Materials Transactions, Vol. 46, No. 1 (2005) pp. 118 to 122
#2005 Journal of Japan Research Institute for Advanced Copper-Base Materials and Technologies
Damping Properties of Ductile Cu-Al-Mn-Based Shape Memory Alloys*1
Naoki Koeda1; *2 , Toshihiro Omori1; *2 , Yuji Sutou2 , Hidekazu Suzuki3 ,
Masami Wakita3 , Ryosuke Kainuma1 and Kiyohito Ishida1
1
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Tohoku University Biomedical Engineering Research Organization, Sendai 980-8575, Japan
3
CHUO SPRING CO., LTD., Research & Development Division, Miyoshi 470-0225, Japan
2
The damping property tan of Cu-Al-Mn-based alloys, where tan is nearly equal to internal friction Q1 , was investigated using a
Dynamic Mechanical Spectrometer (DMS). It was found that the dependences of frequency and strain amplitude on tan are significantly
different between the parent + martensite two-phase and the martensite single-phase states, i.e., tan is mainly influenced by frequency in the
two-phase state and by strain amplitude in the martensite state. It was also found that the relative grain size d=D is a function of the damping
capacity, where d and D are the grain diameter and the diameter of the wire, respectively, and that tan increases with increasing d=D. The
maximum values of tan ¼ 0:54 and tan ¼ 0:07 were obtained in the two-phase state and in the martensite state, respectively, in the specimen
of d=D 1.
(Received July 28, 2004; Accepted November 11, 2004)
Keywords: copper-aluminum-manganese, shape memory, martensitic transformation, damping, internal friction, mobility, martensite variant,
grain size
1.
Introduction
Recently, high damping materials are drawing much
attention in engineering applications because of the increasing need for the reduction of vibration and noise in various
fields. Among conventional damping alloys, shape memory
alloys (SMAs) are well-known as materials showing both
high strength and high damping capacity. It is believed that
the damping capacity of SMAs is mainly due to the energy
loss by the movement of the martensite variant interfaces and
the parent/martensite habit planes.1) However, conventional
SMAs such as Ti-Ni, Cu-Al-Ni and Cu-Zn-Al show poor
cold-workability because of their ordered structures and high
cost in the case of the Ti-Ni alloys.
The present authors have recently developed Cu-Al-Mnbased shape memory alloys with excellent cold-workability
and cost performance.2–4) The phase region exhibiting
martensitic transformation in the Cu-Al binary system is
significantly extended to the low Al content by the addition of
Mn, and the A2/B2 and B2/L21 order-disorder transition
temperatures decreases with decreasing Al content.5) Thereby, Cu-Al-Mn alloys with low Al content below 18 at% have
an excellent cold-workability. In addition, excellent shape
memory properties, which are comparable to those of Ti-Ni
alloys, can be obtained by microstructural control in Cu-AlMn based alloys.6–9) Those results imply that Cu-Al-Mn
alloys have a high damping capacity based on the high
mobility of the martensite variant interfaces and the parent/
martensite habit planes. In the present study, the damping
properties of ductile Cu-Al-Mn-based alloys focusing on the
effect of the grain size were investigated.
*1This
Paper was Originally Published in Japanese in Journal of the JRICu
Vol. 42 No. 1 (2003) 198–201.
*2Graduate Student, Tohoku University
2.
Experimental Procedures
Cu72 Al17 Mn11 and Cu72:4 Al16:9 Mn10:0 Co0:5 B0:2 alloys
were prepared by induction melting in an argon atmosphere.
The cast alloys were hot-rolled at 800 C followed by coldrolling, and then the specimens were cold-drawn to a
diameter of 0.5 mm and 0.35 mm, respectively, and cut into
length of 40 mm. All the wire specimens were solutiontreated at 900 C and quenched in water, then the specimens
with various grain sizes were obtained by changing the
solution-treatment time (1 min–30 min). They were then
finally aged at 200 C for 15 min to stabilize the martensitic
transformation temperatures.
Martensitic transformation temperatures, Ms : martensitic
transformation starting temperature, Mf : martensitic transformation finishing temperature, As : reverse martensitic
transformation starting temperature and Af : reverse martensitic transformation finishing temperature, are determined by
Differential Scanning Calorimetry (DSC) with cooling and
heating rates of 10 C/min. They were defined as the
temperatures at which DSC curve deviated from its base
line due to the martensitic transformation as shown in Fig. 1.
Damping property tan of Cu-Al-Mn alloys was investigated using a Dynamic Mechanical Spectrometer (DMS) in
the tensile mode, where is the loss angle. An oscillating
force is applied to a sample in the DMS measurement. Based
on the measured displacement and phase lag, the sample
modulus tan are defined. The tan is indicated by following
relationship:
tan ¼ = ¼ W=2W Q1
where is logarithmic decrement, W is energy dissipated in
a full cycle, W is maximum stored energy and Q1 is internal
friction. The ranges of strain amplitude, frequency and
heating/cooling rate are 1:3 104 –1:0 103 , 0.5–20 Hz
and 2 C/min, respectively. The stress changes to hold the
strain constant.
Damping Properties of Ductile Cu-Al-Mn-Based Shape Memory Alloys
cooling
DSC
Mf
Ms
100
80
0.10
0.08
0.06
0.04
0.02
0
tanφ
Heat Flow
endothermic
tanφ
Young's
modulus
60
DMS
40
tanφ
(b)
heating
As
Af
DSC
100
80
Young's
modulus
0.10 DMS
0.08
0.06
tanφ
0.04
0.02
0
-150
-100
60
40
-50
0
Temperature, T / °C
Young's modulus, E / GPa
(a)
Young's modulus, E / GPa
Heat Flow
exothermic
Strain Amplitude=5 10-4, Frequency=1 Hz
d/D = 0.42
planes and the martensite variant interfaces, the habit planes
have a higher ability of damping due to higher mobility than
that of the martensite variant interfaces. These kinds of
characteristic features of the damping capacity of SMAs have
been reported by Sugimoto et al.10)
Since the tan is measured under oscillation stress loading
in DMS, martensitic transformation temperatures determined
by DMS measurement should be different from those
detected by DSC measurement without stress loading. The
stress loading is estimated from the static tensile test which
shows that 0.05% strain level of DMS corresponds to 20 MPa
stress level. Furthermore, the dependence of critical stress for
martensitic transformation on temperature, i.e. d=dT, is
about 2.1 in the same Cu-Al-Mn polycrystalline alloy.11,12)
Therefore, the martensitic transformation temperatures determined by DMS are expected to rise by about 10 C.
In the present paper, DMS curves only during the heating
process are presented, because the cooling curves show
tendencies similar to those of the corresponding heating as
demonstrated in Fig. 1.
3.2
Dependence of frequency and strain amplitude on
tan Figures 2 and 3 show the dependence of frequency and
strain amplitude on tan in Cu72 Al17 Mn11 alloys, where the
DMS curves are shown in Figs. 2(a) and 3(a), and three kinds
50
(a)
Strain Amplitude=5 10-4, d/D=0.72
0.25
Frequency
0.5 Hz
1 Hz
10 Hz
20 Hz
Fig. 1 DMS and DSC curves during (a) cooling and (b) heating.
0.20
Damping properties due to the martensitic transformation
Figure 1 shows the results of the DMS and the DSC
measurements during (a) cooling and (b) heating of the
Cu72 Al17 Mn11 alloy. The d=D indicates relative grain size,
where d and D are the grain diameter and the diameter of the
wire, respectively. During cooling, when the temperature
reaches the Ms determined by DSC, tan , which was low in
the parent phase state, drastically increases and then enters a
steady state with a high level of tan 0:08. Although tan starts to gradually decrease with decreasing temperature at
the Mf , the high level of tan is still maintained in the
martensite single-phase state. Similarly, during heating, one
can see a high level of tan ¼ 0:04{0:06 in the martensite
single-phase state, the maximum tan 0:09 in the martensite + parent two-phase state and a low tan in the parent
phase state. The decrease of Young’s modulus associated
with forward and reverse martensitic transformations is
observed. Furthermore, Young’s modulus in the martensite
phase is higher than that in the austenite phase. The tan drastically increases with decreasing Young’s modulus.
These results suggest that while there is a large energy loss
due to the movement of two kinds of interfaces associated
with the martensite, namely, both the parent/martensite habit
tanφ
3.1
Results and Discussion
0.15
0.10
0.05
0
-150
-100
-50
0
Temperature, T / °C
50
100
(b)
peak
martensite phase
parent phase
0.25
0.20
tanφ
3.
119
0.15
0.10
0.05
0
0
5
10
15
Frequency, F / Hz
20
Fig. 2 Dependence of frequency on tan (a) DMS curves and (b) tan values.
120
N. Koeda et al.
(a)
Frequency=1 Hz, d/D=0.72
Strain Amplitude
1 10-3
5 10-4
1.3 10-4
0.20
tanφ
0.15
0.10
0.05
0
-150
-100
-50
0
Temperature, T / °C
50
100
3.3 Effect of grain size on tan It has been reported that shape memory properties depend
on the relative grain size d=t or d=w due to the constraint
stress among the grains,7,8,13) where d, t and w are grain size,
thickness and width of sheet specimen, respectively. Therefore, the mobility of martensite interfaces is expected to be
affected by the relative grain size. In the present study, the
tan was determined in specimens with various relative grain
size d=D about d=D ¼ 0:09 (d ¼ 45 mm), 0.42 (d ¼ 210 mm)
and 0.71 (d ¼ 355 mm), where D is the diameter of the wire
specimen. Figures 5(a) and (b) show the microstructures of
wire specimens with different d=Ds. With increasing d=D,
each grain is able to penetrate the cross section of the wire
(b)
peak
martensite phase
parent phase
0.25
(a)
tanφ
0.20
0.15
0.10
0.05
0
0
5
10
Strain Amplitude, ε / 10-4
tanφ
Fig. 3 Dependence of strain amplitude on tan (a) DMS curves and
(b) tan values.
Peak (Parent+Martensite)
heating
Parent Phase
TA = Tb+50°C
Ta
Martensite Phase
TM = Ta 50°C
500µm
(b)
Tb
Temperature, T / °C
Fig. 4
Definition of tan value in each phase.
of tan values defined in Fig. 4 are plotted in Figs. 2(b) and
3(b), respectively. In the strain amplitude range of 1:3 104 –1 103 and in the frequency range of 0.5 Hz–20 Hz,
the peak height of tan in the parent + martensite two-phase
state decreases with increasing frequency, but hardly depends
on the strain amplitude. On the other hand, tan in the
martensite phase state increases with increasing strain
amplitude, being almost constant on the frequency. This
difference of the damping behavior between the two-phase
state and the martensite state is attributed to whether it is
related to the transformation. It should be noted that the
specimen with a strain amplitude of 1 103 indicates a
relatively high tan at even the Af , which is caused by the
stress-induced martensite due to the high strain amplitude.
Fig. 5 Microstructure of wire specimens with (a) d=D ¼ 0:42 and
(b) d=D ¼ 0:71.
Damping Properties of Ductile Cu-Al-Mn-Based Shape Memory Alloys
0.6
Strain Amplitude = 5 10-4
Frequency=1 Hz
(a)
0.6
d/D=0.09
d/D=0.46
d/D=0.71
0.5
0.5
0.4
tanφ
tanφ
0.4
0.3
0.2
0.3
0.2
0.1
0
-100
121
0.1
-50
0
Temperature, T / °C
( )
50
( )
0
0.1
0.2
0.4
1
d/D
Fig. 6 tan of specimens with d=D ¼ 0:09, 0.46 and 0.71.
(b)
0.08
0.07
0.06
0.05
tanφ
specimen, and the microstructure changes to a bamboo
structure in the large grain condition over d=D ¼ 1. The
values of tan of wire specimens with different d=Ds are
shown in Fig. 6, where the strain amplitude, the frequency
and heating rate are 5 104 , 1 Hz and 2 C/min, respectively. The relatively low tan in the specimen with the small
d=D increases with increasing d=D in both the two-phase and
martensite phase states. It can be concluded that tan strongly depends on the d=D. The obtained tan values at the
peak in the two-phase state and at the TM defined as Fig. 4 in
the martensite phase state are plotted as a function of d=D in
Figs. 7(a) and (b), respectively. In damping materials based
on martensitic transformations, three separate contributions,
1
1
14)
Q1
Tr , QPT and Qint , to the total tan should be considered.
1
The Qint is an intrinsic part which is composed of the internal
friction contributions of each phase and is strongly dependent
on microstructural properties, especially in the martensite
phase. The tan at the peak in the two-phase state, which
corresponds to the temperature region from Ms (As ) to Mf
1
1
1
(Af ), strongly depends on the QTr
and QPT
. The QTr
is the
transient part of total tan which is related to parent/
martensite transformation kinetics and increases with in1
creasing transformation rate. The QPT
is non-transient part
which is related to the mobility of the parent/martensite habit
planes and is independent of the transformation rate. It is seen
from Figs. 7(a) and (b) that the tan values are divided into
two regions (I and II) depending on the d=D and that the tan values both at the peak and in the martensite phase state
linearly increase with increasing d=D. The slope in region II
is much steeper than that in region I in both cases. This result
can be explained from the standpoint of the grain constraint;
i.e., in region I below d=D ¼ 0:4, the relative grain size is
very small, which means that the grains are three-dimensionally constrained by the surrounding grains. On the other
hand, in region II, the volume fraction of the grains
possessing a free surface increases with increasing d=D and
the microstructure becomes close to the bamboo structure. In
this case, the constraint stress may be drastically released
with increasing d=D. Furthermore, it is noted that the
0.04
0.03
0.02
0.01
( )
( )
0
0.1
0.2
0.4
1
d/D
Fig. 7 tan values (a) at peak and (b) in the martensite state in relation to
d=D.
dependence of tan on d=D at the peak in the two-phase
state is much greater than that in the martensite phase state.
1
1
Therefore, it can be supposed that QTr
and QPT
which are the
internal friction terms related to the martensitic transforma1
tions, are more affected by d=D than Qint
.
It can thus be concluded that relative grain size control is
very useful for the improvement of damping capacity. The
largest tan values both at the peak and in the martensite
phase state are obtained in the alloys with the relative grain
size d=D 1.
In the Cu-Al-Mn system, a strong {112} h110i recrystallization texture can be obtained by the addition of Ni to CuAl-Mn-based alloy and by using thermomechanical process
treatment with strong cold-drawn,6–9) while Cu-Al-Mn
ternary alloy have relatively random texture under the same
condition. The effect of texture on tan in Cu-Al-Mn-based
alloys will be reported in near future.
122
4.
N. Koeda et al.
Conclusions
(1) Cu-Al-Mn-based alloys show a high damping capacity
tan in the martensite state as well as in the parent +
marensite two-phase state, a maximum tan being
obtained in the two-phase state.
(2) In the parent + martensite two-phase state, tan increases with decreasing frequency but hardly depends
on the strain amplitude. In the martensite phase state,
while only slightly depending on the frequency, tan increases with increasing strain amplitude.
(3) tan strongly depends on the relative grain size d=D.
The value of tan drastically increases with increasing
d=D. The largest values of tan ¼ 0:07 and tan ¼
0:54 are obtained in the martensite state and at the peak,
respectively, in the alloy with a relative grain size
d=D 1.
Acknowledgements
This work was supported by Grant-in-Aids for Scientific
Research from the Ministry of Education, Culture, Sports,
Science and Technology, Japan.
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