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Recovery Behaviour of Pure Magnesium in Cyclic Compression–Quick
Unloading-Recovery Process at Room Temperature Investigated by AE
Yunping Li and Manabu Enoki
*
Department of Materials Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
Anelastic recovery of pure magnesium at room temperature was investigated in cyclic compression-quick unloading-recovery process
where acoustic emission (AE) measurement was applied to analyze the dynamic behaviour and mechanism of anelastic recovery process. By
analyzing the RMS voltage of AE signals from both the background and the recovery process, it was observed that the recovery process was
accompanied with a gradual decrease in the strength of AE signals. The AE signals in recovery processes of different strain levels seem to be due
to the same source of detwinning process because the same slope between amplitude and logarithmic AE count of AE signals in different strain
levels was found in the strong elastic waves related to detwinning process. The AE behaviors in recovery process were described in details by AE
count rate and AE incubation time. The relations between twinning or detwinning and AE counts in both deformation and anelastic recovery
process could be expressed by a general equation. [doi:10.2320/matertrans.MC200705]
(Received October 24, 2007; Accepted May 21, 2008; Published July 2, 2008)
Keywords: acoustic emission, pure magnesium, psuedoelasticity, anelastic recovery, detwinning, twinning
1. Introduction
Anelastic recovery of magnesium and its alloys has been
thought to be resulted from the detwinning process conven-
tionally when the external stress is retreated or lowered.
1–5)
The results of Gharghouri et al.
1)
showed that the hysteresis
loops of pure magnesium in cyclic tension and compression
are due to f10
112gtwinning which grows when the materials
are stressed and partially reverts when unloaded. The
pseudoelasticity in magnesium and its alloys is very similar
to the stress induced martensitic transition (MT) in which
there is also twinning and detwinning in loading and
unloading processes, respectively.
5)
Lots of researches about
the cyclic transition behaviour of MT by AE technique have
been conducted because the twinning and detwinning
processes are strong AE sources and the dynamic internal
structure evolution can be analyzed effectively by AE.
6)
Magnesium demonstrates different behaviour and mecha-
nism in loading and the following unloading process
compared with the other materials without the pseudoelas-
ticity. The fatigue and energy absorption, when magnesium
or its alloys are used as the damping structure, are also
affected by such cyclic movements of twinning boundaries.
Then, precisely understanding the dynamic behaviour and
mechanism of the anelastic recovery is an important topic for
both engineers and researchers.
Traditionally, pseudoelasticity is analyzed in hysteresis
loops. The anelastic recovery strain "r, the strain difference
before and after the anelastic recovery, can be determined
from the hysteresis loops by using the nominal Young’s
modulus.
7)
However, this method will result in a large
error because it was by an indirect measuring method.
Besides, the unloading curve of magnesium is composed
of both the elastic and anelastic unloading curves which
are not separated automatically, and it is difficult to ana-
lyze the anelastic recovery behaviour and mechanism in-
dependently.
6,7)
In the previous research,
8,9)
the anelastic recovery behav-
iour of magnesium was obtained by unloading the specimen
with relatively high speed so that anelastic recovery lags
behind elastic recovery and were analyzed independently.
AE measurement was applied to investigate the behavior
of anelastic recovery process. The main objective of the
present research is to get the dynamic behaviours and
mechanism of anelastic recovery in more details in terms of
AE measurements. The relationship between recovery by
detwinning and deformation by twinning will be discussed
for the first time.
2. Experimental
Commercial extruded pure magnesium without heat
treatment with purity of 99.95% was selected as the present
research materials. Samples are with average grain size of
about 35 mmas shown in Fig. 1. Microstructure was ob-
served by optical microscope at the center of the side
surface in samples after polishing and etching by nitric
acid solution. Cylindrical specimens were machined into
size of 15 15 mm.
Fig. 1 Microstructure of the pure magnesium in present research.
*
Corresponding author, E-mail: enoki@rme.mm.t.u-tokyo.ac.jp
Materials Transactions, Vol. 49, No. 8 (2008) pp. 1800 to 1805
#2008 The Japan Institute of Metals
Cyclic compression was performed from the strain level
of about 0.1% to about 5% along the extrusion direction.
The deformation rate was in an intermediate level of
1:67 104/s. The specimen was unloaded with a speed of
about 0.56/s in order to get a clear separation of anelastic
recovery and elastic recovery. AE system used was mDISP
(PAC USA) with a threshold of 40 dB and high pass filter
(HPF) of 100 kHz. AE sensor was a low noise type (M304A,
Fuji Ceramics, Japan) and closely contacted to the sample
surface by polymer flocculant in a specially designed
compression jig as shown in Fig. 2. The voltage of AE
signals, AE count as well as the cumulative AE counts will be
used in describing the recovery behavior. The analysis in the
relation between recovery and deformation was partially
based the results in previous researches.
8,10)
3. Results and Discussion
3.1 Cyclic compression curve
Figure 3(a) shows the monotonous compression and cyclic
compression-quick unloading-recovery curves. In each cycle,
the stress was quickly unloaded to zero and then recovered
for about 60 min, which leads to broad hysteresis loops with
clear separation of elastic recovery and anelastic recovery
(Fig. 3(b)). After recovery, the decrease of peak stress can be
observed. The stress decrease is reasonably thought to be due
to the recovery in which the internal stress was relaxed.
However, the stress will increase greatly as the strain exceeds
the previous strain level before unloading and continues to
keep the entire shape similar to the monotonous one. The
yielding stress in present research showed to be a little lower
than the previous results
9)
because in present research, the
grain size of the sample was observed to be a little larger
than the previous one. However, the entire deformation
curves in these two kinds of samples were very similar. Our
previous research
8)
and other report
1)
showed that the
hysteresis loops during cyclic loading of magnesium and its
alloys is due to detwinning process during unloading stage in
which the elastic twins disappeared as soon as the applied
stress was lowered to a certain level. Reed-Hill et al.
11)
also
observed the similar pseudoelastic behaviour of Zr when
compressed at 77 k while unloading at room temperature,
pointing out that such psuedoelasticity of Zr can be ex-
plained on the assumption that there are stress-induced
movements of f10
112gtwinning boundaries which result in
the loading-unloading hysteresis loops. Recently, C. H.
Caceres et al.
7)
reported the similar pseudoelastic behaviour
of cast AZ91 magnesium alloy under cyclic loading-unload-
ing process, by an in-situ observation of the surface of the
AE System
Note PC
Sample
Oil film
AE sensor
Hole
Jig
Jig Preamplifier
Cyclic process
HPF
µ
Disp
Fig. 2 Experimental setup for cyclic compression- quick unloading-
recovery process and AE measurement.
(a) (b)
Fig. 3 (a) Cyclic and monotonous compression curves, and (b) the details of the typical hysteresis loops after quick unloading.
Recovery Behaviour of Pure Magnesium in Cyclic Compression–Quick Unloading-Recovery Process at Room Temperature 1801
specimen. Present hysteresis loops formed in cyclic process
are thought to be in good agreement with the previous results
that twinning–detwinning process is related to the hysteresis
loops closely. Some of twins partially reverted when applied
load was slightly decreased. Twins may become either
slightly narrower or shorter with the decrease of applied load.
In case of very thin twins, complete reversal seems to occur,
but upon reloading, the twin reappeared on the same location.
Present results of magnesium were in good agreement with
previous results. However, it has to be noted that we ob-
served near linear unloading curve when high unloading
rate was applied, which resulted in an elastic recovery
stage followed by the anelastic recovery. Present result in
anelastic recovery was thought to be somewhat not consistent
with the previous explanations
1,11,12)
that detwinning process
occurred simultaneously in the unloading process because
the detwinning process lagged behind significantly at high
unloading rate in present research.
3.2 AE signals in anelastic recovery process
Figure 4 shows the amplified root mean square (RMS)
voltage of AE signals during the recovery stage at strain level
of about 4.26% as well as the signals of background. The
AE signal strength of recovery decreases to a noise level
eventually with increasing time, showing a similar behaviour
to the traditional recovery process of some properties at
elevated temperature. This result indicates that present AE
system is an effective method in investigating the recovery of
magnesium in a specific time range. The recovery time
dependence of cumulative AE counts Nat a threshold of
40 dB when the sample was recovered for about 60 min at
different strain levels are shown in Fig. 5. All AE behaviours
in anelastic recovery processes show similar trends in which
the AE count rate was highest at the initial stage of the
recovery process. The AE behaviours are in some extent
similar to the strain recovery behaviour that recovery process
begins with highest rate and slows down rapidly with the
increase of time.
Figure 6 shows the distribution of AE event count as a
function of signal amplitude in the anelastic recovery process
at two strain levels. In both graphs, linear behaviours between
logðNeÞand AE amplitude are observed. From M. Ohtsu
13)
such kind of linear distribution behaviour between AE
amplitude and event count generally demonstrate the single
AE generation source. The slopes in the two graphs are
observed to be nearly in the same value, showing the same
source of AE in the anelastic recovery process at different
strain levels.
13)
It was supposed that very high stress (stress concentration)
was generated during the deformation process in immediate
vicinity of deformation twins. These stresses and the
associated strain energy arised from the resistance of matrix
to the macroscopic change of shape in the twinned volume.
When the applied stress is retreated or decreased, internal
stresses around the twins would result in an opposite effect of
the deformation by detwinning at least partially. Elastic twins
should disappear spontaneously or in a very short period after
unloading, however some ‘‘true twins’’ in some favorable
condition (such as in a position with very high anti-resolved
shear stress) should also shrink continuously when the
applied stress is decreased or retreated. The detwinning of the
‘‘true twins’’ should proceed in a competitive process of the
driving force such as the stress concentration or high strain
energy with the resistances from the vicinity such as the
dislocations around the interface of the twins, the defects of
the matrix etc. With the increase of time, the relaxation of
matrix by the annihilation of dislocations, ordering of
dislocation configurations or disappearance of point defects
will result in a favorable condition for the detwinning
process. As described above, the anelastic recovery of pure
magnesium was due to (at least partially) the detwinning
process. It can be naturally concerned to the martensitic
transition in which AE signals were believed to be from the
detwinning process. As described by O. A. Bartenev et al.,
14)
disappearance of twinning in martensitic transition can
produce much stronger AE signals than that from the
dislocation annihilation or slipping. In present condition,
such strong AE signal after deformation can be reasonably
ascribed to the detwinning process.
3.3 Relation between AE and anelastic recovery process
Strain recovery curve in Fig. 5 can be accurately de-
scribed by
Fig. 4 RMS voltage of AE signals in recovery process (at strain 4.26%)
and the noise level in room temperature.
Fig. 5 AE behaviors in anelastic recovery process at different strain levels.
1802 Y. Li and M. Enoki
"¼RT
lnðtÞþRT
lnð2Þ¼AlnðtÞþBð1Þ
where "is the anelastic strain, Rthe universal gas constant,
tthe recovery time, the theoretical relaxation time from
present strain to zero, and t0and constants. The recovery
curve at strain of 4.26% drawn in Fig. 7 is shown to be in
good agreement to eq. (1) where A¼RT
¼4:68 103,
and B¼RT
lnð2Þ¼3:83 are selected. Equation (1) is a
traditional form of the recovery in the properties of materials
at high temperature in case of the thermal activated process.
In present research, the anelastic recovery process of
detwinning is thought to be also a thermal activated process
if considering the process in the whole aspect, because the
detwinning process is driven by the internal stress in which
recovery behavior of internal stress at a certain temperature
is well known to be a thermal activated process.
The applied strain dependences of the anelastic recovery
strain "rand the corresponding cumulative AE counts Nafter
recovered for 60 min in each cycle are described in refer.
9)
Before the strain of about 2.0%, "rincreases greatly with the
increase of strain level while the increasing rate decreases in
the later stage as if the recovery process was interrupted by
some factors not favoring in the recovery process. Nreleased
in each recovery process grows greatly with the increase of
strain. However, after strain of about 2.0%, the cumulative
AE counts decreases gradually. The different changing
behaviours of these two parameters show that the mecha-
nisms of anelastic recovery and the AE event formation
mechanism must be different. The AE signals in the anelastic
recovery process are reasonably thought to be due to the
detwinning process, because the detwinning process is a very
important source of AE and the anelastic recovery of pure
magnesium is related to detwinning closely.
6)
It is thought
that the anelastic recovery strain is due to at least two
mechanisms, detwinning and the annihilation of dislocations
where the annihilation of dislocations is a thermal activated
process
15)
and the elastic energy released is too weak to be
detected by present AE system. From above explanation, it
can be known that the anelastic recovery by detwinning and
the overall anelastic recovery process (both detwinning and
dislocation annihilation) are different. At lower strain level
(lower than about 1.0%), the recovery from detwinning and
the overall anelastic recovery have a similar behaviour. In
the later stage, due to the decrease of the fraction of anelastic
recovery by detwinning, the increasing rate of overall
anelastic recovery strain decreased accordingly. The exact
changing behaviour of the anelastic recovery from detwin-
ning or dislocation will be discussed in another paper.
16)
The AE signals accompanied with the anelastic recovery
process was described in details as mentioned above. Then,
what is the relationship between AE signal and anelastic
recovery strain? Figure 8 shows the relationship of overall
AE counts and the anelastic recovery strain before the strain
level of 1.0% by the red circles and the red line. A nonlinear
fit to the experimental data was applied and a cubic relation
was observed between these two parameters. This result can
be explained by the cubic relation between the anelastic
strain from detwinning and the detwinning volume, and the
cumulative AE counts Nis proportional to the energy
released in detwinning which is proportional to the volume
of the detwinning. According to this theory, we can obtain
an equation showing the behaviour of Nas a function of the
recovery time on the basis of that the relation between AE
Fig. 7 Strain recovery behaviour after quickly unloading at strain of
4.26%.
(a) (b)
Fig. 6 Amplitude distributions of AE signals at strain levels of (a) 2.0% and (b) 4.6%.
Recovery Behaviour of Pure Magnesium in Cyclic Compression–Quick Unloading-Recovery Process at Room Temperature 1803
and anelastic recovery strain is fixed as a function of
recovery time,
N/"r3ð2Þ
and
"r¼"0"tð3Þ
where "0is the initial strain immediately after the elastic
recovery or the theoretical starting recovery point where the
AE signal is started to release. "tis the strain at time t.
It has to be mentioned that, physical meaning of eq. (2)
should express the direct relation between the anelastic
recovery strain from detwinning and Neven at higher strain
level because the AE signals are only related to the
detwinning process as mentioned above while the anelastic
recovery includes both information of recovery from
detwinning and dislocation annihilation.
Inserting eq. (1) into eq. (2) and eq. (3) based on the
assumption of that the relation between "rand Ndoes not
vary with the increase of recovery time, and "ris propor-
tional to the anelastic recovery strain from detwinning all
the time.
N¼K"0þ
RT
lnðtÞ
RT
lnð2Þ
3
ð4Þ
In present situation, Tis room temperature, a constant,
N¼Kð"0þAlnðtÞBÞ3ð5Þ
Equation (5) is the general AE behaviour during anelastic
recovery of pure magnesium. Given appropriate values of
K,"0, the fitting result shows a very good agreement with
the experimental result as shown in Fig. 9 for the recovery
process at strain level of 4.26%. Then, we can deduce
an equation from eq. (5) directly by applying differential
processing by time t,
dN=dt ¼Vð"0þAlnðtÞBÞ2
tð6Þ
where Vis equal to 3 K/A with a value of about 5:90 104,
other parameters are same to that in Fig. 10(a). Equation (6)
shows the behaviour of AE count rate in the anelastic
recovery process. The decreasing rate of AE count rate
shows a decrease of detwinning rate with the increase of
recovery time.
With the increase of recovery time, the interval time range
between the two neighboring AE events or detwinning steps
will increase accordingly. This is because that the internal
stress decreases gradually with the increase of recovery time,
and the detwinning process has to need longer incubation
time or the time for storing enough energy to activate the
detwinning. Supposed that all the AE signals have the same
count per event with a value of F, and then the incubation
time Ican be obtained from eq. (4).
I¼
F
dN=dt ¼
F
Vð"0þAlnðtÞBÞ2
tð7Þ
where Iis the incubation time of the AE signals in recovery
process, and Fthe average AE count number per event in the
entire recovery process. In present situation Fis about 4.55
obtained from the experimental data. A plotting of eq. (7)
shows a good agreement with the experimental incubation
time as shown in Fig. 10(b).
In present research, the anelastic recovery process at room
temperature described by the AE count rate and the AE
incubation time. It has to be noted that these two parameters
are different to the traditional parameters of the materials
properties such as the grain size, and yield stress etc because
the AE count rate and AE incubation time can dynamically
and directly express the internal evolution behavior of
materials in recovery process.
3.4 Consistency between deformation and recovery
Twinning plays an important role in the deformation
process of pure magnesium as described in our previous
research.
10)
For a given grain orientation, "tw is the strain
accommodated by twinning that is thought to be related to
the characteristic shear of twinning system S, Schmid factor
m, which is supposed to be decreased with increasing strain
", as well as the volume fraction of twinned grain
17)
by
"tw ¼mS¼miSMð8Þ
m¼Mmi;M¼1C"ð9Þ
Fig. 8 Relations between AE behavior and twinning behavior in both
deformation and recovery of pure magnesium.
Fig. 9 Time dependence of cumulative AE counts in anelastic recovery
process and the fitting results by eq. (5) (4.26%), and Kis with a value of
around 4:29 106.
1804 Y. Li and M. Enoki
where Cis a constant for a specific deformation process.
10)
It is found that the relation between cumulative AE counts
and the twinning strain can be expressed by following
equation in the initial stage of deformation process,
10)
N1=P¼k"tw ð10Þ
where Pis an exponent constant with a value of about
1:26 0:02 in all cases, and kis varied according to
experimental condition. The relation between Nand "rin
each recovery process before the applied strain level of 1.0%
for both vertical and parallel samples is also plotted in Fig. 8.
It is interesting to find similar expressions between
eqs. (10) and (2) in both deformation and anelastic recovery
process. Equation (10) expresses the relation between AE
and twinning behavior in deformation process, and eq. (2)
shows the relation between AE and detwinning behavior. The
two processes with contrary direction are reasonably thought
to should have similar equation. The relation between Nand
"tw can not be expressed by eq. (10) any more with increasing
strain level because the AE signals emitted from twinning
nucleation are much more than that from the twinning growth
and the twinning changes from twinning nucleation process
to twinning growth with increasing strain level
8)
in deforma-
tion process. For the anelastic recovery process, at higher
strain level, the decrease of Nand the increase of "rshow
that fraction of anelastic recovery strain from detwinning
decreases accordingly. The relation between Nand "rdoes
not follow eq. (2) any more at higher strain level. From
present result in both deformation and anelastic recovery,
a good consistence between deformation and recovery in
the relation between AE and the corresponding twinning
(detwinning) is established.
4. Conclusions
Anelastic recovery of pure magnesium in cyclic compres-
sion-quick unloading-recovery process was investigated in
detail by AE measurements and the results obtained are as
follows:
(1) By analyzing the RMS voltage of AE signals from both
the background and the recovery process, it was
observed that the recovery process of pure magnesium
was accompanied with a gradual decrease in the
strength of AE signals.
(2) The AE signals in recovery processes of different strain
levels seems to be due to the same source of detwinning
process because the same slope between voltage and
logarithmic AE count of AE signals in different strain
levels was found in the strong elastic waves related to
detwinning process.
(3) The relations between twinning or detwinning and AE
counts in both deformation and anelastic recovery
process could be expressed by a general equation.
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(a) (b)
Fig. 10 Recovery time dependence of (a) incubation time and (b) count rate of AE signals in anelastic recovery process at strain of 4.26%.
Recovery Behaviour of Pure Magnesium in Cyclic Compression–Quick Unloading-Recovery Process at Room Temperature 1805
