Hot Deformation Resistance of an AA5083 Alloy under High Strain

China Steel Technical Report, No. 27,Shi-Rong
Chung-Yung Wu, Yen-Liang Yeh and Yi-Llang Ou
Hot Deformation Resistance of an AA5083 Alloy
under High Strain Rates
New Materials Research & Development Department
China Steel Corporation
To produce hot-rolled plates having a superiorly precise dimensional quality, axisymmetric compression tests
using the Gleeble 3800 simulator were carried out to assess hot deformation resistance of an AA5083 alloy
under high strain rates. Sharp temperature rises and load cell ringing characterized by vibrational load
responses were encountered at strain rates higher than 20 s-1 while sample buckling occurred at low
temperatures. The load cell ringing was corrected using a moving average method with a two-way filtering
operation to correct phase distortion. Isothermal flow curves were obtained by fitting the instantaneous
temperatures into a binomial function, while the buckling was removed by controlling the sample height.
Through the corrections, a hyperbolic sine equation was derived and data of hot tensile test having strain
rates lower than 3 s-1 were successfully extended to 100 s-1. Effects of temperature, strain rate and work
hardening behaviors on the flow curves were quantitatively analyzed accordingly and a new constitutive
equation was constructed to predict the hot deformation resistance of the AA5083 alloy for high speed rolling.
Keywords: Axisymmetric compression test, Load cell ringing, Temperature rise, Zener-Hollomon parameter,
Hyperbolic sine equation
To produce aluminum plates having a superiorly
precise dimensional quality, a formula Eq.1, was
previously proposed to predict hot deformation resistance of an AA5083 alloy(1), where σ, Th, ε, εp and
flow stress, homologous temperature being the test
temperature T divided by solidus of the alloy (843 K),
strain, peak strain 0.14 and strain rate, respectively. The
formula followed the basic form of Eq.2 and could
faithfully describe the flow behaviors of work hardening
at low temperatures as well as work softening at high
temperatures. It was derived from friction-free tensile
tests using strain rates lower than 3 s-1. Tensile strain as
high as 0.7 could be obtained at high temperatures,
nevertheless, such high strain data were not available at
low temperatures because of limited elongation. Similarly, the elongation decreased with increasing strain
σ = (-570 + 814 / Th – 195 / Th2) × [1.16 × (ε / εp) -0.45Th + 0.42
– 0.13 × (ε / εp) ] × ( / 2)0.37Th - 0.19 ··············· (1)
σ = f(T) × f(εn) × f(
) ································· (2)
In the present work axisymmetric compression
tests using the Gleeble 3800 simulator were carried out
to extend the experimental strain rate to 100 s-1. With
the advent of high speed compression tests, load cell
ringing(2), load response appears as a wave form and
sharp temperature rises were encountered. In addition,
multi-pass compressions using a long sample could be
successfully made when the strain rate was relatively
low, but buckling occurred at low temperatures when
the strain rate was high. Thus, a direct use of the data
under high strain rates is difficult.
Correction of load cell ringing was made firstly,
temperature rise was normalized using the temperature
function of Eq.1, and buckle behaviors were correlated
with sample length h, diameter d and Young’s modulus
E on the basis of Eq.3. Hyperbolic sine function Eq.4,
was subsequently used to link the data of the high
speed compression tests with those of the hot tensile
test because it could be extended over orders magnitude
of the strain rate(3). Here Z is Zener-Hollomon parameter,
Q is activation energy for hot deformation, R is the
universal gas constant, A and n are numerical constants,
Hot Deformation Resistance of an AA5083 Alloy under High Strain Rates
Buckle load limit = (π3 E d4/ 256h2) ············ (3)
× eQ/RT = A [sinh(α)]n ····················· (4)
It was hoped that Eq.1 could be appropriately
modified and be applied to a hot rolling mill for the
production of the superiorly precise dimensional plates
running at high speeds.
2.1 Sample preparation
Cylinder samples having a diameter of 10 mm and
15 to 21 mm high were cut from a direct chill cast slab,
which was 520 mm thick and 1660 mm wide and
homogenized at 520C for 8 h. Major chemical compositions of the slab are listed in Table 1. To minimize
variations of microstructure or cast porosities, the
cylinder center was located at a constant depth of
70 mm below free surface of the rolling plain. Metallurgical examinations revealed that the average grain
size was 160 μm there.
2.2 Compression test using the Gleeble 3800
Tests were carried out according to the procedures
suggested by Roebuck et al(4). Prior to the test, a hole of
1.7 mm diameter and 5 mm deep was drilled into the
plane of mid-length to insert a thermocouple, end faces
of the cylinder were coated with Ni-paste and cushioned
with graphite foils, the sample was then fitted onto the
two anvil faces of the simulator. Samples were electrically heated at 2 C/s to target temperature, soaked
there for another 90 s and then compressed with the
Hydrawedge system using a constant strain rate mode.
Maximum nominal strain rate was 120 s-1 and data of
load, displacement and temperature were recorded by a
maximum acquisition rate 50 kHz.
The sample temperature during the compression
stage remained relatively constant and a smooth flow
curve could be obtained when the applied strain rate
was low. However, the temperature rose sharply and
load cell ringing appeared when the strain rate was
higher than 20 s-1. Figure 1 shows typical curves of
mean pressure and sample temperature rise observed at
350C using a nominal strain rate 50 s-1.
2.3 Correction of load cell ringing and temperature
The ringing signal in Fig.1 was attributed to the
Table 1
Fig.1. Load cell ringing and temperature rise during a
compression test at 350C using a nominal strain rate 50 s-1.
resonant response of the dynamic system among the
testpiece, load cell and Hydrawedge module when
subjected to a short duration of excitation. Close
examination revealed that the force spectrum
bandwidth increased when the strain rate increased
beyond 20 s-1 providing a wider energy distribution to
excite the system resonant response during higher
strain rates. The force signal contained a step-like
slow-varying signal overlapped with an oscillation
component. The latter can be mathematically modeled
as an impulse response of a second order system using
Eq.5, where symbols A, ζ, ωn, t, ωd and φ denote
amplitude factor, damping ratio, natural frequency,
time, damped natural frequency and phase angle,
respectively. The ringing part of the load signal was
fitted to Eq.5, substracted from the orignal signal and
mean pressure on the sample could be obtained
f= Ae
cos (ωd t + φ) ······················· (5)
However, this approach involved mode
identification and often compounded with inherent
nonlinearity of the system stiffness during plastic
deformation. Thus, a moving average filter was used to
cover all the operating conditions. It was found that the
oscillation frequency was around 580 Hz within the
scope of the present work. The number of the filter tap
was appropriately chosen to assure the cutoff frequency
was below that frequency. For a sampling rate of 50
kHz, a 100-tap moving average filter was used. It's
-3 dB cutoff frequency was 310 Hz, which was
sufficient to smooth out ripple of load signal, as shown
in Fig.2. To further correct the delay due to filter operation,
Major chemical compositions of the AA5083 alloy
Shi-Rong Chen, Chung-Yung Wu, Yen-Liang Yeh and Yi-Llang Ou
the load data sequence was filtered in both forward and
backward directions to achieve a zero phase distortion.
Buckling was observed in those samples higher
than 18 mm when compressed at temperatures below
350C using high strain rates. Figure 4 shows the top
surface of a 18mm high sample having become oval
after being compressed at 330C using a strain rate
50 s-1 because longitudinal axis has been severely
tilted. The degree of the buckling was found to increase
significantly with decreasing temperature. Abe et al
reported that Young’s modulus of Al- 5.6 Mg (at%)
alloy dropped sharply at temperatures below 350C (5),
but a linear relationship between 200C and 400C was
proposed by Naimon et al(6). The present results
supported Abe’s observation because the Naimon’s
linear proposal failed to define the critical temperature
Fig.2. Ringing frequency could be removed by a moving
average filter with 100 taps.
After the correction of the load cell ringing,
instantaneous temperatures were fitted into the temperature function of Eq.1 and isothermal flow curves
were used exclusively. Friction hill of the isothermal
flow curves were subsequently corrected using a constant coefficient of friction 0.02 because the degree of
sample barreling was minor.
3.1 Flow behaviors under high strain rate
Flow stress, as expected, increased with decreasing
the temperature. Strain rate dependence of the flow
curves tested at 400C is given in Fig.3, where a
corrected curve of strain rate 100 s-1 is included. Compared with the work softening curves at low strain rates
0.08 s-1 and 0.56 s-1, it is evident that the stress
increases with increasing the strain rate as well as the
degree of work hardening. Thus, flow curves at strain
rates higher than 5.5 s-1 were dominated by work
hardening i.e., stress increases progressively with
increasing the strain within the experimental ranges.
Fig.4. Longitudinal axis buckled when a sample was
18 mm high and compressed at 330C using a strain rate 50 s-1.
As a result, Abe’s data were fitted into Eq.3 and
the buckling could be successfully removed by
decreasing the sample height. Alternatively, it could
also be avoided by decreasing the strain rate but further
investigation is required because the effect of strain rate
on Young’s modulus is currently not clear.
3.2 Hyperbolic sine equation
The stress at a strain of 0.20, σ0.2, in each curve
was intercepted and validated by the hyperbolic sine
function Eq.4. Prior to this, the previously measured Q,
173200 J/mol, was used to calculate the Zener-Hollomon
parameter Z. This parameter was firstly correlated with
the stress and the following exponential function Eq.6
was obtained.
Z= 8.57 × 108 × exp(0.082 × σ 0.2) ·············· (6)
Fig.3. Strain rate dependence of the flow curves tested at
As reported earlier(7,8), α value in Eq.4 can be
derived as the ratio of the exponent 0.082 in Eq.6 and n
value of power law equation, Z = A1 σ0.2n. However,
this equation could not be successfully derived because
of high σ0.2. Thus, a constant α value of 0.015 MPa-1,
proposed by Sheppard(9,10), was introduced in the
present work.
Hot Deformation Resistance of an AA5083 Alloy under High Strain Rates
Figure 5 shows strain rate dependence against the
stress, while the stress against temperature is demonstrated in Fig.6. Slope of each curve was obtained by
linear regression analyses and averaged as described
previously(1,3). Through a simple multiplication over the
mean slope of Figs.5 and 6 and the universal gas constant, the newly derived Q is 174700 J/mol. This value is
close to those measured by Sheppard, 171400 J/mol(9,10),
Wang(11) and our previous report(1).
Fig.7. Relationship between stress σ0.2 and the Zener
-Hollomon parameter. (● denote hot tensile data, ● high
speed compression data)
3.3 Compound function of strain rate, temperature
and work hardening behaviors
Strain rate dependence against the stress σ0.2.
Modification of Eq.1 was carried out in a sequence of
strain rate sensitivity factor m, followed by the temperature function and then work hardening exponent
n. Strain rate sensitivity factor was correlated with
homologous temperature Th, as shown in Fig.8. It is
clear that the m increased progressively with increasing
temperature but its value remained almost unchanged
with the introduction of high strain rate compressions.
The current observation that m increases with increasing
temperature is consistent with earlier reports by
Lloyd(12) and Chida et al(13), but contrary to Motomura
et al(14) and Kitamura et al(15) who proposed that m was
a constant during hot deformation.
Fig.6. Stress σ0.2 dependence against the inverse temperature.
The Z parameters of the experimental σ0.2 were
accordingly re-calculated based on the present Q and a
new Eq.7 was drawn. The correlation between the Z
parameter and the stress σ0.2 is demonstrated in Fig.7
where the black spots denote hot tensile data and the
light spots, the compression data under high strain
rates, respectively. It is evident that the data of high
strain rates can be correlated with those of hot tensile
data having strain rates lower than 3 s -1. The current
results support the earlier conclusion that the hyperbolic sine equation can be extended over orders magnitude of the strain rate(3).
Ln ( × e174700 / RT) = 24.98 + 5.23 ×
Ln sinh(0.015 × σ0.2)······ (7)
Strain rate sensitivity factor increased with
increasing the homologous temperature. (symbols ●  
denote strain at 0.10, 0.15 and 0.20, respectively)
A strain rate of 15 s-1 was chosen as a standard rate
and the following linear equation for the sensitivity
factor m was drawn. In Fig.8, the bold line is plotted
according to Eq.8, while the dot line denotes Chida’s
formula. It can be seen that the present m values are
higher but the reason is not clear. Additionally, both the
Shi-Rong Chen, Chung-Yung Wu, Yen-Liang Yeh and Yi-Llang Ou
two lines similarly converge at about 185C i.e., the
effect of m is numerically predicted to disappear below
this temperature.
/ 15)0.42Th - 0.23 ························ (8)
Figure 9 shows all the stress data at strains of 0.10
to 0.65 with an interval of 0.05 within 250 to 450C.
Before the correction using Eq.8, raw data of hot tensile and Gleeble compression fests are denoted by
dimond morks. Both the two data scattered largely, but
they narrowed down to black spots when Eq.8 was
applied. Thereafter, regression analyses of the temperature effect over those black spots revealed that the
flow stress could be described by a binomial function
Eq.9, as demonstrated by the parabolic line inside
Fig.10. Comparisons of predicted flow curves using Eq. 10
and the measured data ( ) compressed at 300C.
σ = (-479 + 694 / Th – 145 / Th2) ×
[1.11 × (ε / 0.26)-0.45Th + 0.42 - 0.06 × (ε / 0.26)]
× ( / 15)0.42Th - 0.23 ···························· (11)
Fig.9. Flow stress increased parabolically with increasing
the inverse homologous temperature after being corrected
by Eq.8. (● corrected; before correction,  hot tensile
test,  high speed compression test)
Figure 11 shows a comparison between the present
work and the published equations. It can be seen that
the experimental data could be well explained by the
present equation. In contrast, large deviations of
Chida’s equation(12) appeared in high stress regions
where the temperature has been extended beyond its
lower limit (300C). Deviations were similarly found in
Takuda’s equation (15) particularly at low stress regions
where the flow curves were dominated by work softening.
f(T) = -479 + 694 / Th - 145 / Th2 ·············· (9)
Function to describe the behaviors of both work
hardening and work softening was derived in a similar
way as reported previously. Since peak strain of the
flow curves increases with increasing the strain rate,
higher strains were used to minimize discrepancies and
the following Eq.10 was obtained. Fig.10 shows that
predicted stress-strain curves (solid lines) using Eq.10
for those compressed at 300C and under various strain
rates are close to the observed data (inserted marks)
although deviations appeared at lower strains.
Through an additive combination of Eqs.8 to 10, a
new formula Eq.11 was consequently derived to predict
the hot deformation resistance of the AA5083 alloy.
f(εn) = 1.11 × (ε / 0.26)-0.45Th + 0.42 - 0.06 × (ε / 0.26)
··············································· (10)
Fig.11. A comparison between the present work and the
previously proposed equations. (●present work, Chida’s
Eq., Takuda’s Eq.)
Hot deformation resistance of the AA5083 alloy
under high strain rate compression tested up to 100 s-1
has been thoroughly investigated over the respects of
Hot Deformation Resistance of an AA5083 Alloy under High Strain Rates
load cell ringing, instantaneous temperature rise, sample buckling and work hardening behaviors. The effects
of the temperature T, strain ε and strain rate
on the
flow stress σ have been quantitatively assessed and
following conclusions are drawn:
(1) Vibrational force signals during high speed compressions containing a ringing frequency about 580
Hz have been successfully corrected by a moving
average filter with 100 taps.
(2) By using the experimentally apparent activation
energy for hot deformation 174700 J/mol and an α
value 0.015 MPa-1, the flow stress at the strain 0.2
can be described by the following equation:
Ln ( × e174700 / RT) = 24.98 + 5.23 ×
Ln [sinh(0.015 × σ0.2)]
(3) Within the experimental ranges of: 250 to 450C,
strains 0.10 to 0.70, and strain rates 0.06 to 100 s-1,
flow stress can be described by the equation:
σ = (-479 + 694 / Th – 145 / Th2) ×
[1.11 × (ε / 0.26)-0.45Th + 0.42 - 0.06 × (ε / 0.26)]
× ( / 15)0.42Th - 0.23
where homologous temperature Th is the test temperature divided by solidus of the alloy (843 K), reference
strain and strain rate are 0.26 and 15 s-1, respectively.
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