finite element investigation of equal channel angular
TRANSCRIPT
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 two-dimensional plane strain condition at elevated temperatures. Material properties were assumed by hardening, softening, and no hardeningbehaviors based on the measured experiment data. The effects of friction conditions, die geometries, and processing routes were also examinedunder the same processing condition. Based on the value of average strain and standard deviation of the strain distribution, the magnitude anduniformity of deformation was determined depending on process conditions. In addition, damage parameters based on plastic work and Cockroftand Latham criteria were calculated to check the likeliness of surface cracking. Finally, non-isothermal analyses were carried out to explore theeffect 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 thatinduces severe plastic shear deformation without changingthe cross-sectional shape of the workpiece.1) As thistechnique greatly refines the grain size, it is an effectivemethod of obtaining materials with high strength andtoughness. Also, it is desirable to make the deformationpattern and strain distribution as uniform as possible to obtainrather homogeneous mechanical properties of the finalproduct.
The main advantage of the ECAE process compared withother forming processes is that multi-pass operations can becarried out without changing the cross-sectional shape. Thus,the workpiece can undergo different processing routes as it isrotated between passes and the strain is accumulated. Thus,the processing route is a very important factor that directlyinfluences the deformation pattern and strain distribution inthe final deformed workpiece.
Many studies of the ECAE process have been conductedexperimentally so far, following the theoretical work bySegal.2) In this work, the required load and imposed strainwere calculated by neglecting frictions at the die interface.Iwahashi et al.3) extended the work of Segal for generalshaped die geometry and Furukawa et al.4) evaluated theshearing characteristics and patterns for the multi-pass ECAEprocess. Kamachi et al.5) compared the strain distribution anddeformed geometry between theoretical and experimentalresults of the ECAE process. Also Stolyarov et al.6) carriedout the experiments with CP-Ti and proposed optimalprocessing conditions to obtain better physical and mechan-ical properties.
For better understanding of the deformation behaviornumerically, Prangnell et al.7) presented a simplified finiteelement model neglecting the frictional effect and Bowen etal.8) studied deformation behavior of the billet under variousconditions by both finite element analyses and experiments.Semiatin et al.9) investigated the effect of material properties
and die geometries on deformation pattern and surfacecracking by numerical simulations. Delo and Semiatin10)
have demonstrated the instability of deformation in the hotECAE process due to softening behavior. Kim et al.11) alsonumerically investigated the plastic flow and deformationduring the ECAE.
Kamachi et al.12) and Horita et al.13) reported that theVickers hardness distribution can be considered to beglobally uniform in the specimen after the ECAE process.However, they reported some inhomogeneity in microstruc-ture or wavy and ill-defined grain boundaries, respectively.On the other hand, Chung et al.14) found that the distributionof Vickers hardness was inhomogeneous and that it wasqualitatively consistent with the strain distribution obtainedfrom finite volume method simulation results. Thus, furtherinvestigation of the strain distribution which will affect boththe distribution of hardness and microstructure is required.
In this study, the effects of various ECAE processparameters were examined using finite element analyses.For verification of these simulations, the stress componentsobtained from numerical results were first compared to thereported results by Semiatin et al.9) from the literature. Inaddition, experimentally obtained values of the Vickershardness in three cross-sections of a circular ECAE specimenwere compared to the three-dimensional non-isothermalsimulation results of strain distribution.
For examination of the effects of various ECAE processparameters such as material properties, friction conditions,die geometries, and processing routes on deformation behav-ior and strain distribution, numerous two-dimensional finiteelement analyses under the plane-strain and isothermalconditions were carried out. However, in the actual ECAEprocess temperature of the workpiece rises due to heatgeneration by plastic and frictional work.15) Thus, the non-isothermal analysis was carried out to investigate the effect ofprocessing temperature. For numerical investigations, thematerial property was determined by compression test usingThermecmaster at various temperatures and strain rates.16)
Based on the measured data, the effect of material propertieson deformation during the process was investigated by*Corresponding author, E-mail: [email protected]
Materials Transactions, Vol. 45, No. 7 (2004) pp. 2165 to 2171Special Issue on Ultrafine Grained Structures#2004 The Japan Institute of Metals
assuming hardening, softening, and no hardening materialbehaviors.
According to Semiatin and Delo,17) the surface cracking ofthe specimen often occurs in the hot ECAE process. Kim etal.18) investigated the limitation and applicability of theductile fracture criteria based on plastic work and Cockcroftand Latham. Similar to this work, damage factors based onplastic work and Cockcroft and Latham were calculated toestimate the likeliness of surface cracking of the workpieceduring the ECAE process.
2. FE Models
Both isothermal and non-isothermal two-dimensionalsimulations were carried out using CAMPform-2D,19) an in-house metal forming simulator developed based on rigidthermo-viscoplastic formulation and constant shear frictionmodel, to investigate the effect of various ECAE processparameters. Since the details of mathematical formulation areavailable in the literature,20) it is omitted here.
Figure 1 displays the ECAE process parameters inves-tigated in the current study. The die channel geometry used insimulations was 10� 10� 70mm3 and � ¼ 90�. In simu-lations, 700 quadrilateral elements were used for the work-piece. All the simulations were carried out with a constantplunger speed of 8mm/s.
The material properties of the CP-Ti specimen used insimulations were obtained from hot compression tests usingThermecmaster at temperatures in the range of 300 to 600�Cand strain rates from 0.001 s�1 to 10 s�1.16) A typical datameasured is given in Fig. 2.
As shown in Fig. 3, the material properties used inisothermal simulations were assumed as strain hardeningand softening, or no hardening behavior based on theexperimental data. All isothermal simulations were carriedout with a strain rate sensitivity m of 0.02. For no hardeningmaterial with n ¼ 0, however, simulation was done with m ¼0:02 or 0.15 to investigate the effect of m value.
3. Results and Discussion
3.1 Verification of FE modelIn order to validate the FE model used in this work,
comparison of the stress components between the work by
Die Corner angles (Ψ):0°, 45°, 90°
Shear friction factor (mf):
Processing routes:A route : no rotation
C route : 180° rotation
Material properties:nKσ ε ε= K : strength coefficient
n : strain hardenabilitym : strain rate sensitivity
τ : friction stressmf : shear friction factork : shear strength
Processing Temperature:300°C, 450°C, 600°C
x
z
Φ=90°
y
m·
= − m f kτ
Fig. 1 The ECAE process parameters used in FE simulations.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
100
200
300
400
500
600
= 1s–1
350°C300°C
400°C450°C
500°C550°C
600°C
Strain
Stre
ss, σ
/MPa
ε·
Fig. 2 Flow curves for CP-Ti obtained from hot compression test at
various temperatures with constant strain rate of 1 s�1.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
100
200
300
400
500
600
700
800
= 1s–1
Stre
ss, σ
/MPa
Strain
Experimental Hypothetical propertiesStrain SofteningNo HardeningStrain Hardening
300 °C450 °C600 °C
ε·
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.
Material behaviorSemiatin et al.9Þ CAMPform-2D
�x �y �xy �x �y �xy
Strain hardening15 �324 5 �10 �347 �4
(m ¼ 0:02)
Strain hardening�11 �384 �4 �14 �370 �7
(m ¼ 0:15)
No hardening�1 �314 1 �12 �305 �10
(m ¼ 0:15)
Flow softening�1 �224 0 �14 �227 �6
(m ¼ 0:15)
Sect.1
x
z
30 10 20 10
Unit : mm
Sect.2
Sect.3
Fig. 4 Positions of the Vickers hardness measurements of the CP-Ti
specimen.
2166 J.-H. Lee, I.-H. Son and Y.-T. Im
0 10140
150
160
170
180
190V
icke
rs H
ard
nes
s (H
v)
Depth (mm)
Section 1 Section 2 Section 3
1 2 3 4 5 6 7 8 9
Fig. 5 Measured Vickers hardness data at different depths.
0 100.5
1.0
1.5
2.0
2.5
Str
ain
Depth (mm)
Section 1 Section 2 Section 3
(a)
(b)
x
z
1 2 3 4 5 6 7 8 9
Fig. 6 (a) Deformed pattern, and (b) predicted strain distribution data at
different depths.
(d)
(c)
(a)
(b)
1.261.14
1.03
0.911.03
1.14
0.46
1.03
1.14
0.911.03
0.34
0.801.031.03
1.141.14
1.14
1.14
0.460.461.14
1.140.3
4
0.91
0.460.91
1.14
0.80
1.37
0.910.80
0.46
1.260.1
1
0.80 0.571.031.141.37
1.141.37
1.16
1.16
1.021.16
0.29
1.161.02
0.29
1.02
1.16
0.29 0.291.16
1.02
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�.
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
(a) (b)
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
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�.
Finite Element Investigation of Equal Channel Angular Extrusion Process 2167
Semiatin et al.9) and the current study using the materialproperties reported by Semiatin et al.9) was made as shown inTable 1. This table shows that the results of the current studywere in good agreement with the published data in reference.
In addition, since the main interest of the currentinvestigation is to determine the strain distribution in theECAE specimen, the strain distribution was compared toactual Vickers hardness measurements in three cross-sectionsof a circular ECAE specimen. The three-dimensional versionof the current in-house FE program CAMPform-3D20) wasused for the simulation.
A cylindrical CP-Ti specimen with 10mm diameter and70mm length was extruded at 350�C through one pass of theECAE process with die corner angle of 45 degrees. TheVickers hardness measurements were taken at three cross-sections, 30 (section 1), 40 (section 2), and 60 (section 3) mmfrom the left edge of the deformed workpiece as shown inFig. 4. In addition, the measurement was made at 9 locations,roughly at increments of 1mm from the top surface of theworkpiece. The distributions of Vickers hardness measure-ments at each cross-section and the corresponding distribu-tions of strain and the deformed pattern obtained fromsimulations are shown in Figs. 5 and 6, respectively. Thesection 3 was taken at 60mm from the left edge of thedeformed workpiece as it better shows the frictional effectnear the bottom die. These two figures show the non-uniformdistributions of hardness and strain in thickness direction.The general trends are similar although there are somediscrepancies between the two. Similar non-uniformity ofhardness and microstructure distributions in aluminum isreported by Chung et al.14) and Kamachi et al.,12) respec-tively. Since most earlier works claimed the uniformity ofcross-sectional hardness distribution, it is necessary toinvestigate this in further investigations.
3.2 Isothermal FE simulationsFigure 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 reducesthe amount of non-uniform deformation around the contactregion near the lower die and leads to more uniformdistribution of the effective strain. Higher value of mincreased the separation of the material from the top die.As shown in Fig. 7, the deformation patterns and straindistributions for strain hardening, no hardening, and strainsoftening material behaviors with the same value of m werevery similar. In the stable part or central part of the workpiece
(a)
(b)
2.44
0.10
7.11
0.101.667.89
-205.71
88.57
15.00-58.57
15.00 15.00
162.14-58.57
88.57530.00
88.57 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 strainhardening behavior and � ¼ 0�.
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
(a)
(b)
(c)
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.
Table 2 Mean strain and standard deviation at various conditions with
strain hardening behavior.
Die corner angle Friction factor"mean "dev(�) (mf )
00.05 1.066 0.197
0.4 1.381 0.331
450.05 1.023 0.231
0.4 1.067 0.252
2168 J.-H. Lee, I.-H. Son and Y.-T. Im
(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�.
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
(a)
(b)
(c)
Fig. 12 Strain distribution at different depths for route A after: (a) 1, (b) 3,
and (c) 5 passes with no hardening behavior withmf ¼ 0:05,m ¼ 0:02 and
� ¼ 0�.
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9S
trai
n
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
(a)
(b)
(c)
Fig. 13 Strain distribution at different depths for route C after: (a) 1, (b) 3,
and (c) 5 passes with no hardening behavior withmf ¼ 0:05,m ¼ 0:02 and
� ¼ 0�.
Finite Element Investigation of Equal Channel Angular Extrusion Process 2169
it can be seen that the level of strain gradually decreases fromtop to bottom surfaces in the thickness direction.
Figure 8 shows the effect of friction condition on the straindistribution. In this figure, strain values were plottedaccording to the distance from the left edge of the workpieceby increments of 10mm at three different depths of 0.5, 5.0,and 9.5mm from the top surface of the workpiece. As thehigh friction restricts material flow at the bottom die, non-uniformity of the distribution of effective strain increased.Contrary to the lower friction case which had the higheststrain value near the top surface of the workpiece, the case ofhigher friction showed the highest level of strain near thebottom of the workpiece.
The examination of distributions of strain rate and stresscomponent �x provided more quantitative insight to the effectof friction conditions. The strain rate contours in thedeformation zone became locally denser and more uniformfor a low friction condition. In the stress component �xdistribution, attention was paid to the stress state at thesurface of the workpiece. It was known that the tensile stressdeveloped in the surface of the specimen might lead tosurface cracking. From the distribution of the stress compo-nent �x in Fig. 9, it can be seen that the level of the tensilestress �x was higher for the case with the higher frictioncondition. Also Fig. 9 shows that while the lower frictioncase showed a smooth surface, the surface quality especiallyat the bottom was noticeably deteriorated for the higherfriction case.
The effect of die corner angles is shown in Fig. 10. It canbe seen that the case of die corner angle of 0 degree showedthe highest amount of non-uniformity and the highest level ofstrain was found at the bottom part of the workpiece. Incomparison, the uniformity was increased with higher diecorner angles and the highest level of strain was found at thetop of the workpiece. Although the deformation shape is notshown here, the case of die corner angle of 90 degrees waseasily extruded with large separation of the workpiece fromthe top die. Therefore the die geometry with the high cornerangles generates more uniform strain distribution.
Table 2 shows the average and standard deviation of thestrain at the center of the workpiece in the thickness directionto quantitatively investigate the magnitude and uniformity ofthe strain distribution. As can be seen in Table 2, in bothcases of die corner angle of 0 and 45 degrees, the average andthe standard deviation increased with increasing value of theshear friction factor. It means that the deformation was moresevere and non-uniformity increased as the friction becamehigher. When friction factor was 0.05, only the standard
(a)
(b)
0.801.031.03
1.141.14
1.14
1.14
0.460.461.14
1.140.3
4
0.91
0.460.91
1.14
0.91
1.031.141.14
0.34
0.57
0.91
1.14
0.46
1.14
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�.
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
0 10 300.0
0.5
1.0
1.5
2.0
Str
ain
Distance (mm)
Depth (mm) 0.5 5.0 9.5
(a)
(b)
(c)
20 40 50 60
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)
(b)
64.648.07 8.07
85.86
57.57 64.64 64.6485.86
71.7171.71
8.07 15.1478.79
15.14
50.5043.4336.36 43.43
50.50
510.79
432.
36
471.57
510.79
236.29
471.57
236.29 197.07
471.57
275.50432.36
393.14393.14
118.64
393.14
197.07314.71
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�.
2170 J.-H. Lee, I.-H. Son and Y.-T. Im
deviation also increased with increasing value of die cornerangle. On the other hand, when the friction factor was 0.4, themagnitude and standard deviation decreased conversely.
Figure 11 shows the accumulated deforming patternsaccording to processing routes, route A and C, respectively.Route A has no rotation of the workpiece when it enters thenext pass, while route C rotated the workpiece by 180�
between each pass. The shearing patterns were examined fora total of five passes. In the previous study, the shearingpatterns of these two routes were examined theoretically withreference to macroscopic distortions.4) The currently ob-tained grid patterns from FE simulations were in goodagreement with these theoretical results as shown in Fig. 11.
Figures 12 and 13 show the distribution of strain obtainedfrom the simulation of the two routes, respectively. It can beseen that for route A the amount of non-uniformity clearlyincreases with increasing number of passes. On the otherhand, for route C, the amount of non-uniformity in the stablepart of the workpiece does not dramatically increase depend-ing on the number of passes. From this, it can be inferred thatroute C will likely be better than route A for obtaininguniform distribution and consequently microstructure withmore equiaxed grains.
3.3 Non-isothermal simulationsFigure 14 shows the effect of considering heat transfer in
simulations. The isothermal case assuming strain softeningmaterial behavior is compared to the non-isothermal simu-lation with working temperature of 300�C in this figure.Although the levels of strain are similar, it can be seen thatthe strain distribution and the deformation shape of the rightend of the workpiece are quite different due to the non-isothermal effect. Thus, other non-isothermal simulations atworking temperatures of 450�C and 600�C were compared asshown in Fig. 15. This figure shows that the distribution ofstrain is not greatly changed by variation of workingtemperature.
The distribution of damage parameters as introduced in theearlier work18) was also examined in Fig. 16 to investigate thetendency having the likeliness of inducing surface cracking.It can be seen that the levels and distributions of predicteddamage parameters vary according to isothermal or non-isothermal condition. Through the comparison betweenisothermal and nonisothermal simulations, it was found thatthe temperature had a great influence on the materialbehavior, the strain distribution, and the occurrence of thesurface cracking and thus the heat transfer effect should beproperly considered in numerical simulations.
4. Conclusions
In this study, the effects of ECAE process parameters ondeformation pattern and strain distribution were numericallyinvestigated. The mean strain and standard deviation wereemployed to determine the magnitude and uniformity ofstrain distribution. From these results, it was found that the
material with low strain rate sensitivity, low friction, andlarge corner angle might lead to more uniform deformationand homogeneous distribution of strains. However, in orderto obtain the higher deformation levels, the high friction andsmall corner angle might be preferable and the ECAE processwith processing route C more desirable than route A in termsof uniformity of accumulated deformation pattern. It was alsofound that the temperature had a great influence on thematerial behavior, the strain distribution, and the occurrenceof the surface cracking for the material investigated in thepresent study. In addition, damage parameter could be usedas an indicator to examine the surface quality of theworkpiece including the likeliness of surface cracking. Basedon this study, the numerical simulations can be easily used todesign a better ECAE process including multi-passes.
Acknowledgement
The authors wish to thank for grant No. R01-2002-000-00248-0 from the Basic Research Program of the KoreaScience and Engineering Foundation.
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Finite Element Investigation of Equal Channel Angular Extrusion Process 2171