FLOW STRESS MICROSTRUCTURES AND MODELING
IN HOT EXTRUSION OF MAGNESIUM ALLOYS
H.J. McQueen*, M. Myshlaev**, M. Sauerborn and A. Mwembela*
* Mechanical Engineering, Concordia University
Montreal, Canada H3G 1M8
** Baikov Institute of Metallurgy, RAS, Moscow
117911
Russia
in several grades and tempers (i.e. fabricated, annealed and
hard-rolled). With minimum weight penalty of any metal,
magnesium thick-sheet construction provides the rigidity
necessary in a structure, without the need for costly assembly
of ribs and similar reinforcing members [6-8]. Wrought
magnesium has been widely utilized in transportation,
handling equipment and sports equipment [6].
Abstract
The hot ductility and strength, as well as constitutive equations
were determined for Mg-3Al-lZn (AZ31), Mg-5,5Al-3Zn
(AZ63) Mg-8Al-lZn (AZ91) and Mg-6Zn-0.6Zr (ZK60) by
torsion testing across the range 180-450°C, 0.01 to 1.0 s"1.
Optical observations show that twinning occurs extensively at
low strain to reorient grains without suitable slip planes. At
180°, slip is normally limited to the basal system except when
stress concentrations at grain or twin boundaries enhance other
systems. However as T rises above 300°C, thermally activated
pyramidal or prismatic slip causes noticeable dynamic recovery
near the twin and grain boundaries, as observed in TEM. The
development of misoriented regions leads tp formation of
dynamic recrystallization grains. These restoration mechanisms markedly raises the ductility above 300°C. The constitutive equations were employed in extrusion modeling.
Magnesium alloys with a hexagonal crystal structure, are much
more workable at elevated temperatures than at 20°C. Below
about 150°C, slip is mainly limited to the hexagonal basal
planes, since the critical yield stress on prismatic or pyramidal
planes is higher by a factor of 10. This falls to a factor of 2 by
about 400°C [9,10]. However, the critical twinning stress on
pyramidal planes (six orientations in each grain) is only
slightly higher than basal slip [1,11-13]. The reorientation
through about 80° brings twin basal planes to a much higher
shear stress than in the matrix grain. In addition, high temperature enhances dynamic recovery (DRV) in which dislocations climb, annihilate and arrange into simple, low-energy
sub grain boundaries (SGB) [10,14-17]. Where the substructure
is more dense, dynamic recrystallization (DRX) may nucleate
providing new randomly oriented grains, which deform easily
[10,13,17-20]. Moreover, working in one high temperature
operation, without repeated annealing and reworking, reduces
the time involved and eliminates die equipment for extra
stages. Hot formed parts can be made to closer dimensional
tolerances than cold formed because of less springback [6].
Introduction
Magnesium and its alloys are attractive for many engineering
structural and non-structural applications because they exhibit
good machinability and hot formability, high strength-toweight ratios of both the wrought and cast alloys [1],
Expanded application in the automotive industry has been
mainly as die castings because of the high productivity,
dimensional and surface quality and mechanical properties
[2,3]. Fabrication by mechanical forming has great potential
because the products have greater strength and ductility; the
processing requires optimization for competitive productivity
and appearance [4,5]. Wrought magnesium alloys are produced
as bars, billets and shapes, wire, sheet and plate, forgings and
tubing, with moderate mechanical properties.
The alloy
AZ31B is most widely usedfor sheet and plate and is available
In the present project, as-cast alloys were subjected to hot
torsion testing to establish the hot strength and ductility
dependence on temperature T and strain rate E. With the
expectation of finding a window for forming with improved
ductility and microstructure. The results were later employed
for modeling and estimation of the extrudability of the alloys.
Magnesium Technology 2000
Edited by H.I. Kaplan, J. Hryn, and B. Clow
The Minerals, Metals & Materials Society, 2000
355
Experimental Techniques
The specimens of AZ31 and AZ31-Mn with compositions Mg2.8Al-0.88Zn-0.01Mn and Mg-3.2Al-l.lZn-0.34Mn respectively and were supplied as ingots by Timminco, Toronto,
Ontario. The as-cast specimens were quite coarse grained, with
segregated second phase. Comparison was made to AZ63 (6%
Al), AZ91 (9% Al) andZK60 (6%Zn). The specimens with gage
length, L=22.2mm and radius, r=3.2mm were deformed in the
range 180 - 450°C and 0.01-1 s"1 by means of a servocontrolled, hydraulic motor with a rotary potentiometer for
twist measurement [21-25]. The fixed grip was attached to a
torque cell mounted on a tail stock and the lathe-bed frame. The
specimens were heated in an argon atmosphere by a radiant
furnace. The testing program was applied through a computer
which also recorded the torque-twist measurements. Tests were
conducted to failure; specimens were quenched in two (2)
seconds. Sections normal to a radius just below the surface were
prepared for optical and transmission microscopy bymethods
described elsewhere [24-27].
O
•
V
i<r'
ALLOY AZ31 Mn
1 8 0 - C T 360'C
240-C D 420-C
300-C ■ 450-C
io°
IO1
c - B.aSZ MP»
ic;
le^
io*
ie*
ic'
SINHImn
/ m
■
r
I.
z
'//
/j
ALLOY AZ31 Mn
O
•
■ V
i - 1.01_1
.1
•
1
C - OJll i"
/ /
//
/
/v
■
/
•
■f/
S-4..D
Q - 1 3 S KJItnol
A (sinh aup) n == sexp(Qiw:RT)=Z
Fig. 2. The constitutive analysis according to Eqn. 3 is
illustrated for dependence of a) a on 8 and b) a on T [21].
Because of the radial gradient in strain e and strain rate I, flow
stress a related to the outer annulus was calculated by the FieldsBackofen formula [21-25]:
a = (V3 (torque)/2jtr3)(3+m+n)
(1)
where m is the strain rate sensitivity and n' is the strain
hardening rate which is zero at the flow curve peak Op, ep The
outer annulus strain is:
£ = (2jtr/Y3 L)/(no. of twists)
(2)
both o and e are equivalent to uniaxial tension through the von
Mises convention.
Mechanical Results
250
300
3S0
The a-e curves workhardened to a peak about 0.6 at low T and
0.3 at high T. At 150-240°C, fracture occurred near the peak,
but at higher T a plateau developed with a gradual decline to
failure [22-25]. As seen in Fig. 1, rising T and falling E
decreases a p about 250 to 25 MPa and Ef from 0.5 to 2.5. The
flow curve shapes were similar for AZ63, AZ91 and ZK60,
following the same variation with T and e. As-cast AZ91
exhibited hot shortness above 350°C; a preliminary TMP at
400
TEMPSIATURE T. ' C
Fig. 1. In hot torsion of AZ31 Mn a) a declines as T rises,
higher for higher e ; b) 6f mounts as T rises, lower for higher e.
356
Fig. 3 . Optical microstructures of ZK60: a)240°C, 0.1 s 1 , Ef = 0.15, twins in many grains, x200; b) 360°C, 0.1 s"1, ef = 0.75,
DRX grains at twins andGB.xlOO and c)420°C, 1.0 s"1, e f =0.31 DRX grains atGB,x200 [24].
Fig. 4. TEMmicrostructures of AZ31: a) 180°C, 1.0 s"1, s f =0.45 bands of twins; b) as a), fine cells at twin intersection; c) 360°C,
1.0 s'\ £ f = 1.30 DRX grains (A, B, C, D, E, F)atGBand d)300°C, 0.1 s"1, E f =0.95 DRVin twinned region [26].
and s = 4.0 for AZ31-Mn, it was possible to calculate OJJ W
(=2.3Rns) to be 130 kJ/mol and 138 kJ/mol for AZ31 and
AZ31-Mn respectively (A = 2.75 and 1.16 x 10 7 s 1 ). The
activation energy for AZ91 was 125 kJ/mol (n = 1.5) and for
ZK60 was 140 kJ/mol (n = 1.9) [22,23,25]. These Q ^ values
are compatible with creep results [28],
300°C homogenized and refined the structure, so that
satisfactory straining was observed up to 450°C. The flowcurve shapes were similar to those observed in compression in
Mg-0.8A1 alloy and the peak strength values were consistent
[12-13], AZ91 exhibited crp = 92 MPa, e f = 1.5 at 360°C, 1 s 1
being less ductile than AZ31 because of increased second phase
volume fraction [22]. ZK60 exhibited o p = 90 MPa and e f = 0.3
for the same condition, thus being less ductile than AZ31 [25].
Observation By Optical Means
The peak stresses CJP were subjected to constitutive analysis for
T and e dependence according to [22-23]:
A (sinh aop) n = E exp (Qrw/RT) = Z
Optical microscopy of the shoulder showed fairly uniform
equiaxed grains with precipitates at grain boundary (GB); AZ31,
AZ31Mn and ZK60 were fairly similar, but the volume of
particles increased with Al content in AZ63 and AZ91 [23-27].
It should be realized that as T increased the strain of
observation
also increased, so it is possible that
microstructural evolution at higher e masks phenomena that
occurred at low E. Specimens deformed at 180-240°C exhibited
twinning in about half the grains, indicating that this is a low
strain phenomena (Fig. 3). In compression tests, Humphreys
etal. [11-13] showed that extensive twinning had reoriented a
large volume by E « 0.12 over the range 180-400°C. The twins
intersect each other and cause offsets at GB. The basal slip is
not visible optically. The two boundaries of a twin are initially
closely spaced, slightly bulged, parallel lines, which
(3)
where, A, a (0.052 MPa"1) n OJJ W are material constants and
R=8.31 J/K mol. The Zener-Hollomon parameter Z incorporates
the two control variables T and e and is usually constant during
a hot forming test (it is likely to vary during a hot working
operation because of cold tooling and friction). In Fig. 2, the
relation between log E andlog(sinhao) is seen to be linear and
approximately parallel; the average values of n are about 1.8
and 1.9 for AZ31 and AZ31-Mn respectively. In the Arrhenius
plot of log (sinhaa) versus (1000/T), it is possible to draw
parallel lines through the data; from the slope s = 3.6 for AZ31
357
In the range 180-240°C, twins were frequently observed with
smooth boundaries and with much higher dislocation density
than the matrix around them; parallel twins resulted in such
alternating bands (Fig. 4) [26,27]. However, some twins exhibited subgrains which tended to produce an irregular boundary.
Twin intersections were observed and these contained very
small diamond-shaped cells (Fig. 4b). In some cases, they were
enlarged as a result of DRV and in one case, at 240°C a very
small DRX nucleus was observed. This and DRX below are
consistent with the observations ofKaibyshev etal. [30-37].
Radius (X10E2)
Fig. 5. Model of extrusion for flat die (R = 31) shows grid
distortion after complete formation of the deformation zone.
At 300 and 360°C, medium DRX grains with low dislocation
densities were observed in necklaces presumably along the
original GB (Fig. 4c) [26,27]. Smaller grains may have been
related to twins, but because of the higher Ef, than at 240°C,
very fine grains wouldhave been expected to grow. Twins were
frequently observed to have undergone various degrees of
recovery; the twinning dislocations apparently reacted with
slip dislocations to form SGB. Regions of elongated subgrains
were noted and interpreted as originating from parallel twins
(Fig. 4d). Occasionally, an unrecovered twin was observed,
likely having been formed in a grain core shortly before
fracture. Even less commonly, a twin was observed in a DRX
-2.0Q0-
completely cross a matrix region (defined by GB or earlier
twins); with rising strain, the twins may thicken. The matrix
may develop secondary twins, but the twins slip without
twinning. At 300 and 360°C twinning is still noticeable, more
so at higher i. Many GB exhibit serrations which are noticeably different from the lower T above at high e, although they
are larger at lower e. Serrations arise from formation of subgrain boundaries (SGB) which are indicative of slip on other
planes than basal; this can happen near the GB, due to stress
concentrations arising from different basal slip and twinning
orientations of neighboring grains. A wide region along the
GB is often referred to as the mantle and the center of the
grains, as the core. At lower 8, DRX grains are observed as
single rows or necklaces along some GB and also in some
twins, which are still recognizable, being fairly straight.
-IAZ31 R64 T400 V5 ml D90
nStep 120 Strain Rate ( Effective )
A 0.0005
C S3.5215
•2.400 -j
At 420 and 450°C DRX grains are found as a mantle on most
initial grains, while the cores remain; at450°C, 0.01 s"1, a few
regions showed complete DRX (as commonly occurs for
multiple slip in Cu, Ni and ^-Fe [10,17-20]). The DRX grains
are now quite large but still smaller than the original ones.
Twins were difficult to distinguish from GB even at the highest
e with the least DRX and lowest e, because they were distorted
and rotated into the elongation direction of the grains. The
behavior was similar for AZ63, AZ91 and ZK60.
The
development of DRX along GB is consistant with the
observation on Mg-0.8A1 [11-13].
j AZ31 R64 T400 V5 m l D90 .
~i Step 161 Strain ( Effective )
Obj 4
=
=
=
=
=
=
=
=
=
0.0
0.3813
0.7637
1.14551.5274
1.9093
2.2911
2.5730
3.0548
3.4367
Transmission Electron Microscopy (TEM)
Observation by TEM is generally limited to smaller fields
because of the higher magnifications used to resolve finer
details.
Nevertheless, in this investigation quite large
transparent areas were developed so the microstructure could be
assessed as a whole. Unlike Al, Cu, Ni, y-Fe which are fairly
uniform, the structure of these Mg alloys is quite
heterogeneous; Mg-3Al-lZn in comparison to Al-5Mg had
similar strength, very varied microstructure and much lower
ductility [29]. The microstructures are described in descending
Z and hence rising ef as for the optical examinations.
0.000
0.155
0.912
Radius (X10E2)
Fig. 6. In extrustion model of AZ31 for TB 400°C and VR =
5 mm/s a) strain rate for R = 64, max e = 83 s"1 whereas, for R
= 31 andV R = 2.6 mm/s max e 15 s 1 b) strain for R = 64,
max E =3.44 [46].
358
grain [26]. Since DRX grains are quite small, the interactions
with neighbors is likely to induce multiple slip thus promoting
DRV and impeding twinning.
Moreover, for age hardening AI-Mg-Si alloys, extrusion heating can be utilized as solution treatment and quenching as extrudate exits prepares the material foraging treatment; this avoids
the need for long solution furnaces and quenching tanks [40].
At 420 and 450°C, DRX grains in the mantle are large and the
grain cores are reduced and further apart [26,27]. The level of
DRV in all the grains is now much higher and twins are seldom
observed (Bf is now about 10 times that at which they had
formed). Regions of elongated subgrains may have also
originated from twins. While on the whole, the degree and
extent of DRV and DRX is much greater than at lower T, the
mircrostructure is far from homogeneous as in metals such as Al
with high DRV, or as y-Fe with uniform DRX. Extraordinarily,
occasional low T features, such as a straight twin or a twin
intersection is observed.
The axisymmetric, direct extrusion process (L = 305mm, r =
89mm) was modeled with DEFORM (™)finite element software.
A mesh was created for a two dimensional slice from center to
chamber wall with node density being much greater in regions
of expected strain concentration and variation [43-45]. The
equipment modeled consisted of a cool ram block (175°C) and a
heated chamber and die at T B , all of which were defined as rigid
[46]. The friction coefficient m was set as 1.0 (sticking
friction, internal shearing) for square dies and 0.4 (lubricated)
for conical dies. The thermal properties, such as heat capacity
and conductivity of billet and tooling, as well as the billettooling transfer coefficient (200W/m2K) were taken from the
literature. The billets were considered as elastic plastic
materials, with flow stress equal to the plateau or peak in
torsion tests; the constitutive equations derived above were
employed [22-25,46]. In the modeling, the ram is given a
series of small displacements at a defined rate until it reaches
the yield value and the billet upsets into the chamber. Nodes
near the die exit begin to displace and a stress is assigned to
each in relation to T and E and hence o in the next step of ram
advance. Repetition through 300 to 700 steps leads first to
definition of a fairly stable deformation zone and finally a
maximus exit TM, shortly after which the run is halted to limit
computer memory and time.
Magnesium Extrusion
Mechanically formed parts generally show superior strength
and toughness to die cast ones, which are likely to have the
advantage of lower cost and minimal machining. Extrusion
produces long products of intricate section with good surface
finish. If individual parts can be adapted by cutting to length,
bending and drilling of holes, the application would be quite
competitive with die castings. It is versatile in that a single
press can produce a variety of sections from different alloys
through additional investment in dies. Pressure demands rise
with increase in extrusion ratio (R=ln) [area of billet/area of
extrudate], in intricacy and thinness of the section, in rate of
production (ram speed VR) but it can be reduced by raising
initial billet temperature TB [38-42]. However, it is known that
as R and VR (rate of strain energy conversion) and TB increase
the exit temperature TM rises leading to surface defects through
incipient melting. Through studies of wire grids embedded in
billets and macrostructural examination, the distribution of
strain was observed to increase markedly from center to surface
[38-40], The potential for strengthening of Mg alloys can be
inferred from the well-established behavior of Al alloys
[14,29,39,40]. In the case of Al alloys (no DRX), the DRV
substructure could easily be retained for strengthening by
cooling at exit (non uniform SRX seriously weakens).
After the run, the progress of various parameters can be
examined with stroke and location namely; T, e, E, velocity,
highest and mean stress a m (of principal stresses) and the press
load L (Table 1) [44-46]. The distributions of these parameters
(and of T in the tooling) can be graphically displayed for any
step. One purpose of this was to permit comparison to results
from gridded billets to confirm that the modeling was
reasonable. The results for square dies are described in entirety
before looking at conical dies. The distortion of an originally
square grid provided some concept of the deformation zone and
the friction at the chamber walls leading to the dead zone where
it meets the flat die (Fig. 5). A sequence of steps showing node
AZ31 R31 T400 V2.6 m l D90
Step 164 Stress ( Mean )
IX!
O
Obj 4 (X10E2)
A =-3.3902
= -3.473S
= -Z-35S8
= -2.4401
= -1.9234
= -1.4066
= -0.8SS9
= -0-3732
= 0.1435
= 0.6S02
0.4S6
Radius (x10E2)
0-912
Radius (X10E2)
Fig. 7. Mean stress in extrusion of AZ31 for R = 31, VR = 2.5
mm/s andT B = 400°C, reaches 66 MPa at die corner [46].
Fig. 8. Temperature distribution during extrusion of AZ31 for
TB = 400°C. R = 31 VR = 2.6 mm/s results in T M = 496°C [46].
359
The deformation work transforms into heat so T is expected to
rise with a distribution related to 8, s and a. However, heat is
flowing out of the billet into the tooling and also in the
emerging extrudate; the properties controlling this are quite
separate from the mechanical ones [44,46]. The contours away
from the deformation zone indicate a decline below T B , notably
near the cold ram block. The rise in T is comparatively gradual
and reaches a maximum, only after some hundred steps. The
coincidence of TM with e and & generally enhances the ductility
at the die corner "(Fig. 8). However, if TM exceeds the incipient
melting point (of segregated phases), fissures will form; the
model is oblivious to this, leaving estimates of defect
formation to the metallurgists knowledge about the physical
and mechanical limitations of the alloys. The creation of the
hot zone leads to a rapid decline in press load (Fig. 9) as was
shown experimentally by Sheppard, et al. [38,41,42]. Once a
stable deformation zone is developed, the load drops gradually
as a result of decrease in friction force, as the billet shortens in
this direct extrusion; this effect was not examined because of
memory limitations and being less crucial than initial stages.
Load stroke curves
AZ31,T=400°C
9=90°, R=64, V R =5 mm/s, m=1
V H =5 mm/s, m=0.4
8=60°, R=64,
\ ^ V R =5 mm/s, m=0.4
\ * « « 1 9 = S 0 " , R=31,
^**e=60°,R=31,
V„=2.6 mm/s, m=0.4
^
\V„=5 mm/s, m=1
1=90°, R=31,
J=90°, R=31,
V„=2.6 mm/s, m=1
l | I . U | l l l l | l l l . | l l . . | l . l l
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Stroke length (mm)
Fig. 9. Load-stroke curves for extrusion modeling of
AZ31, 400°C and b) AZ31, AZ63, AZ91 andZK60 [23,46],
a)
The extrusion process was also modeled for conical dies of 60°
and 45° to the axis [46]; clearly because of the greatly
increased die surface compared to 0°, the total friction and load
increase markedly. In consequence, the value of m was lowered
from 1 to 0.4 by assuming suitable lubrication, although the
means to attain this is unknown to the authors. The inserted
billets had square ends, i.e., not machined to match the die
contour; as a result, the upsetting process to the point of
extrudate emergence was much more extensive in terms of ram
displacement and number of model steps. The square grid and
velocity diagrams indicate much more homogeneous flow
without the severe dead zone at the intersection of die and
chamber wall (Fig. 10). The contours of all parameters were
changed from the approximate circles with the common chord
at the die exit. The decreasing contours intersected the conical
surface successively closer to the chamber wall, so that the
deformation and hot zones were much larger and more diffuse.
These distributions are to be elaborated elsewhere [47].
velocities illustrates how the extrudate emerges [46]. Back
tracking of points across the section of the extrusion or of
lines of points parallel to the axis, backward in time as they
moved with the plastic flow, shows the deformation zone even
better than the square grid distortion [44,45].
The distribution of strain and strain rate were almost
independent of TB and of material (Fig. 6) [46] (including Al
matrix composites) [44,45], as were the grid distortion and
velocity development. The contours of decreasing 8 and e are
almost circles of increasing radius resting on the die opening as
a chord. At TB= 400°C, R = 31 and VR= 2.6 m/s, max 8 = 3 and
max 8 = 15 s"\ were attained at the die corner; they reached a
stable condition shortly after extrusion emergence. When VR
was increased, there was little change in e distribution but e
and the values for the contours rose in an almost linear
relationship. When R was increased, there was room for more
circle contours at smaller radii and both E ^ and I , as well as
levels at any fixed location, rose. The patterns were generally
in agreement with estimates derived from grid tests [46]. The
occurrence of the max e and 8 at the die corner indicate that to be
the critical point for cracking [38-40],
Because of the diminished friction, the load for the 60° die was
reduced relative to the flat one. However, the load for the 45°
die was higher then the 60° one, because of the increased die
surface at constant m [46,47], Because the hot zone was less
intense, the drop in load after the peak was much less than that
for the flat die. For fixed R, V R , T B , the maximum values of e,
E, a m andT M , were reduced; although they still coincided at the
die throat surface. One can estimate that the incidence of
surface defects are reduced and processing could be altered to
higher V R , or lower T B , depending on press capabilities.
The distributions of a and o m were fairly similar to those of e
and 8 and also the changes with rising R and VR [44-46]. As an
elastic-plastic material, ois strongly dependent on 8 but not on
s; however, it is ameliorated by the rise in T discussed below.
For the condition above, o m = 66 MPa and TM> = 495°C. At the
back of the billet near the ram, a m has a high negative value,
since all components are compressive; the metal is near
yielding. In the deformation zone, o m tends to decrease as 1 or
2 components move towards tensile values in relation to the
complex strain field and to increase as e rises (decrease as T
rises) (Fig. 7). Near the die exit the value of o m rapidly reaches
a positive value (any negative components move towards zero).
The maximum o m and the maximum stress (= a m + a ), both
tensile occur at the die corner, in coincidence with maximum s
and I encouraging defect formation. The maximum values are
found early upon break out of the extrusion and decrease as the
hot zone forms. In conjunction, the pressure or load increases
rapidly to cause upsetting and reach a maximum at breakout.
TABLE J: Results of the Modeling of AZ31
m
Die
(mm/si angle
(dea.)
R
31
31
31
31
31
31
64
31
31
350
400
425
450
400
400
400
400
400
2.6
2.6
2.6
2.6
1.5
5.0
5.0
2.6
5.0
90
90
90
90
■90
90
90
60
60
64 | 400 5.0 | 60
360
Tm„
464
496
516
529
479
523
555
0.4 484
0.4 514
0.4 548
p
2n» max —E3I
(Mm
(MPai (MPai
13.77
10.83
9.65
8.47
10.05
553.36
435.21
387.79
340.37
403.86
470.97
507.94
354.03
390.20
464.14
1172
12.64
8.81
9.71
11.55
92.00
66.00
65.76
60.89
63.68
70.53
7575
48.31
90.00
49.74
Emax
3.06 16.49
2.86 15.00
3.07 15.22
2.91 16.26
2.98j 8.89
3.04 38.01
3.44 83.52
2.26 13.96
3.19 26.68
3.53 65.52
For the extrudate conditions determined with maximum ranges
of 2-4 in strain, of 8-80 s"1 and of 450-550°C (Table 1), one can
estimate the microstructures from the torsion observations.
The original grain structure, twinned as needed upon entering
the deformation zone. The microstructure did not reach any
stable condition, because as E increases both e and T are rising,
having opposing effects; estimates should thus be based upon Z
values. Moreover, there is a strong variation in e, e and T
across the extrudate, all being less as radius decreases [38-40];
Z clearly decreases because of the rapid decline in E. One can
thus expect a high extent of DRX with fine grains and a fine
substructure near the surface. There would be larger DRX grains
with coarser substructure in both mantle and core. If such a
heterogeneous microstructure were preserved, it would provide a
strong and fairly tough product, probably not as useful a combination as in Al alloys where substructures would be more
uniform. However, it is possible that SRX could take place if
the cooling were slower; this was not examined in the present
study. The literature tends to indicate that uncontrolled cooling
in air would lead to considerable SRX; this is likely to be non
uniform and degrade the mechanical properties [38-40].
:
Conclusions
The torsion testing and associated microscopy provided
significant information on dependence on strain, strain rate and
temperature of the peak flow stress, the fracture strain and the
evolution of microstructure. The derived constitutive equations
were used to carry out finite element modeling, which derived
the dependence of maximum loads on extrusion ratio, ram
speed, die angle and billet temperature. The indication of
maximum values of E, E, a m andT M at the die corner provided an
opportunity to estimate the limiting condition for avoiding
surface defects on the basis of the torsion ductility and alloy
incipient melting point. The distributions of e, E and TM,
especially with the last 2 combined into Z made it possible to
estimate the microstructures at the point of extrusion; however,
these might be considerably altered by static recrystallization
during slow cooling.
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AZ31 R31 T400 V2.6 m0.4 D60
I Step 286 Stress ( Mean )
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B
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□
E
F
G
H
I
4(rlOE2)
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