compression tests using Thermecmaster at temperatures in the range of 300 to 600 C and strain rates from 0.001 s1 to 10 s1 .16) A typical data measured is given in Fig. 2. As shown in Fig. 3, the material properties used in isothermal simulations were assumed as strain hardening and softening, or no hardening behavior based on the experimental data. All isothermal simulations were carried out with a strain rate sensitivity m of 0.02. For no hardening material with n ¼ 0, however, simulation was done with m ¼ 0:02 or 0.15 to investigate the effect of m value. 3.
Results and Discussion
3.1 Verification of FE model In order to validate the FE model used in this work, comparison of the stress components between the work by
0.8
Fig. 2 Flow curves for CP-Ti obtained from hot compression test at various temperatures with constant strain rate of 1 s1 .
assuming hardening, softening, and no hardening material behaviors. According to Semiatin and Delo,17) the surface cracking of the specimen often occurs in the hot ECAE process. Kim et al.18) investigated the limitation and applicability of the ductile fracture criteria based on plastic work and Cockcroft and Latham. Similar to this work, damage factors based on plastic work and Cockcroft and Latham were calculated to estimate the likeliness of surface cracking of the workpiece during the ECAE process. 2.
0.7
Strain
0 0.0
·
ε = 1s–1 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Strain Fig. 3 Flow curves for CP-Ti used in isothermal simulations.
Table 1 Comparison of the stress components at the center of deformation zone between Semiatin et al.9Þ and the current study. Semiatin et al.9Þ
Material behavior
y
x Strain hardening (m ¼ 0:02) Strain hardening (m ¼ 0:15) No hardening (m ¼ 0:15) Flow softening (m ¼ 0:15)
xy
x
y
xy
15
324
5
10
347
4
11
384
4
14
370
7
1
314
1
12
305
10
1
224
0
14
227
6
Sect. 1
30
CAMPform-2D
Sect. 2
10
Sect. 3
20
10
z x
Unit : mm
Fig. 4 Positions of the Vickers hardness measurements of the CP-Ti specimen.
Finite Element Investigation of Equal Channel Angular Extrusion Process
Vickers Hardness (Hv)
190
(a) z
Section 1 Section 2 Section 3
180
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x 170
(b)
160
2.5
150
Section 1 Section 2 Section 3
2.0
0
3
2
1
4
5
6
7
8
9
Strain
140 10
Depth (mm)
1.5
1.0
Fig. 5
Measured Vickers hardness data at different depths. 0.5 1
0
2
4
3
5
6
7
8
9
10
Depth (mm) Fig. 6 (a) Deformed pattern, and (b) predicted strain distribution data at different depths.
0.1 1
(a)
1.37 1.14 1.03 0.57
1.2 6
0.80
(b)
1.14
34
0. 91
0.
1.37 1.14
1.37 0.46
1.14 1.14 0.91 0.46
1.14 0.46
0.91 0.80
0 .80
1 .1 4 3 1 .0 3 0 1. 0 0.8 0.46
1.14 1.14
(c) 1.14 1.03 0.91 0.34
1.14 1.03 0.91
03
46
1.
0.
1.03 1.1 4 1.26
(d) 1.02
1.16 0.29
1.02 1.16
1.16 0.29
1.16 1.02
1 .1 6
6
1 .0
2
29
1 .1
0.
0.29
Fig. 7 Deformation pattern and strain distribution according to the material properties: (a) strain hardening (m ¼ 0:02), (b) strain softening (m ¼ 0:02), (c) no hardening (m ¼ 0:02), and (d) no hardening (m ¼ 0:15) behaviors with mf ¼ 0:05 and ¼ 45 .
(a)
4.0
Depth (mm) 0.5 5.0 9.5
3.5 3.0
(b) 4.0 3.0 2.5
Strain
2.5
Strain
Depth (mm) 0.5 5.0 9.5
3.5
2.0 1.5
2.0 1.5
1.0
1.0
0.5
0.5
0.0
0.0 0
10
20
30
40
Distance (mm)
50
60
0
10
20
30
40
50
60
Distance (mm)
Fig. 8 Strain distribution at different depths according to the friction conditions: (a) mf ¼ 0:05 and (b) mf ¼ 0:4 with strain hardening behavior and ¼ 0 .
2168
J.-H. Lee, I.-H. Son and Y.-T. Im
(a)
(b)
7 .1 1 2 .4 4 10 0.
5 .7 1 -2 0 15.0 0 7 .5 88 -58.57 15.00
7.89 66 1. 0 1 0.
14 62. -5 8.57 1 7 88 .5 7 8 8 .5 530.00
15.00
15.00
Fig. 9 Distribution of strain rate and stress component x according to the friction conditions: (a) mf ¼ 0:05 and (b) mf ¼ 0:4 with strain hardening behavior and ¼ 0 .
3.2 Isothermal FE simulations Figure 7 shows the deformation pattern and strain distribution according to the material properties of Fig. 3. Figures 7(c) and (d) reveal that the lower value of m reduces the amount of non-uniform deformation around the contact region near the lower die and leads to more uniform distribution of the effective strain. Higher value of m increased the separation of the material from the top die. As shown in Fig. 7, the deformation patterns and strain distributions for strain hardening, no hardening, and strain softening material behaviors with the same value of m were very similar. In the stable part or central part of the workpiece
Table 2 Mean strain and standard deviation at various conditions with strain hardening behavior. Die corner angle ()
Friction factor (mf )
"mean
"dev
0.05
1.066
0.197
0.4
1.381
0.331
0.05
1.023
0.231
0.4
1.067
0.252
0
45
(a) 2.0
Strain
1.5
1.0 Depth (mm) 0.5 5.0 9.5
0.5
0.0 0
10
20
30
40
50
60
Distance (mm)
(b) 2.0
Depth (mm) 0.5 5.0 9.5
Strain
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
Distance (mm)
(c) 2.0
Depth (mm) 0.5 5.0 9.5
1.5
Strain
Semiatin et al.9) and the current study using the material properties reported by Semiatin et al.9) was made as shown in Table 1. This table shows that the results of the current study were in good agreement with the published data in reference. In addition, since the main interest of the current investigation is to determine the strain distribution in the ECAE specimen, the strain distribution was compared to actual Vickers hardness measurements in three cross-sections of a circular ECAE specimen. The three-dimensional version of the current in-house FE program CAMPform-3D20) was used for the simulation. A cylindrical CP-Ti specimen with 10 mm diameter and 70 mm length was extruded at 350 C through one pass of the ECAE process with die corner angle of 45 degrees. The Vickers hardness measurements were taken at three crosssections, 30 (section 1), 40 (section 2), and 60 (section 3) mm from the left edge of the deformed workpiece as shown in Fig. 4. In addition, the measurement was made at 9 locations, roughly at increments of 1 mm from the top surface of the workpiece. The distributions of Vickers hardness measurements at each cross-section and the corresponding distributions of strain and the deformed pattern obtained from simulations are shown in Figs. 5 and 6, respectively. The section 3 was taken at 60 mm from the left edge of the deformed workpiece as it better shows the frictional effect near the bottom die. These two figures show the non-uniform distributions of hardness and strain in thickness direction. The general trends are similar although there are some discrepancies between the two. Similar non-uniformity of hardness and microstructure distributions in aluminum is reported by Chung et al.14) and Kamachi et al.,12) respectively. Since most earlier works claimed the uniformity of cross-sectional hardness distribution, it is necessary to investigate this in further investigations.
1.0
0.5
0.0 0
10
20
30
40
50
60
Distance (mm)
Fig. 10 Strain distribution at different depths according to die corner angles: (a) ¼ 0 , (b) ¼ 45 , and (c) ¼ 90 with no hardening behavior and mf ¼ 0:05.
Finite Element Investigation of Equal Channel Angular Extrusion Process
2169
(a)
(b)
(c)
(d)
(e)
Fig. 11 Shearing patterns for route A and C after: (a) 1, (b) 2, (c) 3, (d) 4, and (e) 5 passes with no hardening behavior with mf ¼ 0:05, m ¼ 0:02, and ¼ 0 .
(a)
9
Depth (mm) 0.5 5.0 9.5
8 7
(a)
9
7
6
6
5
Strain
Strain
Depth (mm) 0.5 5.0 9.5
8
4 3 2
5 4 3 2
1
1
0 0
10
20
30
40
50
0
60
0
10
Distance (mm)
(b)
9
(b)
7 6
5
5
4 3
3 2
1
1
0 20
30
40
50
0
60
0
10
Distance (mm)
(c)
(c)
7
6
6
5
5
Strain
Strain
8
7
4 3 Depth (mm) 0.5 5.0 9.5
0 0
10
20
30
40
30
40
50
60
9
8
1
20
Distance (mm)
9
2
60
4
2
10
50
Depth (mm) 0.5 5.0 9.5
8
6
0
40
9
Strain
Strain
7
30
Distance (mm) Depth (mm) 0.5 5.0 9.5
8
20
50
60
Distance (mm) Fig. 12 Strain distribution at different depths for route A after: (a) 1, (b) 3, and (c) 5 passes with no hardening behavior with mf ¼ 0:05, m ¼ 0:02 and ¼ 0 .
4 3 Depth (mm) 0.5 5.0 9.5
2 1 0 0
10
20
30
40
50
60
Distance (mm)
Fig. 13 Strain distribution at different depths for route C after: (a) 1, (b) 3, and (c) 5 passes with no hardening behavior with mf ¼ 0:05, m ¼ 0:02 and ¼ 0 .
1.14 1.14 0.91 0.46
0.
1.14 0.46
1.14
1.14 1.14
0.46
0.34
0.
57
(b) 0.91
1 .1 4 3 1 .0 3 0 1. 0 0.8 0.46
1.14 1.14
1.14 1.03 0 .91
Fig. 14 Strain distribution: (a) isothermal analysis of strain softening behavior and (b) non-isothermal analysis of 300 C with mf ¼ 0:05 and ¼ 45 .
(a)
2.0
Depth (mm) 0.5 5.0 9.5
Strain
1.5
1.0
0.5
0.0 0
(b)
10
20
30
40
50
2.0
Depth (mm) 0.5 5.0 9.5
1.5
Strain
60
Distance (mm)
1.0
0.5
0.0 0
10
20
30
40
50
60
Distance (mm)
(c)
2.0
Depth (mm) 0.5 5.0 9.5
Strain
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
Distance (mm)
Fig. 15 Strain distribution at different depths according to the processing temperatures: (a) 300 C, (b) 450 C, and (d) 600 C with mf ¼ 0:05 and ¼ 45 .
(a) 8 5 .8
6
57.57
64.64
7 1 .7 1 64.64
64.64 8.0 7
8.07
7 1 .7 1 6 .8 85
it can be seen that the level of strain gradually decreases from top to bottom surfaces in the thickness direction. Figure 8 shows the effect of friction condition on the strain distribution. In this figure, strain values were plotted according to the distance from the left edge of the workpiece by increments of 10 mm at three different depths of 0.5, 5.0, and 9.5 mm from the top surface of the workpiece. As the high friction restricts material flow at the bottom die, nonuniformity of the distribution of effective strain increased. Contrary to the lower friction case which had the highest strain value near the top surface of the workpiece, the case of higher friction showed the highest level of strain near the bottom of the workpiece. The examination of distributions of strain rate and stress component x provided more quantitative insight to the effect of friction conditions. The strain rate contours in the deformation zone became locally denser and more uniform for a low friction condition. In the stress component x distribution, attention was paid to the stress state at the surface of the workpiece. It was known that the tensile stress developed in the surface of the specimen might lead to surface cracking. From the distribution of the stress component x in Fig. 9, it can be seen that the level of the tensile stress x was higher for the case with the higher friction condition. Also Fig. 9 shows that while the lower friction case showed a smooth surface, the surface quality especially at the bottom was noticeably deteriorated for the higher friction case. The effect of die corner angles is shown in Fig. 10. It can be seen that the case of die corner angle of 0 degree showed the highest amount of non-uniformity and the highest level of strain was found at the bottom part of the workpiece. In comparison, the uniformity was increased with higher die corner angles and the highest level of strain was found at the top of the workpiece. Although the deformation shape is not shown here, the case of die corner angle of 90 degrees was easily extruded with large separation of the workpiece from the top die. Therefore the die geometry with the high corner angles generates more uniform strain distribution. Table 2 shows the average and standard deviation of the strain at the center of the workpiece in the thickness direction to quantitatively investigate the magnitude and uniformity of the strain distribution. As can be seen in Table 2, in both cases of die corner angle of 0 and 45 degrees, the average and the standard deviation increased with increasing value of the shear friction factor. It means that the deformation was more severe and non-uniformity increased as the friction became higher. When friction factor was 0.05, only the standard
7 4 7 1 .5 9 .7 0 51 236.29
471.57
471.57
510 .79
36
1.14
4
2.
3 0.
91
(a)
J.-H. Lee, I.-H. Son and Y.-T. Im
236.29
197 .07
43
2170
(b) 43.43
50.50
50.50
15. 14
43 .4 3 15.1 4
36.36 8.07
7 8 .7
9
4 31
1 .7
393.14
197.07
393.14
118.64
393.14 432.36 275.50
Fig. 16 The damage factor based on Cockcroft and Latham and plastic work criteria: (a) isothermal analysis of the strain softening behavior and (b) non-isothermal analysis of 300 C with mf ¼ 0:05 and ¼ 45 .
Finite Element Investigation of Equal Channel Angular Extrusion Process
2171
deviation also increased with increasing value of die corner angle. On the other hand, when the friction factor was 0.4, the magnitude and standard deviation decreased conversely. Figure 11 shows the accumulated deforming patterns according to processing routes, route A and C, respectively. Route A has no rotation of the workpiece when it enters the next pass, while route C rotated the workpiece by 180 between each pass. The shearing patterns were examined for a total of five passes. In the previous study, the shearing patterns of these two routes were examined theoretically with reference to macroscopic distortions.4) The currently obtained grid patterns from FE simulations were in good agreement with these theoretical results as shown in Fig. 11. Figures 12 and 13 show the distribution of strain obtained from the simulation of the two routes, respectively. It can be seen that for route A the amount of non-uniformity clearly increases with increasing number of passes. On the other hand, for route C, the amount of non-uniformity in the stable part of the workpiece does not dramatically increase depending on the number of passes. From this, it can be inferred that route C will likely be better than route A for obtaining uniform distribution and consequently microstructure with more equiaxed grains.
material with low strain rate sensitivity, low friction, and large corner angle might lead to more uniform deformation and homogeneous distribution of strains. However, in order to obtain the higher deformation levels, the high friction and small corner angle might be preferable and the ECAE process with processing route C more desirable than route A in terms of uniformity of accumulated deformation pattern. It was also found that the temperature had a great influence on the material behavior, the strain distribution, and the occurrence of the surface cracking for the material investigated in the present study. In addition, damage parameter could be used as an indicator to examine the surface quality of the workpiece including the likeliness of surface cracking. Based on this study, the numerical simulations can be easily used to design a better ECAE process including multi-passes.
3.3 Non-isothermal simulations Figure 14 shows the effect of considering heat transfer in simulations. The isothermal case assuming strain softening material behavior is compared to the non-isothermal simulation with working temperature of 300 C in this figure. Although the levels of strain are similar, it can be seen that the strain distribution and the deformation shape of the right end of the workpiece are quite different due to the nonisothermal effect. Thus, other non-isothermal simulations at working temperatures of 450 C and 600 C were compared as shown in Fig. 15. This figure shows that the distribution of strain is not greatly changed by variation of working temperature. The distribution of damage parameters as introduced in the earlier work18) was also examined in Fig. 16 to investigate the tendency having the likeliness of inducing surface cracking. It can be seen that the levels and distributions of predicted damage parameters vary according to isothermal or nonisothermal condition. Through the comparison between isothermal and nonisothermal simulations, it was found that the temperature had a great influence on the material behavior, the strain distribution, and the occurrence of the surface cracking and thus the heat transfer effect should be properly considered in numerical simulations.
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4.
Conclusions
In this study, the effects of ECAE process parameters on deformation pattern and strain distribution were numerically investigated. The mean strain and standard deviation were employed to determine the magnitude and uniformity of strain distribution. From these results, it was found that the
Acknowledgement The authors wish to thank for grant No. R01-2002-00000248-0 from the Basic Research Program of the Korea Science and Engineering Foundation. REFERENCES
