Elastic constants of bcc austenite and 2H orthorhombic martensite in CuAlNi shape memory alloy
Introduction
Shape memory alloys (SMA) exhibit unique thermomechanical behaviors due to thermoelastic martensitic transformations (MT) driven by the external stress or temperature [1], [2], [3]. It is of essential interest to know the elastic constants of the austenite and martensite phases, since they reflect the fundamental thermodynamic properties; i.e., very interesting physical information can be deduced not just from the values of elastic constants but mainly from their temperature and stress dependencies [3]. Knowledge of the elastic constants of both austenite and martensite phases is also important in modelling of SMA functional mechanical behaviors, since the crystal domains (separated by mobile phase or twin interfaces responsible for shape memory phenomena) interact elastically.
Elastic properties of the cubic high temperature phases in SMAs are relatively well known [2], [3], [4], [5], including their temperature [3], [4], [5] and stress [2], [3] dependencies. As a particular case to be focused on in this work, the β1 austenite phase in Cu-based SMAs is known for its very large elastic anisotropy. It transforms to various martensitic phases (18R), (2H), (6R) depending on composition, temperature, magnitude and sense of uniaxial stress [1]. Before the martensitic transformation occurs at Ms temperature, the body-centered cubic (bcc) structure of the austenite [4] exhibits several kinds of anomalies (elastic, diffraction, phonon) over a broad temperature range above Ms. These anomalies can be viewed as a reflection of the enhanced instability of the bcc structure approaching its stability limit. In particular, variation of the elastic constants of the β1 austenite phase with temperature in the vicinity of the phase transition has been thoroughly investigated [3], [4], [5]. It is now generally accepted that the main characteristic feature of the pretransformation elastic instability of Cu-based SMAs is the simultaneous decrease of the elastic constant C′ (softening) and increase of the C44 constant (hardening) with decreasing temperature. The experimental results published so far [3], [4], however, prove that the softening is far from complete and that C′ remains finite even just above Ms and the same is true for the softening of the [1 1 0] TA1 phonon branch as another premartensitic instability observed in inelastic neutron scattering experiments [3].
There exist only very limited experimental data for the elastic properties of the low temperature (high stress) martensite phases in SMAs. This is mainly because of the experimental difficulties related to the preparation of multiple, sufficiently large single crystals of low symmetry martensite phases needed for the ultrasonic experimental methods commonly used to evaluate the elastic constants. Nevertheless, as regards the elastic properties of the lower symmetry martensite phases in Cu-based SMAs, some very limited data exist. Elastic constants of the 2H martensite phase in CuAlNi alloy were determined solely by Yasunaga et al. [8] using resonant ultrasound spectroscopy (RUS) technique. These constants, although never verified, as far as we know, are frequently referenced in the literature and widely used in SMA modelling. Elastic constants of the 18R monoclinic martensite in a different CuZnAl alloy were reported by Rodríguez et al. [7] and their temperature dependence investigated by Gonzàlez-Comas et al. [6]. In the present work, elastic constants of the bcc austenite (β1) and orthorhombic 2H martensite phase () in CuAlNi single crystal were evaluated using an optimization approach towards pulse-echo overlapping acoustic method. This newly proposed modification of the standard direct method (Section 2.3) is particularly suitable for evaluation of elastic constants of low symmetry martensite phases in SMAs. It facilitates the work and reduces experimental errors.
A deformation technique allowing the mutually conversion of the austenite and martensite single crystal variants (Section 3.2) was developed. The elastic constants of both austenite and martensite phases thus could be firstly evaluated on the same single crystal piece at the same temperature. Taking advantage of that, the inheritance of soft acoustic modes from bcc β1 austenite to orthorhombic 2H martensite phase is investigated in Section 4.3. The inheritance of elastic properties (anisotropy of Young’s modulus) is discussed in Section 4.4 as a model example for elastic property changes associated with the martensitic transformation in SMAs.
Section snippets
CuAlNi single crystal
A single crystal of Cu–14.3Al–4.2%Ni (wt.%) alloy was grown by the Bridgman method. The transformation temperatures were determined by DSC as Ms(2H) = 288 K and austenite start temperature, As = 313 K. Due to the thermal hysteresis, this crystal may exist at room temperature either in the bcc austenite or in the 2H martensite phase. Four specimens (Table 1) were spark cut in the austenite phase in a prism shape (Table 2) with crystallographic orientations of the faces given in Table 1. The crystal
Elastic constants of the austenite phase
The pulse-echo measurements were performed at room temperature T = 296 K on three austenite cubes in nine available crystal directions (Table 1). The measured and calculated wave velocities for longitudinal and transverse waves are given in Table 3. The denoted error intervals stem from the orientation uncertainty. They were determined by the Monte Carlo simulation approach introduced above. Some data are missing in the table because only a weak echo could be detected in some ultrasound
Austenite elastic constants
As concerns the elastic constants of the CuAlNi austenite, numerous results were reported in the literature [8], [11], [12], [13], [16], [17], [18]. Due to the strong elastic anisotropy, the value of C′ is very low compared to the constants C11, C12 and C44. Our results for C11 and C44 (Table 4) agree with the literature data. However, there are differences in the values of C12, C′ and A. Table 8 shows a summary of the literature data of C′ we are aware of. Since C′ varies with temperature
Summary and conclusions
Single crystals of CuAlNi alloy existing at room temperature either in austenite or martensite state were grown and cut into the cube shape (a ∼ 5.6 mm) in austenite state. Taking advantage of the easy deformation twinning in the martensite state, multiple parallelepiped shaped samples were prepared by a compression deformation method. Ultrasonic pulse-echo measurements of the velocities of acoustic wave propagation were carried out on the austenite cubes as well as on the martensite
Acknowledgements
Support of the Marie-Curie RTN Multimat (Contract No. MRTN-CT-2004-505226) is gratefully acknowledged. The work has been further supported by Czech Grant Agency under the project no. 106/03/1073, the Grant Agency of Academy of Sciences A1048107, the project of the Institute of Thermomechanics ASCR No. AV0Z 20760514 and project MAT2004-1291 (CICyT, Spain).
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