Effect of grain size and texture on pseudoelasticity in Cu–Al–Mn-based shape memory wire

Abstract

The effect of the relative grain size d/D (d: grain size, D: wire diameter) on stress–strain characteristics was investigated in Cu–Al–Mn-based shape memory alloy (SMA) wires. The yield stress (σ_y), the work-hardening rate after yielding (dσPE/dε) and the stress hysteresis (Δσ) in the wires with a random texture decrease with increasing d/D. The transformation strain (ε_TS) and the maximum pseudoelastic strain $({\epsilon }_{\mathrm{PE}}^{\mathrm{MAX}})$ increase with increasing d/D. The effect of grain size on pseudoelastic behaviors can be clarified from the volume fraction of three-dimensionally constrained grains and the σ_y, dσ_PE/dε and Δσ increase proportionally with increasing (1 − (d/D))² while the ε_TS decreases proportionally with increasing (1 − (d/D))². Consequently, the effect of grain size on the pseudoelastic behaviors can be expressed using the Taylor and inverse Schmid factors. The σ_y and the ε_TS for wires with a 〈1 1 0〉 fiber texture are larger and smaller than those for wires with a random texture, respectively.

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 ${\mathrm{\beta }}_1^{\prime }$ (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.