Effect of grain size and texture on pseudoelasticity in Cu–Al–Mn-based shape memory wire
Introduction
Cu-based shape memory alloys (SMAs) such as Cu–Al- and Cu–Zn-based alloys are commercially attractive for practical applications of the shape memory effect (SME) and pseudoelasticity (PE) because of their low cost and their advantages with regard to electrical and thermal conductivities [1], [2]. The recoverable strain of the polycrystalline Cu-based SMAs depends on the grain size (d) relative to the size of the specimen, including sheet thickness (t) and wire diameter (D), and increases with increasing relative grain size (d/t and d/D), which is equal to the decrement of the grain constraint [3], [4]. In Cu–Zn SMAs with extremely large grains, a large recoverable strain of about 10% has been obtained [5]. However, the polycrystalline Cu-based SMAs with a coarse grain size are generally brittle and tend to cause intergranular fractures due to the high degree of order in the parent β phase with a B2, D03 or L21 structure and the extremely high elastic anisotropy ratio in the β phase [2]. Therefore, the fatigue strength of those SMAs with coarse grains is very low [6], [7] and only a limited recoverable strain of about 2% can be used for practical applications in the polycrystalline Cu-based SMAs, although grain refining has been attempted to improve the ductility and the fatigue strength [1], [2].
It is also known that the recoverable strain of Cu-based SMA single crystals strongly depends on the crystal orientation. According to theoretical calculations, the development of a favorable texture should improve the recoverable strain in the polycrystalline Cu-based SMAs [8], [9], [10]. In fact, a large recoverable strain of 6% can be obtained in Cu-based thin film with a favorable texture prepared by splat quenching [11], [12]. Only limited enhancement of recoverable strain due to the formation of the texture by conventional fabrication methods using thermomechanical heat treatment, however, has been demonstrated in the polycrystalline Cu–Zn–Al SMAs [10]. Furthermore, a low cold-workability of about 10% and 30% in Cu–Al- and Cu–Zn-based SMAs, respectively, has restricted the practical applications of their SM components which consist of thin sheets, fine wires, tubes, etc. [1], [13].
Recently, Kainuma et al. [14], [15] have reported that excellent ductility can be obtained by controlling the degree of order in the β phase of the Cu–Al–Mn SMAs. Fig. 1 shows the vertical section of the phase diagram of the Cu–Al–10at.%Mn system [16]. It is seen that both the transition temperatures of order–disorder transitions, β (A2) → β2 (B2) and β2 → β1 (L21), drastically decrease with decreasing Al content. The Cu–Al–Mn SMAs with an Al content below 18 at.%, which have a low degree of order in the β phase, show excellent cold-workability over 60% in cold-rolling reduction and also exhibit SME and PE based on cubic β1 (L21) to monoclinic (18R) [14], [15]. Very recently, the present authors have found that in the Cu–Al–Mn–Ni alloys, a strong {1 1 2}〈1 1 0〉 recrystallization texture was developed by cold-rolling with heavy reduction over 60% followed by solution-treatment, and an PE strain of about 7% was obtained in the direction 45° from the rolling direction (RD) for the {1 1 2}〈1 1 0〉 textured sheet specimen [17], [18]. It was also demonstrated that the degree of the PE strain strongly depends on the relative grain size in the Cu–Al–Mn-based SMA sheets, and that, in particular, a large PE strain over 6% can be obtained in specimens with columnar grains even if the specimens have a random texture [18].
In order to predict and understand the stress–strain behaviors of polycrystalline SMAs, numerical calculations based on the Taylor [19], [20] and Sachs models [21] have been demonstrated [8], [9], [10], [22], [23], [24], [25], [26], [27]. In the Taylor model, the grain constraint effect in the stress-induced martensitic (SIM) transformation is considered, and the strain compatibility at grain boundaries is maintained. On the contrary, in the Sachs model, strain compatibility at grain boundaries is not maintained and each grain behaves as the same applied stress components since the effect of grain constraints on the polycrystalline alloy is ignored. In the Cu-based SMAs, however, the yield stress and recovery strain estimated on the basis of both models do not agree with experimental results which fall between the values predicted from Taylor-type and Sachs-type models [9], [27]. Such disagreement in the Cu-based SMAs should suggest a strong dependence of grain size on the stress–strain behaviors which has not yet been systematically demonstrated in a wide range of grain sizes, and therefore, the prediction of the stress–strain behaviors for polycrystalline alloys with various grain sizes using such models is required.
In the present study, the effect of the relative grain size d/D on the PE behaviors for the Cu–Al–Mn-based SMA wires was investigated. The PE properties of the textured Cu–Al–Mn–Ni SMA wires were also demonstrated. The experimental data of the yield stress and the PE strain were compared with the theoretical results predicted on the basis of Taylor and Sachs models and a new model on the grain size dependence on the PE properties is herein proposed.
Section snippets
Experimental procedures
Several kinds of alloys, i.e., Cu72Al17Mn11 (designated as CAM), (Cu72Al17Mn11)99.8–B0.2 (designated as CAM-B), (Cu72.5Al17Mn10.5)99.5–Co0.5 (designated as CAM-C), and (Cu73Al17Mn10)97.8–Ni2B0.2 (designated as CAM-NB), were prepared by induction melting in an argon atmosphere. Boron was added for grain refining which can be achieved by the grain boundary pinning effect due to the dispersed particles of MnB [28], and specimens with huge grains were obtained by secondary recrystallization which
Model calculations
The theoretical calculations and their results are described before presentation of the experimental results. The yield stress σy and the transformation strain εTS, which should be equal to the maximum PE strain due to SIM transformation in the random textured polycrystalline alloys with grain constraint effect, can be estimated by the following equations [22], [23], [24]:where ΔS is the entropy change of the martensitic transformation per unit volume, η is
Effect of grain size on the stress–strain behaviors
Figs. 4(a)–(c) show the stress–strain curves obtained by cyclic tensile testing at Ms + 50 K in the (a) CAM-C alloy with the d/D = 6.0, (b) CAM alloy with d/D = 0.217 and (c) CAM-B alloy with d/D = 0.06, respectively. It can be seen that the yield stress σy and the work-hardening rate dσPE/dε defined in Fig. 4(b) increase with decreasing d/D, where σy is defined as the stress at which macroscopic SIM transformation occurs and is relevant for comparison with the prediction of the rigid perfectly plastic
Conclusions
The effects of grain size and the texture on the stress–strain behaviors of SIM transformation and the transformation temperatures were investigated in the Cu–Al–Mn-based SMAs. The results obtained are as follows:
- 1.
In the Cu–Al–Mn-based SMA wire with a random texture, the yield stress σy, the work-hardening rate dσPE/dε, the stress hysteresis Δσ, the transformation strain εTS and the maximum pseudoelastic recovery strain due to the SIM transformation strongly depended on the relative grain
Acknowledgments
The authors thank Mr. H Suzuki of Chuo Spring Co. LTD, Japan for carrying out the mechanical testing. This work was supported by a Grant-in-Aid for Scientific Research and Development from the Ministry of Education, Science, Sports and Culture of Japan.
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