Dynamic mechanical damping analysis of up/step-quenched Cu-Zn-Sn-based shape memory alloys

The effect of thermal quenching procedures on the damping properties of Cu-Zn-Sn-based SMAs is reported. Three compositions of Cu-Zn-Sn-based SMAs designated A (Cu-15.6Zn-12.1Sn), B (Cu-26.1Zn-9.3Sn), and C (Cu-29.6Zn-8.9Sn) samples produced by the casting process were subjected to direct quenching, up-quenching, and step-quenching treatments. The microstructure of the samples was examined using the backscattered electron microscope with fixtures for energy-dispersive spectroscopy analysis. The damping properties were assessed on a dynamic mechanical analyzer and presented in terms of tan delta. The microstructures of Cu-Zn-Sn-based SMAs consist of γ-Cu5Zn8 and Cu4 major phases containing some black dot precipitation and a small amount of white circular precipitates in the parent phase. For the A alloys, the step-quenched samples exhibited the highest damping capacity with peak internal friction of 0.041 at 37 °C, which is greater than 0.028 at 37 °C and 0.26 at 25 °C obtained for the up-quenched and direct-quenched samples respectively. The step-quenched B alloys show the highest damping capacity with peak internal friction of 0.104 at 227 °C, which is far greater than 0.053 at 23 °C and 0.034 at 35 °C obtained for the up-quenched and direct-quenched samples respectively. For the C alloys, the up-quenched samples show the highest damping capacity with peak internal friction of 0.053 at 235 °C, which is greater than the peak values of 0.037 at 23 8 °C obtained for the step-quenched samples. Direct-quenched samples gave the lowest damping capacity with a peak value of 0.027 at 235 °C. In general, step-quenching treatment effectively improved the damping properties of Cu-Zn-Sn-based SMAs.


Introduction
Shape memory alloys are technically one of the most intriguing advance engineering materials to select for hightech applications.They are characterized by two distinct functional features that distinguish them from conventional metal alloys: (i) shape memory effect (SME), which enables them to regain the original geometry after deformation upon heating; and (ii) superelasticity (SE) or pseudoelasticity, which is the ability to recover a significant strain (up to 8%) during loading and unloading [1].SMAs are also known to exhibit strong damping effect, good mechanical strength and corrosion resistance properties [2][3][4].Based on their interesting functional, physical, and mechanical properties, the commercial utilization of SMAs has been progressively increased (in automotive, biomedical, aerospace, marine and military applications) as the global market of SMAs is projected to reach 33.89 billion US dollars by the year 2027 [5].
The damping capacity of materials is considered a critical factor in materials selection, especially in structural applications where dynamic loads are inevitable [6,7].Damping capacity is a material property that measures the capacity of the material to absorb elastic strain energy induced by mechanical vibration [8,9].Damping may occur as structural damping or due to internal friction in the material [10].Structural damping is based on energy absorption and dissipation while damping due to internal friction is governed by the mechanism of interaction of dislocations with variant interfaces in the materials microstructure [6,10].In shape memory alloys (SMAs), damping capacity is related to the changes that occur in their microstructure during martensitic transformation [11].SMAs have been reported to be very effective in energy dissipation applications due to their high damping capacity arising from movement between the martensite variant interfaces and the parent martensite habit planes [12].This justifies the recent utilization of SMAs in applications such as structural connectors, brace frames, and dampers where undesirable noise and vibrations need to be passively attenuated [13].NiTi and Cu-based SMAs have been prominent in applications requiring vibration control [14], but the Cu-based SMAs have drawn more research attention because of their relatively low cost, ease of fabrication, and superior electrical and thermal conductivity [15].Among Cu-Zn-Al, Cu-Zn-Ni, and Cu-Zn-Sn SMAs which are most prominent under the Cu-Zn system, the damping properties of Cu-Zn-Sn SMAs have not been well reported leading to paucity of scientific data needed to design and expand their commercial utilization for structural vibration control applications [16].
Damping properties are largely sensitive to SMA composition, microstructure, and defect concentration like vacancies and dislocations [17].These microstructural characteristics can be altered significantly by the application of certain thermal treatment procedures, suggesting that heat treatment have effect on damping properties [18].Several studies have been carried out on the effect of heat treatment on the damping properties of Cu-based SMAs, among these works include Alaneme et al [19], Hsu et al [20], Li et al [21], and Gang-Ling et al [22].Alaneme et al [19] recently studied the mechanical and damping behavior of Cu-Zn-Sn SMA modified with Ni.The microstructure of the un-modified Cu-Zn-Sn SMA subjected to homogenization treatment at 600 °C was characterized by several binary intermetallic phases (Cu 3 Zn, Cu 6 Sn 5 , and CuSn).The study observed that the Ni 3 Sn 2 phase was only found in the samples that were modified with Ni.The damping capacity of the alloy samples was observed to increase with Ni content reaching a peak value of 0.031 at 4 wt%Ni.Hsu et al [20] studied the influence of aging treatment on the microstructure evolution and shape memory properties of Cu-Zn-Sn SMAs.It is observed that aging heat treatment conducted above 285 °C for 5 min leads to a drastic reduction in the shape memory effect (SME) of the alloy due to precipitation of γ(Cu 5 Zn 8 ) phase.Li et al [21] studied the damping behaviour of Cu-based SMA subjected to aging treatment and observed that ageing leads to the formation of bainitic structures, which influences the damping characteristics of the alloy.The study upheld that the martensitic transformation and damping capacity of Cu-Al-Mn alloy decrease with the increase in the volume fraction of bainite which is a function of the thermal cycle.Gang-Ling et al [22] studied the damping behaviour of Cu-Al-Mn SMA at ambient temperature.The study observed that the damping characteristics of the Cu-based SMA increase with solution treatment temperature to a peak value at 825 °C, beyond which the damping capacity begins to decline.
The adoption of heat treatment procedures has been projected to be one of the best options for improving the properties of Cu-based SMAs [23][24][25][26][27][28].The up-quenching and step-quenching treatment procedures have a significant impact on the vacancy concentration, dislocation, and precipitation behavior of Cu-based SMAs and these factors have a strong influence on their damping properties [29][30][31][32].Cai et al [33] reported the influence of direct-quenching, up-quenching, and step-quenching treatments on the vacancy behavior and damping properties of Cu-Al-Mn SMA modified with Ni.It is observed that the mobility of martensite boundaries in the direct-quenched samples is pinned by the large concentration of vacancies while the up/step-quenched samples had less concentration of vacancies which resulted in better interface mobility and improvement in their functional properties (damping and shape memory capacity).Step-quenched samples had better damping properties compared to the up-quenched samples due to the greater reduction of vacancy migration imposed by the Ni quaternary alloying element in the up-quenched samples.Yang et al [29] reported the effect of up/stepquenching treatment on the shape memory properties of Cu-Al-Mn SMA.It is observed that the heating rate during the treatment process is the main factor with determines whether the up/step-quenched samples can improve shape memory properties by suppressing the stabilization of martensite.The step-quenched and upquenched samples have fewer quenched-in vacancies when compared to the direct-quenched samples.In a related study, Yang et al [34] suggested that reducing vacancy concentration using up or step-quenching treatment can prevent martensitic stabilization.The study noted that the occurrence of martensitic stabilization is closely related to the behaviors of vacancies, such as kinetic stabilization and pinning of moving interfaces by vacancies.These studies have shown that up-quenching and step-quenching treatments significantly affect the functional characteristics such as the damping properties of Cu-based SMAs.
Cu-Zn-Sn-based SMAs are continually being used in numerous industrial applications such as in heat exchanger tubing [35] as well as hydraulic fittings, connector pipes, valves and pumps [36].The majority of these areas of applications expose them to vibrations and mechanical shocks.For instance, a connector pipe in hydraulic coupling systems incurs hydraulic shock each time a submersible pump is turned-on [37].Therefore, the study of the damping behaviour of Cu-Zn-Sn based alloys is necessary to evaluate their reliability in service.No report has explored the effect of up-quenching and step-quenching treatments on the damping behavior of Cu-Zn-Sn-based SMAs which is the drive of our investigation.The study on the best quenching thermal procedure and design of Cu-Zn-Sn-based SMAs composition for optimum damping properties remains an inadequately explored area of research.The aim of this study is therefore to investigate the influence of heat treatment on the damping characteristics of Cu-Zn-Sn-Fe SMAs.

Materials
Cu-Zn-Sn-Fe SMAs were produced using 99.9% pure copper, 99.8% pure zinc, 99.8% pure tin, and 99.2% pure iron.The Cu-Zn-Sn-Fe alloy ingots were produced by melting the raw materials in a crucible furnace and casting them into split molds made of stainless steel.Three categories of the Cu-Zn-Sn-based alloys were produced and labeled A, B, and C samples.The chemical composition (wt.%) of the alloys were 15.64 Zn, 12.12 Sn, 1.05 Fe, and balance with Cu for sample A; 26.11 Zn, 9.34 Sn, 0.82 Fe, and balance with Cu for sample B; and 29.55 Zn, 8.92 Sn, 0.70 Fe, and balance with Cu for sample C. The alloys were water quenched after being homogenized for 5 h at 550 °C in a heat treatment furnace.This operation is necessary to reduce the amount of structural and chemical imperfections in the casting.Part of the samples were heated to a solution treatment temperature of 550 °C for 5 h, and then quenched in water at ambient temperature and these samples were referred to as directquenched (DQ) samples.Some samples referred to the step-quenched (SQ) samples were subjected to quenching treatment in water at 100 °C for 15 min before quenching in water at ambient temperature.The upquenched (UQ) samples were obtained by heating some of the DQ samples in water at 100 °C for 15 min before quenching in water at ambient temperature.The thermal quenching treatments for the DQ, UQ, and SQ samples are presented in table 1 following procedures stipulated in Anaele et al [38], and the schematic representation of the various treatments is shown in figure 1.

Microstructural analysis
A succession of grinding, polishing, and etching processes was used to prepare the alloy samples to a mirror surface following the procedures stipulated in Anaele et al [38].The polished samples were etched by rubbing them for 20 s in a solution containing 95 ml ethanol, 10 ml HCl, and 5 g ferric chloride.After etching, the microstructural characterization was carried out using the HeliosG4-FIB SEM with fixtures for energy dispersive  spectroscopy (EDS), and the micrographs were taken in backscattered electron (BSE) mode.The EDS measurements were used to determine the compositions of the alloys.The area fraction of the phases and grain size were analyzed using IMAGE-J program.

Damping test
The damping behavior of the Cu-Zn-Sn-based SMAs with respect to temperature was assessed on a NETZSCH 242 model dynamic mechanical analyzer (DMA).Rectangular-shaped samples with dimensions of 40 mm × 5 mm × 2 mm were subjected to a three-point bending deformation mode by the ASTME756-05 [39] standard.The damping test conditions were set to strain amplitude (ε) of 10 μm, vibration frequencies (f) of 1 Hz and 2 Hz, temperature range (T) from 25 to 250 °C, and heating rate (Ʈ) of 8 K min −1 .The DMA results showed the dependence of storage modulus (E′) and the loss modulus (E″) with temperature [11].Storage modulus (E′) relates to the elastic responses of materials and determines the capacity of a material to absorb and store mechanical energy generated during periodic deformation or vibrations [40].E′ is an important consideration when designing against structural instability such as the springback effect which involves dimensional alteration caused by residual stresses [41].The loss modulus (E″) is proportional to the mechanical energy dissipated in the form of heat under static and dynamic loading conditions [9].The ratio of energy dissipated by heat per cycle to mechanical energy absorbed or stored in the material subjected to stress is known as the damping capacity (tan δ) of the material [42].Damping capacity (tan δ) in terms of the energy loss in the material due to viscous friction is determined mathematically using the relation in equation (1) [43]: The damping capacity of a material can thus be determined precisely in terms of the loss tangent (Tan δ) signal recorded over a period of time [44].Tan δ attains peak as a result of the internal friction associated with martensitic transformations in SMAs [45].

Microstructural characterization
The SEM micrographs of Cu-Zn-Sn-based alloys subjected to various heat treatments are presented in figure 2. The IMAGE-J software was used to determine the grain size and area fraction of the precipitate phases and the values were reported at 95% confidence interval.The XRD analysis was carried out on the Cu-Zn-Sn-based alloys to determine the composition of the phases.The microstructures comprise of two major phases.The light phase is found to be γ-Cu 5 Zn 8 , while the dark phase is Cu 4 .Some black particles and a small amount of white circular precipitates were dispersed in the parent phase.The BSE image of the up-quenched A alloy is presented in figure 2(a).The microstructure is dendritic and contains a 1.92 ± 0.03% area fraction of precipitates dispersed in the parent Cu 4 and γ-Cu 5 Zn 8 phases.The microstructure of the step-quenched A samples is presented in figure 2(b).The microstructure is similar to those of the up-quenched A alloy in terms of phase composition but the grains structures are dendritic and lamellar in morphology.The step-quenched A alloy samples had an average grain size of 17.06 ±1.13 μm which is less than 24.08 1.98  μm obtained for the up-quenched A samples.The area fraction of the precipitates was determined to be 1.22 ± 0.03% which is observed to be less than those of the up-quenched A samples.The micrograph of the up-quenched B alloy samples is presented in figure 2(c).The microstructure is characterized by Cu 4 and γ-Cu 5 Zn 8 major phases containing some black and white precipitates.The morphology of the grains is globular and has an average grain size of 66.94 2.46  μm. Figure 2(d) presents the micrograph of the step-quenched samples of B alloy.The microstructure is similar to those of the up-quenched B alloy sample except that the grains are elongated and contain some fine dendrites.The average grain size is determined to be 34.20 2.08  μm which is smaller compared to the grain size of the up-quenched B alloy samples.Also, the amount of precipitates in the up-quenched B alloys is 2.81 ± 0.05% which is greater than the 1.62 ± 0.04% obtained for the step-quenched B samples.The BSE micrograph of the up-quenched C alloy is presented in figure 2(e).The microstructures consist of Cu 4 and γ-Cu 5 Zn 8 main phase containing some precipitate.The grain structures are dendritic with an average grain size of 16.78 1.74   μm.The micrograph of the step-quenched C alloy is presented in figure 2(f).The microstructure exhibits similar characteristics to those of the up-quenched alloy C samples.However, the average grain size is determined to be 18.15 1.25  μm which is higher than the grain size of the up-quenched samples.Additionally, it is found that the area fraction of the precipitate phases is 0.83 ± 0.02%, which is lower than the 1.34 ± 0.03% obtained for the up-quenched C samples.The microstructures are consistent when compared to the alloys with similar compositions reported by Alaneme et al [19], Anaele et al [38], and Celik et al [46].For all the alloy categories (A, B, and C) investigated, the up-quenched samples yielded more area fraction of the precipitate phases than the step-quenched samples.The results suggest that step-quenching treatment tends to suppress the precipitation of a second phase in the parent matrix whereas up-quenching treatment induces the formation of precipitates in the microstructure.This observation is in line with the result presented by Stosic et al [25] where the precipitation behavior of Cu-Zn-Al SMA is reported to be sensitive to the type of quenching treatment as well as the alloy composition.Figures 2(g) and (h) present the microstructures of the direct-quenched A and B alloy respectively.The microstructure of the direct-quenched A alloy (figure 2(g)) is composed of two distinct phases which are Cu4 (dark) and γ-Cu5Zn8 (bright) phases with elongated and globular grain morphology.A similar result is obtained for the direct-quenched B alloy (figure 2(h)) except that the white and black precipitates which represent the Sn-rich and Fe-rich phases are more pronounced.

Effect of quenching treatments on the storage modulus, loss modulus, and damping behavior of alloy a samples
The effect of direct-quenching, up-quenching, and step-quenching treatments on the storage modulus of alloy A sample is presented in figure 3. It is observed that the storage moduli of the samples of A alloy subjected to various quenching procedures at 1 Hz (figure 3(a)) and 2 Hz (figure 3(b)) over a temperature range of 23 to 250 °C, decrease continuously with increase in temperature.The step-quenched alloy A sample exhibits the highest storage modulus of 172 GPa at 57 °C whereas the storage modulus of the up-quenched alloy A sample attains a peak value of 112 GPa at 30 °C.The direct-quenched alloy A sample had the least storage modulus (102 GPa at 55 °C).The SEM micrographs presented in figures 2(b), (d), and (f) showed that the step-quenched samples are characterized by fine dendritic structures with larger grain boundary areas and consequently higher interfacial density which enhanced their capability to store energy [47].This accounts why the modulus properties of the step-quenched samples are considerably greater than the up-quenched and direct-quenched samples.The variation in damping frequency in the range of 1 to 2 Hz had no significant effect on the storage modulus of the alloy samples.
The effect of quenching treatment procedures on the loss modulus of alloy A samples at 1 Hz and 2 Hz is presented in figures 4(a) and (b) respectively.It is observed that the loss modulus of the alloy samples exhibits an intermittent decrease in the temperature range of 23 to 170 °C, but beyond this temperature range, there is a regime of sporadic increase in the loss modulus with temperature.Step-quenched samples exhibited a maximum loss modulus value of 6.99 GPa at 37 °C which is by a great margin higher than the peak loss modulus value of 3.10 GPa at 37 °C obtained for the up-quenched samples.The direct-quenched samples had the least loss modulus with two peak values of 2.63 GPa and 3.05 GPa at 41 °C and 239 °C respectively.There is a marginal difference in the loss modulus of the up-quenched and direct-quenched samples for the test temperature range of 23 to 250 °C and frequency range of 1 to 2 Hz.The large difference in the modulus for stepquenched alloys when compared to those of the up-quenched and direct-quenched samples showed that each quenching procedure had diverse effect on the microstructural characteristics which in turn affect their modulus properties.Variation in the damping frequency in the range of 1 to 2 Hz had no significant effect on the loss modulus of A alloy samples.
Figures 5(a) and (b) show the influence of direct-quenching, up-quenching, and step-quenching treatments on the damping capacity of alloy A samples at 1 Hz and 2 Hz frequencies respectively.It is observed from figure 5(a) that the step-quenched A samples exhibited the highest damping capacity with three regimes of a peak internal friction of 0.041, 0.037, and 0.038 at 37 °C, 130 °C, and 245 °C respectively.Peak internal friction of 0.028, 0.029, and 0.030 at 37 °C, 129 °C, and 245 °C respectively, were obtained for the up-quenched samples.The direct-quenched samples exhibited a peak internal friction of 0.026 at 25 °C and 41 °C and 0.031 at 225 °C and 245 °C respectively.There is a marginal difference in the damping capacity of the up-quenched and direct-quenched samples at a test frequency of Stepquenched samples show the highest damping capacity with peak internal friction of 0.040 and 0.038 at 31 °C and 245 °C respectively, which is far greater than those of the up-quenched and direct-quenched samples for the test temperature range of 23 to 250 °C.These values are slightly less when compared to 0.041 at 37 °C obtained at 1 Hz frequency.Peak internal friction of 0.027 (which is lower than 0.029 at 1 Hz) is obtained at 129 °C for the upquenched A alloy samples.Similarly, the direct-quenched samples exhibited a peak internal friction of 0.028 at 225 °C which is lower than 0.031 at 225 °C obtained at 1 Hz frequency.The results suggest that the damping characteristics at a frequency of 1 Hz are marginally higher than those obtained at a frequency of 2 Hz with the variance becoming pronounced with increasing damping temperature.This report agrees with the observations of Alaneme et al [9] where it is stated that more energy is dissipated at lower frequencies due to the characteristic irregular reciprocating motion prevalent at low damping frequency.This accounts for the marginal decrease in damping capacity as the frequency increased from 1 Hz to 2 Hz.

Effect of up/step quenching treatments on damping mechanisms
It has been reported in the literature that the high damping capacity of Cu-based shape memory alloys is attributed to their ability to dissipate energy emanating from the movement of variant interfaces [48,49].The high damping capacity associated with the step-quenched samples of Cu-Zn-Sn-based SMAs may be linked to the marginal pinning effect of the precipitate phases and greater mobility of variant interfaces leading to high internal friction.The analytical results of the BSE images (figure 2) showed that the up-quenched samples had a greater volume fraction of the precipitate phases and larger grain structures than the step-quenched alloys.These precipitates pin down the movement of dislocations and variant interfaces thereby leading to relaxation and consequent reduction in the internal friction as well as the damping capacity [9,30,40,50].Also, Cu-based SMAs with smaller grain sizes have larger grain boundary areas and consequently higher interfacial density  which in turn results in higher damping capacity [47,51].These explanations confirmed the reason for better damping properties realized in the step-quenched samples when compared to the up-quenched and directquenched samples.The up-quenched samples exhibited better damping properties compared to the directquenched samples.This result agrees with the observations of Cai et al [33], where it is explained that the mobility of variant interface boundaries in the direct-quenched samples is pinned by the large concentration of vacancies while the up/step-quenched samples had less concentration of quenched-in vacancies which result to better interface mobility and improvement in their damping properties.
The effect of temperature on the damping characteristics of Cu-Zn-Sn-based SMAs is presented in figure 5.The damping properties of A alloy are observed to exhibit two regimes of thermo-mechanical response, namely: negative response regime and positive response regime.The negative response regime occurs in the temperature range of 23 °C to 170 °C, during which the damping capacity tends to decrease.In this regime, damping occurs by the mechanism of dislocation movement with interfaces.These interface movements tend to decrease due to heavy dislocation network and pinning of the interfaces leading to a decrease in damping capacity [40].The positive response regime occurs at higher temperatures (170 to 250 °C), during which the damping capacity is observed to increase with temperature (figure 5).At higher temperatures, dislocations gain kinetic energy creating internal friction as a result of the stress-induced movement across interfaces.Damping occurs in this regime by the mechanism of dislocation climb and thermally activated structural sliding friction leading to energy dissipation [48].Ivanić et al [42] explained that the interfacial bonding strength between the interfaces weakens and thermally activated dislocations are formed by sliding friction leading to energy dissipation and an increase in damping capacity due to rising internal friction and greater interface mobility.This result agrees with the observations of Alaneme et al [9], Li et al [40], and Ivanic et al [42] where it is confirmed that the damping behavior of Cu-based SMAs is sensitive to the thermal conditions of the alloys.

Effect of varied compositions on damping properties of Cu-Zn-Sn-based alloy
The damping results of B and C alloy samples are presented in figures 6(a) and (b) respectively.The results for alloy B (figure 6(a)) follow a similar trend of positive and negative thermo-dynamic response with those of A alloy samples presented in figure 5, with the exception of step-quenched B samples.The damping behaviour of step-quenched B alloys is characterized by the dominance of dislocation glide mechanism and marginal pinning effect which accounts for the occurrence of positive thermo-mechanical response regime through the temperature range of 23 to 250 °C.The microstructure of the step-quenched B alloy (figure 2(d)) supports this result since it shows relatively lesser area fraction of the precipitate phases which offer lesser impedance to dislocation glide leading to greater internal friction.Consequently, the step-quenched B alloys had the highest damping capacity with peak internal friction of 0.104 at 227 °C, which is far greater than a peak value of 0.053 at 23 °C and 0.034 at 35 °C obtained for the up-quenched and direct-quenched samples respectively.Step/up quenching treatments significantly improved the damping properties of B alloys when compared to the directquenched result.The results for alloy C are presented in figure 6(b).The damping behavior of alloy C is quite different from those of the A and B alloy samples.The damping behaviour of C alloy showed no distinct negative response regime but rather characterized by irregular thermo-mechanical response at lower temperatures due to the interaction of dislocation network and the precipitate phases [30].At higher temperatures (200 C), the internal friction tends to increase with thermally activated interface mobility prevalent at high temperatures as  damping occur by dislocation glide mechanism [48].The up-quenched C alloys show the highest damping capacity with peak internal friction of 0.053 at 238 °C, which is greater than the peak values of 0.037 at 24 5 C and 0.027 at 235 °C obtained for the step-quenched and direct-quenched samples respectively.The higher damping capacity obtained for the up-quenched C alloy samples relative to the step-quenched samples may be linked to their finer grain structures and higher Zn concentration.There is a significant variation in the damping properties of A, B, and C alloys.B alloy samples exhibited far better damping characteristics when compared to A and C alloys for the test temperature range of 23 to 250 °C and at a test frequency of 1 Hz.The high damping capacity of the step-quenched A, B, and C alloy samples as well as the up-quenched C alloys observed in the present study may be linked to their greater mobility of variant interfaces leading to high internal friction [50].Generally, among the three heat treatment processes carried out on A, B, and, C alloy samples, direct-quenching treatment gave the lowest damping capacity for the test temperature range of 23 to 250 °C and at a test frequency of 1 to 2 Hz.The results also suggest that step-quenching treatments are effective procedures for tailoring the damping properties of Cu-Zn-Sn-based SMAs depending on the alloy compositional design.It is therefore concluded that the damping properties of Cu-Zn-Sn-based SMAs are sensitive to their composition and the type of quenching treatment.This result agrees with the observations of Cai et al [33] where it is confirmed that stepquenching treatments are most effective for improving the damping properties of Cu-based SMA.Table 2 compares the results of the damping characteristics of Cu-Zn-Sn-based SMAs in the present study with those of other Cu-based SMAs in the literature.The results showed that the step-quenched B alloys are the most appropriate alloy design and thermal treatment for utilization in various damping applications such as structural connectors, brace frames, hydraulic pumps, and passive dampers.This assertion is based on the damping capacity of the step-quenched B alloy (0.104 at test frequency of 1 Hz) which is superior than most Cu-based SMAs reported in literature that have been recommended for commercialization and applications in hydraulic couplings, connector pipes in pump systems and structural connectors (table 2).The findings from this study showed that Cu-Zn-Sn-Fe SMAs had higher damping capacity than that of quaternary Cu-Al-Ni-Be (0.072 ± 0.004) and Cu-Al-Ni-Ga (0.042 ± 0.002) SMA systems [49], and ternary Cu-Al-Mn (0.09) SMAs [21].

Conclusion
The effect of thermal quenching procedures on the damping properties of Cu-Zn-Sn-based SMAs of varied compositions is reported.The study arrived at the following conclusions: i.The microstructures of Cu-Zn-Sn-based SMAs consist of γ-Cu 5 Zn 8 and Cu 4 major phases containing some black dot precipitation and a small amount of white circular precipitates in the parent phase.
ii.There is a significant variation in the damping properties of A, B, and C alloys of variant compositions of Cu-Zn-Sn-Fe SMAs.
iii.The damping properties of Cu-Zn-Sn-based SMAs are sensitive to their composition and type of quenching treatment.
iv. B alloy samples exhibited better damping characteristics when compared to A and C alloys for the test temperature range of 23 to 250 °C and at a test frequency of 1 to 2 Hz.v.
Step-quenching treatment is effective for improving the damping properties of Cu-Zn-Sn-based SMA.The direct-quenched samples gave the lowest damping capacity for the test temperature range of 23 to 250 °C and at a test frequency of 1 to 2 Hz.vi.The step-quenched B alloys are the most appropriate alloy design and thermal treatment for utilization in various damping applications such as structural connectors, brace frames, hydraulic pumps, and passive dampers.

Figure 2 .
Figure 2. SEM micrographs of the: (a) up-quenched A alloy (b) step-quenched A alloy (c) up-quenched B alloy (d) step-quenched B alloy (e) up-quenched C alloy (f) step-quenched C alloy (g) direct-quenched A alloy (h) direct-quenched B alloy.

Figure 3 .
Figure 3.Effect of quenching treatments on E¢ of alloy A samples at frequencies of (a) 1 Hz (b) 2 Hz.

Figure 4 .
Figure 4. Effect of quenching treatments on E ¢¢ of alloy A samples at frequencies of (a) 1 Hz (b) 2 Hz.

Figure 5 .
Figure 5.Effect of quenching treatments on the damping capacity of alloy A samples at frequencies of (a) 1 Hz and (b) 2 Hz.

Figure 6 .
Figure 6.Damping properties at various quenching treatments at 1 Hz for (a) B alloy samples and (b) C alloy samples.

Table 1 .
Various categories of heat treatments conducted on the alloy samples.
DQ samples were heated in boiling water at 100 °C for 15 min before being quenched in water at room temperature.Solution treated at 550 °C for 5 h, quenched in boiling water at 100 °C for 15 min before being quenched in water at room temperature.

Table 2 .
Effect of heat treatments on damping properties of some Cu-based SMAs (peak values within 25 °C-250 °C were reported at frequency of 1 Hz).