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Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg)
Journal Pre-proof Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg) Sajad Molafilabi, Alireza Sadeghi, Mohammadjafar Hadad PII:
S2588-8404(19)30103-9
DOI:
https://doi.org/10.1016/j.ijlmm.2019.09.001
Reference:
IJLMM 79
To appear in:
International Journal of Lightweight Materials and Manufacture
Received Date: 12 August 2019 Revised Date:
4 September 2019
Accepted Date: 4 September 2019
Please cite this article as: S. Molafilabi, A. Sadeghi, M. Hadad, Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg), International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.09.001. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.
Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg) Sajad Molafilabi, Alireza Sadeghi, Mohammadjafar Hadad*
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Corresponding author email: [email protected], Tel: +982161119958, Fax: +982188013029
1 2 3 4 5 6
Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg)
7 8 9 10 11 12
Abstract
13
Large strain extrusion machining (LSEM) is used to produce pure magnesium strips directly
14
from as-cast billets. LSEM reduces manufacturing steps and the special shear direction inclines
15
the unfavorable strong basal texture of Mg. Finding suitable parameter ranges to control
16
geometry and properties of the produced strip is a great challenge. In the present research, a
17
finite element model is proposed and verified with experiments and previous findings. Next,
18
effects of process parameters (temperature and pressure) on geometrical and microstructural
19
properties of the produced strips are investigated. Studying the involved failure micro-
20
mechanisms shows that the process temperature and hydrostatic pressure have adverse effects on
21
the production of a flawless strip. To reduce the temperature and hydrostatic pressure throughout
22
the LSEM process many different conditions are tested by the FEM model. Among all the
23
examined conditions, 0.85
24
it terms of low temperature, low hydrostatic pressure, and stable machining force. The proposed
25
conditions are applied in the experimental setup and a uniform and flawless strip is obtained.
feed and 530
rotation speed yields the most promising results
26 27 28
Keywords: large strain extrusion machining; magnesium; turning; chip formation, FEM
1
1 2
1- Introduction
3
The large difference in the critical resolved shear stress (
4
hexagonal magnesium results in the formation of a strong basal texture through deformation [1].
5
In rolled magnesium sheets, the hexagonal c-axis aligns with the deformation direction and easy
6
slip of dislocations becomes limited in the sheet thickness direction (c-axis) [2]. Consequently,
7
the rolled sheets exhibit strong anisotropic behavior and their formability is significantly reduced
8
for further sheet forming processes (e.g. deep drawing). Various approaches are used by different
9
researchers to control the formation of the strong basal texture in rolling of Mg sheets [3].
10
Among those, changing the deformation force direction has received significant attention as an
11
alternate approach to weaken the basal texture. Processes such as (1) axisymmetric rolling [4],
12
(2) cross-rolling [5] and (3) large strain extrusion machining [6] are proven to have positive
13
effects on reduction of the basal texture strength. In large strain extrusion machining (LSEM),
14
the formed chip is constrained in a die opening, right after separation from the material bulk.
15
Different configurations and relative motions of tool and workpiece are proposed for LSEM [7].
16
During the process, the shear direction is inclined compared to the produced chip and therefore
17
the basal texture component is inclined [8]. In 1925 sheets were attempted to be directly formed
18
from the bulk of material by large strain machining (LSM) was used to peel a stainless steel disc
19
by a high positive rake angle tool [9][10]. The process required tons of hydraulic force to make
20
the peeling tool stable [11] and eventually, the produced foil was not flat. Later, extrusion was
21
combined with machining by employing a constraining unit above the cutting tool to apply shear
22
strain and increase uniformity [12]. Wire production was the first application of extrusion cutting
23
[13]. Then cutting extrusion was used to produce a 40m long continuous brass strip from a
2
) of different slip systems of
1
cylindrical bar [14]. In 2007 Moscoso [15] studied the microstructures and mechanical properties
2
of LSEM strips and showed that this process could be classified as a severe plastic deformation
3
process [15]–[19]. In the present research, the finite element method (FEM) is used to predict
4
machining force, hydrostatic pressure, and temperature in LSEM of pure magnesium.
5
Simulations were calibrated using experiments. The numerical model was used to locate
6
appropriate LSEM parameters for forming a uniform Mg strip. Then the located LSEM
7
parameters were applied in real experiments and a uniform strip was obtained.
8 9
2- Experimental procedure
10
Linear configuration large-strain extrusion machining (Fig.1) was carried out on a 78 mm
11
diameter pure magnesium bars. The cylindrical bars were clamped on a 5 kW turning machine to
12
carry out the experiments. A special tool was designed to remove chips and simultaneously
13
constrain their expansion. The tool was machined from a cold work tool steel (C 2.00; Cr 12.0)
14
with 60 Rockwell C hardness. The tool was designed to control different dimensions including
15
the undeformed and deformed sections to apply different chip thickness ratios (λ). The rake angle
16
(α) was kept constant through all the experiments equal to 5 degrees. In Fig.1 the schematic
17
configurations of the tool and workpiece are shown.
18
To investigate effects of cutting parameters on different properties of produced LSEM strips, five
19
experimental conditions were selected by alternating the feed and rotation speed. In the first set
20
of experiments, represented by P1, P2, and P3, the feed was set constant equal to 1.060
21
the rotation speed was increased from 190
22
respectively (Fig.2). In the second set of experiments, represented by P3, P4 and P5, the rotation
23
speed (at constant diameter) was constant equal to 1050
for P1 to 530
3
and
and
1050 for P2 and P3
and the feed decreased from 1.060
1
to 0.600 and 0.095
from P3 to P4 and P5 respectively (Fig.2). It should be noted that
2
although λ is constant by changing rotation speed, it may not remain constant when feed is
3
changing. As described in Fig.1,
4
decreased consequently. Other than the depicted conditions in Fig. 2, many other conditions
5
were tested but not reported in the present paper. A large set of samples are studied in this
6
research. Here the two extremes of low and high λ are reported to illustrate the trends of change.
7
Before starting each test, the LSEM tool tolerances were checked, fixed and the lathe was set to
8
proper feed and rotation speed. Molybdenum disulfide (MoS2) was used as a high-temperature
9
lubricator between the cutting and constraining tools. Each test was stopped after producing a
10
three-meter strip. In Fig. 3 the test setup and the produced strip are shown. After LSEM, the strip
11
surfaces were examined by optical microscopy and the dimensions were carefully measured. By
12
measuring the thickness of the produced strip in terms of known tool parameters, the extrusion
13
pressure and the shear strain were calculated using the upper bound equations proposed by De
14
Chiffre [20]. Important to mention that these equations are based on uniform deformation, and
15
localization and fracture at shear bands are not considered. Therefore it can be predicted that the
16
actual values of strain are lower than the values calculated by the upper bound approach. Next,
17
the samples were cold mounted, ground and polished for optical microscopy and hardness
18
measurements.
=
⁄
by increasing the feed t0 increases and lambda is
19 20
3- Finite element modeling
21
To model the thermo-mechanical LSEM process, SFTC-DEFORM (V.11) software was used. In
22
Fig.4 the thermal and displacement boundary conditions on the tool and the workpiece are
23
shown. The tool was fixed in space and the cutting speed was applied on the workpiece boundary
4
1
nodes along the x-axis. The simulation began considering Lagrangian conditions with a rigid tool
2
and a plastic workpiece. After formation of the initial chip geometry, an Eulerian method was
3
used for simulating the steady state cutting. In all the modeling conditions, the mesh size was
4
selected to be 0.1 to 0.33 times the feed [21], [22]. Within and around the deformation zone,
5
smaller elements were used and remeshing was used to prevent mesh distortion. The following
6
simplifying assumptions were made: (1) Owing to the high width to thickness ratio of the strip,
7
the plane strain condition is considered, (2) the cutting speed is constant throughout the test, (3)
8
friction is independent of the pressure and (4) the workpiece and the tool boundaries are far
9
enough from the cutting zone to remain at the room temperature. To introduce deformation
10
characteristics of Mg, sophisticated material and damage models are required to represent
11
localized deformation, fracture at shear bands and formation of serrated chips. However, to
12
reduce calculation time, simplified models are employed. The Johnson-Cook (JC) model was
13
selected to describe the mechanical properties of pure magnesium [23]. The mathematical form
14
of the JC model is expressed by Eq. 1:
15
σ Pl = [A + B (ε Pl ) n ]1 + C. ln(
ε& ε&0
Pl
[
) 1 − T *m
]
,
0 : T < TTransition T − TTransition T* = : TTransition < T < Tmelt Tmelt − TTransition 1 : T > Tmelt
(1)
16
where σ Pl is flow stress, T indicates temperature of work material, Tmelt shows the melting
17
temperature, and TTransition is the temperature that all temperatures lower than that don’t have any
18
effects on flow stress. A is initial yield stress (MPa), B is hardening modulus and n shows the
19
work-hardening exponent. ε&0 is the strain rate which the constants A, B and n will be measured
20
in this strain rate. C is strain-rate-dependent coefficient, can be calculated using compression or
21
tension test in the high strain rate. m is thermal softening coefficient that can be determined using
22
hot compression test. The Cockroft-Latham criterion of 3.58 MPa was considered to simulate 5
1
damage in the produced strip [24]. It must be noted that the simplification approach in selecting
2
material and damage models cause deviation of FEM results with actual experiments. To
3
properly describe the friction condition, it was assumed that the deformation occurs only at the
4
shear plane between the cutting tool tip and the constraining tool tip. Therefore, the interface
5
between the constraining tool and the workpiece was considered frictionless [7]. On the rake face
6
of the cutting tool, constant tau (τ) friction model with 0.5 traction was considered. Colombian
7
friction with
8
approaches to estimate the time length required to reach steady-state conditions [22], [25], [26].
9
In this study since the cutting length is 20 times greater than the undeformed chip thickness,
10
based on [25], the time required to reach the steady-state condition is 0.01 seconds. Moreover,
11
(1) the steady-state chip geometry, (2) the plastic strain field, and (3) the temperature distribution
12
in the workpiece were calculated using simulation.
= 0.3 was assumed for all other faces [7]. Researchers have employed different
13 14
4- Results and discussion
15
4-1- Verification of the FEM model
16
In this research, LSEM parameters are studied and calculated using three different methods: (1)
17
analytical method, (2) finite element modeling, and (3) experimental verification. In Fig.5,
18
values of shear angle and effective strain are calculated and reported using these methods at
19
different chip thickness ratios. Results indicate a clear agreement between the three methods of
20
calculations and verify the FEM model. By increasing λ, both shear angle and effective strain are
21
reduced [28-30]. Previous reports indicate that at chip thickness ratios greater than one (λ>1), the
22
shear strain changes direction and increases by increasing the extrusion ratio [27] [29]. In the
23
next step, the developed FEM model is verified with the experimental PIV (particle image
6
1
velocimetry) results reported by Efe et al. [6] for lead. In Fig.6 the strain rate profile on the ABC
2
route is plotted for the same geometry as described in [6]. The highest strain rate occurs at the
3
shear plane connecting the cutting tool tip and the constraining tool tip. As shown in Fig.6, the
4
calculated strain rate distribution and its maximum value of the FEM model and that of Efe et al.
5
[6] are in close agreement with each other. The calculations are repeated for pure Mg (the dashed
6
black line). Results show 8% higher strain rates for pure Mg compared to lead.
7 8
4-2- Temperature and machining force
9
The finite element temperature and force prediction of different LSEM conditions are presented
10
in Fig.7a and b respectively. As the temperature plots of Fig.7a show, the temperature quickly
11
reaches a plateau. Comparing the steady-state temperatures indicates that by increasing the
12
cutting speed from P1 to P2 and P3 the temperature also increases (Fig.7a). A similar
13
observation is reported by Sagapuram et al. [8] when studying LSEM of magnesium alloys
14
(AZ31B). Increasing the rotation speed also increases the time before reaching stability (t3>t2>t1
15
in Fig.7a). Likewise, by increasing the feed (from P5 to P4 and P3), again the steady-state
16
temperature increases. Effects of feed on temperature during the machining process are also
17
studied by Khan et al. [30] and an identical trend is reported. However, no significant effect of
18
feed on time before the steady-state temperature is detected. Many researchers have studied the
19
effect of feed on machining forces and reported that by increasing feed, the cutting force is
20
increased [31][32][33]. De Chiffre et al. [14] have reported that in extrusion machining similar
21
conditions apply and force is increased by increasing feed. In the present FEM results of the
22
constant rotation speed conditions (P3, P4 and P5 in Fig.7b), by increasing the feed from 0.095
7
1
to 0.6
and 1.06
, the force increases from 25N to 200N and 400N for the P5, P4 and
2
P3 conditions, respectively.
3
However, interpreting the force in the constant feed samples (P1, P2 and P3) is not as
4
straightforward. In general, it is well-accepted that by increasing the cutting speed, machining
5
force should decrease [34]. In the studied conditions, increasing the rotation speed leads to rises
6
in the temperature (Fig.7a). Due to increase in the temperature, work-softening occurs and as a
7
result, the flow stress decreases which in turn reduces the machining force. This is why the
8
machining force for P1 (the lower temperature) is higher than P2 and P3 (the higher
9
temperatures).
10
As shown in Fig.7a, the P3 temperature is higher than P2 and based on the above analysis, the P3
11
machining force is expected to be lower than that of P2. However, in the P2 condition, the shear
12
angle and extrusion ratio (R = A0/Af =1/λ) are smaller (Table 1) and thus less machining force is
13
required. The effect of both parameters (work-softening and deformation zone geometry) causes
14
the machining forces of P2 and P3 to become close to each other (Fig.7b).
15
This raises the question of why temperature does not have the same effect on the constant
16
rotation speed samples (P3, P4 and P5). In these samples, the shear angle is increased from P3 to
17
P5 and its effect is more pronounced compared to the temperature and work-softening effect
18
(Table 1). In Table 1, the FEM and experimentally calculated geometry and strain parameters are
19
reported. As shown in the table, the shear angle and effective strain values of the FEM are
20
smaller than the experimentally calculated ones. This difference which was previously reported
21
for machining by other researchers [35], [36] originates from the deviations of chip thickness
22
ratio (λ) which are larger in the FEM owing to the inaccuracy of the material model. In Fig. 8, a
23
summary of the above discussion is presented which shows the effects of LSEM process
8
1
parameters (feed and rotation speed) on the temperature and machining forces obtained by the
2
FEM.
3 4
4-3- Dynamic recrystallization and work-softening
5
As previously discussed, the high temperatures generated by shear and friction throughout
6
LSEM directly influence the mechanical properties. In the processed samples, Vickers micro-
7
hardness is measured as a work-softening indicator. In Fig.9, the Vickers micro-hardness, shear
8
strain, and effective strain are plotted versus chip thickness ratio (λ). Experimental results show
9
that in the processed samples, by increasing the thickness ratio, λ (or decreasing the extrusion
10
ratio, R) shear and effective strains are decreased. However, different behavior is observed for
11
the Vickers micro hardness versus chip thickness ratio (λ). Generally, it is expected that by
12
increasing extrusion ratio, shear and effective strains, HV increases by more work-hardening
13
[14]. To understand the reason behind higher HV at lower shear strains (and effective strains), in
14
Fig.10a the LSEM temperature obtained from the FEM is plotted against the thickness ratio (λ).
15
Results indicate that by increasing the thickness ratio, the temperature is decreased. At low
16
thickness ratios, the temperature is high and above the dynamic recrystallization (DRX)
17
temperature of pure Mg [6], [8]. By DRX, new grains are formed, dislocation density is
18
decreased, and HV is reduced. At intermediate thickness ratios, the temperature is not high
19
enough to activate DRX and only dynamic recovery occurs. Limited hardness reduction is
20
predicted at this condition. At high thickness ratios, the temperature is not high enough to
21
activate work-softening mechanisms and work-hardening conditions dominate. In Fig.10b and c,
22
optical micrographs of the strip cross section at P3 and P5 test conditions are depicted. In both
23
cases, because of fracture during deformation, serrations are formed on the surface. To
9
1
understand micro-mechanisms involved in LSEM, strip microstructures are studied through
2
optical microscopy. In the test conditions that temperature rises above the recrystallization
3
temperature, new grains are formed. The formation of new fine grains is intensified on shear
4
bands [37]. Simultaneously, at high temperatures and high hydrostatic pressures, Mg strength is
5
reduced and the produced strip in fractured right on the shear bands. On the other hand, for the
6
test conditions that the temperature stays below the DRX threshold, the dislocation slip is unable
7
to accommodate the large strain and twinning systems activate extensively all across the
8
microstructure [19]. Sharp twin tips and edges act as stress concentrators and their weak
9
boundaries provide easy path for crack propagation [38]. Again, the produced strips are
10
fractured, this time on twin boundaries. In Fig.11, the observed fracture mechanisms of the
11
produced strips at high and low temperatures are summarized. For each scenario a representing
12
microstructure is also shown. Careful analysis of the microstructures and the failure modes
13
reveal that to produce a flawless strip, two criteria should be met; (1) temperature should stay
14
low to maintain strength and (2) hydrostatic pressure should also stay low to prevent fracture at
15
the weak regions. This observation is in contradiction with previous results of [6] on AZ31. They
16
reported that high hydrostatic pressure enhances workability and suppresses segmentation at high
17
LSEM temperatures. Comparing the experiments in the present study and those done by [6],
18
important differences can be highlighted both in the test setup and in the materials. It seems that
19
the difference in the material properties of pure and alloyed Mg has the most significant effect
20
and can explain the inconsistent observations.
21
(1) Effect of temperature: The critical resolved shear stress (CRSS) necessary to move
22
dislocations is reduced at elevated temperatures [39]. This reduction is more severe in
23
pure Mg (compared to its alloys) since there are no obstacles against dislocation motion.
10
1
Therefore, compared to AZ31, pure Mg is much softer at high temperatures [40-49]. As a
2
result, AZ31 requires higher stresses (and hydrostatic pressures) to move dislocations on
3
slip systems while equivalent stress levels rupture pure Mg.
4
(2) Effect of deformation mechanism: Owing to the limited number of independent slip
5
systems in Mg alloys, twining has an important role in accommodating deformation [41].
6
By rotating the crystal orientation and preparing easy slip systems for further dislocation
7
motion, twinning plays a work-softening role in Mg deformation [42]. At the same time,
8
as previously discussed, twin tips and boundaries may also act as stress concentrators and
9
initiate cracks and provide easy path for their propagation [42]. In LSEM of AZ31, the
10
worksoftening effect of twinning is not significant since dislocations are pinned with
11
solid solutions and precipitates anyways. Moreover, it has been reported that by addition
12
of alloying elements importance of twining in accommodating deformation is reduced
13
[43]. Therefore, high temperatures are suggested for AZ31 samples to reduce the negative
14
effects of twinning. However, for pure Mg, twining is necessary for accommodating
15
deformation.
16
(3) Recrystallization mechanism: Precipitates and solid solutions have significant effects
17
on recrystallization and twining in Mg alloys [44] [43]. In pure magnesium, contributions
18
of twinning induced dynamic recrystallization (TDRX) and continuous dynamic
19
recrystallization (CDRX) are strongly dependent on strain and deformation temperature
20
[45]. At high temperatures and strains, bulging of grain boundaries (discontinuous
21
dynamic recrystallization - DDRX) is common. However, at lower temperature ranges
22
and high strains, continuous dynamic recrystallization (CDRX) without grain boundary
23
bulging dominates. CDRX imposes large elastic strains on the microstructure which
11
1
trigger fracture and separation in the produced strip [46]. But at lower temperature ranges
2
and low strains, TDRX dominates which is accompanied by formation of new grains
3
inside previous twins. As previously discussed, twins are less detrimental to pure Mg
4
compared to its alloys and therefore TDRX is less harmful to integrity compared to
5
CDRX. As a result, in pure Mg, strain and hydrostatic pressure should be in their lower
6
ranges to prevent CDRX.
7
To draw a conclusion, it appears that the pressure and temperature requirements for successful
8
LSEM of AZ31 reported in [6] are greater than those for pure Mg in this study. Therefore, higher
9
pressure and higher temperature are proposed in their study while the same conditions apply in
10
lower temperatures and lower pressures for pure Mg. Based on the above-mentioned
11
interpretation, many different test conditions were planned at various feeds and rotation speeds to
12
find suitable LSEM conditions. Among all the studied conditions, the condition represented as
13
P6 (0.85
14
of this test condition are shown by blue curves. The FEM modeling indicates that not only is the
15
temperature below DRX criteria (~80oC), but also the machining force is low and unlike the
16
previous samples, its curve is very smooth. The curve smoothness represents conditions without
17
shear localization and strip fracture and fragmentation. In Fig.12a, the initially studied samples
18
(P1 to P5) and the proposed condition (P6) are plotted in a hydrostatic pressure-temperature
19
diagram. The strip cross section shows no sign of shear localization which is produced by
20
lowering both the temperature and the hydrostatic pressure. Fig.12b and c show the top and
21
bottom surfaces of the produced strip at P6 test conditions. Surface marks in the local
22
magnifications (Fig.12d and e) clearly indicate that both surfaces of the strip have touched the
23
die and extrusion has occurred. Another sign of successful LSEM can be seen on the strip edges
and 530
) yields promising results. In Fig.7, the temperature and machining force
12
1
which show movement of material in the transverse direction [15]. It should be noticed that, in
2
this study, the FE model is not used to predict the chip shape to be either continuous or
3
segmented. Second, as shown in Fig.6 the simplified FEM results are close to experiments of [6]
4
(PIV test). It should be noted that strain calculation is dependent on the deformation geometry
5
and not the involved strain accommodation micro-mechanisms (shear banding). Therefore, what
6
has been calculated is FEM and upper bound are independent of shear bands. Interestingly,
7
although localization happens in low λ samples, the actual and upper bound also results match
8
quite well in Fig.5. The results of FEM analysis are used to find the trend and absolute values are
9
not aimed [47-49]. To employ more sophisticated material models Hopkinson tests are required
10
which will be completed for a future continuation of the project. In addition, a large set of
11
samples are studied in this research. Here the two extremes of low and high lambda are reported
12
to illustrate the trends of change. Regarding temperatures, figure 7 shows that the temperature
13
rises over 200C in the P2, P3 and P4 samples. In reference [6] the lamda ranges are comparable
14
and experiment temperatures are started from RT. Moreover, it should be considered that when
15
Mg is freely deformed, deformation mechanisms are very different from what happens in severe
16
plastic deformation and constraint conditions. At such high strains, strain rates and constrains
17
Mg is proven to be more formable.
18 19
5- Conclusions
20
In the present study, a finite element model is proposed for large strain extrusion machining of
21
pure magnesium. The model is verified by previous reports and analytical and experimental data.
22
Five different test conditions are selected with various feed and rotation speeds. Effects of
23
processed parameters on temperature, machining force, geometrical and microstructural
13
1
properties are studied using the FEM and experiments. Based on the obtained results it was
2
found out that the temperature and hydrostatic pressure have significant effects on strip fracture.
3
At all temperatures and high hydrostatic pressures, strips are fractured at the shear bands and
4
twin boundaries respectively. To locate the process parameter with minimum temperature and
5
hydrostatic pressure, various test conditions are simulated in the calibrated FEM model. Based
6
on the simulations, a new test condition is proposed at 0.85
7
The strip produced at the newly proposed condition represents excellent surface quality without
8
any sign of shear localization and fracture.
feed and 530
rotation speed.
9 10
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11
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17 18
19
1 2
Figure 1 – Schematic configurations of the LSEM (a) deformation zone, (b) LSEM tool and (c)
3
the tool and workpiece configuration of the experiment.
4 5
20
1 2
Figure 2 – Experiment conditions at different feeds and rotation speeds.
3 4
21
1 2
Figure 3 – (a) Test setup and (b) the strip produced at the P4 test condition (c) optical
3
microscopy illustrating the top and (d) the bottom strip surfaces.
4 5
22
1 2
Figure 4 – Thermal and displacement boundary conditions.
3 4
23
1 2
Figure 5 – Experimentally measured, finite element calculation and analytical shear angle and
3
effective strain at different extrusion ratios (λ).
4 5
24
1 2
Figure 6 – Verification of the developed FEM model in this paper for lead and magnesium with
3
the experimental PIV results reported by Efe et al [6] for lead.
4 5
25
1 2
Figure 7 – Predicted LSEM (a) temperature and (b) forces calculated by the FEM model for the
3
experiment conditions of Fig.2.
4 5
26
1 2
Figure 8 – Effect of feed and cutting speed on the LSEM results (temperature and machining
3
force) obtained by the FEM.
4 5
27
1 2
Figure 9 – Micro-Vickers hardness, shear strain and effective strain versus thickness ratio (λ) for
3
the studied LSEM conditions.
4 5
28
1 2
Figure 10 – (a) LSEM temperature at different chip thickness ratios for the studied experiment
3
conditions and chip cross-sections for the (b) P3 and (c) P5 test conditions.
4 5
29
1 2
Figure 11 – Micro-mechanisms involved in LSEM at high hydrostatic pressure and high and low
3
temperatures.
4 5
30
1 2
Figure 12- (a) hydrostatic pressure versus temperature for the studied LSEM samples. (b) top and
3
(c) bottom surfaces of the sample processed at P6 condition. (d) and (e) are higher
4
magnifications of the squared areas.
5 6
31
1
Table 1 – Properties of the processed strips measured experimentally and predicted by the FEM. Experimental
P1
Chip thickness ration 0.264
Shear angle (degrees) 79.9
P2
0.245
P3
Finite element modeling (FEM)
2.24
Chip thickness ration 0.267
Shear angle (degrees) 71.3
80.9
2.40
0.253
0.235
81.5
2.50
P4
0.272
79.5
P5
0.853
P6
0.941
#
Effective strain
Effective strain
Hydrostatic pressure
1.864
1.198
68.6
1.404
1.201
0.244
71.1
2.044
1.205
2.18
0.273
68.5
1.927
1.195
52.4
1.05
0.881
40.8
1.653
1.19
47.5
1.06
0.941
43.4
1.506
1.12
2
32
Highlights 1. A finite element model is defined and validated and based on the modeling results and experiments a target condition is explored to machine a continuous extruded strip of pure magnesium. 2. It was found out that the temperature and hydrostatic pressure have significant effects on strip fracture. 3. To locate the process parameter with minimum temperature and hydrostatic pressure, various test conditions are simulated in the calibrated FEM model. 4. At all temperatures and high hydrostatic pressures, strips are fractured at the shear bands and twin boundaries respectively.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S2588-8404(19)30103-9
DOI:
https://doi.org/10.1016/j.ijlmm.2019.09.001
Reference:
IJLMM 79
To appear in:
International Journal of Lightweight Materials and Manufacture
Received Date: 12 August 2019 Revised Date:
4 September 2019
Accepted Date: 4 September 2019
Please cite this article as: S. Molafilabi, A. Sadeghi, M. Hadad, Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg), International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.09.001. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.
Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg) Sajad Molafilabi, Alireza Sadeghi, Mohammadjafar Hadad*
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Corresponding author email: [email protected], Tel: +982161119958, Fax: +982188013029
1 2 3 4 5 6
Investigation of large strain extrusion machining (LSEM) of pure magnesium (Mg)
7 8 9 10 11 12
Abstract
13
Large strain extrusion machining (LSEM) is used to produce pure magnesium strips directly
14
from as-cast billets. LSEM reduces manufacturing steps and the special shear direction inclines
15
the unfavorable strong basal texture of Mg. Finding suitable parameter ranges to control
16
geometry and properties of the produced strip is a great challenge. In the present research, a
17
finite element model is proposed and verified with experiments and previous findings. Next,
18
effects of process parameters (temperature and pressure) on geometrical and microstructural
19
properties of the produced strips are investigated. Studying the involved failure micro-
20
mechanisms shows that the process temperature and hydrostatic pressure have adverse effects on
21
the production of a flawless strip. To reduce the temperature and hydrostatic pressure throughout
22
the LSEM process many different conditions are tested by the FEM model. Among all the
23
examined conditions, 0.85
24
it terms of low temperature, low hydrostatic pressure, and stable machining force. The proposed
25
conditions are applied in the experimental setup and a uniform and flawless strip is obtained.
feed and 530
rotation speed yields the most promising results
26 27 28
Keywords: large strain extrusion machining; magnesium; turning; chip formation, FEM
1
1 2
1- Introduction
3
The large difference in the critical resolved shear stress (
4
hexagonal magnesium results in the formation of a strong basal texture through deformation [1].
5
In rolled magnesium sheets, the hexagonal c-axis aligns with the deformation direction and easy
6
slip of dislocations becomes limited in the sheet thickness direction (c-axis) [2]. Consequently,
7
the rolled sheets exhibit strong anisotropic behavior and their formability is significantly reduced
8
for further sheet forming processes (e.g. deep drawing). Various approaches are used by different
9
researchers to control the formation of the strong basal texture in rolling of Mg sheets [3].
10
Among those, changing the deformation force direction has received significant attention as an
11
alternate approach to weaken the basal texture. Processes such as (1) axisymmetric rolling [4],
12
(2) cross-rolling [5] and (3) large strain extrusion machining [6] are proven to have positive
13
effects on reduction of the basal texture strength. In large strain extrusion machining (LSEM),
14
the formed chip is constrained in a die opening, right after separation from the material bulk.
15
Different configurations and relative motions of tool and workpiece are proposed for LSEM [7].
16
During the process, the shear direction is inclined compared to the produced chip and therefore
17
the basal texture component is inclined [8]. In 1925 sheets were attempted to be directly formed
18
from the bulk of material by large strain machining (LSM) was used to peel a stainless steel disc
19
by a high positive rake angle tool [9][10]. The process required tons of hydraulic force to make
20
the peeling tool stable [11] and eventually, the produced foil was not flat. Later, extrusion was
21
combined with machining by employing a constraining unit above the cutting tool to apply shear
22
strain and increase uniformity [12]. Wire production was the first application of extrusion cutting
23
[13]. Then cutting extrusion was used to produce a 40m long continuous brass strip from a
2
) of different slip systems of
1
cylindrical bar [14]. In 2007 Moscoso [15] studied the microstructures and mechanical properties
2
of LSEM strips and showed that this process could be classified as a severe plastic deformation
3
process [15]–[19]. In the present research, the finite element method (FEM) is used to predict
4
machining force, hydrostatic pressure, and temperature in LSEM of pure magnesium.
5
Simulations were calibrated using experiments. The numerical model was used to locate
6
appropriate LSEM parameters for forming a uniform Mg strip. Then the located LSEM
7
parameters were applied in real experiments and a uniform strip was obtained.
8 9
2- Experimental procedure
10
Linear configuration large-strain extrusion machining (Fig.1) was carried out on a 78 mm
11
diameter pure magnesium bars. The cylindrical bars were clamped on a 5 kW turning machine to
12
carry out the experiments. A special tool was designed to remove chips and simultaneously
13
constrain their expansion. The tool was machined from a cold work tool steel (C 2.00; Cr 12.0)
14
with 60 Rockwell C hardness. The tool was designed to control different dimensions including
15
the undeformed and deformed sections to apply different chip thickness ratios (λ). The rake angle
16
(α) was kept constant through all the experiments equal to 5 degrees. In Fig.1 the schematic
17
configurations of the tool and workpiece are shown.
18
To investigate effects of cutting parameters on different properties of produced LSEM strips, five
19
experimental conditions were selected by alternating the feed and rotation speed. In the first set
20
of experiments, represented by P1, P2, and P3, the feed was set constant equal to 1.060
21
the rotation speed was increased from 190
22
respectively (Fig.2). In the second set of experiments, represented by P3, P4 and P5, the rotation
23
speed (at constant diameter) was constant equal to 1050
for P1 to 530
3
and
and
1050 for P2 and P3
and the feed decreased from 1.060
1
to 0.600 and 0.095
from P3 to P4 and P5 respectively (Fig.2). It should be noted that
2
although λ is constant by changing rotation speed, it may not remain constant when feed is
3
changing. As described in Fig.1,
4
decreased consequently. Other than the depicted conditions in Fig. 2, many other conditions
5
were tested but not reported in the present paper. A large set of samples are studied in this
6
research. Here the two extremes of low and high λ are reported to illustrate the trends of change.
7
Before starting each test, the LSEM tool tolerances were checked, fixed and the lathe was set to
8
proper feed and rotation speed. Molybdenum disulfide (MoS2) was used as a high-temperature
9
lubricator between the cutting and constraining tools. Each test was stopped after producing a
10
three-meter strip. In Fig. 3 the test setup and the produced strip are shown. After LSEM, the strip
11
surfaces were examined by optical microscopy and the dimensions were carefully measured. By
12
measuring the thickness of the produced strip in terms of known tool parameters, the extrusion
13
pressure and the shear strain were calculated using the upper bound equations proposed by De
14
Chiffre [20]. Important to mention that these equations are based on uniform deformation, and
15
localization and fracture at shear bands are not considered. Therefore it can be predicted that the
16
actual values of strain are lower than the values calculated by the upper bound approach. Next,
17
the samples were cold mounted, ground and polished for optical microscopy and hardness
18
measurements.
=
⁄
by increasing the feed t0 increases and lambda is
19 20
3- Finite element modeling
21
To model the thermo-mechanical LSEM process, SFTC-DEFORM (V.11) software was used. In
22
Fig.4 the thermal and displacement boundary conditions on the tool and the workpiece are
23
shown. The tool was fixed in space and the cutting speed was applied on the workpiece boundary
4
1
nodes along the x-axis. The simulation began considering Lagrangian conditions with a rigid tool
2
and a plastic workpiece. After formation of the initial chip geometry, an Eulerian method was
3
used for simulating the steady state cutting. In all the modeling conditions, the mesh size was
4
selected to be 0.1 to 0.33 times the feed [21], [22]. Within and around the deformation zone,
5
smaller elements were used and remeshing was used to prevent mesh distortion. The following
6
simplifying assumptions were made: (1) Owing to the high width to thickness ratio of the strip,
7
the plane strain condition is considered, (2) the cutting speed is constant throughout the test, (3)
8
friction is independent of the pressure and (4) the workpiece and the tool boundaries are far
9
enough from the cutting zone to remain at the room temperature. To introduce deformation
10
characteristics of Mg, sophisticated material and damage models are required to represent
11
localized deformation, fracture at shear bands and formation of serrated chips. However, to
12
reduce calculation time, simplified models are employed. The Johnson-Cook (JC) model was
13
selected to describe the mechanical properties of pure magnesium [23]. The mathematical form
14
of the JC model is expressed by Eq. 1:
15
σ Pl = [A + B (ε Pl ) n ]1 + C. ln(
ε& ε&0
Pl
[
) 1 − T *m
]
,
0 : T < TTransition T − TTransition T* = : TTransition < T < Tmelt Tmelt − TTransition 1 : T > Tmelt
(1)
16
where σ Pl is flow stress, T indicates temperature of work material, Tmelt shows the melting
17
temperature, and TTransition is the temperature that all temperatures lower than that don’t have any
18
effects on flow stress. A is initial yield stress (MPa), B is hardening modulus and n shows the
19
work-hardening exponent. ε&0 is the strain rate which the constants A, B and n will be measured
20
in this strain rate. C is strain-rate-dependent coefficient, can be calculated using compression or
21
tension test in the high strain rate. m is thermal softening coefficient that can be determined using
22
hot compression test. The Cockroft-Latham criterion of 3.58 MPa was considered to simulate 5
1
damage in the produced strip [24]. It must be noted that the simplification approach in selecting
2
material and damage models cause deviation of FEM results with actual experiments. To
3
properly describe the friction condition, it was assumed that the deformation occurs only at the
4
shear plane between the cutting tool tip and the constraining tool tip. Therefore, the interface
5
between the constraining tool and the workpiece was considered frictionless [7]. On the rake face
6
of the cutting tool, constant tau (τ) friction model with 0.5 traction was considered. Colombian
7
friction with
8
approaches to estimate the time length required to reach steady-state conditions [22], [25], [26].
9
In this study since the cutting length is 20 times greater than the undeformed chip thickness,
10
based on [25], the time required to reach the steady-state condition is 0.01 seconds. Moreover,
11
(1) the steady-state chip geometry, (2) the plastic strain field, and (3) the temperature distribution
12
in the workpiece were calculated using simulation.
= 0.3 was assumed for all other faces [7]. Researchers have employed different
13 14
4- Results and discussion
15
4-1- Verification of the FEM model
16
In this research, LSEM parameters are studied and calculated using three different methods: (1)
17
analytical method, (2) finite element modeling, and (3) experimental verification. In Fig.5,
18
values of shear angle and effective strain are calculated and reported using these methods at
19
different chip thickness ratios. Results indicate a clear agreement between the three methods of
20
calculations and verify the FEM model. By increasing λ, both shear angle and effective strain are
21
reduced [28-30]. Previous reports indicate that at chip thickness ratios greater than one (λ>1), the
22
shear strain changes direction and increases by increasing the extrusion ratio [27] [29]. In the
23
next step, the developed FEM model is verified with the experimental PIV (particle image
6
1
velocimetry) results reported by Efe et al. [6] for lead. In Fig.6 the strain rate profile on the ABC
2
route is plotted for the same geometry as described in [6]. The highest strain rate occurs at the
3
shear plane connecting the cutting tool tip and the constraining tool tip. As shown in Fig.6, the
4
calculated strain rate distribution and its maximum value of the FEM model and that of Efe et al.
5
[6] are in close agreement with each other. The calculations are repeated for pure Mg (the dashed
6
black line). Results show 8% higher strain rates for pure Mg compared to lead.
7 8
4-2- Temperature and machining force
9
The finite element temperature and force prediction of different LSEM conditions are presented
10
in Fig.7a and b respectively. As the temperature plots of Fig.7a show, the temperature quickly
11
reaches a plateau. Comparing the steady-state temperatures indicates that by increasing the
12
cutting speed from P1 to P2 and P3 the temperature also increases (Fig.7a). A similar
13
observation is reported by Sagapuram et al. [8] when studying LSEM of magnesium alloys
14
(AZ31B). Increasing the rotation speed also increases the time before reaching stability (t3>t2>t1
15
in Fig.7a). Likewise, by increasing the feed (from P5 to P4 and P3), again the steady-state
16
temperature increases. Effects of feed on temperature during the machining process are also
17
studied by Khan et al. [30] and an identical trend is reported. However, no significant effect of
18
feed on time before the steady-state temperature is detected. Many researchers have studied the
19
effect of feed on machining forces and reported that by increasing feed, the cutting force is
20
increased [31][32][33]. De Chiffre et al. [14] have reported that in extrusion machining similar
21
conditions apply and force is increased by increasing feed. In the present FEM results of the
22
constant rotation speed conditions (P3, P4 and P5 in Fig.7b), by increasing the feed from 0.095
7
1
to 0.6
and 1.06
, the force increases from 25N to 200N and 400N for the P5, P4 and
2
P3 conditions, respectively.
3
However, interpreting the force in the constant feed samples (P1, P2 and P3) is not as
4
straightforward. In general, it is well-accepted that by increasing the cutting speed, machining
5
force should decrease [34]. In the studied conditions, increasing the rotation speed leads to rises
6
in the temperature (Fig.7a). Due to increase in the temperature, work-softening occurs and as a
7
result, the flow stress decreases which in turn reduces the machining force. This is why the
8
machining force for P1 (the lower temperature) is higher than P2 and P3 (the higher
9
temperatures).
10
As shown in Fig.7a, the P3 temperature is higher than P2 and based on the above analysis, the P3
11
machining force is expected to be lower than that of P2. However, in the P2 condition, the shear
12
angle and extrusion ratio (R = A0/Af =1/λ) are smaller (Table 1) and thus less machining force is
13
required. The effect of both parameters (work-softening and deformation zone geometry) causes
14
the machining forces of P2 and P3 to become close to each other (Fig.7b).
15
This raises the question of why temperature does not have the same effect on the constant
16
rotation speed samples (P3, P4 and P5). In these samples, the shear angle is increased from P3 to
17
P5 and its effect is more pronounced compared to the temperature and work-softening effect
18
(Table 1). In Table 1, the FEM and experimentally calculated geometry and strain parameters are
19
reported. As shown in the table, the shear angle and effective strain values of the FEM are
20
smaller than the experimentally calculated ones. This difference which was previously reported
21
for machining by other researchers [35], [36] originates from the deviations of chip thickness
22
ratio (λ) which are larger in the FEM owing to the inaccuracy of the material model. In Fig. 8, a
23
summary of the above discussion is presented which shows the effects of LSEM process
8
1
parameters (feed and rotation speed) on the temperature and machining forces obtained by the
2
FEM.
3 4
4-3- Dynamic recrystallization and work-softening
5
As previously discussed, the high temperatures generated by shear and friction throughout
6
LSEM directly influence the mechanical properties. In the processed samples, Vickers micro-
7
hardness is measured as a work-softening indicator. In Fig.9, the Vickers micro-hardness, shear
8
strain, and effective strain are plotted versus chip thickness ratio (λ). Experimental results show
9
that in the processed samples, by increasing the thickness ratio, λ (or decreasing the extrusion
10
ratio, R) shear and effective strains are decreased. However, different behavior is observed for
11
the Vickers micro hardness versus chip thickness ratio (λ). Generally, it is expected that by
12
increasing extrusion ratio, shear and effective strains, HV increases by more work-hardening
13
[14]. To understand the reason behind higher HV at lower shear strains (and effective strains), in
14
Fig.10a the LSEM temperature obtained from the FEM is plotted against the thickness ratio (λ).
15
Results indicate that by increasing the thickness ratio, the temperature is decreased. At low
16
thickness ratios, the temperature is high and above the dynamic recrystallization (DRX)
17
temperature of pure Mg [6], [8]. By DRX, new grains are formed, dislocation density is
18
decreased, and HV is reduced. At intermediate thickness ratios, the temperature is not high
19
enough to activate DRX and only dynamic recovery occurs. Limited hardness reduction is
20
predicted at this condition. At high thickness ratios, the temperature is not high enough to
21
activate work-softening mechanisms and work-hardening conditions dominate. In Fig.10b and c,
22
optical micrographs of the strip cross section at P3 and P5 test conditions are depicted. In both
23
cases, because of fracture during deformation, serrations are formed on the surface. To
9
1
understand micro-mechanisms involved in LSEM, strip microstructures are studied through
2
optical microscopy. In the test conditions that temperature rises above the recrystallization
3
temperature, new grains are formed. The formation of new fine grains is intensified on shear
4
bands [37]. Simultaneously, at high temperatures and high hydrostatic pressures, Mg strength is
5
reduced and the produced strip in fractured right on the shear bands. On the other hand, for the
6
test conditions that the temperature stays below the DRX threshold, the dislocation slip is unable
7
to accommodate the large strain and twinning systems activate extensively all across the
8
microstructure [19]. Sharp twin tips and edges act as stress concentrators and their weak
9
boundaries provide easy path for crack propagation [38]. Again, the produced strips are
10
fractured, this time on twin boundaries. In Fig.11, the observed fracture mechanisms of the
11
produced strips at high and low temperatures are summarized. For each scenario a representing
12
microstructure is also shown. Careful analysis of the microstructures and the failure modes
13
reveal that to produce a flawless strip, two criteria should be met; (1) temperature should stay
14
low to maintain strength and (2) hydrostatic pressure should also stay low to prevent fracture at
15
the weak regions. This observation is in contradiction with previous results of [6] on AZ31. They
16
reported that high hydrostatic pressure enhances workability and suppresses segmentation at high
17
LSEM temperatures. Comparing the experiments in the present study and those done by [6],
18
important differences can be highlighted both in the test setup and in the materials. It seems that
19
the difference in the material properties of pure and alloyed Mg has the most significant effect
20
and can explain the inconsistent observations.
21
(1) Effect of temperature: The critical resolved shear stress (CRSS) necessary to move
22
dislocations is reduced at elevated temperatures [39]. This reduction is more severe in
23
pure Mg (compared to its alloys) since there are no obstacles against dislocation motion.
10
1
Therefore, compared to AZ31, pure Mg is much softer at high temperatures [40-49]. As a
2
result, AZ31 requires higher stresses (and hydrostatic pressures) to move dislocations on
3
slip systems while equivalent stress levels rupture pure Mg.
4
(2) Effect of deformation mechanism: Owing to the limited number of independent slip
5
systems in Mg alloys, twining has an important role in accommodating deformation [41].
6
By rotating the crystal orientation and preparing easy slip systems for further dislocation
7
motion, twinning plays a work-softening role in Mg deformation [42]. At the same time,
8
as previously discussed, twin tips and boundaries may also act as stress concentrators and
9
initiate cracks and provide easy path for their propagation [42]. In LSEM of AZ31, the
10
worksoftening effect of twinning is not significant since dislocations are pinned with
11
solid solutions and precipitates anyways. Moreover, it has been reported that by addition
12
of alloying elements importance of twining in accommodating deformation is reduced
13
[43]. Therefore, high temperatures are suggested for AZ31 samples to reduce the negative
14
effects of twinning. However, for pure Mg, twining is necessary for accommodating
15
deformation.
16
(3) Recrystallization mechanism: Precipitates and solid solutions have significant effects
17
on recrystallization and twining in Mg alloys [44] [43]. In pure magnesium, contributions
18
of twinning induced dynamic recrystallization (TDRX) and continuous dynamic
19
recrystallization (CDRX) are strongly dependent on strain and deformation temperature
20
[45]. At high temperatures and strains, bulging of grain boundaries (discontinuous
21
dynamic recrystallization - DDRX) is common. However, at lower temperature ranges
22
and high strains, continuous dynamic recrystallization (CDRX) without grain boundary
23
bulging dominates. CDRX imposes large elastic strains on the microstructure which
11
1
trigger fracture and separation in the produced strip [46]. But at lower temperature ranges
2
and low strains, TDRX dominates which is accompanied by formation of new grains
3
inside previous twins. As previously discussed, twins are less detrimental to pure Mg
4
compared to its alloys and therefore TDRX is less harmful to integrity compared to
5
CDRX. As a result, in pure Mg, strain and hydrostatic pressure should be in their lower
6
ranges to prevent CDRX.
7
To draw a conclusion, it appears that the pressure and temperature requirements for successful
8
LSEM of AZ31 reported in [6] are greater than those for pure Mg in this study. Therefore, higher
9
pressure and higher temperature are proposed in their study while the same conditions apply in
10
lower temperatures and lower pressures for pure Mg. Based on the above-mentioned
11
interpretation, many different test conditions were planned at various feeds and rotation speeds to
12
find suitable LSEM conditions. Among all the studied conditions, the condition represented as
13
P6 (0.85
14
of this test condition are shown by blue curves. The FEM modeling indicates that not only is the
15
temperature below DRX criteria (~80oC), but also the machining force is low and unlike the
16
previous samples, its curve is very smooth. The curve smoothness represents conditions without
17
shear localization and strip fracture and fragmentation. In Fig.12a, the initially studied samples
18
(P1 to P5) and the proposed condition (P6) are plotted in a hydrostatic pressure-temperature
19
diagram. The strip cross section shows no sign of shear localization which is produced by
20
lowering both the temperature and the hydrostatic pressure. Fig.12b and c show the top and
21
bottom surfaces of the produced strip at P6 test conditions. Surface marks in the local
22
magnifications (Fig.12d and e) clearly indicate that both surfaces of the strip have touched the
23
die and extrusion has occurred. Another sign of successful LSEM can be seen on the strip edges
and 530
) yields promising results. In Fig.7, the temperature and machining force
12
1
which show movement of material in the transverse direction [15]. It should be noticed that, in
2
this study, the FE model is not used to predict the chip shape to be either continuous or
3
segmented. Second, as shown in Fig.6 the simplified FEM results are close to experiments of [6]
4
(PIV test). It should be noted that strain calculation is dependent on the deformation geometry
5
and not the involved strain accommodation micro-mechanisms (shear banding). Therefore, what
6
has been calculated is FEM and upper bound are independent of shear bands. Interestingly,
7
although localization happens in low λ samples, the actual and upper bound also results match
8
quite well in Fig.5. The results of FEM analysis are used to find the trend and absolute values are
9
not aimed [47-49]. To employ more sophisticated material models Hopkinson tests are required
10
which will be completed for a future continuation of the project. In addition, a large set of
11
samples are studied in this research. Here the two extremes of low and high lambda are reported
12
to illustrate the trends of change. Regarding temperatures, figure 7 shows that the temperature
13
rises over 200C in the P2, P3 and P4 samples. In reference [6] the lamda ranges are comparable
14
and experiment temperatures are started from RT. Moreover, it should be considered that when
15
Mg is freely deformed, deformation mechanisms are very different from what happens in severe
16
plastic deformation and constraint conditions. At such high strains, strain rates and constrains
17
Mg is proven to be more formable.
18 19
5- Conclusions
20
In the present study, a finite element model is proposed for large strain extrusion machining of
21
pure magnesium. The model is verified by previous reports and analytical and experimental data.
22
Five different test conditions are selected with various feed and rotation speeds. Effects of
23
processed parameters on temperature, machining force, geometrical and microstructural
13
1
properties are studied using the FEM and experiments. Based on the obtained results it was
2
found out that the temperature and hydrostatic pressure have significant effects on strip fracture.
3
At all temperatures and high hydrostatic pressures, strips are fractured at the shear bands and
4
twin boundaries respectively. To locate the process parameter with minimum temperature and
5
hydrostatic pressure, various test conditions are simulated in the calibrated FEM model. Based
6
on the simulations, a new test condition is proposed at 0.85
7
The strip produced at the newly proposed condition represents excellent surface quality without
8
any sign of shear localization and fracture.
feed and 530
rotation speed.
9 10
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17 18
19
1 2
Figure 1 – Schematic configurations of the LSEM (a) deformation zone, (b) LSEM tool and (c)
3
the tool and workpiece configuration of the experiment.
4 5
20
1 2
Figure 2 – Experiment conditions at different feeds and rotation speeds.
3 4
21
1 2
Figure 3 – (a) Test setup and (b) the strip produced at the P4 test condition (c) optical
3
microscopy illustrating the top and (d) the bottom strip surfaces.
4 5
22
1 2
Figure 4 – Thermal and displacement boundary conditions.
3 4
23
1 2
Figure 5 – Experimentally measured, finite element calculation and analytical shear angle and
3
effective strain at different extrusion ratios (λ).
4 5
24
1 2
Figure 6 – Verification of the developed FEM model in this paper for lead and magnesium with
3
the experimental PIV results reported by Efe et al [6] for lead.
4 5
25
1 2
Figure 7 – Predicted LSEM (a) temperature and (b) forces calculated by the FEM model for the
3
experiment conditions of Fig.2.
4 5
26
1 2
Figure 8 – Effect of feed and cutting speed on the LSEM results (temperature and machining
3
force) obtained by the FEM.
4 5
27
1 2
Figure 9 – Micro-Vickers hardness, shear strain and effective strain versus thickness ratio (λ) for
3
the studied LSEM conditions.
4 5
28
1 2
Figure 10 – (a) LSEM temperature at different chip thickness ratios for the studied experiment
3
conditions and chip cross-sections for the (b) P3 and (c) P5 test conditions.
4 5
29
1 2
Figure 11 – Micro-mechanisms involved in LSEM at high hydrostatic pressure and high and low
3
temperatures.
4 5
30
1 2
Figure 12- (a) hydrostatic pressure versus temperature for the studied LSEM samples. (b) top and
3
(c) bottom surfaces of the sample processed at P6 condition. (d) and (e) are higher
4
magnifications of the squared areas.
5 6
31
1
Table 1 – Properties of the processed strips measured experimentally and predicted by the FEM. Experimental
P1
Chip thickness ration 0.264
Shear angle (degrees) 79.9
P2
0.245
P3
Finite element modeling (FEM)
2.24
Chip thickness ration 0.267
Shear angle (degrees) 71.3
80.9
2.40
0.253
0.235
81.5
2.50
P4
0.272
79.5
P5
0.853
P6
0.941
#
Effective strain
Effective strain
Hydrostatic pressure
1.864
1.198
68.6
1.404
1.201
0.244
71.1
2.044
1.205
2.18
0.273
68.5
1.927
1.195
52.4
1.05
0.881
40.8
1.653
1.19
47.5
1.06
0.941
43.4
1.506
1.12
2
32
Highlights 1. A finite element model is defined and validated and based on the modeling results and experiments a target condition is explored to machine a continuous extruded strip of pure magnesium. 2. It was found out that the temperature and hydrostatic pressure have significant effects on strip fracture. 3. To locate the process parameter with minimum temperature and hydrostatic pressure, various test conditions are simulated in the calibrated FEM model. 4. At all temperatures and high hydrostatic pressures, strips are fractured at the shear bands and twin boundaries respectively.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: