Regular Article Equilibrium stress during the response of shape memory alloys to an abrupt heat pulse Shahaf Vollach ⁎, Ran Caciularu, Doron Shilo Department of Mechanical Engineering, Technion, Haifa 32000, Israel abstract article info Article history: Received 7 April 2017 Received in revised form 28 June 2017 Accepted 17 July 2017 Available online xxxx Previous studies of the responses of shape memory alloys (SMA) under a rapid heat pulse revealed the existence of a critical plateau stress that determines the performances of high rate SMA actuators. In this letter, we inves- tigate the effects of temperature and initial stress on the plateau stress. Calculations based on the integration of the Clausius-Clapeyron equation while considering the inhomogeneity of the transformation temperature were in good agreement with the measured data. Our results indicate that the plateau stress represents equilibrium conditions and that actuation performances can be increased significantly by increasing the initial stress. © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. The reverse martensitic phase transformation is the physical mech- anism responsible for the actuation performances of shape memory al- loys (SMA). This transformation is very fast due to its diffusionless and athermal nature [1–4]. However, it is usually studied at slow rates [5– 6]. For example, in cases where the phase transformation is induced by a temperature change, the rate of heating or cooling is usually several orders of magnitude slower than the true phase transformation rate [7]. Recently, we demonstrated a unique high rate experiment in which a SMA wire was heated by an electric pulse with a characteristic time of approximately 1 μs [8,9]. These experiments were used to study the true kinetics of the phase transformation under conditions at which the transformation rate is unrestricted by the rate of heat transfer or mechanical inertia [10]. The results revealed two characteristic times, in the range of 20–30 μs that describe the initial stages of the phase transformation [10]. In addition, we suggested a kinetic law and a model, which fit the experimental results performed at different tem- peratures and for different wire dimensions [10]. The high rate experiments also revealed that after a few millisec- onds, the stress reaches a plateau and remains at a constant value for a long time (until the wire cools down after a few seconds) [10]. This ob- servation implies that the plateau value represents equilibrium condi- tions and was therefore denoted as σ eq . This definition of σ eq based on rapid heat pulse experiments is different than the commonly used defini- tion of the equilibrium stress as the average/plateau transformation stress during slow rate mechanical tests that are performed under constant temperature [5,6]. It should be clarified that the phase transformation is hysteretic and therefore equilibrium thermodynamics do not strictly apply. In the context of this paper, we use a broader definition of equilib- rium as a state in which the Gibb's free energy difference between the two phases, i.e., the driving force for the transformation, reaches a constant value that is equal to the resistance of the material to the phase transfor- mation. This definition still fulfills the laws of thermodynamics. The value of σ eq determines the force and energy outputs of SMA actu- ators activated by pulse heating and is therefore of significant practical im- portance [9–11]. In the previous study [10], it was found that σ eq is the only material response parameter that is affected by temperature, but this effect was not studied. In this article, we first measure the relation between the temperature and σ eq and compare the results with the Clausius-Clapeyron equation that reflects a system under thermodynamic equilibrium. We then show that the initial stress also has a significant effect on σ eq . This ob- servation seems to contradict the fact that an equilibrium state does not depend on the initial conditions. We address this contradiction by devel- oping a thermodynamic model that considers that different regions within the SMA material have different transition temperatures. The model calcu- lations are in good agreement with the experimental results and indicate the significant effect of transformation temperature inhomogeneity. In the high rate experiments, a detwinned NiTi wire was heated by an electric pulse with a peak of 10 5 –10 6 W and an overall duration of b 5 μs [9,10]. The NiTi wire was fixed at both ends such that there were no moving masses, except the local motion of the wire itself [10]. Dedicated force sensors with a bandwidth of 350 kHz and a re- sponse time of approximately 1 μs (see details in Ref. [9]) were attached to both ends of the NiTi wire to measure the mechanical response di- rectly associated with the phase transformation. The average temperature of the wire as a function of time, t, can be expressed as. Tt ðÞ¼ T R þ U in t ðÞ C p − H∙xt ðÞ C p − Qt ðÞ C p ð1Þ where T R is room temperature. The second term represents the Scripta Materialia 141 (2017) 50–53 ⁎ Corresponding author. E-mail address: cieux@campus.technion.ac.il (S. Vollach). http://dx.doi.org/10.1016/j.scriptamat.2017.07.016 1359-6462/© 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 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