Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) WW Part 12 doc

(b) Glass fiber Vinyl ester resin Vinyl ester + carbon particles Carbon-particle - glass-fiber-reinforced plastics Figure Schematics of the structural design for CFGFRP (a) and CPGFRP (b) in the shape of rod The CFGFRP and CPGFRP consisting of unidirectional reinforced fiber have a diameter of mm The schematic structural designs for the CMC are shown in Fig The composites were fabricated by the filament winding method using Si3 N4 particles (Ube Industries Co., Ltd SN-COA) as the matrix and SiC fiber (Nippon Carbon Co., Ltd NL-401) as the reinforcement for strengthening or toughening the composite A portion of the fibers was replaced with tungsten wire (Nippon tungsten Co., Ltd φ 30 µm) The conductive particles of TiN (Japan New Metals Co., Ltd.) were dispersed in part of the Si3 N4 matrix The volume fraction of the conductive phase, which includes 40 vol% of TiN particles, was 0.13% These conductive phases were formed near the surface (500 µm in (a) Si3N4 a percolation structure consisting of conductive has been successfully achieved The self-diagnosis functions of these mater evaluated through simultaneous measurements and electrical resistance change as a function strain in tensile loading tests The resistance ch defined as relative change in resistance (R − R0 cated by R/R0 in which R0 denotes initial resi fore loading The two types of loading selected a normal tensile test until specimen fracture cyclic loading–unloading test below the maxim level Figure shows the electrical resistance ch the applied stress for CFGFRP and CPGFRP a tion of the applied strain in the tensile tests Th in both specimens were increased linearly in pro the strains until fracture occurred of the carbon fi glass fiber The CFGFRP indicates a slight chang tance below a 0.6% strain due to the elongation fiber and shows a tremendous change around owing to the fracture of the conductive fiber; nam sistance of CFGFRP exhibits a nonlinear respo applied strain as shown in Fig 4(a) The initial r R0 for CPGFRP was higher than that for CFGFR of a slight electrical contact between carbon pa the percolation structure As can be seen from the CPGFRP indicates a linear increase in resist increasing tensile strain The response of the res applied strain appears at 0.01% strain (100 µ lower The linear increase in the resistance cont til the fracture of the composite Comparing Fig (b) illustrates CPGFRP’s higher sensitivity at strain level and the wider detectable strain pared to CFGFRP These results mean that the p (b) SiC fiber Tungsten wire (conductive fiber) Si3N4-SiC fiber-W fiber Si3N4 +T (conductive Si3N4-SiC fiber-(Si3N4 + TiN) Figure Structural design for CMC containing tungsten wire (a) and TiN particles (b) Figure SEM photographs of polished transverse section (a) and longitudinal section (b) of CPGFRP with unidirectional glass fiber structure formed with the carbon particle enables more sensitive and adaptable diagnosis of damage than the structure consisting of carbon fiber The strong response of resistance for CPGFRP was attributed to a local break in electrical contact between carbon particles because of the micro crack formation in the matrix or in the rearrangement in the percolation structure under tensile stress It should be noted that the dispersion of the carbon particles had no effect on the strength of the composite, since the fracture stress and mode for CPGFRP were similar to those of GFRP without carbon particles Figure shows the change of resistance to the applied strain as a function of time in the cyclic loading tests for CFGFRP and CPGFRP These FRP were loaded and unloaded cyclically under a gradual increase in stress The resistance of CFGFRP showed poor response below 0.6% strain and a drastic increase above 0.7% strain as shown in Fig 5(a) From Fig 5(b), it can be seen that the change in resistance of CPGFRP corresponded well with strain fluctuation (3) It is noteworthy that the resistance decreased 50 400 350 40 ∆R/Ro 300 R0 = Ω 250 30 200 20 150 100 10 50 Stress / MPa Stress / MPa 300 Stress 350 ∆R/Ro 400 (b) Stress ∆R /R0 / % (a) but did not completely return to zero at the u state The residual resistance in CPGFRP appea the application of 0.2% strain, and then increa the increase to the maximum applied strain T mum resistance during loading, indicated by R the residual resistance change after unloading, d Rres , were arranged according to the maximum plied in the past as shown in Fig The residual r of CFGFRP appeared around the 0.4% strain and discontinuously above 0.6% The appearance of re sistance for CFGFRP owing to fracture of the car was limited in a narrow strain range The change ual resistance of CPGFRP correlated closely with maximum strain over the wide strain range as Fig 6(b), suggesting that the CPGFRP has the diagnose the maximum strain based on measure past residual resistance at an unloading state (3 parison of Fig 6(a) and (b) shows that the CPG forms a more useful diagnostic function of damag over the wide strain range than does the CFGFR R0 = 1200 Ω 250 200 150 100 50 0.5 Strain / % 1.5 0 0.5 Strain / % 1.5 Figure Changes in electrical resistance (solid line) and applied stress (dashed line) as a function of applied strain in tensile tests for CFGFRP (a) and CPGFRP (b) 10 20 30 40 50 0.5 Time / 40 Strain R0 = 1200 Ω 25 20 15 10 0.5 20 40 60 80 1.5 20 15 10 100 Time / Figure Change in resistance (solid line) and applied strain (dashed line) as a function of time in cyclic loading test for the CFGFRP (a) and CPGFRP (b) 0.5 Figure Maximum resistance change at loading stat ual resistance change at unloading state as a function strain in cyclic loading tests for the CFGFRP (a) and C The microstructure of CPGFRP after the loading– unloading cycle induced 0.6% strain and 2.1% strain was observed by scanning electron microscopy (SEM) as shown in Fig (2) Clearly, the number of micro cracks in the matrix increased with the increase in applied strain Although the elongation of CPGFRP affected the elasticity after unloading, the percolation structure did not return reversibly (a) Strain / % 25 0 ∆ Rmax ∆ Rres 30 30 ∆Rmax, ∆Rres / % Strain / % 35 ∆R/Ro 1.5 1.5 35 (b) ∆R /Ro / % (b) Strain / % to the initial state because of the micro crack in the matrix The irreversible change in the p structure in the conductive phase was partly re for the appearance of obvious residual resistan wide strain range (b) Figure Scanning electron micrographs of CPGFRP after removing 0.6% strain (a) and 2.1% strain (b) 500 Figure SEM cross sections of polished CMC specimens The arrows point to the tungsten wire (a) or to the area containing TiN particles (b) Self-Diagnosis Function of CMC The conductive phases in the CMC observed by SEM are shown in Fig (4) Three tungsten wires were embedded near the tensile surface The conductive phase containing dispersed TiN particles and SiC fibers was observed as the bright area Some voids (white bareas) appeared in the conductive phase; however, these defects were thought to be insignificant for the damage diagnosis function because the amount was negligible The interface between these conductive phases and the Si3 N4 matrix did not show a remarkable reaction and exhibited good adhesiveness The self-diagnosis functions of the CMC were evaluated by simultaneous measurements of stress and electrical resistance change R as a function of applied strain in fourpoint bending tests The loading was performed two ways: (1) a normal bending test until specimen fracture and (2) cyclic loading–unloading tests below the maximum stress level The dependence of the applied load and change in resistance on displacement for the CMC is shown in Fig (4) Similar fracture behavior peculiar to CMCs was in both composites in which a part of the ultim was kept after fracture at a displacement of abou The peculiar load–displacement curve explained extraction of SiC fibers from the Si3 N4 matrix in Fig 10 The difference in the ultimate load a load-displacement curve for both composites wa to be due to the uneven quality of SiC–Si3 N4 ph not to the difference in conductive phase The non sponse of resistance changes to displacement was in both composites The CMC with tungsten wir a slight change in resistance in a small deforma then a drastic change was accompanied by their ture as shown in Fig 9(a) The CMC containing T cles exhibited a distinct change in resistance from displacement to the fracture in the composite in Fig 9(b) These results suggest that the mon resistance for CMCs with percolation structures tageous for diagnosing damages to the composite Figure 11 shows the hysteresis of resistanc in loading–unloading bending tests under the (b) (a) 200 Load ∆R 0.4 0.2 100 0 0.1 0.2 0.3 Displacement / mm 300 0.4 Load / N R0 = 280 Ω 0.6 ∆R / Q Load / N 300 R0 = 62 Ω 200 100 0 0.1 0.2 0.3 Displacement / mm Figure Change in load and resistance as a function of displacement in the four-point bending tests for the CMC containing tungsten wire (a) or TiN particles (b) 100 µm 200 Figure 10 SEM images of fractured surface for the CMC specimens containing tungsten wire (a) or TiN particles (b) load (4) The resistance of CMCs containing tungsten wire showed no change at the loading and unloading state, which was expected from Fig 9(a) The applied load of some 50% of the ultimate load induced the increase in the resistance for the CMCs containing TiN particles, and then the increased resistance remained at about 80% of the maximum resistance after unloading It should be noted that the loading–unloading cycle induced elastic deformation for the CMCs without residual strain Hence, the residual resistance was thought to be due to irreversible local fracture in the conductive phase The residual phenomenon in resistance change for the CMCs was more remarkable than that for FRP shown in Fig 5(b), which was attributed to the brittleness of the ceramic in the matrix Figure 12 presents an attempt at repeatedly varying the resistance for the CMC with tungsten wire or TiN 200 (b) 200 R0 = 218 Ω R0 = 57 Ω 0.5 100 50 Load / N 150 ∆R / Q Load / N 150 0.5 100 50 Load 0 0.02 0.04 Displacement / mm 0.06 ∆R 0 0.02 0.04 Displacement / mm 0.06 Figure 11 Change in load and resistance as a function of displacement in the loading–unloading tests for the CMC containing tungsten wire (a) or TiN particles (b) The applied maximum load was 150 kN ∆R / Q (a) particles in cyclic bending test The applied however, kept constant at 150 kN The resid tance for the CMCs with tungsten wire ind change, while that for the composites containing ticles after unloading rapidly increased up to It should be noted that the residual resistanc tionally increased with an increasing number tions after 20 cycles The linear response of re sistance was thought to be attributed to the prop micro cracking in the conductive Si3 N4 –TiN ph result further confirms that the CMCs contai particles have the ability to diagnose cumulativ to the composite through measurements of the resistance The electrical conductive FRP and CMC signed and produced by adding a conductive Load / N and performance of the composites when embedde tar/concrete blocks and concrete piles 100 Specimen and Experiment 0 20 40 60 80 Number of repetitions / cycles 100 Figure 12 Change in resistance as a function of number of repetitions in the cyclic bending tests for the CMC containing tungsten wire and TiN particles particles, and the self-diagnosis functions for these conductive composites were investigated Compared with the composites that include conductive fiber or wire the composites with the percolation structure consisting of conductive particles were found to be capable of diagnosing deformation or damage in the composites The composites containing carbon particles appeared capable of diagnozing damage at the sensitivity level of a small strain and in a detectable strain range Concerning the detectable strain level, the FRP showed an excellent response to the resistance change and to the applied strain This is a suitable range for the health monitoring of structural materials such as concrete construction It was also found through measurements of the residual resistance that the FRP composites are capable of memorizing the maximum applied strain or stress The CMCs with percolation structures consisting of TiN particles exhibited superior resistance to small deformation changes It should finally be noted that the CMC materials proved capable of diagnosing cumulative damage for the composites by evaluating the residual resistance, and that these self-diagnosis functions are easily obtained by simple measurements of electrical resistance Two kinds of glass-fiber reinforced plastics co were fabricated in this study The first composite carbon fibers substituted for some of the glass electrical conductivity was called CF The second c involved carbon powders dispersed in a part of t that formed the percolation structures as a conduc (CP) The CF and CP composites were embedded tar specimens and concrete specimens reinforced bars or rods by the following procedures Figur shows the structure and arrangement of the co in the three concrete specimens types The first rectangular mortar block specimen with the CP ites The second type is a rectangular concrete bl men with the CP and CF composites and two s The third type is a concrete pile specimen havin composites and 16 steel bars The pile type specim been pre-stressed at 14.3 MPa applied by the tens of the steel bars, while the block type was free stress Figure 14 illustrates the methods used for ben for the block and the pile type specimens with lengths and distances The electrical resistanc ( R/R0 , where R is an increase of resistanc is an initial resistance) of the composites was m simultaneously in the loading tests The stra measurement attached on the tension-side surfa specimen was also used Photographs the actua tests for the block and the pile specimens are Fig 15 Mortar Block Tests APPLICATION OF THE SELF-DIAGNOSIS COMPOSITE TO CONCRETE STRUCTURES A new type composite was developed that had a selfdiagnosis function for health monitoring and damage detection in materials (1–7) The composite, which has electrical conductivity as well as reinforced fibers, provides a signal of electrical resistance change corresponding to the degree of damage in the material This self-diagnosis composite offers also some advantages in properties, cost, and simplicity, compared with other materials or systems such the an optical fiber and the strain gauge A concrete The CP composite was embedded in the tensi the mortar specimens in order to demonstrate diagnosis function Figure 16 shows the applied resistance change of the CP composite as a fu displacement in a bending test The embedded posite was located mm apart from the ten face of the mortar The load–displacement curve discontinuous changes at points A and B, whi spond to the crack formation and propagation in th specimen, respectively The crack formation and tion are shown in photographs of the mortar s The resistance of the CP composite begins to (b) 100 21 400 270 50 100 12 17 Typ 21 Type - 34 12 Figure 13 Structure and arrangement of the composites in the three types of concrete specimens (a) Type-1, a rectangular mortar block specimen with the CP composite (b) Type-2, a rectangular concrete block specimen with the CP and CF composites (c) Type-3, a concrete pile specimen with CP composite D1 D2 D3 L Type Bending test L / mm D1 / mm D2 / mm D3 / mm points 160 50 - 50 points 400 100 100 100 points 8000 3000 1000 3000 Figure 14 Different bending tests for the block-and-pile type specimens with different length and distances corresponding to type-1, type-2, and type-3 slightly before crack formation Note that the in resistance appears simultaneously with the m formation and that a discontinuous resistanc is generated in response to the crack propaga residual resistance was observed in the FRP m ter unloading at point D The resistance chan bedded CP composite corresponds well to the pr of damage inflicted on the mortar specimen On the results demonstrate that the embedded CP has the ability to diagnose micro crack formati gation and loading history in cement-based materials The behavior of residual resistance for the CP embedded in a mortar specimen was investigate by cyclic bending tests Figure 17 presents the sis of resistance changes by cyclic loading–unloa under 40% of ultimate load The application of lo micro crack formation, and then the crack was cl unloading state as shown in Fig 17 It should that the crack was eliminated, but the behav micro crack induced residual resistance after u The application of higher load (60% of ultimate lo higher residual resistance after unloading The suggested that the CP composite embedded in t specimen has the ability to diagnose the closed m namely the hysteresis of micro crack formation ation of the residual resistance even after the closed (c) Figure 15 Bending tests in progress for the mortar block specimens (a), the concrete block specimens (b), and the pile specimens (c) 35 (a) C (b) Load / kN 30 25 B 20 D 15 A Load 10 (c) ∆R/R0 R0 = 4200 Ω 0 0.5 1.5 2.5 Displacement / mm (d) Figure 16 Changes in resistance (solid line) and applied load (dashed line) in a bending test for CPGFRP rod embedded in mortar specimen These points (A–D) on the graph correspond to the photographs of the mortar specimen 899 3.5 0 0.5 Displacement / mm 1.5 Figure 17 Changes in resistance (dashed line) and applied load (solid line) in the cyclic loading– unloading tests, under 40% of the ultimate load Concrete Block Tests Figure 18 shows the results of load, strain, and R/R0 of CP and CF composites as a function of time in the bending test for the concrete block (6) The stain change, which followed closely the loading curve, indicates that a micro crack formed at about 200µ strain and the steel bars yielded at about 1000µ strain The strain gauge was broken in the loading test owing to the crack propagation in the surface of the concrete specimen The R/R0 of the CP composite is initiated at about 300 s, which corresponds to the stage of crack formation The R/R0 of the CP composite increased with an increased load up to the maximum load at about 1000 s The R/R0 of CF is scarcely detected until the high load level when it increases suddenly near the maximum load Both the CP and CF composites not break in the test because of their high strength and flexibility It should be noted that the CP composite shows good sensitivity in the small stain range as well as a continuous response in the wide strain range up to the final fracture of the specimen Figure 19 provides the results of a cyclic loading test for the block-type specimen (6) In all, eight cycles of loading and unloading with an increased load level were carried out in this test The strain change and the R/R0 of CP composite responded well to the load curve from a lower load level, while the R/R0 of CF did not act until a higher load was applied It was also found that the CP composite’s residual resistance appeared only after the cycles of the medium load level The block specimen is shown in Fig 20 (a–c) as it appeared in the cyclic bending test (6) The cracks are clearly initiated from the tension-side surface at a low load, and they grow with an increased load level until the specimen finally breaks owing to steel bar fracture Concrete Pile Tests Figure 21 gives the results of the cyclic bending test for the type-3 concrete pile specimen (6) The specimen included only the CP composite because of the sensitivity under a small load, which was higher than that composite as confirmed in Figs 18 and 19 This t to increase the sensitivity of the CP composite arranged near the tension-side surface of the p men Figure 21(d) is the result from the enlarg axis of the CP composite in Fig 21(c) The R/ CP composite in the pile responds well in a w of loading as shown in Fig 21(c) The CP com cated near the tension-side surface of the pile indicates good sensitivity in the lower load levels in Fig 21(d) The R/R0 of the CP composite in load range is very similar to the strain chang 21(b), which means that the CP composite can smaller strain before the crack forms in the pil In these pile tests there is no clear indication ual resistance phenomena as detected in the b probably because of the effect of pre-stress in specimens The appearances of the pile specimen in the cy ing test are shown in Fig 22(a–c) (6) The crack a low load, its growth occurs with an increased finally the pile fractures after the test has ended Performance of the Self-diagnosis Composites In the bending tests of the concrete block, the C ite produced good results compared to the CF c Remarkably, the electrical resistance of the CP ite increased under a small strain to detect a m formation at about 200µ, and it responded well to formations before the crack formation The CP showed continuous resistance change up to a la level near the final fracture of the concrete stru inforced by steel bars It was also found that th posites embedded in mortar/cement block specim the ability to diagnose the hysteresis of micro cra tion by the evaluation of the residual resistance unloading Figure 11 Above left: Orientation of M, H, and σ relative to the twinned sample High-speed video frames (a), (b), and (c) show the sample in the initial vertically compressed (σ ≈ MPa) state (H = 0), in an intermediate state, and in the final magnetically saturated (and fully strained vertically by 6%) state, respectively Below: Selected field-induced strain curves at various external opposing stresses at room temperature for a Ni49.7 Mn28.5 Ga21.7 single crystal (8) response because the component of the applied field parallel to the twin planes of a given orientation is less than the twin-motion coercivity For fields above this threshold, the strain increases rapidly toward the linear value predicted by the thermodynamic models The physical origin of this threshold field in polycrystalline samples is different from that associated with σ0 and the initiation of twin-boundary motion FIELD-INDUCED STRAIN UNDER LOAD With the background developed so far, it is now possible to describe and analyze in more detail the measurements of field-induced strain under load that form the basis for use of FSMAs as actuator materials dc Actuation under Static Stress Figure 11 shows the results of field-induced strain measurements in a Ni49.8 Mn28.5 Ga21.7 single crystal at room temperature for various axial external stresses that oppose the field-induced strain The sketch at the upper left shows the orientation of the magnetization, magnetic external stress relative to the twinned sample T photographs are frames from a high-speed (1200 video taken on the sample close to the initially state (approximately MPa) at H = (frame a) 15 ms into the actuation (frame b), and at satura about 23 ms (frame c) The structure in frame (a nated by the dark twin bands (M parallel to s frame (b) the lighter twin bands (M parallel to H than half the area on the front surface In fram sample is essentially filled by the light-colored tw (except for the thin twin band that apparently pinned) The graph in Fig 11 shows the ε-H loops w abrupt strain changes of several percent, occurri narrow field range On returning the field to zer cant hysteresis is evident With increasing extern the threshold field for strain actuation increase strain at saturation decreases At low external s field-induced stain does not reset to ε = upon of the field This suggests that Ceff is small in At strain levels in excess of 0.7 MPa, the samp Alternating-Field Actuation under Dynamic Load The quasi-static, field-induced strain measurements shown in Fig 11 have also been carried out at actuation frequencies up to 330 Hz To perform these measurements, the static load was replaced with a spring against which the sample extends under a transverse field (Fig 13) Figure 14 shows a set of field-induced strain curves taken at Hz drive, Hz actuation in the system shown in Fig 13 (46) The sample is a single crystal of Ni–Mn–Ga measuring × × mm, with the field applied normal to the × mm face and the strain measured along the mm direction The saturation strain at any given stress level increases with increasing stress, reaching a maximum value near 1.4 MPa Note the much smaller hysteresis in this case compared to the quasi-static situation shown in Fig 11 For larger stresses, the saturation strain decreases, and the hysteresis as well as the threshold field for actuation increase When the sample is driven to higher frequencies than in Fig 14, the saturation strain is unchanged up to an Field (MA/m) (b) Strain (%) to condition a) when H = The hysteresis appears nonmonotonic in applied stress Nearly the full transformation strain is achieved in this sample for stresses less than 0.5 MPa Some samples have shown strains of 6.1% at saturation (8,45) The data of Fig 11 can be modeled with Eq using the measured Ni–Mn–Ga parameters (see Table 1) The hysteresis is accounted for in an ad-hoc manner by adding to the applied field a coercive (offset) field Hc = ±σo εo /(µo Ms ) = 93.3 kA/m (1.17 kOe) The model results displayed in Fig 12(a) and (b) show that these parameters give a reasonable reproduction of the major trends in the experimental data, namely the shape of ε(H), as well as the increase in threshold field and decrease in strain with increasing external stress The model does not account for the observed change in coercivity with external stress The predicted decrease in saturation strain with increasing stress, Fig 12 (b), is consistent with observations The limitations of the model in fitting the data may be the result of neglecting magnetostatic effects in the model It is not the result of a stress-induced anisotropy (3σ λ/2) adding to Ku as external stress is increased Based on the measured magnetostriction of the martensitic phase, λs = −145 × 10−6 (28), the magnetoelastic anisotropy at σ = MPa is more than two orders of magnitude smaller than Ku 0 Stress (MPa) Figure 12 a) Calculated strain versus applied field c Eq (3) b) Calculated strain at peak field versus stress laid experimental points from the full set of data d Fig 11 (8) actuation frequency of about 100 Hz Beyond th the peak output strain drops off sharply How clear from the data in Fig 15 that the drop-o ponse is due to the reduction in the applied fie a drive frequency of about 50 Hz, the inductive of the field coils becomes sufficiently large that supply can no longer deliver the current neede erate a field sufficient to saturate the strain P plies must be designed to match the impedan load over the operating bandwidth Pulsed-mag measurements with a drive-field rise time of cate that single-crystal samples of Ni–Mn–Ga c at a rate that keeps up with the rise time of (47) This implies a bandwidth of at least kHz materials Figure 13 Test system, schematic (left) and photograph (right) The FSMA sample is subjected to a bias stress along one axis and an ac magnetic field along an orthogonal axis A micrometer advances the sample into the spring to establish the desired bias stress level The sample elongation under applied field is measured with an eddy-current proximity sensor The apparatus measures approximately 12 × 15 × 30 cm (46) DISCUSSION Engineering Parameters James and Wuttig (18) have observed the rearrangement of twin boundaries in martensitic Fe70 Pd30 accompanying a field-induced 0.5% extensional strain Similarly, Ni–Mn– Ga crystals show extensional strains under quasistatic excitation of ε > 4% at room temperature (8,45) AC strains in excess of 3% in Ni–Mn–Ga crystals at room temperature have been reported (46) The response of active magnetic materials is generally described by the magnetostrictivity defined as dij = ∂ε1 /∂ Hj , where the subscripts refer to directions in Cartesian coordinates Magnetostrictive materials such as Terfenol-D are often operated under field bias In the case of the FSMA data shown in Fig 14, application of a bias field of about kOe and an ac field of ± 1kOe about that bias, would result in actuation at the drive frequency with an output strain of about 2% peak-to-peak The value of d31 under such actuation is about 1% per kOe or 12.5 × 10−8 m/A This value compares Strain (%) 1.1 0.9 100 150 200 250 Actuation frequency (Hz) Figure 15 Frequency dependence of peak field gener system shown in Fig 13 (upper curve) and the strain at The decrease in actuation strain above a drive frequen has been identified as due to the decrease in field app sample (46) favorably with the value of d33 for Terfenol-D in Table compares the magnetostrictivities, dij active FSMAs and the leading magnetostrictive Terfenol-D, Fe2 (Tb0.3 Dy0.7 ) The negative (positive) sign of d33 (d31 ) for N reflects the fact that it contracts along the axis in magnetization increases and expands along the axis of M The magnetomechanical coupling coef is defined for a magnetically driven actuator by of the output mechanical energy to the total inp (magnetic plus mechanical) For purposes of det the coupling coefficient, the following relations clamped and free permeabilities or free and clamp moduli, can be derived: µε = (1 − k2 )µσ or C H = (1 (6) From Fig and the data in Table 1, the latte suggests that k approaches unity for these mater is, they couple magnetic energy to a mechanical near-perfect efficiency (48) (The free modulus, C H as Ctb in Table and the clamped modulus, C M is C0 in Table 1.) The introduction of an external stress in the dynamic model when Ceff = predicts a strain creases linearly with applied stress, Eq (3), and F 1.4 Table Comparison of Currently Achieved Field-Induced Strain and Magnetoelastic Coupli Coefficients d33 and d31 in FePd and Ni–Mn–Ga F with the Magnetostrictive Material, Terfenol-D 1.9 0.3 2.1 σext = 0.13 MPa −6 50 Stress Dependence of ε(H ) 1.6 0.5 −8 −4 −2 Field (kOe) Active Magnetic ε H-field d33 d31 Material (%) (kA/m) (10−8 m/A) (10−8 m/A Figure 14 Field-induced strain data for several values of applied stress at an actuation frequency of Hz The sample elongates against the spring for both positive and negative field cycles, giving an actuation frequency twice the drive frequency Fe70 Pd30 Ni50 Mn28 Ga22 Terfenol-D a b 0.5 6.1a 3.1b 0.2 Quasi-static actuation ac actuation 800 400 400 40 +0.63 −25 −13 +6 −0.63 +25 +13 −3 Figure 16 (a) Field-induced strain versus stress predicted by single-variant thermodynamic model (32) (b) Field-induced strain versus stress observed in Ni2 MnGa at −15◦ C (38) (c) Fieldinduced strain versus stress calculated with no restoring force (30) (d) Field-induced strain versus stress observed in Ni–Mn–Ga at room temperature (36) Figure 16(b) shows one set of strain versus stress data for Ni2 MnGa at −15◦ C and H =12 T (29) The saturation strain achieved here is less than ε0 , suggesting that many of the twin variants are not responding to the applied magnetic field These unresponsive twins may present an elastic resistance (Ceff = 0) to the deformation caused by motion of the active twin boundaries The observed blocking stress of 9.2 MPa (σ at which ε = 0) is calculated from Eq (3) to be MPa (using Ku = 2.45 × 105 J/m3 and εo = 0.05) In contrast, Murray et al (36) have noted that different Ni–Mn–Ga crystals may respond to an applied field with little or no restoring force, namely Ceff ≈ When the stored elastic energy is omitted from Eq (2), the free energy cannot be minimized for |δf | < 0.5 Instead, an instability arises in which the twin boundary moves completely (δf = ±0.5) in the direction favored by the field if µ0 Ms H > σ ε o and in the opposite direction if µ0 Ms H < σ ε o There is no internal elastic opposition to this motion when there are no unfavorably oriented twin planes In such situations, the strain under load does not decrease linearly with stress but rather maintains a constant value until a critical stress is reached, σ c = µo Ms H/εo , at which point the strain vanishes abruptly as in Fig 16(c) Recent data on Ni–Mn–Ga at room temperature, Fig 16(d), support this instability model (36) In addition, the field-induced strain in these FSMAs is more bistable (like a Barkhausen jump), whereas the FSMAs whose response is shown in Fig 16 (b) show smoother, more reversible ε (H) as depicted in Fig (36) Likhachev et al (49) have recently shown data for the strain dependence of Ni48 Mn30 Ga22 that fall between these two limits and are well des their model It thus appears that a range of e(H, σ ) respo be able to be achieved with FSMAs Smaller out with larger blocking stress may be achieved in s tals, Fig 16 (b), or larger output strain with sma ing stress may be observed in other crystals, F The reasons behind these different types of res not yet well understood In the present case, the temperatures and compositions (and hence diffe netic anisotropies, magnetizations, and mecha perties) may be factors Another difference bet two samples contrasted in Fig 16 is that the on (b) shows a much finer twin structure (measured microns) with multiple twin systems present Th represented in panel (d) shows a much coarser t ture (twin spacing of order 0.5 – mm), and only o of twin boundaries is present It may be possible of the variously oriented twin systems in the for ple may not respond to the applied field and hen a mechanism for storing energy elastically (0.5C the active twins respond to the field Comparison with Shape-Memory Effects Here, we compare the field-induced strain ob FSMAs with (1) the thermoelastic shape mem (pseudoplasticity) and (2) stress-assisted m transformations (superelasticity) This thermoelastic shape-memory effect achieves a shape change by structural transformation of the material between a twinned phase and a different untwinned phase By contrast, the shape changes so far observed in FSMAs are induced by a magnetic field fully within the martensitic state It involves the field-induced motion of twin boundaries Thus, the effect in FSMAs may be faster and more efficient compared to the thermoelastic shape-memory effect where the need for heat transfer limits the kinetics Second, when a material showing the shape-memory effect is subjected to a stress at a temperature just above the martensite start temperature, the stress can facilitate the transformation to the martensitic phase Once twinned martensite is formed, the stress can result in a large (several percent) macroscopic deformation of the material (superelasticity) Upon removal of the stress, the material re-transforms to the austenitic phase and the large deformation is erased This effect can be much faster than thermally induced shape changes associated with the martensitic transformation FSMAs have been shown to exhibit stress-induced martensite that then responds to a magnetic field with an additional strain (19) When the external stress is removed, the material reverts to the austenitic phase and the large field-induced strain decreases to the smaller value typical of the austenitic phase Comparison with Magnetostriction The field-induced strain observed in FSMAs is similar in some ways to the magnetostriction generally observed in ferromagnetic materials In both cases, the strains conserve volume to first order Thus, the strain measured from the demagnetized or equi-twin-variant state in a direction perpendicular to the field will be ε⊥ ≈ −ε /2, where ε is the field-induced strain parallel to the field Nonuniform initial distributions of domain magnetizations or twin variants can upset this relation (as in field-biased or pre-stressed samples such as that shown in Fig 11 where ε⊥ ≈ −ε ) The bending effect across the twin boundary (which is also a 90◦ domain wall), shown in Fig for Ni–Mn–Ga, would also occur in an appropriately cut ferromagnetic crystal such as Fe ( at 45◦ to bar axis) if a single 90◦ domain wall could be the direction of magnetization The FSM is tied to the crystallography, not to the of M That is, it is possible to rotate M FSMA strain, only conventional magnetost FSMAs that are characterized by relativ anisotropy In magnetostrictive materials other hand, field-induced strain is a result o tization rotation relative to the crystallogr strain is tied to M, and not to the crystal orientation In the ferromagnetic martensitic phase creased magnetocrystalline anisotropy re austenite means that saturation of the m tion requires stronger magnetic fields than i ite If TC > Tmart , there is no large FSMA field strain between Tmart and TC because the m in the austenitic phase and twins are not The FSMA strain shows a peak on heating Tmart (28,49) If TC < Tmart , there is a static each variant of the martensitic phase abov it cannot be controlled by a field because It can be controlled by an applied stress tostrictive strain becomes possible below T second-order magnetic transformation; it h perature dependence governed by [M(T)/M (51) (Here, l defines the symmetry of the low crystal field term: l = is uniaxial and l = The crystal strain in an FSMA, on the other pears in the martensitic phase by a first-or tural transformation below Tmart [James an (2)] Field-induced strains in FSMAs decreas strength of the magnetocrystalline anisotro martensitic phase decreases below µ0 Ms H anisotropy martensite, the field may rotate out moving the twin boundaries, and th change in macroscopic strain The field-de of strain in FSMAs—that not show disco ε(H) versus σ behavior in Fig 16(b) and (d dicted to be linear in H below saturation in t anisotropy limit (18,32) Reduced anisotrop troduce strong nonlinearities in ε(H) (18,31 the other hand, the magnetostrictive strai ble in a given field H < Ha will be greater, th the anisotropy The field dependence of mag tive strains in a hard-axis magnetization p quadratic in H or M below saturation (42) latter case, the field-induced strain is smaller and more linear in the applied field for h < 1, and the blocking stresses can be greater Micromagnetic and analytic thermodynamic models are able to describe the main features of the magnetization patterns in the twinned FSMAs and the forms of ε (H, σ ), and M(H) in single-crystal FSMAs, respectively Field-induced strains in FSMAs show some incidental similarities to magnetostrictive strains but are essentially different, arising from the field-induced motion of twin boundaries in a martensitic phase that is strongly distorted by a first-order transformation not connected to TC The field-induced strains occur at smaller fields as the stress required to nucleate twin boundary motion, σo , decreases Decreased magnetocrystalline anisotropy or increased external stress limits the magnitude of the field-induced strains Unlike the thermoelastic shape-memory effect, large magneticfield-induced strain in FSMAs so far is observed fully within the martensitic state ACKNOWLEDGMENTS The authors acknowledge fruitful discussions with R.D James and M Wuttig The work at MIT described in this review was carried out largely by S.J Murray, M Marioni, and C.P Henry It has been supported by the Finnish Ministry of Science and Technology (TEKES) with a consortium of Finnish companies, by a subcontract from Boeing Corporation on a DARPA contract, by grants from the Lord Corporation, Mid´ Technologies, and the Office of Naval e Research, as well as by contracts from DARPA, ACX Corporation, and Mid´ Technologies The crystals used in our e study were grown by Dr V.V Kokorin, Institute of Metallurgy, Kiev (Fig 1) and by Dr Tom Lograsso of Ames Laboratory, Department of Energy (Figs 6, 11, and 14) BIBLIOGRAPHY V.A Chernenko, E Cesari, V.V Kokorin, and N Vitenko Scrip Metall Mater 33: 1239 (1995) R.D James and M Wuttig SPIE 2715: 420 (1996) K Ullakko J Mat Eng Perform 5: 405 (1996) K Ullakko, J.K Huang, C Kantner, V.V Kokorin, and R.C O’Handley Appl Phys Lett 69: 1966 (1996) K Ullakko, J.K Huang, V.V Kokorin, and R.C O’Handley Scripta Mater 36: 1133 (1997) G.H Haertling J Am Ceram Soc 82: 797 (1999) Phys Rev B57: 2659 (1998) 13 T Kanomata, K Shirahawa and T Kaneko, J Ma Mtls 76–82, 65 (1987) 14 A.A Gonzalez-Comas, E Obrad´ , L Manosa, A P o Chernenko, B.J Hattink, and A Labarta Phys Rev (1999) 15 M Taya Unpublished results (1998) 16 K Inoue, K Enami, Y Yamaguchi, K Ohoyama Y Matsuoka, and K Inoue J Phys Soc Jpn 69: 17 A.N Vasil’ev, S.A Klestov, R.Z Levitin, V.V Sn Kokorin, and V.A Chernenko Sov Phys JETP 82: 18 R.D James and M Wuttig Phil Mag A77: 1273 ( 19 R Hayashi S.M Thesis Massachusetts Institute logy June 1998 20 S.J Murray, R Hayashi, M Marioni, S.M Allen O’Handley SPIE Conf 3675: 204 (1999) 21 R Hayashi, S.J Murray, M Marioni, M.J Farinelli, and R.C O’Handley Sensors and Actuators A81: 22 P.J Webster, K.R.A Zieback, S.L Town, and M.S Mag B49: 295 (1984) 23 R.W Overholser, M Wuttig, and D.A Nueman Mater 40: 1095 (1999) 24 A Sozinov, A.A Likhachev, and K Ullakko SPIE March (2001) 25 K Ullakko, Y Ezer, A Sozinov, G Kimmel, P Yako V.K Lindroos Scripta Mater 44: 475 (2001) 26 S.J Murray Ph.D Thesis Massachusetts Institute ogy, January (2000) 27 S.J Murray, M Farinelli, C Kantner, J.K Huang, and R.C O’Handley J Appl Phys 83: 7297 (1998) 28 R Tickle and R.D James J Magn Magn Mate (1999) 29 S.J Murray, M Marioni, A Kukla, J Robi O’Handley, and S.M Allen J Appl Phys 87: 5744 30 A.A Likhachev and K Ullakko Phys Lett A275: 31 R.C O’Handley J Appl Phys 83: 3263 (1998) 32 A.A Likhachev and K Ullakko EuroPhys J B2: 33 A.A Likhachev and K Ullakko EuroPhys J B14: 34 V.A.L’vov, E.V Gomonaj, and V.A Chernenko J dens Matter 10: 4587 (1998) 35 S.J Murray, R.C O’Handley, and S.M Allen Proc 604: 279, (2000) 36 R.D James and D Kinderlehrer Phil Mag 68: 23 Appl Phys 76, 7012 (1994) 37 R Tickle, R.D James, T Shield, M Wuttig, and V IEEE Trans Magn., 35: 4301 (1999) 38 R.D James Unpublished Manuscript (1999) 39 Q Pan and R.D James J Appl Phys 87: (2000) 47 M Marioni, unpublished 48 A.E Clark Personal communication (2001) 49 A.A Likhachev, A Sozinov, and K Ullakko SPIE Conf Proc., March (2001) 50 G.H Wu, C.H Yu, L.Q Meng, J.L Chen, F.M Yang, S.S Ai, W.S Zhan, Z Wang, Y.F Zheng, and L.C Zhao Appl Phys Lett 75: 2990 (1999) 51 E Callen J Appl Phys 39: 516 (1968) SHAPE MEMORY ALLOYS, TYPES AND FUNCTIONALITIES J VAN HUMBEECK K.U Leuven-MTM Katholieke Universiteit Leuven Heverlee, Belgium R STALMANS Flexmet Aarschot, Belgium SHAPE-MEMORY ALLOY SYSTEMS Many systems exhibit martensitic transformation Generally, they are subdivided into ferrous and nonferrous martensites A classification of the nonferrous martensites was first given by Delaey et al (1) (Table 1), and ferrous alloys that exhibit a shape-memory effect were first reviewed by Maki and Tamura (2) (Table 2) r Ni–Ti alloys r HTSMA r other systems Fe-Based Alloys (2,4,6) The austenite (fcc-γ phase) in ferrous alloys can formed to these three kinds of martensites, depe composition or stress: γ -α (bcc), γ → ε (hcp) an martensite Although a shape-memory effect has been ob all three types of transformation, most attenti veloping a commercial alloy has been given to t that have a γ → ε transformation These alloys h stacking fault energy in austenite (Fe–Cr–Ni, Fe alloys) The austenite to ε-martensite transforma ceeds by the a/6 [112] Schockley partial dislocat trail a stacking fault ribbon on every {111} austen and change the crystal structure to martensite T memory effect, which is of the one-way type, resul from reverse motion of the Schockley partial dis during heating A complete shape-memory effect has been re both single-crystal (7,8) and polycrystalline Fe–M loys (9,10) that contain suitable amounts of M A 9% shape-memory strain in single crystals (8 in polycrystals (9) have been reported Any factors that impede the reversibility of th of partial dislocations lead to incomplete recove turn a poor shape-memory effect Table Classification of Nonferrous Martensitesa Group Alloy System Terminal solid solutions based on an element that has allotropic phases Cobalt and its alloys Rare-earth metals and their alloys Titanium, zirconium, and their alloys Alkali metals and their alloys and thallium Others such as Pu, Ur, Hg, and alloys Intermetallic solid solutions that have a bcc-parent phase β-Hume–Rothery phases of Cu-, Ag-, and Au-based alloys β-Ni–Al alloys Ni–Ti–X alloys Alloys that show cubic to tetragonal trans (incl Quasi-martensite) Indium-based alloys Manganese-based alloys (paramagn ↔ antiferromagn.) A15 compounds Others: Ru–Ta, Ru–Nb, Y–Cu, LaCd, LaAgx –In1−x a Ref T.E.: Thermoelastic martensite, non-T.E.: Nonthermoelastic martensite The internal factors that hamper recovery include alloy composition, N´ el temperature, transformation temperae ture, and lattice defects External factors are applied stress and strain, deformation, recovery annealing temperature, and thermomechanical treatment For example, Murakami et al (11) showed that Fe–Mn– Si alloys that contained 28–33% Mn and 4–6% Si exhibit a nearly perfect shape-memory effect But alloys whose Mn content is less than 20% have also been developed successfully Cr (less than 20%) and Ni are added to improve the corrosion resistance of commercial Fe-based alloys So far, Fe-based alloys are not successful SMA They exhibit only a (limited) one-way shape-memory effect after a labor-intensive thermomechanical treatment No significant two-way effect or pseudoelastic properties have been reported, whereas only moderate damping capacity might have some interest Therefore the only reported successful applications of these Fe-based alloys are couplings This type of application is based on the one-way effect The recovery stresses are moderate but sufficient (12) Cu-Based Alloys [(1,3,13–16)] Copper-based shape-memory alloys are derived from Cu–Zn, Cu–Al, and Cu–Sn systems The composition range of these alloys corresponds to that of the well-known β-Hume–Rothery phase In most shape-memory alloys, this phase has a disordered bcc structure at high temperatures but orders to a B2, D03 , or L21 form at lower temperatures The shear elastic constant of the β phase exhibits anomalous behavior as temperature decreases, that is, it is lowered till the lattice instability with respect to ¯ {110} shears at some temperature and transforms β to martensite The temperature of the transformation to martensite, Ms , varies with the alloy composition The elastic anisotropy of the β phase is much higher compared to normal metals and alloys and increases further as the martensitic transformation is approached Cu–Zn and Cu–Al martensites are of three types α , β or γ : the subscript 1, 2, or is added to indicate the ordering schemes in β, namely, B2 (2) or D03 (1) or L21 (3) Some conversion from one martensitic structure to another, for example β → γ , may also take place The net result is a coalescence of plates within a self-accommodating group and even coalescence of groups Heating this deformed martensitic microstructure transforms it to the β phase, and the shape-memory effect accompanies the change Copper-based shape-memory alloys presently derived from Cu–Zn and Cu–Al systems, and are added for various metallurgical reasons Th martensite in these alloys is only or predomin β1, or , type where γ martensite is the minor co in the latter case Alloys that have α martensite far not been used Therefore, alloys of β1, or m are the subject in this part Two criteria should be taken into account lecting an alloy composition to obtain a compl crostructure that transforms to martensite: (1) Th must be stable across as wide a temperature possible The less wide this temperature range, the cooling rate required to retain the β phas diffusional decomposition (2) Transformation tures must fall within a range that satisfies th ment for the shape-memory application (−150 The three alloy systems in Table satisfy thes They are used nowadays, but in limited amoun from composition, transformation temperature strongly influenced by other factors The Influence of Chemical Factors on the Trans Temperature The Influence of Composition Several author tempted to quantify the Ms –composition relatio several Cu-based alloys An overview is given i ferent authors weight the same element differe main reason for this discrepancy might be that ples measured have different thermomechanical that is, one has probably not measured “identical Indeed, composition is not the only chemical fact fects the Ms temperature The type and degree o the β and the martensite lattice also affect the Ms treatments can, therefore, influence the transform discussed in the following sections Quenching and the Order State of the β Phase T formation temperatures of Cu-based alloys are sitive to minute changes of the degree of ord β phase Such changes are easily brought quenching from intermediate and high temperatu form of dilute disorder in an otherwise well-orde rial The effect is noticeable in both Cu–Zn–Al (1 Cu–Al–Be 9–12 Al 0.4–1 Be −80 to +80 (β ) Cu–Al–Ni (19,20) alloys and manifests as a suppression of the transformation temperatures thereby stabilizing the β phase relative to the martensitic The suppression is temporary, but it is easily recoverable in Cu–Zn–Al alloys by aging in the β condition at as low a temperature as room temperature However, the recovery of Cu–Al–Ni alloys tends to be more sluggish and requires higher aging temperatures For example, Cu–Al–Ni alloys aged at 300◦ C for hour can have transformation temperatures up to 60◦ C higher than the as-quenched alloys Aging and the Order State of Martensite Aging a Cu–Zn– Al alloy in the martensitic condition can appreciably shift the reverse transformation temperatures of the martensite to the β phase (21) This shift to higher temperatures stabilizes the martensitic relative to the β phase This stabilization is brought about by a thermally activated diffusional process and, is it presumed, alters the ordered state inherited by the martensite from the β to a relatively disordered state (21,22) The effect is more pronounced in the presence of excess vacancies retained after a prior quench from higher temperatures A quench to a temperature above the Ms followed by a hold at the same temperature (step quenching) to rid the alloy of excess vacancies reduces the problem considerably (21) But even then, stabilization of martensite can recur during subsequent aging, and the effect is worse, the higher the aging temperature in the martensitic condition Manganese or nickel addition to Cu–Zn–Al, it has been shown, too lessens the problem of stabilization This happens possibly through a slowing of diffusion in the martensite in the presence of the added elements More interestingly, the effects it has been shown are inhibited, even in the absence of these elements, by dislocations introduced into the β phase during hot rolling (23) or through transformation cycling (24) Further understanding of the role of these dislocations in such inhibition might provide the information needed to improve the stability of these alloys for use at higher temperatures Stabilization of Cu–Al–Ni martensite is much slower compared to Cu–Zn–Al (19,25) The former alloys thus are more thermally stable than Cu– Zn–Al and are more suited for use at higher temperatures Ni (5%) B (AlB2 or AlB12 ) Ti (Cu2 TiAl) good β-stabili Poor reproduc excellent β sta (T > 200◦ C Influence of Other Factors on the Trans Temperature Besides the chemical factors such position and order; certain nonchemical factors influence the Ms temperature Among the latter a butions from defects such as vacancies, dislocatio boundaries, and precipitates Influence of Nonequilibrium Precipitates Pr like the γ phase can be formed in Cu–Zn–Al by fl ing to an intermediate temperature after prior di followed by quenching (17) These precipitates the transformation temperatures with respect nominal values and also may produce variatio transformation temperature range and the hyste accompanies the transformation The exact cha pend on the coherency, size, and distribution of th itates The variations are brought about by an a in the chemical, stored, elastic, and frictional en the transformation because of the presence of tional phase Stored elastic energy plays a domi when the precipitates are small and coherent a their presence does not appreciably change the tion of the matrix This usually leads to a suppress Ms and to minor changes in the hysteresis, prov precipitates are deformed in the transformatio semi- or incoherent precipitates that substanti the composition of the matrix and impede the g martensitic plates lead to changes in the Ms that d the partitioning of the elements and an enlarged h (26) Precipitation and concomitant changes in tra tion temperatures can be disadvantageous if the duced inadvertently during service, but they can porated in the heat treatment schedule to fine transformation temperatures or when wider hys required The Influence of Grain-Refining Elements t Precipitates Copper-based shape-memory alloy rapid grain growth at higher dissolution temp When grain sizes are of the order of millime the elastic anisotropy in the β phase is high, th β lattice of alloying elements that change the transformation temperatures (2) Part of these elements remain in solution within the β matrix Depending on the atom size, this can give rise to solid-solution hardening that decreases the Ms and eventually the other transformation temperatures (29) (3) They can also have a chemical contribution, which means that the global composition determines the transformation temperatures on a purely thermodynamic basis (4) The precipitates limit grain growth during annealing, which influences the transformation temperatures, as discussed in the next section The Influence of Grain Size Several authors have shown that small grain size results in stabilizing the parent phase and depressing the transformation temperatures up to 40◦ C (30,31) This effect is observed in alloys with and without the special addition of grain-refining elements, which indicates the restraining effect of grain size itself on the transformation Lowering of transformation temperatures is attributed to the increasing grain restraint as grain size decreases This is the conclusion of most authors (32,33) and is also consistent with Hornbogen’s argument that the increase in yield stress σy is proportional to the stress required to start the transformation (20) Hornbogen’s important assumption is that matrix strengthening increases the undercooling T(= T0 − Ms ) but does not influence necessarily the T0 temperatures T0 is the temperature at which the free energy of the β phase is equal to the free energy of the martensitic phase Adnyana (30) and Jianxin (33) found a linear relationship between the Ms temperature and the yield stress derived via the classic Hall–Petch relationship for Cu–Zn–Al alloys The restraining effect of grain size is, however, also influenced by the grain size (gs) to thickness (t) ratio At high gs/t ratios, the contribution of the free surface becomes important and Ms no longer changes linearly with gs, as observed by Wood (34) This is consistent with the conclusion of Mukunthan and Brown (35) who showed that the flow stress in all specimens decreases as specimen thickness decreases when the value of t/d becomes smaller than a critical value These authors showed further that this critical value of t/d increases as both grain size and stacking fault energy decrease These elements that contribute to high stacking fault energy have an effect similar to a small grain size Influence of Defects Often it is not only the effect of the grain size or the grain size thickness ratio that relationship is also found between martensitic pl ness and fracture stress (36) Specific defect configurations can be introduce mal cycling and also by two-way memory trainin fluence of such defects, notably dislocations, has cussed in some recent literature It has been sugg the changing character of the same dislocation in martensitic phases alters the relative phase stab two phases Ni–Ti Alloys Ni50 –Ti50 and near equiatomic Ni–Ti alloys are explored system of all shape-memory alloys and most the whole SMA market Ni50 –Ti50 is an int phase that has some solubility at higher temper The science and technology of Ni–Ti is overw documented The influence of composition and t chanical processing on functional properties is w stood and described in the literature Therefore to some very interesting and relevant publication (37–41) The basic concept of processing Ni–Ti alloys i martensitic and β phases have to be strengthene plastic deformation during shape-memory or pse loading This occurs by classic methods: strain h and during cold deformation, solution hardening cipitation hardening Ni–Ti alloys have the sign vantage that these techniques can be easily appl excellent ductility and a very interesting but co precipitation process (42) The compositions of Ni–Ti SMA are approxim tween 48 and 52 at% Ni and the transformation tures of the B2 structure to the martensitic phas a monoclinic B19 structure are very sensitive to content (a decrease of about 150◦ C for an increas Ni) Transformation temperatures can be chosen −40 and +100◦ C Ni–Ti alloys have the best shape-memory be all SMA Even in the polycrystalline state, 8% covery is possible, 8% pseudoelastic strain is c reversible above Af , and the recovery stress is of th 800 MPa In some cases, the martensitic transformati ceded by the so-called R-phase transition The tion is a B2 ↔ rhombohedral transformation tha second-order characteristics (43) The most specific characteristics of this R-ph sition are that it shows clear one- and two-way nary alloys (52): Ternary Ni–Ti Alloy Systems Adding third elements opens even more possibilities for adapting binary Ni–Ti alloys to more specific needs of applications Adding a third element implies a relative replacement of Ni and/or Ti Therefore, it must be always very well indicated which metal, Ni or Ti or both, is replaced by the third element Alloying third elements influences the transformation temperatures and also affects hysteresis, strength, ductility, shape-memory characteristics, and the B2→(R)→B19 sequence The influence of several elements has been described in (44–48) Although more application oriented, one can distinguish four purposes to add third elements: to decrease (Cu) or increase (Nb) hysteresis, to lower transformation temperatures (Fe, Cr, Co, Al), to increase transformation temperatures (Hf, Zr, Pd, Pt, Au), and to strengthen the matrix (Mo, W, O, C) Some ternary alloys have been developed for large-scale applications We will summarize only the two most well developed: Ni–Ti–Cu and Ni–Ti–Nb Ti–Ni–Cu Ternary Ti–Ni–Cu alloys in which mainly Ni is substituted by Cu are certainly as important as binary Ti–Ni Increasing the Cu content decreases the deformation stress in the martensitic state and also decreases the pseudoelastic hysteresis without affecting the Ms temperature significantly (49) However, addition of more than 10% Cu embrittles the alloys and hampers formability It should also be remembered that Ti–Ni transforms from a B2 into a monoclinic phase, but Ti–Ni–Cu that contains more than 15 at% Cu transforms from a B2 into an orthorhombic phase Ti-Ni-Cu that has less than 15 at% Cu transforms in two stages (37) A disadvantage of most Ti–Ni–Cu alloys is that the transformation temperatures not decrease below room temperature Cr or Fe can be alloyed to obtain pseudoelastic alloys at room temperature that have small hystereses An Ni39.8 –Ti49.8 Cu10 Cr0.4 alloy was developed that has small hysteresis (130 Mpa), one-fourth compared with Ni50 -Ti50 , and an Ms below room temperature (50) Stress rate is much lower σ P−M stresses are much higher The superelastic window is much larger High-Temperature Shape-Memory Alloys (5) Actual shape memory alloys (SMA) are limited imal Af temperatures of 120◦ C: Ms is genera 100◦ C However, because market demands for S expanded greatly, the need for SMA that tran higher temperatures than presently available is ing The main application areas of interest a tors in the automobile and oil industries and devices There is also an interest in robotics becaus memory alloys that have high transformation tures allow faster cooling, which would signific crease the bandwidth in which the robot can ope Although many alloy systems have high tra tion temperatures, no large-scale applications h developed A major breakthrough has not been yet mainly due to the following problems: (mu performance than the successful Ni–Ti alloys, sta of martensite, decomposition of the martensitic phase, and brittleness due to high elastic anisotro to the presence of brittle phases or precipitates Another condition for a good shape-memory eff the stress to induce martensite or the stress to martensite is (much) lower than the critical stres mal slip Because the critical stress for slip gen creases as temperature increases, this condition difficult to fulfil, especially at high temperatures HTSMA should be designed at such a compositi thermomechanical treatment that strengthenin nisms are incorporated to increase the critical slip Table summarizes the systems under inve For references to this table, see (5) OTHER TYPES OF SHAPE MEMORY ALLOYS β-Ti Alloys In spite of the good biocompatibility of NiTi-alloy remain on the long-term stability or on the d bad surface treatment leading to Ni leaching S Ni–(Ti–X) Thermoelastic β2 ⇔ B19 , B19 X = Hf, Zr Ni–Al Thermoelastic B2 ⇔ 3R (7R) (L1 o structure) Cu, Co, Ag Ni–Mn Thermoelastic (?) B2 ⇔ θ (L1 o structure) Zr-based intermetallics Cu–Zr Zr2 –Cu–Ni Zr2 –Cu–Co a B19 monoclinic Fe, Co, Mn, B Al, Ti, Cu for Ni Mg, Al, Si, Ti, V, Sn, Cr, Co, Fe, Mo for Mn Ti, Ni Based on Ni–X intermetallic compounds that form a pseudobinary with Ni–Ti To increase transformation temperatures To improve ductility To decrease Ms and to improve shape-memory characteristics To increase Ms and to improve shape-memory characteristics To improve ductility 120 100 500 200 Nonthermoelastic Nonthermoelastic Thermoelastic Ref known for his high allergic reaction, Ni-less shape memory alloys could be attractive Such alloys might be developed based on the allotropic transformation in Ti, a highly biocompatible material Pure titanium shows an allotropic transformation from β (bcc) to α (hexagonal) phase at 1155 K Transition elements (TM) stabilise the β-phase Thus the temperature of the (α + β)/β transition decreases with increasing concentration of the alloying element β-phase Ti alloys can be martensitically transformed if they are quenched from the stable β-phase Two types of martensite, respectively α and α can be formed, depending on the composition and the solution treatment conditions (53) The α -martensite is hexagonal, while α has an orthorhombic structure (54) It is the α -martensite that shows the shape memory effect The shape memory effect was first studied in detail by Baker in a Ti-35 wt% Nb alloy (127) Since then several observations of SME especially in Ti-Mo base alloys have been reported (57,58, 59,60,61) A systematic work on the influence of different alloying elements on the shape memory effect can be found in (62), a patent deposited J Albrecht, T Duerig and D Richter The authors come to the conclusion that α -martensite can be obtained when the following condition is fulfilled: −1100 ≤ ε Ai Xi + Bi Xi2 ≤ −700 where Xi is the atomic percentage for each element, Ai and Bi are constants given in the patent for each elem Fe, Ni, Co, Mn, Cr, Mo, Zr, Nb, Sn, Cu) Ta was no although it also offers its contribution to SME as in (61) Generally, a shape recovery in the order of obtained based on strain-induced martensite and stresses up to 170 MPa have been reported (60) advantage is that those alloys are very prone to tion and decomposition due to the fact that the β retained after quenching in its metastable state petes with ω-phase during quenching Also spi composition of α -martensite in Ti-Mo and Ti-Nb observed (53) The sensitivity to decomposition ate temperatures is less, if not, important at r perature Therefor pseudoelastic β-Ti alloys coul interesting alternative to Ni-Ti alloys for exam thodontic wires Such an alloy has recently been by Lei et al (63) Ti–11Mo–3Al–2V–4Nb was se optimization Good pseudoelasticity of the order obtained after cold working and heat treatment Magnetic-Field-Induced Martensitic Transformation T Kakeshita et al (64) defined a magnetoelasti sitic transformation: when a magnetic field i (above Af ) to an alloy that exhibits a thermoelasti sitic transformation, martensite variants may b while a magnetic field is applied and revert to t phase when the magnetic field is removed This observed in Fe31.9 –Ni9.8 –Co4.1 –Ti (at%) (64,65) A Shape-memory alloys have different shape-memory effects and can be used in different ways These effects and ways of use are described in general terms here As explained before, binary and ternary Ni–Ti alloys are probably used for more than 90% of new SMA applications Therefore, quantitative data refer to Ni–Ti alloys, unless otherwise stated One-Way Shape-Memory Effect A shape memory element can be deformed in its martensitic state to almost any “cold shape.” The basic restriction is that the deformations may not exceed a certain limit, typically 8% These apparent plastic deformations can be recovered completely during heating when the reverse transformation occurs and results in the original “hot shape.” This strain and shape recovery during heating is called the one-way shape-memory effect because only the hot shape is memorized (Fig 1) The physical basis for this one-way effect is a reverse martensitic transformation from a preferentially oriented martensitic phase and shape to the original hightemperature phase and shape, as explained more in detail earlier and in many review papers on shape-memory alloys The preferential orientation of the martensitic variants originates from the application of stress either below Mf that causes martensitic reorientation, or during the forward transformation that causes preferentially oriented formation of martensite Thus, the apparent plastic strain is caused by the preferential orientation of martensite T