Gang Liu
Department of Materials Science and
Engineering,
Delft University of Technology,
Mekelweg 2,
2628 CD Delft, The Netherlands;
School of Materials Science and Engineering,
Harbin Institute of Technology,
P.O. Box 435,
Harbin 150001, China
Jie Zhou1
e-mail: [email protected]
Jurek Duszczyk
Department of Materials Science and
Engineering,
Delft University of Technology,
Mekelweg 2,
2628 CD Delft, The Netherlands
Finite Element Simulation of
Magnesium Extrusion to
Manufacture a Cross-Shaped
Profile
At present, a fundamental knowledge of the thermal and mechanical interactions occurring during the extrusion of magnesium is lacking. This acts as a serious technological
barrier to the cost-effective manufacturing of lightweight magnesium alloy profiles. In the
present research, a three-dimensional finite element (FE) simulation of extrusion to produce a magnesium alloy profile with a cross shape was carried out as an efficient means
to gain this understanding. It revealed the redistribution of temperatures in the billet
throughout the process from the transient state to the steady state, the formation of the
deformation zone and dead metal zone, and varying fields of effective stress, effective
strain, effective strain rate, and temperature close to the die orifice. The predicted extrudate temperature and extrusion pressure were compared with experimental measurements. The key to controlling the extrudate temperature and extrusion process was found
to lie in the capabilities of predicting the temperature evolution during transient extrusion, as affected by extrusion conditions. The relationship between ram speed and the
extrudate temperature increase from the initial billet temperature was established and
experimentally validated. 关DOI: 10.1115/1.2714590兴
Keywords: extrusion manufacturing, finite element analysis, magnesium
1
Introduction
Extrusion is a bulk-forming process usually used to manufacture long, straight, semi-finished metal products in the forms of
bars, tubes, strips, and solid and hollow profiles. It is applicable to
various metals, categorized in different ranges of operating temperatures, for example, aluminum, magnesium and zinc over a
temperature range of 300– 600° C; copper, titanium, zirconium,
beryllium, and uranium over 600– 1000° C; and nickel and steel
above 1000° C 关1兴. While the principle of the process for these
metals and their alloys is the same, their behavior, i.e., the relationship between the material and deformation conditions, may
vary considerably. Each material may allow extrusion deformation
within specific limits and therefore special technology for extruding a particular material must be developed, with such parameters
as workpiece material characteristics 共workability and solidus
temperature兲 and process conditions 共billet temperature, reduction
ratio, ram speed, and permissible pressure兲 taken into consideration.
Many of these parameters are interrelated with each other and
the most important parameter is the extrusion temperature. One
should note that due to heat generation from plastic deformation
and friction and heat dissipation to the extrusion tooling and surroundings during the process, the actual extrusion temperature is
not the same as the initial billet temperature. Moreover, it varies
throughout a process cycle. Therefore, a critical analysis of the
thermal and mechanical response of the billet material to deformation is of fundamental importance to the understanding and
optimization of the process. Most of the preceding research on the
thermomechanical characteristics of the extrusion process has
been specific to aluminum as well as copper alloys and very little
1
Corresponding author.
Contributed by the Manufacturing Engineering Division of ASME for publication
in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received
April 19, 2006; final manuscript received January 15, 2007. Review conducted by
Jian Cao.
to magnesium. It is just generally understood that the extrusion of
magnesium is quite similar to that of aluminum in terms of press
size and achievable extrudate dimensions. However, due to the
hexagonal lattice structure of magnesium often in combination
with the presence of phases with low melting points in magnesium
alloys, the permissible exit speed is much more restricted, in comparison with that for low- and medium-strength aluminum alloys.
As a consequence, the applicable ranges of process variables
共mainly billet temperature and ram speed兲 are highly restricted. In
this case, rational selection of these variables is of critical importance for the throughput and yield of the process and the quality of
the product. In addition, magnesium has a stacking fault energy
value lower than aluminium and thus dynamic recrystallization is
prone to occur during extrusion, in contrast to dynamic recovery
in the case of aluminium extrusion as a dominant restoration
mechanism. As a result of thermally activated dynamic recrystallization, softening is pronounced after the extrusion pressure peak
关2兴, which affects the further evolution of the temperature of the
workpiece. At present, many peculiarities of magnesium extrusion
with respect to thermomechanical response are not fully understood, while it is expected that the process will be increasingly
used for the manufacturing of semi-finished wrought magnesium
products mostly for automotive applications 关3兴.
The thermomechanical response of a magnesium alloy as affected by extrusion conditions is highly complex. Local parameters, such as flow stress, strain, strain rate, and temperature, are
not experimentally measurable. In such a case, finite element 共FE兲
simulation can play a unique role in gaining an understanding of
the thermomechanical interactions occurring inside deforming
magnesium during extrusion. For example, assuming the ZK60
magnesium alloy 共Mg– Zn– Zr兲 to be thermoplastic, Ogawa et al.
关4兴 made use of FE simulation to define temperature limits for
backward 共i.e., indirect兲 extrusion at a given speed. Chandrasekaran and Yong 关5兴 used two-dimensional FE simulation to establish
the size and capacity of a press to extrude the AZ31 magnesium
alloy 共Mg– Al– Zn兲 axisymmetrically over a range of tempera-
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Table 1 Physical properties of the billet and extrusion tooling
Properties
Heat capacity 共N / mm2 ° C兲
Thermal conductivity 共W / m ° C兲
Heat transfer coefficient between
tooling and billet 共N / ° C s mm2兲
Heat transfer coefficient between
tooling/billet and air 共N / ° C s mm2兲
Emissivity
AZ31
H13
2.09684 at 327° C
2.27484 at 527° C
96
11
5.6
28.4
11
0.02
0.02
0.12
0.7
Fig. 1 Cross section of the extrudate with the shaded area
selected for simulation
tures. Song et al. 关6兴 applied a more realistic rigid-viscoplastic
material model to predict the behavior of the AZ31 alloy during
extrusion to produce a sheet, with heat exchanges between the
workpiece and extrusion tooling incorporated. Lapovok et al. 关7兴
took one step further by using FE simulation to construct a limit
diagram for extrusion from an AZ31 billet with a diameter of
75 mm into round bars at different reduction ratios. The preceding
studies using FE simulation as an efficient means undoubtedly
contribute to gaining a fundamental understanding of the manufacturing process. However, these simulations deal with simple
shapes. The shape factor of the extrudate has not yet been taken
into account, while in real extrusion manufacturing complex sections take a vast majority of the extrusions commercially produced for structural or nonstructural applications. In the case of
extruding a round billet into a profile, the relationship between
extrudate temperature and process conditions is lacking. It is more
complex than in the case of extruding the same billet into a round
bar or a square bar, as a result of increased complexities in metal
flow and enhanced heat generation from friction and heat conduction due to increased contact area and sharp edges. Obviously, the
simulation of extrusion to manufacture a shaped profile requires
three-dimensional FE simulation, which is at present still highly
demanding on software, hardware, and user’s skills.
In the present research, an attempt was made to simulate the
direct extrusion process to manufacture a shaped magnesium profile. It concerned the characterization of the thermomechanical
response of a wrought magnesium alloy during extrusion in terms
of the evolutions of stress, strain, strain rate, and temperature as
affected by ram speed. Temperature redistribution and temperature
evolution throughout an extrusion cycle were of major interest.
The results would ultimately be used for the establishment of a
generic relationship between ram speed and extrudate temperature
change, suitable for a wide range of extrudate section shapes
within a shape category, e.g., simple solid, after a shape factor is
incorporated into this relationship.
2
Simulation and Experimental Details
2.1 Materials and Geometry. A wrought magnesium alloy
AZ31 with 3% aluminum, 1% zinc, and balance magnesium by
weight was used as the billet material both in computer simulation
and experimental verification. The billet had a diameter of
48.8 mm and a length of 200 mm. The extrusion tooling composed of a die, a container, and a stem was made of the H13
hot-work tool steel. The physical properties of the billet and extrusion tooling are listed in Table 1.
Figure 1 shows the cross section of the extrudate as the end
product of the extrusion process. To save computational time for
the simulation of the process from the transient state to the steady
state, was only one-eighth of the object 共the shaded area兲 modeled
to take advantage of its symmetry. The artificial symmetrical
planes were assumed to be immobile with no material moving
across.
Table 2 gives the dimensions and temperatures of the billet and
extrusion tooling used in computer simulation, which were identical to those applied in extrusion experiments. As AZ31 normally
608 / Vol. 129, JUNE 2007
does not contain the eutectic Mg17Al12 phase with a melting point
at 437° C and it starts to melt at the solidus temperature of 605° C,
the initial billet temperature was chosen to be at a relatively high
level 共450° C兲 in order to allow ram speed to vary over a wide
range from 2 to 12 mm/ s, without running the risk of reaching the
press force limit during experiments at high ram speeds. The container had an insider diameter of 50 mm and therefore a clearance
of 1.2 mm was left to facilitate the loading of the billet into the
container. As a result, upsetting took place before the billet was
extruded.
2.2 FE Model, Material Data and Boundary Conditions.
Figure 2 shows the FE model of the billet and extrusion tooling
with initial finite elements. The tooling was meshed with tetrahedral elements and its heat exchanges with the billet incorporated
in the model. Table 3 gives the simulation parameters used. To
enhance the efficiency of simulation and in the meantime achieve
high resolutions in the areas of particular interest, several windows of higher element densities were applied, especially around
the die orifice. For simulation accuracy and stability, the absolute
mesh density was used to maintain the element size to be nearly
constant at any positions. 共The absolute mesh density is defined as
the number of elements per unit length on the surface of an object.兲 The minimum size of an element was 0.2 mm. The total
number of elements was 47,000– 60,000, depending on the length
of the cross-shaped extrudate. To limit the volume of simulation
database files and increase simulation speed, the extrudate was cut
off at a length of 200 mm when its length exceeded 300 mm. A
small relative interference depth of 0.3 mm was chosen to trigger
automatic remeshing when any element edge on the workpiece
had been penetrated into and the penetration depth exceeded 30%
of the original length of the surface edge that had a contact node
on each end. In the present simulations, the rest of the extrusion
die stack 共die holder, backer, die heater, bolster, and die holder
carrier兲 and container accessories 共resistance heating兲 were all neglected. To limit excessive heat loss through the simplified extrusion tooling during computer simulation, the surrounding temperature of the container and the die was assumed to be 300° C.
The DEFORM 3D version 5.1 software package was used for
the FE simulation of magnesium extrusion. The billet material
共AZ31兲 was considered thermo-viscoplastic and the extrusion
Table 2 Dimensions and initial temperatures of the billet and
extrusion tooling
Billet length 共mm兲
Billet diameter 共mm兲
Container inside diameter 共mm兲
Container outside diameter 共mm兲
Reduction ratio
Die bearing length 共mm兲
Initial billet temperature 共°C兲
Initial tooling temperature 共°C兲
200
48.8
50
132
8.8
5
450
400
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Table 3 Simulation parameters, material data source, and
boundary conditions
Total number of elements
Minimum size of an element 共mm兲
Mesh density type
Relative interference depth
Temperature range in flow stress determination 共°C兲
Strain rate range in flow stress determination 共s−1兲
Surrounding temperature 共°C兲
Friction factor at billet/tooling interfaces
47,000– 60,000
0.2
absolute size
0.3
300– 500
0.03– 90
300
1.0
Fig. 3 The instrumented direct extrusion press used experimental verification
m = 冑3
␶
␴
共1兲
where ␶ is the frictional shear stress and ␴ the effective flow stress
of the billet. In the present study on the direct extrusion process, a
friction factor of 1.0 was chosen at the container/billet interface
according to the results of a ring-upsetting test of the AZ31 magnesium alloy 关9兴. The same friction factor was assumed at the
interfaces between the billet and stem and between the billet and
die. In this case, there was no relative movement between the
workpiece and extrusion tooling, and strong shearing took place
near the interface, which raised the extrusion pressure and contributed to the temperature rise of the workpiece.
Fig. 2 FE model of the billet and extrusion tooling to produce
the cross-shaped profile as illustrated in Fig. 1
tooling a thermo-rigid material. Both of these material models
neglected the elastic behavior of the workpiece 共billet and extrudate兲 and extrusion tooling.
The true flow stress–strain data of the AZ31 alloy over a temperature range of 300– 500° C and a strain rate range of
0.03– 90 s−1 were determined through hot compression tests using
Gleeble 3500. The flow stress data were corrected for deformation
heating during hot compression 关8兴. The corrected flow stresses at
various strains up to 1 were input into the DEFORM simulation
model.
The friction at the workpiece/tooling interfaces was considered
to be of shear type. The friction factor m 共0 艋 m 艋 1兲 is expressed
as
Journal of Manufacturing Science and Engineering
2.3 Extrusion Experiments. Extrusion experiments were carried out to verify the results obtained from computer simulation.
To manufacture the cross-shaped profile as shown in Fig. 1, a
flat-faced die with a uniform bearing length of 5 mm was designed. A hole close to the die face was drilled to allow the temperature of the die to be measured by a thermocouple at a spot
1 mm away from the die bearing. A 2.5 MN well-instrumented
extrusion press having a resistance-heated container and a heated
die was used 共Fig. 3兲. The materials, dimensions, and temperatures of the billet and tooling as well as ram speed were identical
to those applied in computer simulation, as stated earlier. A 3T
multi-wavelength pyrometer with a spot size of 10 mm was
placed 200 mm behind the die exit to measure the exact temperature of the extrudate. The billet was heated in an external furnace
up to 450° C and transported into the container at a preset temperature of 400° C and then extrusion started immediately. During
an extrusion cycle, container temperature, die temperature, extrudate temperature, extrusion pressure, and ram displacement were
measured. These data were displaced in real time on the press
console. After the extrusion cycle, they were subjected to data
processing.
3
Results and Discussion
3.1 Temperature Evolution Throughout the Process. The
patterns of temperature evolution during extrusion at different ram
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Fig. 5 Positions „a… and evolution „b… of the maximum and
minimum temperatures during extrusion at a ram speed of
6 mm/ s, revealed by computer simulation
Fig. 4 Predicted temperature evolution during the extrusion at
a ram speed of 6 mm/ s and at various ram displacements „S…
in both the transient state and the steady state
speeds from 2 mm/ s to 12 mm/ s were quite often the same. Figures 4共a兲 and 4共b兲 show representative temperature evolution during transient-state extrusion at a ram speed of 6 mm/ s. From the
iso-temperature surfaces, it is clear that the temperatures of the
billet in front of the die face increase gradually. Toward a ram
displacement of 15.4 mm, the maximum temperature appears at
the junction between the die bearing and die face where severe
shear occurs and contributes to the local temperature rise. In the
meantime, the temperatures of the billet in contact with the con610 / Vol. 129, JUNE 2007
tainer decrease, as a result of heat loss to and through the container 共the initial container temperature being 50° C lower than
that of the billet兲, although shearing takes place near the billet/
container interface and leads to local heating.
During the subsequent steady-state extrusion, the temperatures
of the billet near the die face increase continuously, especially
along the die bearing. This is illustrated by the iso-surface of
452° C in Figs. 4共d兲, 4共e兲, and 4共f兲, expanding step by step, indicating that with the progress of the process more and more material reaches the temperature of 452° C.
Figure 5共a兲 shows the maximum temperature and minimum
temperature in the billet during extrusion at a ram speed of
6 mm/ s. The maximum temperature appears in the middle of the
surface in the groove of the cross-shaped extrudate. As expected,
the minimum temperature occurs at the center of the rear end of
the billet. Figure 5共b兲 shows that during upsetting up to a ram
displacement of 10 mm, the maximum temperature remains
stable. However, during transient-state extrusion over a short ram
displacement of 5.4 mm from 10 mm to 15.4 mm, the maximum
temperature rises sharply from 450° C to 483.5° C, a rise of
33.5° C, as indicated by Points A and B in Fig. 5共b兲. During the
subsequent steady-state extrusion, the maximum temperature increases only slightly from 482.5° C to 485.5° C. The predicted
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Fig. 6 Iso-surfaces of high effective strain rates outlining the
deformation zone, revealed by computer simulation
maximum temperature evolution throughout the process cycle indicates that the temperature of the workpiece would not go beyond the solidus temperature of the alloy 共605° C for the alloy
AZ31兲 and thus no hot shortness would occur, leading to the defect caused by incipient melting. The results also show that, to
prevent the defect from occurring, measuring the temperature in
the groove of the cross-shaped profile is most important, because
this is where the hottest spot is. If the temperature there does not
exceed the solidus temperature or the lowest melting temperature
of second-phase particles in the workpiece, surface defect would
not occur. Obviously, the temperature margin between the maximum temperature and the critical temperature of the workpiece
allows for an increase in ram speed to approach the maximum
permissible exit speed for a maximum throughput of the process.
Being different from the maximum temperature, the minimum
temperature decreases from the initial billet temperature of 450°C
to 431.7°C during upsetting, due to heat loss to the tooling 共whose
initial temperature was 400° C兲. During transient-state extrusion,
the minimum temperature continues to decrease to 421.5° C, i.e.,
from Point C to D in Fig. 5共b兲. During the further steady-state
extrusion, it remains stable up to a ram displacement of 80 mm. It
then increases gradually until the end of the extrusion cycle, as a
combined result of heat flow from the deformation zone and heat
generation from shearing near the billet/container interface. By
comparing the maximum temperature curve and the minimum
temperature curve in Fig. 5共b兲, it becomes clear that there exist
significant temperature differences in the deforming billet, as a
result of heat generation from plastic deformation and heat transfer between the billet and extrusion tooling. Figure 5共b兲 also indicates that during steady-state extrusion, both the maximum temperature and the minimum temperature increase gently. Thus, the
key to controlling the process closely is the capabilities of predicting the temperature rise during transient-state extrusion, as affected by process variables, i.e., initial billet temperature and ram
speed.
3.2 Deformation Zone and Dead Metal Zone. Figure 6
shows the iso-strain rate surface of 5 s−1 in the deformation zone
that appears like a ring outlining the grooves and the legs of the
Journal of Manufacturing Science and Engineering
Fig. 7 Areas with flow velocities lower than 0.5 mm/ s „dark
color… outlining the dead metal zone at the corners in the front
part of the billet „simulation results…
extrudate. When the material flows into the deformation zone,
severe deformation occurs and a large amount of heat is generated. The material at the center of the profile has a lower strain
rate and therefore it flows through the die with less severe
deformation.
Figure 7 shows the dead metal zone where the material flow
velocity is smaller than 0.5 mm/s, represented by the dark area at
the corners between the container liner and die face. The flow
discontinuity at the boundary between the deformation zone and
dead metal zone is clearly revealed. It is the shearing at this
boundary that leads to the formation of extrusion surface from the
virgin material in the interior of the billet.
3.3 Effective Stress, Strain, Strain Rate, and Temperature
Fields Close to the Die Orifice. Figure 8 shows the fields of
effective stress, effective strain rate, effective strain, and temperature on a cross section in the billet just 0.1 mm away from the die
face. It can be seen that during transient-state extrusion from a
ram displacement of 10.2 mm, Fig. 8共a兲, to 15.4 mm, Fig. 8共b兲,
these field all change significantly. It is interesting to observe that
the peak value of the effective stress does not change with ram
displacement but the stress field does. At a ram displacement of
10.2 mm, the highest effective stress of 62 MPa appears at the
edge of the billet head and also at the junction between the die
face and die bearing, as shown in Fig. 8共a兲. Before the real extrusion starts, there exists a clearance of 1.2 mm between the billet
and container. At the start of transient extrusion, the corner between the die face and the container liner has just been filled and
the material there still has axial compressive stresses and circumferential tensile stresses, resulting in high effective stresses. With
the process proceeding to a ram displacement of 15.4 mm, the
corner is transformed into part of the dead metal zone. Under
three-dimensional compressive stresses, the material has a decreased effective stress of 8 MPa, because the three principal
stresses have quite similar algebraic values.
During transient-state extrusion, the effective strain rate along
the die entrance increases from 10 s−1 to 40 s−1. In the meantime,
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Fig. 8 Effective stress, effective strain rate, effective strain, and temperature fields at different ram displacements „simulation results…
the effective strain in the deformation zone increases dramatically
from 0.2 to 3.29 at the surfaces of the grooves of the profile. The
most notable changes are, however, the temperature distribution
and peak temperature value. It is of interest to see that the spot of
the maximum temperature coincides with that of the maximum
effective strain.
During steady-state extrusion from a ram displacement of
15.4 mm, Fig. 8共b兲, to 136 mm, Fig. 8共d兲, the gradient fields of
these parameters are all quite steady. Only the peak values of the
effective strain and temperature increase slightly. Also notable is
the tendency of temperature distribution toward uniformity, as a
result of decreasing heat conduction into the extrusion tooling
after a certain ram displacement and decreasing heat generation
from shearing at the billet/container interface as the billet shortens. In addition, with increasing temperature in the majority of the
612 / Vol. 129, JUNE 2007
remaining billet, the effective stress of the material close to the die
bearing decreases. Also, extrusion pressure decreases as a result of
dynamic recrystallization 关8兴, leading to a decreasing amount of
heat generated as the process proceeds.
3.4
Comparison With Experimental Measurements.
3.4.1 Extrudate Temperature. To verify the model and the results obtained from simulation, extrusion experiments at different
ram speeds were performed. Figure 9 shows the evolution of extrudate temperature obtained from experimental extrusion at ram
speeds of 2 – 8 mm/ s. It can be seen that after a ram displacement
of 55 mm, extrudate temperature increases steadily and slowly. As
the pyrometer was placed 200 mm away from the die exit in order
to avoid radiations from the die stack with a resistance heater, the
temperatures of the nose of the profile could not be measured and
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Fig. 9 Predicted evolution of extrudate temperature at various
ram speeds
those of the front part of the profile could not be reliably determined. In this case, the extrudate temperatures after a ram displacement of 55 mm were compared with simulation results. Figure 9 also shows that the differences in temperature between the
extrusions produced at different ram speeds remain almost unchanged during steady-state extrusion, after much heat is generated during upsetting and transient-state extrusion to create these
differences. Therefore, the differences in extrudate temperature in
the steady state reflect the extent of the effect of ram speed on
temperature evolution in the transient state. In the following, a
ram displacement of 60 mm is taken as a point for comparison
between experiment and simulation with regard to the temperature
of the extrudate 200 mm behind the die.
Figure 10 compares the extrudate temperature evolution determined from experimental extrusion at a ram speed of 6 mm/ s and
that predicted from FE simulation under the same process conditions. The predicted tendency of temperature evolution is in good
agreement with that from the experiment. The predicted extrudate
temperatures are just a few degrees lower than the measured values. The maximum difference of 5.2° C between the two curves
occurs at a ram displacement of 123.7 mm, which is equal to a
small deviation of 1.1% from the actual extrudate temperature.
3.4.2 Extrusion Pressure. Figure 11 compares the extrusion
pressure/ram displacement diagrams between the experiment and
Fig. 11 Comparison in pressure during the extrusion at a ram
speed of 6 mm/ s between simulation results and experimental
measurements
simulation of extrusion at a ram speed of 6 mm/ s. It can be seen
that billet upsetting takes place before pressure rises. The billet
with an initial diameter of 48.8 mm is forced to fill the container
with a diameter of 50 mm 共see Table 2兲. It is obvious that the
slopes of the pressure increase during upsetting between simulation and experiment are quite different, which may be caused by
the approximations made in the rigid-viscoplastic billet material
model. Of more interest is the comparison in peak pressure between simulation and experiment. It appears that the peak pressure
values are quite similar to each other. The comparison also shows
that the measured pressure peak occurs later, likely due to the
elastic deformation of the billet and extrusion tooling which is
neglected altogether during FE simulation. In the steady state, the
extrusion pressures predicted from simulation are higher than the
measurements, which is in line with the discrepancies in extrudate
temperature as shown in Fig. 10. A lower temperature leads to a
higher extrusion pressure.
3.5 Effect of Ram Speed on Extrudate Temperature
Increase. From the simulations of extrusion at different ram
speeds, the relationship between ram speed and extrudate temperature increase could be established. The extrudate temperature
increase was found to be an exponential function of ram speed,
meaning that the rate of extrudate temperature increase decreased
as ram speed increased. In other words, the higher the ram speed,
the smaller the effect of ram speed on extrudate temperature increase. For convenience, extrudate temperature increase is expressed as a linear function of logarithmic ram speed 共Fig. 12兲
⌬T = 29.304 ln V − 29.64
共2兲
where ⌬T is the difference between the extrudate temperature and
the initial billet temperature; and V is ram speed. In Fig. 12, experimentally measured temperature points are included. It can be
seen that the experimental data fit well in the relationship established through FE simulation. The linear relationship between extrudate temperature increase and logarithmic ram speed is thus
validated.
4
Conclusions
The present three-dimensional FE simulation of extrusion to
produce a cross-shaped magnesium profile, focused on the effect
of ram speed on thermomechanical response, leads to the following conclusions:
Fig. 10 Comparison in extrudate temperature between the experiment and simulation of extrusion at a ram speed of 6 mm/ s
Journal of Manufacturing Science and Engineering
1. During upsetting and transient-state extrusion, the temperatures in the billet change significantly; the temperatures near
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temperature is a linear function of logarithmic ram speed,
which has been experimentally validated. The rate of extrudate temperature increase decreases with rising ram speed.
The higher the ram speed, the smaller the effect of ram
speed on extrudate temperature increase. These results are of
fundamental importance in establishing a generic relationship between ram speed and extrudate temperature change,
suitable for a wide range of extrudate shapes.
Acknowledgment
Thanks are due to Mr. M.A. Leeflang for performing extrusion
experiments to validate the results obtained from computer simulation.
References
Fig. 12 Relationship between ram speed and extrudate temperature increase both predicted and experimentally measured
the die face increase with ram displacement while those in
the rear part of the billet decrease. The maximum temperature occurs in the middle of the surface in the groove of the
cross-shaped profile, while the minimum temperature appears at the center of the rear end of the billet in contact with
stem.
2. During transient-state extrusion, extrudate temperature increases dramatically, while in the steady state it increases
steadily and slowly as a result of near dynamic balance between heat generation and heat dissipation. Therefore, to
control the extrudate temperature and the extrusion process
closely, the prediction of temperature evolution during
transient-state extrusion is the key.
3. The increase in extrudate temperature from the initial billet
614 / Vol. 129, JUNE 2007
关1兴 Laue, K., and Stenger, H., 1981, Extrusion Processes, Machinery, Tooling,
American Society for Metals, Metals Park, OH, Chap. 3.
关2兴 Mueller, K. B., 2002, “Direct and Indirect Extrusion of AZ31,” Magnesium
Technology 2002, TMS, Warrendale, PA, pp. 187–192.
关3兴 Lass, J. F., Bach, F. W., and Schaper, M., 2005, “Adapted Extrusion Technology for Magnesium Alloys,” Magnesium Technology 2005, TMS, Warrendale,
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