Thermomechanical Properties of Shape-Memory Alloy and Polymer ...

Mechanics of Advanced Materials and Structures, 16:236–247, 2009 c Taylor & Francis Group, LLC Copyright ISSN: 1537-6494 print / 1537-6532 online DOI: 10.1080/15376490902746954

Thermomechanical Properties of Shape-Memory Alloy and Polymer and Their Composites Hisaaki Tobushi,1 Elzbieta Pieczyska,2 Yoshihiro Ejiri,1 and Toshimi Sakuragi1 1 2

Department of Mechanical Engineering, Aichi Institute of Technology, Toyota, Japan Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

The shape memory effect and superelasticity appear in shape memory alloy (SMA). The large amount of strain by more than several hundreds percent can be recovered in shape memory polymer (SMP). The shape recovery and shape fixity can be used in SMP elements. These characteristics of shape memory materials (SMMs) can be applied to intelligent elements in various fields. In order to use these characteristics and design the SMM elements properly, it is important to understand the thermomechanical properties of SMAs and SMPs. The deformation behaviors of SMMs differ depending on the thermomechanical loading conditions. The main factors which affect these properties are strain rate, stress rate, temperature, subloop loading, temperature-controlled condition, strain holding condition and cyclic loading. In the present paper, the thermomechanical properties of TiNi shape memory alloy, polyurethane-shape memory polymer and their composite are discussed. Keywords

shape memory alloy, shape memory polymer, composite, cyclic loading, strain rate, fatigue

1.

INTRODUCTION In order to contribute to solving the problems of resources, energy and environment of the earth, the development of high performance materials is required. The development of intelligent or smart materials and their systems is vital since they have various functions, such as sensing, working and crack-healing by themselves, etc. In the intelligent materials, the development of shape memory alloy (SMA) has attracted high attention because the unique properties of the shape memory effect (SME) and superelasticity (SE) [1]. If we use the SME and SE in practical applications, not only large recovery strain but also high recovery stress, energy storage and energy dissipation can be obtained. The main features of the SME and SE are induced due to the martensitic transformation.

Address correspondence to Hisaaki Tobushi, Department of Mechanical Engineering, Aichi Institute of Technology, 1247 Yachigusa, Yakusa-cho, Toyota, 470-0392, Japan. E-mail: tobushi@aitech. ac.jp

In the shape memory materials, shape memory polymer (SMP) has also been developed [2]. In SMP, the shape fixity and shape recovery can be used. Large recovery strain of more than 100% can be obtained in SMP. The main features of SMP appear due to the glass transition. Elastic modulus differs at temperatures above and below the glass transition temperature, and therefore the rigidity of SMP elements vary depending on temperature. Although elastic modulus and yield stress are high at high temperatures and low at low temperatures in SMAs, they are high at low temperatures and low at high temperatures in SMPs. The dependence of rigidity on temperature is therefore quite different between SMA and SMP elements. If the composite materials with SMA and SMP are developed, the new characteristics of the shape memory materials can be obtained. In the present paper, (1) the thermomechanical properties of SMA: the shape memory effect and superelasticity, the conditions for progress of the phase transformation, the influence of strain rate on deformation property, the deformation behavior subjected to the stress-controlled subloop loading, damping and energy storage and the fatigue property, (2) the thermomechanical properties of SMP: the constitutive equation, shape fixity and shape recovery, the deformation properties of foam, the characteristics for holding at low temperature and the secondary-shape forming and (3) the thermomechanical properties of composite with SMA and SMP: the characteristics of composite with SMA and SMP and the bending properties will be discussed. 2.

THERMOMECHANICAL PROPERTIES OF SHAPE-MEMORY ALLOY

2.1. Shape Memory Effect and Superelasticity 2.1.1. Stress-Strain-Temperature Relationship The typical deformation behavior of shape memory alloys is summarized graphically by the three-dimensional stress-straintemperature diagram in Figure 1. In Figure 1, As and A f denote the austenite start and finish temperatures, respectively. In the yield stage of the stress-strain diagram shown in the σ-ε plane, the deformation accompanied with stress plateau appears due to the martensitic transformation. This phenomenon is called the

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FIG. 1. Three-dimensional stress-strain-temperature diagram showing the deformation and shape memory and superelastic behaviors of a Ti-Ni alloy deformed below As and above A f .

stress-induced martensitic transformation (SIMT). The strain induced at a temperature below As , 6%, recovers between As and A f after the applied stress has been removed and the specimen heated, as seen in the ε-T plane, showing the shape memory effect (SME). At a temperature above A f the SIMT is formed, leading to the usual superelastic (SE) loop with upper and lower plateaus.

under constant maximum strain εm = 8% at constant temperature above A f [3] are shown in Figures 3(a) and (b), respectively. The curves are parameterized by the number of cycles N . As seen in Figure 3(a), for N = 1 yielding due to the RPT appears under

2.1.2. Deformation Due to R-phase Transformation The stress-strain curves obtained by the experiments for a TiNi SMA wire with thermomechanical cycles for maximum strain εm of 1% and the stress-strain curves with the loadingunloading cycles under εm = 1% at temperature above A f [3] are shown in Figures 2(a) and (b), respectively. The curves are parameterized by the number of cycles N . As seen in Figure 2(a), yielding due to rearrangement of the rhombohedral phase occurs under stress of 60MPa in the loading process and residual strain of 0.6% appears after unloading. The residual strain disappears by heating under no load, showing SME. The stress-strain curves vary little in N = 1–10. As seen in Figure 2(b), the nonlinear strain induced due to the stress-induced rhombohedral phase transformation (RPT) in the loading process diminishes due to its reverse transformation in the unloading process, resulting in the hysteresis loop of SE. The width of the hysteresis loop is very narrow and the difference in stress between the loading curve and the unloading curve is smaller than 20MPa. The stress-strain curves vary little in N = 1–20. Thus it is ascertained that the properties of SME and SE associated with the RPT are stable for cyclic deformation. 2.1.3. Deformation Due to Martensitic Ttransformation The stress-strain curves for a TiNi SMA wire in the case of thermomechanical cycling maximum strain εm = 6% and the stress-strain curves in the case of cyclic loading-unloading

FIG. 2. Stress-strain curves for SME and SE due to RPT under thermomechanical cycles [3] (a) SME (b) SE.

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2.2. Conditions for Progress of Phase Transformation Let us discuss the conditions for progress of the phase transformation based on the transformation kinetics for the MT in SMAs proposed by Tanaka et al. [4]. It is expressed as follows. z˙ = b M C M T˙ − b M σ˙ ≥ 0 1−z

(1)

and for the reverse transformation z˙ − = b A C A T˙ − b A σ˙ ≥ 0 z

(2)

where σ, T and z represent the stress, temperature and the volume fraction of the martensitic phase (M-phase), respectively. The volume fraction of the parent phase or austenitic phase (Aphase) is 1 − z. An overdot denotes the time derivative. The material parameters b M , C M , b A and C A are determined from the experiments. The conditions for start and finish of the MT are expressed by the following equations, respectively. σ = C M (T − Ms ) σ = C M (T − M f )

(3) (4)

The conditions for the reverse transformation are as follows, respectively. σ = C A (T − As ) σ = C A (T − A f ) FIG. 3. Stress-strain curves for SME and SE due to MT under thermomechanical cycles [3] (a) SME. (b) SE.

stress of 60MPa in the initial region of strain below 1%, and thereafter yielding due to the martensitic transformation (MT) occurs at 280MPa for strain above 1%. The MT stress decreases with an increase in N . The transformation strain induced in the loading process appears as residual strain after unloading and diminishes by heating under no stress, showing SME. As seen in Figure 3(b), the MT-stress σ M and the reverse transformation stress σ A decrease with the increase in N . Both transformation stresses decrease significantly in the early cycles and only slightly afterwards. The amount of decrease in σ M with cycling is larger than that in σ A . The residual strain, which appears after unloading, increases significantly in the early cycles and then only slightly after these cycles. Therefore in order to obtain cyclic stability of the SME and SE in applications, mechanical training before practical use is necessary. In the case of cyclic deformation of a coiled spring, the relationship between force and deflection varies slightly even in 104 cycles [3].

(5) (6)

The parameters Ms , M f , As and A f denote the start and finish temperatures for the MT and the reverse transformation under no load, respectively. From Eq. (1), the condition for progress of the MT becomes as follows since b M < 0. dσ dσ > C M : for dT > 0, < C M : for dT < 0 dT dT

(7)

From Eq. (2), the condition for progress of the reverse transformation becomes as follows since b A > 0. dσ dσ < C A : for dT > 0, > C A : for dT < 0 dT dT

(8)

The conditions for progress of the phase transformation in the subloop loading during the phase transformation are shown on the stress-temperature phase diagram in Figure 4. In Figure 4, M S (z = 0) and M F (z = 1) denote the MT start and finish lines with a slope of C M , respectively, and A S (z = 1) and A F (z = 0) denote the reverse transformation start and finish lines with a slope of C A , respectively. Points A and G in Figure 4 represent respectively the states of progress of the MT and the reverse


FIG. 4.

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Conditions for progress of MT on stress-temperature phase diagram.

transformation, and the volume fractions of the M-phase at each point are z A and z G . The broken lines M A and MG denote the states with the volume fractions z A and z G , respectively. The conditions prescribed by Eqs. (7) and (8) for progress of the phase transformation from the points A and G mean that stress and temperature vary in the directions shown by the arrows in Figure 4. Recovery stress which appears during heating under constant strain increases along the reverse transformation strip [5]. 2.3. Influence of Strain Rate on Deformation Property The stress-strain curves obtained by the strain rate test for a maximum strain εmax of 7.9% at temperature above A f under strain rates dε/dt = 1.67 × 10−4 s−1 and 5 × 10−3 s−1 [6] are shown in Figure 5. As can be seen in Figure 5, in the case of dε/dt = 1.67 × 10−4 s−1 , an overshoot appears at the MT-start point S M followed by the upper stress plateau until the finish point FM in the loading process. In the same manner, an undershoot appears at the start point S A of the reverse transformation (RT) followed by the lower stress plateau until the finish point FA in the unloading process. On the other hand, in the case of

FIG. 5. Stress-strain curves at various strain rates under temperaturecontrolled condition [6].

FIG. 6. Stress-strain curve and variation in temperature under temperatureuncontrolled condition [7].

dε/dt = 5 × 10−3 s−1 , the overshoot, undershoot and clear stress plateau do not appear. The slope of the stress-strain curve is steep in the regions of the MT and the RT. The stress-strain curve and the variation in temperature at dε/dt = 10−2 s−1 during loading and unloading [7] are shown in Figure 6. In the test, the ambient temperature (room temperature) was not controlled. The surface temperature of the specimen was measured through the thermovision camera. The temperature increases based on the MT. At the point S M , the thin transformation band appears in the central part of the specimen. The transformation band in which temperature is high expands with progress of the MT. In Figure 6, the variation in temperature T p denotes the value at the position where the transformation band appeared at first. The variation in temperature T was obtained as an average value of temperature variation on the surface of the specimen. As can be seen in Figure 6, temperature variation T increases up to 28K due to the exothermic MT during loading. At the start point S A of the RT, the temperature is still higher than room temperature by about 25K. In this test, the temperature was not controlled to keep constant, and therefore, heat generated due to the MT is difficult to transfer into air in a short time under the high strain rate and the amount of decrease in temperature T at the point S A is small. Between the start point S A and the finish point FA of the RT, the RT progresses and temperature decreases due to the endothermic RT. The stress-strain curves obtained by the full loop loading under various stress rates are shown in Figure 7. The stressstrain curve obtained under a strain rate of 1.67×10−4 s−1 is also shown in Figure 7. This strain rate is low enough corresponding to the isothermal loading condition. In the case of the constant stress rate, the overshoot and undershoot do not appear and both slopes of the stress-strain curves are steep in the stress-plateau regions due to the phase transformation during

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Therefore the MT stress plateau during the reloading process (Di , Ai+1 ) decreases with an increase in the number of cycles N . The reloading curve (Ci , Di and Ai+1 ) passes through the unloading-start point Ai . Therefore the return-point memory is observed in the case of the strain-controlled condition with low strain rate.

FIG. 7. Stress-strain curves at various stress rates under temperaturecontrolled condition.

loading and unloading. The strain rate increases in proportion to stress rate in the stress-plateau region. The higher the stress rate is, the steeper the slope of the stress-strain curve is. In the case of a low strain rate, the phase-transformation band due to propagation of the interface between the M-phase and the parent phase progresses like Luder’s band in the stress-plateau region and temperature varies slightly. In the case of high strain rate, many phase-transformation bands appear in the whole area of the specimen and temperature varies markedly [7], resulting in the steep slope of the stress-strain curve since the MT stress varies in proportion to temperature.

2.4.2. Deformation Under Constant Stress Rate The stress-strain curves obtained by the subloop loading test under the constant stress rate for the SMA wire at temperature above A f [9] are shown in Figure 9. The MT occurs in the loading process (S M , A1 ). The subloop unloading process corresponds to the path (Ai , Bi , Ci and Di ). The processes (Ai , Bi ) and (Bi , Ci ) correspond to the condition of Eq. (7) and elastic deformation, respectively. The reverse transformation occurs in the unloading process (Ci , Di ). The subloop reloading process corresponds to the path (Di , E i , Fi and Ai+1 ). The processes (Di , E i ) and (E i , Fi ) correspond to the condition of Eq. (8) and elastic deformation, respectively. Strain increases in the early stage of unloading (Ai , Bi ) and decreases in the early stage of reloading (Di , E i ). The variation in strain is larger under a lower stress rate. These strain behaviors in the subloop loading under the constant

2.4.

Deformation Behavior Subjected to Stress-Controlled Subloop Loading 2.4.1. Return-Point Memory The stress-strain curves obtained by the subloop loading test under a low modulus of strain rate dε/dt =1.67 × 10−4 s−1 [8] are shown in Figure 8. In the test, the process (Ai , Bi and Ci ) corresponds to unloading and the process (Ci , Di and Ai+1 ) to reloading. The process (Ai , Bi ) and the process (Ci , Di ) are elastic. The reverse transformation appears in the process (Bi , Ci ) and the MT appears in the process (Di , Ai+1 ). The MT stress decreases under cyclic deformation as observed in Figure 3(b).

FIG. 8.

Stress-strain curves for subloop loading under low strain rate [8].

FIG. 9. Stress-strain curves for subloop loading under constant stress rate [9] (a) dσ /dt = 1MPa/s. (b) dσ /dt = 10MPa/s.


stress rate are quite different from those under a low strain rate as observed in Figure 8. In the reloading process, the stress-strain curve passes through the unloading start point Ai , showing the return-point memory. However, as can be seen in Figure 9, the reloading stress-strain curve does not pass through the unloading start point Ai . Therefore, the return-point memory does not appear under the stress-controlled condition. In the case of the stress-controlled condition, transformation-induced creep and stress relaxation [10] and the neutral loading [11] may appear. 2.5. Damping and Energy Storage The SE stress-strain curve draws the hysteresis loop during loading and unloading. The area under the loading curve denotes the work per unit volume done during loading. Therefore, the area under the unloading curve denotes the recoverable strain energy per unit volume Er . The area inside the hysteresis loop during loading and unloading denotes the dissipated work per unit volume Wd . The relationships between recoverable strain energy density Er and strain rate dε/dt for maximum strain of 6% in the case of the temperature-controlled condition and the temperature-uncontrolled condition [12] are shown in Figure 10(a). Also the relationships between dissipated work density

FIG. 10. Dependence of Er and Wd on strain rate under various temperaturecontrolled conditions [12] (a) Recoverable strain energy density Er . (b) Dissipated work density Wd .

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Wd and dε/dt are shown in Figure 10(b). As can be seen in Figures 10(a) and 10(b), both Er and Wd are constant in the region of low strain rate below dε/dt = 5 × 10−4 s−1 . In the region of higher strain rate above dε/dt = 5 × 10−4 s−1 , while Er decreases and Wd increases in proportion to strain rate in the case of temperature-controlled condition, Er increases and Wd decreases in the case of temperature-uncontrolled condition. As discussed in the previous section, in the case of temperatureuncontrolled condition under high strain rate, there is not enough time for heat generated due to the MT to be transferred into air, and therefore temperature varies significantly, resulting in large variation in stress. Based on large variation in stress, Er increases and Wd decreases under high strain rate. The condition under low strain rate corresponds to the isothermal process and the condition under high strain rate to the adiabatic process. 2.6. Fatigue Life 2.6.1. Bending Fatigue Life of SMA Wire Relationships between strain amplitude εa and the number of cycles to failure N f for a TiNi SE wire [13], obtained in fatigue tests at various temperatures T in water are shown in Figure 11. In the figure, the points with arrows denote the cases where failure did not occur. As can be seen, the slopes of the strain-life curves are steep in the low-cycle fatigue region. The strain-life curve has a plateau shown by a dotted line in the region of εa = 0.6%–0.8% above N f = 5 × 104 cycles. The strain amplitude for this plateau must correspond to the fatigue limit, which is the same as the RPT finish strain as observed in Figure 2. As can be seen in Figure 11, the fatigue life N f decreases in proportion to the increase in temperature in the low-cycle fatigue region. As expressed by Eq. (3), the MT stress increases in proportion to temperature. Therefore, in the case of high temperature, since high stress acts repeatedly, fatigue damage is correspondingly large, resulting in a short life. The relationship between εa and N f in the low-cycle fatigue region is expressed

FIG. 11. Relationship between strain amplitude and number of cycles to failure for TiNi SE wire at various temperatures T [13].

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FIG. 12. Stress-strain curves for highelastic wire at various strain rates [13]. FIG. 13. Fatigue life curves for highelastic wire at various temperatures T [13].

by the following equation

3. β

εa · N f = α

(9)

where α and β represent εa in N f = 1 and the slope of the log εa -log N f curve, respectively. 2.6.2. Fatigue of Highelastic Wire Stress-strain curves for a TiNi highelastic wire, obtained from tension tests under various strain rates, are shown in Figure 12. As can be seen in the figure, the stress-strain curves are almost linear up to a strain of 4% and a stress of 1400MPa, and the width of the hysteresis loop between loading and unloading is very narrow. The modulus of elasticity for the initial loading stage is 55GPa which is smaller than the 70GPa for a TiNi SE wire. This value is about one fourth of the modulus for stainless steel, which is an indication of the high bending flexibility. The residual strain after unloading is small. From the results, it can be seen that the wire has excellent bending flexibility, a high yield stress and the linearity which are necessary for application as a medical guidewire. At the same time, as can be seen in Figure 12, the dependence of the stress-strain curve on strain rate is slight, so that almost constant deformation properties can be obtained under variation in working conditions. Relationships between strain amplitude εa and the number of cycles to failure N f for the highelastic wire, obtained from fatigue tests at various temperatures T in water, are shown in Figure 13. The points with arrows denote the cases where failure did not occur. As can be seen, the slopes of the strain-life curves are steep in the low-cycle fatigue region. In every case, the plateau shown by a dotted line of the strain-life curve is in the region of εa = 0.6%-0.8% above N f = 5×104 cycles. The strain amplitude of the fatigue limit coincides with the fatigue limit of the SE wire. As can be seen in Figure 13, no clear difference in fatigue life appears among the various temperatures. Since the stress-strain relationship does not depend on strain rate and temperature, no influence of frequency and temperature on fatigue life is evident.

THERMOMECHANICAL PROPERTIES OF SHAPE MEMORY POLYMER

3.1. Constitutive Equation In order to express nonlinear time-independent strain, let us consider a nonlinear term expressed by a power function of stress with respect to a linearly elastic term σ/E. A nonlinear term expressed by a power function of stress is also added to a linearly viscous term σ/μ. By considering these nonlinear terms, the nonlinear viscoelastic equation [14] becomes ε˙ =

σ˙ +m E

σ − σy k

m−1

σ˙ σ 1 + + k μ b

σ −1 σc

n −

ε − εs +αT˙ λ (10)

where E, μ, λ, α, σ y and σc denote elastic modulus, viscosity, retardation time, coefficient of thermal expansion, proportional limit of stress in the time-independent term and the viscous term, respectively, and correspond to yield stress and creep limit. If large strain is applied at a constant strain rate in the loading process, seemingly time-independent plastic strain ε p remains after unloading. Let us consider ε p corresponding to timedependent εc in the irrecoverable strain. The irrecoverable strain εs becomes εs = C(εc + ε p )

(11)

where C is a proportional coefficient. The material parameters involved in Eqs. (10) and (11) vary depending on temperature. The mechanical properties of SMP vary markedly in the glass transition region. This appears due to the fact that SMP is composed of soft segments and hard segments and that microBrownian motion of soft segments is activated at temperatures above Tg but is frozen at temperatures below Tg . In order to express the properties in the glass transition region, let us consider the dependence of coefficients in Eqs. (10) and (11) on temperature. The relationship between elastic modulus E and temperature T obtained by the dynamic mechanical tests on SMP is shown


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In the same manner as E, in order to express the deformation properties in the glass transition region, the material parameters k, σ y , μ, σc , λ, and S are expressed by an exponential function of temperature T . These parameters are denoted by x and are expressed as follows Tg x = x g exp a −1 T

(14)

where x g is the value of x at T = Tg . The boundaries of the glass transition region are Tg ± Tw . Each coefficient is constant above and below the glass transition region. 3.2. Shape Fixity and Shape Recovery The stress-strain curves and strain-temperature curves obtained from the test are shown in Figure 15. As seen in Figure 15(a), during the loading process 1 up to maximum strain εm at temperature Th = Tg + 20K, strain increases nonlinearly when stress becomes large. In the cooling process 2 from Th to Tl = Tg -20K under constant εm , stress increases due to thermal stress for resistance to thermal contraction. In the unloading process 3 , the slope of the curve is steep and the strain εu at a termination point of unloading is close to εm . The ratio εu /εm

FIG. 14. Relationship between elastic modulus and temperature (a) Experimental result. (b) Approximate curve.

in Figure 14(a). In Figure 14(a), E is expressed in logarithmic scale and T in a reciprocal normalized by Tg . As seen in Figure 14(a), E varies markedly in the glass transition region but is almost constant above and below the glass transition region (T = Tg ± 15K). As shown in Figure 14(b), the relationship between log E and Tg /T is approximately represented by a straight line with a slope of a. The relationship in the glass transition region Tg − Tw T Tg + Tw is expressed as follows

Tg −1 T

(12)

Tg E = E g exp a −1 T

(13)

logE − logE g = a Thus E becomes

where E g is the value of E at T = Tg . As seen in Figure 14(b), E h and El denote the values of E above and below the glass transition region, respectively.

FIG. 15. Stress-strain curves and strain-temperature curves in tension [14] (a) Stress-strain curves. (b) Strain-temperature curves.

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represents the rate of shape fixity and approaches 1 if εm becomes large. Elastic modulus of SMP is large at Tl and small at Th . We can use excellent shape fixity of SMP elements by applying the difference of elastic modulus between Tl and Th . As seen in Figure 15(b), during the heating process 4 under no-load, strain is recovered. Strain is markedly recovered in the vicinity of Tg . SMP is composed of soft segments and hard segments. MicroBrownian motion of soft segments is frozen at temperatures below Tg but is activated at temperatures above Tg . Therefore the amount of strain recovery is small at low temperature, but becomes large in the vicinity of Tg due to activated micro-Brownian motion. The calculated results by Eqs. (10)–(13) are shown by the solid lines in Figure 15. As can be seen, the calculated results express the inclination of the experimental results for shape fixity and shape recovery. 3.3. Deformation Properties of Foam The stress-strain curves and the strain-temperatue curves obtained by the thermomechanical compression test for SMP foam at εm = 78% [15] are shown in Figure 16. In Figure 16, N de-

notes the number of cycles. As can be seen in Figure 16(a), yielding occurs in the vicinity of a strain of 10%, stress plateau appears thereafter until a strain of 60% and the slope of the curve becomes steep above a strain of 60%. In the region of the stress plateau for strain from 10% to 60%, buckling of cells propagates in the axial direction of compression. In the upswing region above a strain of 60%, the material is compressed uniformly and deformation resistance increases. With respect to the cyclic properties in the loading process 1 , stress decreases slightly in N =2 and decreases gradually thereafter. In the cooling process 2 , stress disappears perfectly at temperature Tl . Therefore εm is maintained and εu = εm , resulting in a rate of shape fixity R f of 100%. As can be seen in Figure 16(b), in the heating process 4 , strain is recovered significantly in the vicinity of Tg . Since the micro-Brownian motion of soft segments of SMP is frozen in the glassy region at temperatures below Tg , strain maintains εm . Since the micro-Brownian motion becomes active if the material is heated up to temperatures in the vicinity of Tg , strain is recovered. The strain-temperature curves do not change under repetition. Irrecoverable strain remaining after heating is small without depending on the number of cycles, and a rate of shape recovery Rr is 99%. 3.4. Characteristics for Holding at Low Temperature Rate of shape fixity R f and rate of shape recovery Rr were defined by the following equations: R f = εu / εm and Rr = (εm − εir )/εm , respectively, where εu and εir represent the strain obtained after holding no-load condition below Tg and the strain obtained after heating up to above Tg under no-load condition, that is, irrecoverable strain, respectively. The dependences of a rate of shape fixity R f and a rate of shape recovery Rr on the leaving time tc , as obtained by the aging test left under no-load below Tg for SMP foam at maximum compressive strain εm = 90%, are shown in Figure 17. The leaving time denotes the duration in which the SMP foam was left under no-load at Tc . As can be seen, a rate of shape fixity R f is larger than 99% even if the time has passed for longer than 5 × 103 hours. Although some amounts of shape are not fixed, these values are small enough. Therefore, the deformed shape can be fixed if it is left below Tg −60K. A rate of shape recovery Rr is larger than 98% without depending on the leaving time. The small irrecoverable part may appear due to decoupling imperfect molecular chain, collapse of cell and reorientation of molecular chain. It is ascertained that a rate of shape fixity and a rate of shape recovery by leaving the shape below Tg are larger than 98% without depending on the leaving time and maximum strain, resulting in superior performance.

FIG. 16. Stress-strain curves and strain-temperature curves for SMP foam in compression [15] (a) Stress-strain curves. (b) Strain-temperature curves.

3.5. Secondary-Shape Forming If SMP is held at temperatures above Tg for a long time, irrecoverable strain appears. The irrecoverable strain can be applied to the secondary-shape forming. The SMP elements can be fabricated by using a simple method with the secondary-shape


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FIG. 18. Dependence of secondary-shape forming S on holding time th at Th =Tg , Tg +10K and Tg +20K [16].

4.

THERMOMECHANICAL PROPERTIES OF COMPOSITE WITH SMA AND SMP

forming. In order to evaluate the secondary-shape forming by using the irrecoverable strain ε p , the rate of secondary-shape forming S is defined by the following equation: S = ε p /ε0 . S denotes a ratio of irrecoverable strain ε p to fixed strain ε0 . The relationships between S and holding time th obtained by the experiment [16] are shown by various symbols in Figure 18. In order to apply the secondary-shape forming to fabricating SMP elements, the equation to evaluate the rate of secondary-shape forming S is necessary. Based on the characteristics of S shown in Figure 18, the dependence of S on th can be expressed by the following equation th −ts S = S p 1 − e−( c ) (15)

4.1. Characteristics of Composite with SMA and SMP The shape memory effect (SME), superelasticity (SE) and large recovery stress appear in SMA. However, both elastic modulus and yield stress or transformation stress are low at low temperature and high at high temperature. This means rigidity of SMA elements is low at low temperature and high at high temperature. In order to obtain the two-way shape memory effect (TWSME), that is, two-way movement of SMA elements, the combination of SMA and bias materials, for example, steel is used in practical applications. On the other hand, the shape fixity (SF) and shape recovery (SR) appear in SMP. However, both elastic modulus and yield stress, that is, proportional limit are low at high temperature and high at low temperature. This means rigidity of SMP elements is low at high temperature and high at low temperature. The relationships between elastic modulus and temperature and those between yield stress and temperature for SMA, SMP and steel are schematically shown in Figure 19. As can be seen, the dependence of elastic modulus and yield stress on temperature are quite different among SMA, SMP and steel. Therefore, if the composite materials with these materials are developed, new properties which themselves can not be obtained can be achieved. For example, if SMA and SMP are combined, the composite material with large recovery strain, high recovery stress, high rigidity, TWSME and light weight can be obtained. Therefore, if the shape memory composites (SMCs) with SMA and SMP are developed, new and higher functionality of the material can be expected.

where S p , ts and c denote the saturated value of S, critical time for the secondary-shape forming not to appear and time constant, respectively. The calculated results by Equation (15) are shown by solid and broken lines in Figure 18. As can be seen, the calculated results express the inclination of the secondary-shape forming.

4.2. Bending Properties In order to confirm the basic characteristics of the SMC with SMA and SMP, the SMC belt was fabricated and the bending actuation characteristics were investigated [17]. A TiNi SMA wire was used for the fiber of the SMC. A polyurethane SMP

FIG. 17. Dependence of shape fixity and shape recovery on leaving time under no-load at Tg -60K [15] (a) Shape fixity R f (b) Shape recovery Rr .

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FIG. 19. Dependence of elastic modulus and yield stress on temperature for SMA, SMP and steel (a) Elastic modulus. (b) Yield stress.

sheet was used for the matrix of the SMC. The SMC belt was fabricated as follows. The lower half of the SMP sheet with thickness of 2.1mm was molded by mixing two kinds of liquid in a block at first. In a few minutes after molding, viscosity of the SMP became high enough to support the SMA wire with diameter of 0.75mm. SMA wires were put on the lower half of the SMP sheet. The SMP was molding again on them for the upper half of the SMP sheet. The SMC sheet was obtained by curing. Specimens of the SMC belt were cut out from the SMC sheet at the same spacing. In order to observe the deformation state of the SMC in bending, the photographs of an original state of the specimen, a

FIG. 21. Force-deflection curves and deflection-temperature curves for SMC in bending [17] (a) Force-deflection curves. (b) Deflection-temperature curves.

shape-fixed state with ymax =10 mm after cooling followed by unloading at Tg -30 K and a shape-recovered state after heating up to Tg + 30 K under no-load are shown in Figure 20(a), (b) and (c), respectively. As can be seen from Figure 20(b), the deformed state ofymax =10mm at Tg + 30 K is almost maintained after cooling down to Tg − 30 K followed by unloading. From the comparison between Figures 20(a) and (c), it can be confirmed that the

FIG. 20. Photographs of SMC at various states in bending [17] (a) Original state of the specimen. (b) Shape-fixed state after cooling. (c) Shape-recovered state after heating.


original shape is almost recovered by heating up to Tg + 30 K under no-load. The relationship between force and deflection and that between deflection and temperature obtained by the shape fixity and recovery test are shown in Figure 21. As can be seen in Figure 21(a), the maximum force appears at deflection of ymax = 10 mm. Force decreased almost to zero during the cooling process 2 under constant ymax . As can be seen in Figure 21(b), deflection decreases at temperatures in the vicinity of A f and Tg during the heating process 4 and becomes almost zero at Tg + 30 K. The rate of shape fixity R f and the rate of shape recovery Rr are defined by the following equation: R f = yu / ymax and Rr = (ymax − yu ) / ymax , respectively, where yu and yh represent the deflection after unloading at Tg −30 K and the deflection after heating up to Tg + 30 K, respectively. The values of the rate of shape fixity R f and the rate of shape recovery Rr are 99–100%, showing the excellent characteristics of shape fixity and shape recovery. 5.

CONCLUSIONS The thermomechanical properties of SMA, SMP and their composites which have not been clarified until now were discussed in this paper. The future subjects are summarized as follows. 1. With respect to SMA, higher performance of SME and SE is requested. If the volume of thermoelastic SMA elements is large, the response speed must be low. The development of magnetoelastic SMA is therefore expected from the viewpoint of response speed of SMA element. The development of the high-temperature SMA is also expected. In order to perform complex motion of SMA elements by the simple configuration, the thermomechanical behavior of SMA is important for loading paths under multi axial stress. 2. With respect to SMP, we can use the function of not only the shape fixity and shape recovery but also gas permeability, volume expansion, dissipation of work, storage of strain energy, refractive index and antithrombotic nature. The development and application of these functions are expected in the wide fields. 3. The development of the composite with SMA and SMP are expected in order to obtain the higher performance of the shape memory properties. The strength of the interface between both materials is important in the practical applications. 4. The development of higher function of the shape memory materials and their systems is highly expected in fields such as industrial, medical, aerospace, etc. ACKNOWLEDGEMENTS The author is grateful to the Scientific Research (C) in Grantsin-Aid for Scientific Research by the Japan Society for Promo-

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