Thermomechanical Characterization of Superelastic Ni-Ti SMA Helical Extension Springs Manufactured by Investment Casting

Shape memory alloy (SMA) helical springs are special mechanical parts that require a previous evaluation of its behavior for application. Therefore, in this paper thermal and mechanical behaviour of superelastic Ni-Ti SMA helical extension springs manufactured by investment casting (IC) are evaluated. Phase transformation temperatures were measured by Electrical Resistance as a function of Temperature (ERT) and Differential Scanning Calorimetry (DSC). Tensile tests were carried out within strain and temperatures ranges. The pitch angle and stiffness of each spring were determined. Results demonstrated that Ni-Ti SMA helical springs produced by IC presented phase transformation corresponding to the superelastic effect (SE). The reversible deformations under tensile test were of the order of 70%. The mechanical behavior as function of temperature revealed a linear relationship between maximum force and spring temperature.


Introduction
Since the discovery of the shape memory phenomenon in Ni-Ti alloys, shape memory alloys (SMA) have been applied in several areas such as aeronautics and biomedical. Ni-Ti SMA have excellent functional properties, biocompatibility and corrosion resistance. However, the high manufacturing costs due to high reactivity of Ti is a main drawback to the advancement of commercial applications [1][2][3] .
In general, the manufacture of Ni-Ti alloys is accomplished through two main techniques, casting processes and powder metallurgy, followed by other processes such as machining, heat treatments, forming and shape setting to obtain mechanical devices 3,4 . Recently, additive manufacturing (AM) processes have also been used to produce Ni-Ti parts 3,5 .
In order to establish an alternative route for the manufacture of Ni-Ti SMA parts, Simões and De Araújo 6 have recently used investment casting (IC) processes to produce various mechanical components such as Belleville washers, wire netting, honeycombs, helical springs and screws. Basically, in their work the Ni-Ti bulk material was obtained previously by a Plasma Skull Push Pull (PSPP) process, validated by De Araújo et al 7 , and submitted to induction melting followed by centrifugal injection in ceramic moulds.
Among the mechanical Ni-Ti SMA parts, helical springs stand out. These mechanical components can be used as actuators and sensors. Amerinatanzi et al 8 evaluated the performance of a Ni-Ti superelastic spring and compared it with a stainless-steel spring applied to an ankle foot orthosis (AFO) hinged ankle support. In odontology, Ni-Ti springs are generally used for tooth movement because of their ability to provide constant forces 9 . Also, in recent decades, studies have shown the effectiveness of using SMA springs for seismic isolation 10 . Due to intrinsic shape memory effect, SMA springs can also be used as thermal actuators in valves 11 . More recently, SMA coil springs have been proposed for use as mechanical vibration attenuators in rotary systems 12,13 .
Ni-Ti SMA springs are manufactured by "shape setting", wherein the wire is wrapped and fixed around a cylinder and then heat treated to obtain the coil spring shape. However, while usual and simple, this process depends on the preliminary fabrication of the Ni-Ti wires 4,14,15 . Thus, it is also important to develop processes for obtaining these components in a single manufacturing step, especially for custom applications. Recently, helical springs produced by investment casting techniques were obtained directly from the molten Ni-Ti and presented good mechanical properties 6,16 .
However, there are not many studies on the thermomechanical behaviour of Ni-Ti alloy products obtained by investment casting. Thus, the international literature still needs to be enriched with new results in this field of research.
Then, this paper analysed the thermal and mechanical behaviour of Ni-Ti SMA helical extension springs obtained by an investment casting process corresponding to induction melting followed centrifugal casting (ICC).

Experimental Procedures
Geometric parameters can affect the helical springs behavior when subjected to large displacements. 17 Four main geometric parameters are usually considered in the designing of SMA helical springs 17,18 : wire diameter (d), spring diameter (D), number of active coils (N a ) and pitch  Figure 1 shows a schematic drawing of a Ni-Ti SMA produced in this work.
process. For this, ceramic moulds were produced from 3D printed wax springs 6 .
After manufacturing, the Ni-Ti springs were submitted to heat treatment in a resistive furnace without protective atmosphere. The heat treatment applied was homogenization at 850ºC for 30min followed by ageing at 500ºC for 2h, both with air cooling 6 .
The SMA characterization starts from the determination of phase transformation temperatures (PTTs). Critical transformation temperatures were measured by electrical resistance measured as a function of temperature (ERT) and differential scanning calorimetry (DSC). ERT is a nondestructive technique that allows analyse the average PTTs in the entire Ni-Ti coil spring. For this, SMA spring is placed into a thermal controlled silicone oil bath and submitted to a constant electrical current of low intensity to cause a potential difference between two points. Subsequently, the helical spring is subjected to cooling/heating between -60°C and 100°C with a 10°C min -1 rate using the thermal controlled bath (Hubber, CC 902 model). On the other hand, DSC is a technique that allows the measurement of the released and absorbed heat associated with the phase transformation in a small sample of the SMA spring. In this work it was used a heating/cooling rate of 10ºC min -1 , from -60°C to 100°C, using a DSC Q 20 model, from TA Instruments.
The as cast Ni-Ti springs were visually inspected with a digital microscope (Bluetek, model MC500), in order to analyse the surface quality and to identify superficial casting defects. Subsequently, the dimensions of the wax springs and manufactured springs were compared with a Profile Projector (Huatec Group, model HB16).
The heat-treated Ni-Ti SMA springs were mechanically characterized at room temperature (~25ºC) using a universal testing machine (Instron, 5582 model) equipped with a load cell of 30kN. A strain rate of 1% min -1 was used.
Initially, springs were loaded until failure to determine the maximum deflection for each spring. After that, quasi The main design parameter is known as spring index, which is the ratio C = D/d. Thus, it was selected the same spring index for all manufactured Ni-Ti SMA springs (C = 6), as summarized in Table 1. SMA helical springs present a nonlinear distribution of shear stress due to phase transformations. However, in the initial linear region of the force (F) vs displacement (y) curve, with small variations in the pitch angle (α), the mechanical behaviour is similar to a conventional linear spring. Thus, it is possible to use a classic mathematical approach 19,20 to calculate the corresponding shear modulus (G) from stiffness (k) for SMA helical springs [18][19][20][21] in the austenitic phase using Eq. (1).
Therefore, from force-displacement curves of superelastic SMA springs, as illustrated in Figure 2, stiffness (k) of the austenite phase is determined in the initial linear region from 10% to 20% of maximum load, before the transformation had taken place 21 .
As previously mentioned, the manufacture process begins with the production of the Ni-Ti SMA material (Ni 50.2 Ti 49.8 , at. %) by a plasma melting process 7 . To manufacture the springs from the Ni-Ti SMA material, it was used an ICC static tensile tests were carried out under three different maximum displacements of 50%, 60% and 70%. A strain rate of 1% min -1 was used during the loading and unloading. Subsequently, tensile tests at four different temperatures (30ºC, 40ºC, 50ºC and 60ºC) were performed only with the SPG-D2.0 spring (Tab. 1) under constant displacement (90%), due to its better mechanical behaviour in comparison with the other springs.
After the mechanical tests, a TESCAN Vega 3 Scanning Electron Microscopy (SEM) was used to examine the fractured surfaces of the Ni-Ti SMA springs. Figure 3 shows the characteristic results obtained from ERT and DSC tests. For the thermal characterization, only the results for the spring SPG-D2.0 are presented, in both the as cast and heat-treated conditions. It was possible to confirm phase transformations in the Ni-Ti SMA springs in both conditions. A typical behaviour characteristic of the formation of the rhombohedral phase (R-phase) during cooling is observed, in both samples. There are many factors that can cause the R-phase formation in Ni-Ti SMA, such as heat treatment after cold work 22 and stress fields due to formation of Ni-rich precipitates 23 . Table 2 summarizes the TTs obtained from ERT and DSC curves (Figure 3). These two techniques yielded different transformation temperatures, which was mainly influenced by the sample state (as cast or HT) and sample dimensions (small sample for DSC and full spring for ERT). In addition, the Ni-Ti SMA materials are highly sensitive to thermomechanical processing and small composition variations 22 . Also, these two methods are based on different physical principles. DSC is a thermal analysis technique in which the heat flow of the material is measured as a function of temperature while ERT is based on changes in electric properties, usually applied to detect transformation temperatures between the martensite and austenite phases 24 .

Thermal characterization
In general, after the heat treatment DSC peaks and ERT curves are more pronounced. According to De Araujo et al 25 , internal stresses tend to increase the TTs of Ni-Ti SMA, which are reduced by the homogenization treatment. This behaviour was observed in heat treated springs, for which the A f temperatures have been reduced. Figure 4 shows the Ni-Ti SMA extension springs manufactured by ICC. The springs present some defects such as burrs, bubbles and superficial roughness, typical of investment casting processes. The springs have matte grey surface, probably due to the reaction between the molten metal and ceramic mould, as pointed by Freitag et al 26 .   The dimensional accuracy was evaluated as the deviation of cast spring dimensions (wire diameter) from original wax model, as shown in Table 3. The maximum dimensional variation (contraction) was approximately 1.7%. Dimensional accuracy in titanium parts manufactured by investment casting is complex due the combination of thermal expansion effects of the coatings and metallic volumetric contraction 27 .

Dimensional and superficial analysis
An axial force applied to a helical springs produce a direct shear force and a torsional moment in the cross section 19,20 . Figure 5 shows a full view of the rupture surface in SEM. Images present fractured surfaces characteristic of torsion, similar to those observed in orthodontic rotary instruments [28][29][30] .
The presence of internal defects appears to be very important in the initiation of the fracture process of the springs. These defects act as points of stress concentration, leaving the spring more susceptible to failure. Notably, there were small voids distributed throughout the fractured surface. SEM analysis of the springs fractured by torsion revealed evidence of rupture along planes perpendicular at 45º to the longitudinal axis, typical behavior of brittle materials 31 .

Tensile tests
Tensile tests were performed to analyse the mechanical behaviour of the cast Ni-Ti SMA helical springs. Each spring specimen was heated to a temperature above A f and cooling below room temperature. Wire diameter is one of the four geometric parameters usually considered for Table 3. Dimensional verification of the spring wire diameter (d). the design of helical springs. Figure 6 shows the effect of variations of wire diameter on the force-displacement responses of the manufactured SMA springs. The increase of only 0.5 mm in the wire diameter can double the force values to produce the same deflection. The maximum force reached was 24N, 48N and 103N for the springs SPG-D1.0. SPG-D1.5 and SPG-D2.0, respectively, for 70% of maximum deflection. According Shahinpoor and Schneider 32 , there are three types of superelastic behavior in SMA work-hardened: superelasticity, linear superelasticity (when martensite is cold worked by about 10%), and nonlinear superelasticity (for which transformation occurs with strain at practically constant stress, presenting narrow hysteresis and small residual strain). Interestingly, the Ni-Ti SMA helical springs manufactured by ICC exhibit a quasi-linear superelasticity, recovering almost all the imposed strains, with narrow stress hysteresis, which is similar to the results of other previous studies 33,34 . Probably, this behavior results from the interaction between the nucleation of martensite in the Ni-Ti matrix phase (austenite) and residual stresses in precipitates during martensitic transformation 35,36 .

Test temperature influence
Isothermal mechanical responses of the Ni-Ti SMA springs manufactured by ICC are shown in Figure 7 for tests at 30, 40, 50 and 60ºC. The springs change mechanical behaviour with temperature increase, showing a linear relationship between maximum force and test temperature. The force rate obtained from maximum force vs temperature linear relationship was of the order of 1.6 N/ o C.
From Figure 7, two considerable features are observed. First, the start point corresponding to the stress-induced martensite region increases with temperature. Full superelasticity was observed under tensile strain only at room temperature (30 o C), but not at 40ºC, 50ºC and 60ºC, due to the presence of higher levels of residual strain (10%). The increase of stress levels caused by the increase of applied forces at temperatures higher than 30ºC might have caused higher residual strains, due to possible plastic deformation of the material. Further, during transformation, the deformation is highly non-homogeneous, which might result in some voids of SMA which were not transformed from austenite into stress-induced martensite or vice-versa. These conclusions were based on previous characterization studies of shape memory alloys 37 .

Stiffness (k) and shear modulus (G)
Although the SMA springs have nonlinear characteristics, it is possible to use the austenite stiffness to define mechanical aspects of the spring. Table 4 presents the measured stiffness (as defined in Fig. 2) and estimated shear modulus (Eq. 1) for the heat-treated Ni-Ti SMA springs. The obtained values are in the range found in the literature (25 ~ 40GPa) for Ni-Ti SMA in austenitic phase 17,18 .

Conclusions
This paper investigated the thermomechanical characterization of Ni-Ti shape memory alloy helical springs manufactured by centrifugal investment casting. The main conclusions that can be outlined from the obtained results are: Ni-Ti SMA helical extension springs were successfully manufactured using investment casting. It was found that transformation temperatures decreased after heat treatment, in relation to as cast springs. In general, the reverse transformation temperatures ranging from -38.6 ℃ to 49.4 ℃ for as cast springs and -4.7ºC to 30.6ºC for heat treated springs.
At room temperature, the Ni-Ti SMA springs manufactured by investment casting exhibit a quasi-linear superelasticity behaviour (without force plateau) with residual strain around 1%. The maximum displacement supported without rupture were 70% for SPG-D1.0, SPG-D1.5, SPG-D2.0. The wire diameter affects significantly mechanical behaviour of the springs and an increase of only 0.5 mm in the wire diameter can double the force values to produce the same deformation.
The estimated austenitic shear modulus of the Ni-Ti SMA was between 25 and 35GPa, in agreement with literature . The maximum force in the Ni-Ti SMA springs (2 mm of wire diameter) increases linearly with temperature, with a force rate of the order of 1,6 N/ o C.

Acknowledgments
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