Torsion Coupling
6.1 Introduction
Stress (s)
Temperature (T) TMf TMs TAs TAf
Austenite Martensite
FIGURE 6.1 Stress–temperature diagram of an SMA.
Stress (s)
Temperature (T)
Magnetic field (H) Martensite
Austenite
FIGURE 6.3 Schematics of three-dimensional phase transformation diagram of FSMAs.
FIGURE 6.2 Stress–strain curve of an SMA with (a) SE loop at T > TAf and (b) SME loop at T < TMs.
(a) sMs
s
e sy
A
B C
D
O E EA
EM
O (b)
s
eres e
A
B
because it is not an elastic deformation. Th e SMA is in the fully martensite phase at the temperature below TMs and the loading path OA is involved in the martensite variant rearrangement.
However, if the SMA is loaded beyond point A in Figure 6.2b, it is under the elastic deformation with a slope of EM similar to BC in Figure 6.2a.
6.1.2 Ferromagnetic Shape Memory Alloy As described before, the phase transformation of SMAs can be controlled by stress and temperature. Their relationship can be described by a stress–temperature phase diagram as shown in Figure 6.1. Recently, attention has been paid to some SMAs accom- panying a change in ferromagnetism at phase transformation and having low hysteresis. Th is is because the transformation charac- teristics such as transition point (martensite start temperature, TMs) and macroscopically observed strain, caused by the transfor- mation, are possibly controlled by an applied magnetic fi eld (H).
Th e response of transformation is fast in this case because the characteristic time is governed by the formation and growth of martensite, which is induced by an applied magnetic fi eld. It is fast, thus, it is plausible to produce an actuator having reversible straining with quick response to a signal imposed or detected.
Such an alloy with both ferromagnetic property and SMA behav- iors is called ferromagnetic shape memory alloy (FSMA) and it is considered as a strong candidate for fast responsive actuator material. Th e relationship of phase transformation, stress (s), temperature (T), and magnetic fi eld (H) can be presented as a three-dimensional phase transformation diagram as shown schematically in Figure 6.3.
Currently, only a limited numbers of FSMAs have been found as listed in Table 6.1. Many researchers have extensively studied NiMnGa, Fe–Ni–Co–Ti, Fe–Pt, and Fe–Pd FSMAs to examine SME and superelasticity. Th ese alloys have also been considered as a possible candidate actuator materials. Among these alloys, NiMnGa [4,5] and Fe–Ni–Co–Ti [20,21] alloys have been known to exhibit good SMEs. However, the marten- sitic transformation start temperature (TMs) of the latter alloy is below −150°C. It is too low to be practically used. Further, Kakeshita et al. even reported magnetoelastic martensitic transformation in Fe–Ni–Co–Ti by using a strongly applied magnetic fi eld up to 2.3 × 107 A/m. Th ey also reported that martensitic transformation is not induced by an applied mag- netic fi eld until 4.8 × 106 A/m is reached [25]. Th ese results show that a very strong applied magnetic fi eld is needed to directly induce martensitic transformation. Th is is not suitable
for applications as an actuator material where a compact elec- tromagnet is needed.
However, the variant rearrangement mechanism under con- stant magnetic fi eld maybe still useful for some applications. Th e change of the surface morphology on a single crystal specimen can be observed during the process of cooling. As shown in Figure 6.4a of a single crystal FePd whose temperature is just below TMf (= 0°C), the boundary and the contrast of the two vari- ants are not distinct. When this specimen is further cooled at
−20°C, its surface morphology exhibits a distinct boundary with a clear contrast of black and white colors (Figure 6.4b). Th is is
because the lattice parameter change (e.g., c/a ratio, Figure 6.4c [43,44]) of the FePd martensite gradually decreases with decreas- ing temperature. Th e gradual change of the lattice parameter results in an increase of the angle j formed by two martensite variants (CV1 and CV2) (Figure 6.4d). As j increases during cooling, the contrast of the boundary between CV1 and CV2 (Figure 6.4a and b) also is enhanced. Th e change of the volume fraction between variants (variant rearrangement) such as CV1 and CV2 in Figure 6.4d will result in additional straining of the FePd specimen. Th is can be done by applying a magnetic fi eld since the FePd is a ferromagnetic material. Such a straining, which is due to the magnetic fi eld–induced martensite variants rearrangement, can be detected. When the FePd single crystal specimen is fully covered by the pair of CVs at −20°C, a magnetic fi eld is applied along the length of the specimen. As shown in Figure 6.5, the strain of the magnetic fi eld–induced martensite rearrangement is a function of the magnetic fl ux density, where the negative magnetic fl ux density means that the direction of the fi eld is opposite. A strain of 0.4% is obtained and it is revers- ible and repeatable with any bias stress, although some studies have reported [20] that the application of a bias stress is required simultaneously with the applied magnetic fi eld in order to induce such a reversible strain in FSMAs as shown in Figure 6.5.
A single crystalline FePd specimen is subjected to a compres- sion test at −20°C and the amount of strain accompanied with the stress-induced variant rearrangement is measured. Surface morphology change of the specimen is also observed during the tests. Figure 6.6 shows the surface morphology change during the fi rst loading and the stress–strain curves of the fi rst two cycles of loading and unloading tests. During the fi rst loading process (Figure 6.6a through e), the volume fraction of CV1 increases at the expense of CV2. When the stress reaches 10 MPa, the specimen is fully covered by a single variant of CV1 and the process of the variant rearrangement is completed (Figure 6.6e), while the strain reaches to 5.2%. During the fi rst unloading pro- cess, the volume fraction of CV1 decreases and the unloading curve (white circles in Figure 6.6f) is slightly lower than that the loading curve (black circles). Th e specimen exhibits about 5.0%
TABLE 6.1 List of Current FSMAs
Type Alloy TMs References
Heusler Ni2MnGa −150°C to 150°C [2–19]
Fe–Ni–Co–Ti <−150°C [20–29]
Iron-based alloys Fe-23–25Pt <−48°C [30–38]
Fe-28–31Pd −197°C to 80°C [39–53]
Fe–Pd–Ni <RT [54,55]
Cobalt-based alloy NiAlCo [56,57]
Observation direction
Q: Less distinct contrast corresponding to photo (a)
R: Distinct contrast corresponding to photo (b)
P: No contrast
CV1 CV2
CV1 CV2
j
j a
a c c
a a c c (101)
FCC
−2⬚C
(a) 100 μm
(b)
Martensite Austenite
Temperature (c)
(d)
c/a
1 P
Q R
−20⬚C
FIGURE 6.4 (a) and (b) Changing contrast of the twinning boundary aft er martensitic transformation. (c) Schematic illustration of the rela- tionship between c/a ratio and temperature in Fe–Pd alloy. (d) Increasing angle j with decreasing temperature.
−0.4
−0.1 0.1 0.2 0.3 0.4 0.5
0
Strain (%)
−0.2 0 0.2 0.4
Magnetic field (T)
FIGURE 6.5 Magnetic fi eld-induced strain as a function of magnetic fl ux density measured in Fe–Pd single crystal.
reversible strain and 0.3% irreversible strain in the fi rst loading unloading cycle. Th e stress–strain curve of the second test cycle (square dots in Figure 6.6f) almost follows the one of the fi rst cycle. However, no reversible strain is measured in the second test and the repeatable strain is 5.0%. Th is repeatable strain under compressive stress could be utilized as a useful actuation method if the applied magnetic fl ux gradient that provides the stress is applied to the specimen so as to induce the strain by the above variant rearrangement mechanism.
Similarly, the superelastic behavior, SME, and magnetic prop- erties have been studied in Fe–Pt alloys by some groups [30–38].
As shown in Table 6.1, Fe–Pt alloys also have the TMs much lower than room temperature [30,31]. Kakeshita et al. [38] have also reported that the martensitic transformation can be induced by a large applied magnetic fi eld, as large as 2.0 × 107 A/m. Th e TMs
of Fe–Pd alloys can be tailored by compositions of Pd between 80°C and −200°C [39,40,43]. However, currently most of FSMA actuator studies have focused on NiMnGa and Fe–Pd alloys.
6.1.3 Driving Mechanisms for FSMA-Based Actuators
FSMAs have both characteristics of thermoelastic SMAs and ferromagnetic properties. In principle, the phase transforma- tion and straining also can be controlled by the magnetic fi eld.
Th e relationship of phase transformation, stress (s), temperature (T), and magnetic fi eld (H) can be presented as a three-dimen- sional phase transformation diagram as shown schematically in Figure 6.3. Th e three-dimensional surface in the diagram
separates the martensite and austenite phases. Th is diagram can help us to determine a favorable driving mechanism for FSMAs as actuator materials, especially as controlled solely by an applied magnetic fi eld. Th is control method by the magnetic fi eld on FSMAs will be faster than the one by thermal conduction on SMAs. Several driving mechanisms (by the magnetic fi eld) of actuators based on FSMAs have been proposed and studied.
The following sections summarize the three main driving mechanisms.
6.1.3.1 Magnetic Field–Induced Phase Transformation
Th e phase transformations of FSMAs can be controlled or aff ected by a magnetic fi eld. Th is is called the magnetic fi eld–
induced martensitic phase transformation [7,60]. Th erefore, the superelasticity may also be controlled or produced by the mag- netic fi eld and a large reversible displacement is obtained. Th is property is advantageous when applied to an actuator device.
Th e forward transformation (austenite → martensite), induced by a magnetic fi eld, has been found in NiMnGa, while the reverse transformation (martensite → austenite), induced by a magnetic fi eld, also occurs in FePd [60]. As shown in Figure 6.7, the slope, dH/dT, of FePd is negative and that of NiMnGa is positive. Th is phenomenon can be explained by the Clapeyron–
Clausius relationship [59]
= Ms M− A d
d ( )
H h
T T M M (6.1)
Strain (%) 1st cycle loading
1st cycle unloading 2nd cycle loading 2nd cycle unloading
Stress (MPa)
00 5 10 15
(a) 0.0 MPa (b) 3.2 MPa (c) 4.8 MPa (d) 7.5 MPa (e) 9.5 MPa
(f)
1 2 3 4 5 6
FIGURE 6.6 (a)–(e) Change of volume ratio of CVs for the fi rst loading and (f) stress–strain curves for the fi rst two cycles of loading and unloading.
where
h is the enthalpy H is the magnetic fi eld
MM is the magnetization of martensite phase MA is that of the austenite phase
For the case of FePd, (MM – MA) is negative before the saturation of magnetization [60]. Hence, Equation 6.1 implies that dH/dT is negative, resulting in promoting the martensite → austenite phase transformation by applying the magnetic fi eld. However, for the case of NiMnGa, its magnetization in the martensite phase is larger than that in the austenite phase [4,58], thus, dH/dT in Equation 6.1 is positive, resulting in promoting the austenite → martensite phase transformation. It has been reported that the magnetic fi eld can induce phase transformation in FSMAs, but this eff ect is very small in both NiMnGa and FePd alloys because of a small magnetization diff erence (MM – MA) between martensite and austenite phases.
6.1.3.2 Variant Rearrangement in Fully Martensite Phase by Magnetic Field
In addition to the above superelasticity, a rearrangement (change) in variants in a fully martensitic phase due to the application of stress in SMAs will occur and additional strain can be obtained as shown in Figure 6.2b. Here, stress controls variants with diff er- ent transformation strain. Th is variant rearrangement induced by the application of the magnetic fi eld is also possible in FSMAs.
Many studies have concentrated on this mechanism [2,5,6,8–
19,28,29,53]. In this case, the magnetic fi eld controls variants with diff erent magnetization. Variants having diff erent magneti- zation may have diff erent transformation strains. Th us, the mag- netic fi eld may change overall strain of an FSMA, when it is in a martensitic state. Th is is also advantageous when an FSMA is used as an actuator. If the magnetic fi eld can really discriminate martensite variants with a diff erent transformation strain, an FSMA can be used as a high damping material as well. First, the movement of variant or martensite boundaries accompanies energy dissipation. Th is is manifested by a hysteresis, even though it is small in thermoelastic transformation. Secondly, mechanical
vibration interacts with the oscillating magnetic fi eld that moves boundaries of magnetic domain or variant in martensite phase.
Currently, the variant rearrangement induced by the magnetic fi eld is eff ective in a single crystal FSMA, i.e., NiMnGa. However, a bias stress is needed in order to induce single variant in single crystal FSMA so a large strain can be obtained. Although 5%
reversible strain has been reported by this driving mechanism, the output stress is only as high as 10 MPa. Th is is not suitable for actuators that require a high output force. Furthermore, NiMnGa is very brittle; therefore, it is only suitable for the applications where NiMnGa is under a compression mode.
6.1.3.3 SIM Phase Transformation by Magnetic Field Gradient
It is well-known that ferromagnetic material feels a force when it is in a nonuniform magnetic fi eld. Th is force can be large enough to induce the SIM in a superelastic FSMA. Th is is called hybrid mech- anism [59]. Th e hybrid mechanism consists of chain reactions:
Magnetic fi eld gradient causes magnetic force or moment, which introduces stress in an FSMA → SIM transformation → the FSMA becomes much soft er and exhibits a large deformation. In reality, the hybrid mechanism can also be utilized, when an actuator is designed. Th at is, a large force can be applied to an actuator by a compact electromagnet with a high magnetic fi eld gradient, result- ing in a larger displacement with fast response. In this driving mechanism, FePd FSMA, which exhibits 1.6% superelastic strain, is more suitable because it has a large magnetization factor, with the same order as iron [59]. Th is can be easily seen by a demonstra- tion as shown in Figure 6.8, where two identical cantilever beams made of FePd and NiMnGa are subjected to a magnetic fi eld. As shown in Figure 6.8b, the FePd beam bends signifi cantly because FePd has a much larger magnetization than NiMnGa. In addition, FePd is very ductile, which is suitable for any actuator application.
In summary, Table 6.2 shows the comparison among the three driving mechanisms proposed for FSMAs. Mechanism (a) is not practical because a large magnetic fi eld is needed to change the transformation temperatures (i.e., inducing phase transforma- tion). For example, for NiMnGa in Table 6.2, TMs can be changed
H Parallel to
H-axis Austenite Martensite
s s
T
(a)
H
Austenite Martensite
T
(b)
FIGURE 6.7 Schematics of the phase transformation diagram of (a) FePd and (b) NiMnGa. (From Liang, Y., Kazo, H., and Taya, M., Mech.
Mater., 38, 564, 2006. With permission.)
by a 4 × 106 A/m magnetic fi eld, however, the electromagnet will be too huge to use for practical applications. A conventional compact solenoid cannot produce such a high magnetic fi eld.
Mechanism (b) is not achievable for polycrystal FSMA because only a very small strain is available. For example, only the order of 10−4 strain can be obtained for polycrystal FePd in a fi eld up to 8 × 105 A/m [61]. Even though a large strain can be produced by a small magnetic fi eld in single crystals of NiMnGa using mecha- nism (b), the output force is still as small as several MPa.
Th erefore, for the current available FSMA such as the FePd alloy, mechanism (c) (hybrid mechanism) shows the best performance among these mechanisms.