Materials Transactions, Vol. 48, No. 3 (2007) pp. 395 to 399
Special Issue on Smart and Harmonic Biomaterials
#2007 The Japan Institute of Metals
Damping Capacity of Ti-Nb-Al Shape Memory -Titanium Alloy
with f001g h110i Texture
Tomonari Inamura1 , Hideki Hosoda1 , Kenji Wakashima1 , Jae Il Kim2 ,
Hee Young Kim3 and Shuichi Miyazaki3
1
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Materials Science and Engineering, Dong-A University, 840 Hadan 2-dong, Saha-gu, Busan, 604-714, Korea
3
Institute of Materials Science, University of Tsukuba, Tsukuba 305-8573, Japan
2
Damping capacity (tan ) of Ti-24 mol%Nb-3 mol%Al (Ti-Nb-Al) shape memory alloy (SMA) with f001g h110i texture was examined
upon cooling from 423 K to 123 K by dynamic mechanical analysis (DMA) in a tensile mode. The f001g h110i texture was well developed by a
cold-rolling with reduction in thickness of 99% followed by a heat treatment at 873 K for 3.6 ks. The apparent phase of the material at room
temperature was the -phase (bcc) containing small amount of -phase (hcp) and the martensite start temperature (Ms ) of the -00 (Corthorhombic) thermoelastic martensitic transformation was about 250 K. The -phase was equiaxed and averaged grain size was 2 mm. The
angle between the longitudinal direction of the DMA specimens and the rolling direction (RD) was defined as and was 0, 30, 45, 60 and 90
degrees on the normal plane. Damping capacity, tan , depended on the stress-amplitude (o ) and . The peak height of tan during the
martensitic transformation, tan , was proportional to o for each and also proportional to the maximum transformation strain along the
loading direction ("MAX ) which is determined by the crystallography of the transformation. A proportional relationship between tan and
o "MAX was found and indicated that the interaction between the transformation and the applied stress plays an important role in the damping of
the textured SMA. [doi:10.2320/matertrans.48.395]
(Received October 16, 2006; Accepted January 19, 2007; Published February 25, 2007)
Keywords: -titanium, texture, Internal friction, anisotropy
1.
Introduction
Some -Ti alloys have a martensitic transformation from
(bcc) to 00 (C-centered orthorhombic).1,2) This transformation is thermoelastic thus these alloys exhibit the shape
memory effect and the superelasticity.3–5) We have systematically investigated the shape memory effect and the
superelasticity of Ti-Nb and Ti-Mo alloys with third elements
belonging to the 13- and 14-groups in the periodic table.6–11)
Most -Ti alloys possess good workability. It is possible to
fabricate cold-rolled sheet of the alloys, unlike Ti-Ni, with a
reduction rate higher than 90%. Strong textures are developed and anisotropy in superelastic property inevitably
appears in the sheet. It is possible to control and improve
the superelastic behavior using the orientation effect in the
textured shape memory alloys (SMAs). It is, therefore,
valuable to examine which textures can be developed in the
-Ti based SMAs and to investigate the effect of texture on
the shape memory effect and the superelasticity. It has been
revealed that well developed f001g h110i and f112g h110i
textures can be obtained by suitable thermomechanical
treatments in Ti-Nb based alloys,12–15) where subscript indicates -phase, hereafter. The orientation effect in the
transformation strain becomes significant in these textured
SMAs and the superelastic strain comparable to the lattice
deformation strain is obtained.12–15)
It is known that high damping due to hysteretic movement
of interfaces occurs in SMAs.16) Damping is one of
characteristic functions of SMA as well as superelasticity
and shape memory effect. The effect of texture on the
damping capacity in -titanium SMA has not been examined
yet. The objective of this study is to investigate the
orientation dependence of the damping capacity of Ti-NbAl shape memory alloy with a well developed texture.
2.
Experimental Procedures
Ti-Nb-Al alloy with a nominal composition of Ti24 mol%Nb-3 mol%Al was prepared by Ar arc-melting
method with a non-consumable W-electrode in Ar-1%H2
reduction atmosphere. High purity starting elements of Ti
(99.99%), Nb (99.9%) and Al (99.99%) were used. The
change in weight due to arc-melting was less than 0.1 mass%
and was therefore judged to be negligible, requiring no
chemical analysis. It should be noted, however, that the
oxygen content of similar ingots was 200400 ppm by
weight. The oxygen content of this ingot is therefore believed
to be similar. The ingot was sealed into an evacuated quartz
tube, homogenized at 1273 K for 7.2 ks and then quenched by
breaking the quartz tube in water.
Cold-rolling with a reduction in thickness of 99% was carried
out after homogenization. The final thickness of the as-rolled
sheet was 0.10 mm. Rectangular specimens of 15 mm 1 mm 0:10 mm were cut from the as-rolled sheet. The
longitudinal direction of the specimens was systematically
varied within the plane of the as-rolled sheet (the ND-plane).
The angle between the longitudinal axis of the specimens and
the rolling-direction (RD) was defined to be and set to be 0
(RD), 30, 45, 60 or 90 (the transverse direction, TD) degrees.
The damaged layer introduced by cutting was removed by
mechanical polishing. Specimens were encased in Ti-foil and
sealed into evacuated quartz tubes, prior to heat treatment at
873 K for 3.6 ks and quenched into water. The - phase
boundary in the present alloy is estimated to be around the
heat-treatment temperature.17)
Thin-foils for Transmission Electron Microscopy (TEM)
observation were prepared by a twin-jet polishing technique
in a solution of 5 pct sulfuric acid + 2 pct hydrofluoric
acid + 93 pct methanol at 243 K. TEM observation was
made using a Philips CM200 operated at 200 kV. Electron
396
T. Inamura et al.
backscatter pattern (EBSP) analysis was made to characterize
the texture after the heat treatment using a HITACHI S4300SE(N) scanning electron microscope equipped with a
OXFORD INCA Crystal EBSP detector. Specimens for
EBSP analysis were finished by electro-polishing in a
solution of 6 pct perchloric acid + 35 pct buthanol + 59 pct
methanol at 233 K. The specimen was heated above 373 K by
a heat-gun to eliminate any martensite formed during electropolishing.
Storage modulus (E) and damping capacity (tan ) were
measured as functions of temperature using a dynamic
mechanical analyzer (DMA) NETZSCH DMA242C in
tensile mode, where is the phase-lag between the applied
stress and the resultant strain. Liquid nitrogen was pumped
into a specimen chamber with a thermocouple put in the
vicinity of the specimen. The specimen was heated to 423 K
and then cooled down to 123 K at a rate of 5 K/min. A
sinusoidal dynamic tensile stress was applied to the specimen
during cooling. Stress amplitude (o ) was 10, 20 or 30 MPa.
The static stress (mean stress) was set to 1:3o with a
minimum total-stress of 0:3dy and a maximum of 2:3o . A
dynamic stress frequency ( f ) was set to 1 Hz.
3.
Results and Discussion
3.1 Microstructures
Figure 1(a) is a TEM bright field image of the alloy after
the heat treatment at 873 K. The apparent phase was and the
dislocations introduced by the cold-work were not fully
annihilated. No formation of isothermal !-phase was
confirmed. Precipitation of -phase (hcp) was observed at
sub-boundaries as indicated by arrows. Figure 1(b) and (c)
shows a selected area diffraction (SAD) pattern taken from
the -particle encircled in Fig. 1(a) and its key diagram,
respectively. The electron beam was almost parallel to ½100
and ½21 1 0 in the SAD, where subscript indicates -phase
hereafter. The orientation relationship between and was
close to the Burgers OR i.e., ð0001Þ == ð01 1Þ and ½112 0 ==
½111 .18)
Figure 2(a) shows an image quality map obtained by the
EBSP analysis. The -grains were equiaxed and averaged
grain size was 2 mm, where the grain boundary was defined to
be the boundary with misorientation angle higher than 3
degrees. Black points seen in Fig. 2(a) are un-solved points in
(b)
(a)
0111 α
020β
011β
0111 α
β(bcc)
α(hcp)
Table 1 Crystallographic direction for each loading direction in the
texture.
0
30
45
60
90
hhkli
h110i
h410i
h100i
h410i
h110i
EBSP and probably correspond to the -phase. Figure 2(b)
shows a 001 pole figure corresponding to Fig. 2(a).
f001g h110i texture, which is originated to the rollingtexture,19) was developed and 90% of the grains belonged to
this texture within 7 degrees. The texture strength relative to
the random orientation was 65. Table 1 summarizes the
corresponding direction for each in the f001g h110i
texture. In addition to the EBSP analysis, the development of
the f001g h110i texture was confirmed by X-ray pole figure
analysis with a beam-size of 1 mm 1 mm in the same
material.14) The f001g h110i texture was, therefore, judged
to be formed entire the material.
3.2 Temperature dependence of tan Figure 3(a), (b), (c), (d) and (e) shows the temperature
dependence of the storage modulus (E) and tan under
various o upon cooling for ¼ 0 (RD), 30, 45, 60 and 90
(TD) degrees, respectively. E at 423 K is about 60 GPa along
RD and TD whereas it is 40 GPa at ¼ 45 degrees. This
anisotropy in E is due to that the Young’s modulus of the
parent -phase becomes minimum along h100i in this
RD
16
TD
8
4
2
1
0.5
0.13
10µm
Fig. 2
011β
Fig. 1 TEM image of Ti-Nb-Al heat-treated at 873 K for 3.6 ks after the
cold-rolling (a) bright field image, (b) selected area diffraction pattern
taken from the encircled region and (c) key diagram of (b) The arrows
indicate the -phase.
32
RD
0110 α
0001 α
0.5µm
RD
(b)
(a)
002β
(c)
(a) Image quality map and (b) 001 pole figure of the heat-treated material.
001
Damping Capacity of Ti-Nb-Al Shape Memory -Titanium Alloy with f001g h110i Texture
σo
(a)
(b)
10MPa
50
0
30MPa
0.1
φ = 0°
(RD)
20MPa
Tan δ
σo
0.1
10MPa
φ = 30°
30MPa
20MPa
10MPa
50
50 100 150 200 250 300 350 400 450
Temperature, T / K
(c)
(d)
σo
20MPa
30MPa
0
10MPa
20MPa
30MPa
0
Tan δ
φ = 45°
0.1
100 150 200 250 300 350 400 450
Temperature, T / K
σo
50
10MPa
E / GPa
E / GPa
50
σo
30MPa
20MPa
10MPa
σo
0.1
φ = 60°
30MPa
20MPa
10MPa
0
0
50 100 150 200 250 300 350 400 450
Temperature, T / K
(e)
σo
0
0
Tan δ
10MPa
20MPa
30MPa
E / GPa
E / GPa
0
Tan δ
σo
50
20MPa
30MPa
397
50
100 150 200 250 300 350 400 450
Temperature, T / K
σo
10MPa
20MPa
30MPa
E / GPa
50
Tan δ
0
σo
0.1
30MPa
φ = 90°
(TD)
20MPa
10MPa
0
Fig. 3 Temperature dependence of the storage modulus (E) and the
damping capacity (tan ) along of (a) 0 degree (RD), (b) 30 degrees, (c)
45 degrees, (d) 60 degrees and (e) 90 degrees (TD).
50 100 150 200 250 300 350 400 450
Temperature, T / K
alloy.20) E decreased to a minimum at about 200 K with
decreasing temperature from 423 K in each loading direction
for each o . The gradual decrease in E upon cooling from
423 K to about 250 K is suggested to be due to the instability
of -phase toward the 00 -martensitic transformation. The
rapid decrease in E around 250 K corresponds to the rapid
increase in tan as seen in Figs. 3. The temperature at which
the rapid increase of tan occurs is the martensite start
temperature (Ms ).16) The proportionality relation between Ms
and the applied stress, the Clausius-Clapeyron relationship, is
held in SMA in general. The proportionality relation between
Ms and o was, however, not recognized clearly in the present
study. This was probably due to that the applied stress was
not static and o was relatively low, compared to the stresslevel of conventional tensile tests. Ms under zero stress was,
therefore, not obtained by the Clausius-Clapeyron relationship but estimated to be around 230 K250 K by averaging
Ms under various o . The martensite finish temperature (Mf )
could not be detected due to the limitation in cooling capacity
of the equipment and the material is not fully transformed
into martensite even at the lowest temperature of the
measurement. The anelastic strain contributing to tan is,
therefore, considered to be mainly the transformation strain,
i.e., due to the hysteretic movement of 00 = interface.
398
T. Inamura et al.
0.20
φ = 0° (RD)
φ = 30°
φ = 45°
φ = 60°
φ = 90° (TD)
∆tanδ
0.15
bo
co
0.10
ao
ab
0.05
Fig. 5 The Au-Cd type lattice correspondence.
3.0
0.00
10
20
30
Stress amplitude, σo / MPa
Fig. 4 Stress amplitude (o ) dependence of the peak height of tan ( tan ).
ε MAX (%)
0
2.0
1.0
0.0
0.20
3.3
σ o = 30MPa
σ o = 20MPa
σ o = 10MPa
∆tanδ
0.15
0.10
0.05
0.00
0
10 20 30 40 50 60 70 80 90
φ (degree)
Fig. 6 dependence of the maximum transformation strain ("MAX ) and
tan .
0.20
σ o = 30MPa
σ o = 20MPa
σ o = 10MPa
0.15
∆tanδ
Stress amplitude and orientation dependence of
tan The temperature for the peak value of tan was about
175 K in each loading direction for each o . The peak value
of tan was significantly increased along ¼ 0 and 90
degrees (RD and TD) and decreased to a minimum along
¼ 45 degrees. The peak value of tan for o ¼ 30 MPa was
higher than 0.15 along RD and TD whereas it is about 0.1
along ¼ 45 degrees. Figure 4 shows o dependence of
tan for each loading direction, where tan is defined to
be the difference between the base-line and the peak value of
tan . tan increases with increasing o and is seen to be
proportional to o for each loading direction. This is in
agreement with the result obtained in a polycrystalline CuAl-Ni SMA without texture.21) The proportionality factor
between tan and o depends on the loading direction as
seen in Fig. 4. tan along ¼ 0 and 90 degrees (==h110i )
was sensitive to o compared to that along ¼ 45
degrees == h100i . It was confirmed that the damping
capacity strongly depends on the stress amplitude and the
crystallographic direction of the loading.
Figure 5 shows the Au-Cd type lattice correspondence
which is plausible to the -00 martensitic transformation.22)
In the present alloy, the internal twinning for the latticeinvariant deformation does not occur and the transformation
strain is equivalent to the lattice deformation strain with
neglecting a small rotation.23) There are six lattice correspondence variants. The maximum transformation strain
among the six variants ("MAX ) in the f001g h110i texture
was calculated for each loading direction using the lattice
parameters of a ¼ 0:3281 nm, a00 ¼ 0:3183 nm, b00 ¼
0:4775 nm and c00 ¼ 0:4635 nm,23) where subscript 00
indicates the 00 -martensite. Figure 6 shows dependence
of tan for each o together with "MAX . It is clearly seen
that tan and "MAX exhibit similar dependence. The
relationship between tan and "MAX for each o is
summarized in Fig. 7. A proportional relation between
tan and "MAX was confirmed for each o and the
proportionality factor depended on o .
0.10
0.05
0.00
0.0
0.5
1.0
1.5
2.0
Maximum transformation strain, ε
2.5
MAX
3.0
(%)
Fig. 7 Relationship between tan and "MAX for each o .
The critical stress to induce martensite becomes zero and
the spontaneous transformation occurs below Ms in general.
The six variants are formed with the same volume fraction
under zero stress and the average transformation strain
becomes almost zero. External stress assists the formation of
a specific variant of martensite, which has the largest
Damping Capacity of Ti-Nb-Al Shape Memory -Titanium Alloy with f001g h110i Texture
along the loading direction ("MAX ) for each o .
(4) tan was proportional to o "MAX . This indicates that
the interaction between the applied stress and the
transformation plays an important role in the damping
behavior of the textured material.
0.2
0.15
∆tanδ
399
Acknowledgements
0.1
0.05
0
0
20
40
60
80
100
This work was partially supported by a Grant-in-Aid for
Fundamental Scientific Research Kiban B (No. 17360334,
2005–2007), Wakate B (No. 18760522, 2006–2007), Scientific Research of Priority Areas 438, Next-Generation
Actuators Leading Breakthroughs (No. 17040013, 2005–
2006) and the 21st COE program from the Ministry of
Education, Culture, Sports, Science and Technology, Japan.
σoε MAX / 10 J
4
REFERENCES
Fig. 8 Relationship between tan and o "MAX .
interaction with the stress (ij "ij , work done for a unit
volume) among the variants, where ij is the external stress
and "ij is the transformation strain. It is plausible to regard
o "MAX as an index of the work done here. Figure 8 shows
tan as a function of o "MAX . A proportional relationship
is seen between tan and o "MAX . The volume fraction of
the specific variant and the anelastic strain along the loading
direction increase under the external stress to reduce the
potential energy of the external stress according to the
interaction. This indicates that the interaction between the
transformation and the applied stress plays an important role
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4.
Conclusions
Damping capacity, tan , of Ti-Nb-Al shape memory alloy
with well developed f001g h110i texture was examined
upon cooling from 423 K to 123 K by dynamic mechanical
analysis in a tensile mode and following conclusions were
obtained.
(1) Ms was about 250 K and the storage modulus, E, takes
the minimum value along ¼ 45 degrees above Ms in
accordance with the anisotropy of the Young’s modulus
of the parent -phase.
(2) Damping capacity exhibited strong orientation dependence and stress-amplitude dependence in the textured
material. Tan along RT and TD is much higher than
that along ¼ 45 degrees in the f001g h110i texture.
(3) The peak height of tan during the martensitic transformation, tan , was proportional to the stress
amplitude (o ) in each loading directions and also
proportional to the maximum transformation strain
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