PHILOSOPHICAL MAGAZINE LETTERS, 2002 VOL. 82, NO. 9, 511±517
Dynamic deformation of shape-memory alloys: evidence of domino detwinning? Yong Liuy School of Mechanical and Production Engineering, Nanyang Technological University, Singapore
Yulong Li Department of Aircraft Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, PR China
Zeliang Xie School of Materials Engineering, Nanyang Technological University, Singapore
and K. T. Ramesh Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, USA [Received in ®nal form 3 May 2002 and accepted 10 May 2002]
Abstract Deformation of NiTi shape-memory alloys (SMAs) under dynamic tension has been studied. It is found that the stress plateau associated with detwinning ¡1 still exists at the highest strain rate tested (300 s ). Beyond the stress plateau, when dislocation mechanisms dominate the deformation process, the strainhardening e ect is more strongly dependent on strain rate. The dynamically deformed specimens exhibit a shape-recovery process and a two-way memory e ect which are identical with that for the alloy deformed under quasistatic conditions. The observations suggest that the detwinning process takes place in SMAs under dynamic tension.
} 1. Introduction Deformation mechanisms in shape-memory alloys (SMAs) provide an important research subject since they are strongly related to the subsequent shape-memory phenomenon. In martensitic SMAs, a `detwinning’ mechanism through variant reorientation is the major deformation mechanism (Otsuka and Shimizu 1986, Wayman 1992, Liu et al. 2000) which is partially responsible for the shape-memory e ect. Although the ®rst SMA was discovered about half a century ago, understanding of the deformation mechanism in SMAs is still unsatisfactory and this has been a serious drawback in the engineering applications of these materials. Experimental observations have shown that the detwinning process is directional and is strongly related to the deformation mode and microstructure textures (Liu et al. 1998, 1999a). Accompanying the detwinning process, a stress plateau is often y Email:
[email protected] Philosophical Magazine Letters ISSN 0950±0839 print/ISSN 1362±3036 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080 /0950083021015386 9
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generated on a macroscopic scale (®gure 1). The end of the stress plateau is, however, not the end of the detwinning process. The remaining lattice twins, having `unfavourable ’ orientations to the loading direction, will continue to detwin at higher stresses (Liu et al. 2000). For highly textured SMAs, the plateau strain can reach about 6%. Beyond about 10% strain, dislocation mechanisms are more likely to operate. Experimental results further show that a longer plateau strain normally corresponds to a larger shape-recovery strain. Based on the experimental observations, a recent theoretical analysis (Zheng and Liu 2002) has suggested that two di erent detwinning mechanisms exist, namely domino detwinning and assisted detwinning. Domino detwinning is a process in which subsequent detwinning can be triggered by an initially detwinned volume without requiring an increase in the external load. Its driving force is the internal stress impulse generated by the initially detwinned volume which increases the resolved shear stress of the surrounding lattice twins having less favourable orientations to the loading direction. Di erent from domino detwinning, assisted detwinning requires a continuous increase in external force to proceed and takes place beyond the stress-plateau region (Zheng and Liu 2002). Analysis shows that the end of domino detwinning corresponds to the end of the stress plateau. In line with the experimental observations, in highly textured SMAs, domino detwinning is enhanced along certain directions and longer plateau strains are expected. The rate dependence of the detwinning mechanism is of signi®cant interest both for application and for fundamental understanding of the shape-memory phenomenon. The unique combination of novel properties provides SMAs with the potential
Figure 1. Schematic diagram of the current understanding of the martensite deformation process in SMAs. Under tension, the lattice twins are detwinned leading to macroscopic deformation up to about 6% strain under constant load. Further deformation is realized through further detwinning and dislocation mechanisms.
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to be used as a primary actuating mechanism for devices with dimensions in the micrometre to millimetre range (especially devices requiring large forces over relatively large displacements). Three factors may control the actuation speed, namely detwinning speed, heating rate and cooling rate. For actuation mechanisms using thin-®lm SMAs, in which heating and cooling rates can be su ciently high with the help of novel designs, the speed limit of the detwinning process is thus of primary importance. So far, it has been found di cult to determine experimentally the speed limit of the detwinning process. In the present research, a tension Kolsky bar (Chichili and Ramesh 1995) was used to subject the NiTi samples to tensile deformation at high strain rates. Several samples were tested under dynamic tension at ¡1 strain rate up to 300 s and strain amplitude up to 15%. The highest strain rate of ¡1 300 s achieved in the present research is also the highest strain rate used to date to study the deformation mechanism of SMAs under tension. The experiments have been carefully repeated. The reason for using dynamic tension rather than dynamic compression is the di erent deformation mechanisms that operate. Under compression the deformation mechanism is mainly associated with dislocation generation rather than detwinning (Liu et al. 1998). } 2. Detwinning under tension deformation It is known that, in SMAs, the thermally formed martensite consists mainly of lattice twins as a result of strain accommodation (Saburi and Wayman 1979, Knowles and Smith 1981, Miyazaki et al. 1989, Liu et al. 1999a, 2000). A typical NiTi martensite is shown in ®gure 2 (a). The martensite plates A, B and C are well self-accommodate d to each other. In each plate, the parallel bands are lattice twins. Under externally applied stresses the self-accommodate d twinned lattice will become a twin-free lattice through variant reorientation without changing the crystal symmetry, a process known as detwinning. The macroscopic deformation due to detwinning can be recovered through a reverse phase transformation upon heating. Figure 2 (b) is a transmission electron micrograph of detwinned martensite observed in a NiTi specimen that has been deformed to 6% strain under tension. Electron di raction and high-resolution transmission electron microscopy (HRTEM) analysis have veri®ed that the martensite plates (A, B and C) do not have twin relationships and no twins have been observed inside these plates. They are all detwinned without signi®cant formation of dislocations. Based on an extensive transmission electron microscopy study (Liu et al. 1998, 1999a, 2000), the martensite plates most probably consist of h011 i type II twins before detwinning. Some parallel dark lines are visible in plates B and A. Their origin is not clear at the moment; however, HRTEM shows they are not traces of twin planes. Atomic arrangement along the dark-line regions in ®gure 2 (b) has been studied with the help of HRTEM. Image analysis shows that the dark lines are parallel to the (001) plane. Figure 2 (c) is one of the inverse fast Fourier transform HRTEM images corresponding to the area indicated by a white arrow in ®gure 2 (b). A mask ®lter was applied to keep the major crystallographi c information while only reducing the noise of the corresponding high-resolutio n transmission electron micrograph. Figure 2 (c) clearly shows no mirror-plane symmetry with respect to the (001) plane, and the atomic arrangements are identical on both sides of the dark line, which ®ts well the NiTi lattice structure predicted (Otsuka et al. 1971, Kudoh et al. 1985) in ®gure 2 (d). In addition to a high strain ®eld in the dark-line region, a mismatch of (100) and
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(d) Figure 2. (a) Thermally formed martensite in a NiTi SMA typically consists of 100% lattice twins shown by parallel bands in self-accommodated martensite plates A, B and C. (b) Under tension deformation to 6% strain, the lattice twins are mostly detwinned in the observed area with insigni®cant formation of dislocations; B==‰010 ŠM . Plates A, B and C are not twin-related and no lattice twins are found inside each plate. (c) Inverse fast Fourier transform HRTEM image of an area along the dark line in (b). (d) Atomic structure of NiTi martensite viewed from [010]M . A conventional unit cell is shown: (*), Ni atom; (*), Ti atom.
(101) atomic positions between two sides of the dark line is visible. Rotation distortion of the lattice is also present and is shown by the white arrows in ®gure 2 (c). } 3. Dynamic tension deformation and shape-recovery Comparing the stress±strain curves under quasistatic (low strain rate of ¡1 ¡1 0.002 s ) and dynamic (high strain rate of 300 s ) tension loads, the deformation characteristics are similar. As shown in ®gure 3 (a), a stress plateau (region II) that provides up to 4% strain still exist in the stress±strain curve for the highest rate achievable. The plateau stress slightly increases with increasing strain rate, and it seems to obey a linear relation within the tested range (®gure 3 (b)). In the stressplateau region, the di erence between the stress±strain curves for dynamic and quasistatic tension is not as signi®cant as that in the strain region IV. In region IV, the stress level increases more strongly with increasing strain rate (Liu et al. 2002), showing the conventional strain-rate dependence associated with dislocation mechanisms (Nicholas 1980; Stou er and Dame 1996). It has been reported that, for ¡1 low-carbon steels at about 4% strain, the stress level under a strain rate of 300 s is nearly twice that during quasistatic deformations (Rajendran and Bless 1985). The stress plateau that appears under dynamic tension suggests that the detwin¡1 ning can proceed at a strain rate of at least 300 s . The shape-recovery process of the dynamically tested specimens has been further determined using a thermal mechanical analyser. For a specimen deformed to 7% strain, a shape-recovery of about 3.6% strain is recorded during the ®rst heating (®gure 3 (c)). During the subsequent cooling and second thermal cycle, a two-way memory e ect (TWME) exists, being 0.9% two-way memory strain for a specimen deformed to 7% and 2.5% two-way memory strain for a sample deformed to 15% strain (Liu et al. 2002). These results are identical with those observed in a NiTi SMA tested under a quasistatic mode (Liu et al. 1999b). The TWME is known to relate to an internal stress ®eld of dislocation networks that direct the growth of the martensite variants to preferential orientations. Detwinning is a necessary condition to have shape-memory but is not
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Figure 3. (a) Stress±strain curves of martensitic NiTi under tension at strain rates between ¡1 0.002 and 300 s . (b) Yield stress of martensite in NiTi as a function of strain rate. (c) Shape recovery and TWME of the dynamically deformed samples (7% strain) upon heating and subsequent thermal cycling.
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su cient for obtaining a TWME. On the other hand, a severe deformation leading to the formation of a high density of dislocations will lead to poor shape-recovery and poor TWME. Maximum shape-recovery and TWME were obtained when the material was deformed to about 12% under tension (Liu et al. 1999b). Since shape-memory in NiTi requires detwinning as a pre-condition, one can further conclude that the detwinning process has taken place during dynamic deformation to 7% strain. Note that, during dynamic deformations, the specimen’s temperature may increase signi®cantly because of insu cient time available for heat dissipation. These results are signi®cantly di erent from those on stress-induced phase transformation s in SMAs where the stress±strain pro®le changes signi®cantly when even `slightly’ increasing the strain rate (Shaw and Kyriakides 1995), and in steels where the dislocation mechanism dominates the deformation process. The present research shows that the detwinning process responsible for the stress plateau is able to progress at rather high speeds (corresponding to the highest strain rates) under constant load. This seems to provide further evidence of domino detwinning involved in the deformation of martensitic NiTi SMA. ACKNOWLEDGEMENTS Yong Liu wishes to acknowledge the Nanyang Technological University Academic Research Fund RG 16/00. REFERENCES Chichili, D. R., and Ramesh, K. T ., 1995, Int. J. Solids Struct., 32, 2609. Knowles, K. M., and Smith, D. A ., 1981, Acta metall., 29, 101. Kudoh, Y., Tokonami, M., Miyazaki, S., and Otsuka, K ., 1985, Acta metall., 33, 2049. Liu, Y., Li, Y. L., and Ramesh, K. T ., 2002, Phil. Mag. A, 82 (to be published). Liu, Y., Xie, Z. L., Van Humbeeck, J., and Delaey, L ., 1998, Acta mater., 46, 4325; 1999a, ibid., 47, 645. Liu, Y., Xie, Z. L., Van Humbeeck, J., Delaey, L., and Liu, Y. N ., 2000, Phil. Mag. A, 80, 1935. Liu, Y. N., Liu, Y., and Van Humbeeck, J ., 1999b, Acta mater., 47, 199. Miyazaki, S., Otsuka, K., and Wayman, C. M ., 1989, Acta metall., 37, 1873. Nicholas, T., 1980, Technical Report AFWAL-TR-80-4053, Materials Laboratory, Wright± Patterson Air Force Base, Dayton, Ohio. Otsuka, K., Sawamura, T., and Shimizu, K ., 1971, Phys. stat. sol. (a), 5, 457. Otsuka, K., and Shimizu, K ., 1986, Int. Metals Rev., 31, 93. Rajendran, A. M., and Bless, S. J ., 1985, Technical Report AFWAL-TR-85-4009, Materials Laboratory, Wright±Patterson Air Force Base, Dayton, Ohio. Saburi, T., and Wayman, C. M ., 1979, Acta metall., 27, 979. Shaw, J. A., and Kyriakides, S ., 1995, J. Mech. Phys. Solids, 43, 1243. Stouffer, D. C., and Dame, L. T . (editors), 1996, Inelastic Deformation of Metals (New York: Wiley). Wayman, C. M ., 1992, Prog. Mater. Sci., 36, 203. Zheng, Q. S., and Liu, Y ., 2002, Phil. Mag. A, 82, 665.
