Dynamic and creep and recovery performance of Fe 3 O 4 nanoparticle and carbonyl iron microparticle water-based magnetorheological fluid

Abstract

This study investigates dynamic mechanical properties and creep and recovery behaviors of disc-shaped magnetic Fe₃O₄ nanoparticles with carbonyl iron (CI) flake-shaped microparticles in water-based MR fluid. The experimental study is performed using a parallel plate rheometer. Dynamic performance and creep and recovery behaviors help understand deformation mechanism for its practical applications in MR devices like seismic vibration control, active dampers, earthquake dampers, etc., under applied strain, and stress levels. The oscillatory experiment reveals a transition from viscoelastic-to-viscous behavior at the critical strain of 0.1%. The storage modulus $(G^{'})$ of CI/Fe₃O₄ MR fluid showed a stable plateau region over the small strain area and storage modulus $(G^{'})$ independent of strain amplitude. The frequency experiment demonstrated that storage moduli $(G^{'})$ exhibit elastic response and stable plateau region over the complete external frequency range, suggesting the distinguished solid-like behavior of the MR fluid. Creep and recovery experiments showed that fluid acts as a linear viscoelastic material at lower stress levels. As the stress levels increase, the contribution of retardation strain and viscous strain decreases, and it acts like nonlinear viscoelastic material. In summary, this work is expected to obtain MR fluid results for application in MR devices under applied strain, frequencies, and constant stress levels.

Keywords

Magnetorheological fluid storage modulus magnetic field strain dynamic efficiency creep and recovery creep compliance

1. Introduction

Magnetorheological fluids (MRFs) are a type of smart materials whose properties vary rapidly and reversibly under external stimuli (Ginder, 1998). The MR fluid comprises magnetic particles of micron-sized carbonyl iron (CI) and metal oxides dispersed into a non-magnetic carrier medium. Under the applied external magnetic field, the magnetic particles are aggregated alongside the direction of a magnetic field to form a chain structure because of the magnetic dipole-dipole interaction among the magnetic particles (Choi et al., 2020; Li et al., 2004). The formed chain structure increases the viscosity of the fluid, and thus MR fluid changes rapidly from a liquid-like to a solid-like state in milliseconds (Biao et al., 2014; Ghaffari et al., 2014; Maurya and Sarkar, 2020a). Furthermore, water-based MR fluid has a 5°C–90°C working temperature range beyond this temperature; water evaporation occurs (Jolly et al., 1999). MRF-240BS is a standard water-based MR fluid prepared by LORD Corporation, whose operating temperature range is 0°C–70°C. So water-based MR fluids have numerous applications for controlling the temperature of devices. Water-based MR fluids have a fast response, ease of control, good dispersal of fine abrasives, low cost, lower environmental pollution, and excellent cooling characteristics, improving polishing efficiency (Dorosti et al., 2019).

The MR effect of MR fluids is described as the reversible process that the magnetic field can rapidly and easily control their properties. Based on these reversible characteristics and rapid responsiveness to an external magnetic field water-based MR fluid has attracted substantial interest in tunable vibration absorbers. It is noted that MR fluids devices often work in various operating modes under the magnetic field, where MR fluids are subjected to instantaneous strain, vibration frequency, shear stress levels, and loads. For example, dynamic mechanical performance and creep and recovery properties are the critical estimation parameter for devices and structural elements which are subjected under vibration frequency and constant load, respectively. Therefore, the dynamic mechanical performance and creep and recovery properties measurements are very useful for some engineering applications. Some engineering applications of MR fluids in such conditions are car suspension, shock absorbers in buses and motorcycles, seismic vibration control which will operate under the resonance frequency of the building and bridges by absorbing external impacts, shock waves, and oscillations that can cause harm, within the structure (Choi et al., 2020; Dyke et al., 1996), the MR dampers can be used in a prosthetic knee to give fast shock absorbing and make the user feel more natural feet under axial force (Ravishankar and Mahale, 2015). However, the advancement in MR fluids and MR devices is essential to the understanding of MR fluids response under such working modes and conditions. The water-based MR fluid behaviors in such modes and conditions have not been deliberated widely and are not well understand. Furthermore, analysis of creep and recovery behaviors of water-based MR fluids is rarely available, which is extremely essential for such engineering applications.

Creep is a time-dependent mechanical performance of materials that helps to understand their deformation mechanism of MR fluid under a constant applied load. Creep compliance and the ratio of elastic strain are the important estimation criterion for structure elements observed at constant stress levels (Xu et al., 2012). Under oscillatory sweep mode, storage modulus $(G^{'})$ showed a plateau region over the small strain area $γ \leq γ_{crt}$ and both $G^{'}$ and $G^{″}$ independent of strain rate. At a high strain rate, $γ \geq γ_{crt}$ both $G^{'}$ and $G^{″}$ decrease with an increment in strain rate. Under frequency sweep mode, the storage moduli $(G^{'})$ of the MR fluid was exhibited an elastic response and an almost stable plateau area over the whole frequency test range. The viscoelasticity of MR fluid depends on an applied strain rate and magnetic field (Li et al., 2002). Creep and recovery experiments showed that at lower stress, MR fluid acts as linear viscoelastic materials. As the stress levels increase, the contribution of retardation and viscous strains decreases, and MR fluid acts like nonlinear viscoelastic materials. The instantaneous creep strain decreases sharply, and elastic recovery strain increases with the increasing magnetic field.

This study performed using disc-shaped (iron oxide) nanoparticles as a supplement with micron-sized flake-shaped CI particles and suspended in water. The Fe₃O₄ nanoparticles improved the MR fluid performances as the Fe₃O₄ nanoparticles packed the voids among the micron-sized CI particles and toughened the particle-particle chain structure (Maurya and Sarkar, 2020b). The researchers with nanoparticles least analyzed CI and water-based MR fluid while it has better MR performances than hydrocarbon-based MR fluid under similar working conditions (Cheng et al., 2008). The dynamic experiments were performed under oscillatory and frequency mode to understand the mechanical performance of MR fluid at external strain and angular frequency, respectively, in the off-state and on-state of the magnetic field. Then, the creep and recovery performance of the fluid is investigated and analyzed to understand the viscoelastic properties at different steady stress levels and the magnetic field. The viscoelastic properties are directly correlated to applied constant stress levels and magnetic fields (Li et al., 2002). Based on the above experiments, we characterized the MR fluid to use in various temperature-controlled vibration absorber devices where MR fluid is subjected to instantaneous strain, vibration frequency, and constant load.

2. Experiments and methods

2.1. Materials

MR fluid was prepared with CI microparticles 65 wt% and iron (II, III) oxide (Fe₃O₄) nanoparticles 1 wt% by dispersing in Millipore water. MR suspension mixture was stirred 3 h continuously at 400 rpm rotating speed using a mechanical stirrer at room temperature. Magnetic CI particle has a flake shape with 6–10 µm (SEM) average particle size. The flake-shape CI particles have an enhanced rheological response and settling stability than the spherical shape CI particle (Upadhyay et al., 2013). Iron oxide particles have disc-shaped with an average particle size of 50–100 nm (SEM). CI and iron oxide bought from Sigma Aldrich (Germany) with the 7.86 g/mL density at 25°C, 55.85 molecular weight, with 97% purity and 4.8–5.1 g/mL density at 25°C, 231.53 molecular weight, with 97% purity, 20–50 m²/g surface area, respectively. Both CI particles and iron oxide (Fe₃O₄) particles were applied with no additional cleansing and chemical dealing. Note that 1 wt% of iron oxide concentration was taken because more than 1 wt% of iron oxide would not much enhance the on-state magnetorheological response (Maurya and Sarkar, 2020b).

2.2. Experimental setup and measurements

The rheological response, dynamic mechanical properties, and creep and recovery performances of MR fluid were studied using a commercial parallel plate-plate (PP20, Anton Paar Co., Austria) rheometer (Physica MCR 102, Anton Paar Co., Austria) equipped with the magnetorheological module, as presented in Figure 1(a) and (b). The parallel plate measuring tool system has maintained 0.5 mm gap thickness for all the experiments between two plates with a 20 mm rotating head diameter. Since the volume of MR fluids sample controlled for each experiment was 0.25πd²h = 0.25π × 20^2 × 0.5 = 0.157 mL. During the experiment process, MR fluids sample was laid at the center of the base plate in the gap, and the magnetic field between the base plate and rotating plate was generated by the coil fixed under the bottom plate of the rheometer, as shown in the schematic diagram of MR shell in Figure 1(b). The magnetic field passes normally to the parallel plates, and a magnetic cover (yoke) is employed to intensify the magnetic field and to make it identical over the radius of parallel plates where MR fluid was placed.

Figure 1.

Measurement setup of (a) rheological equipment (Anton Paar MCR 102) and (b) schematic diagram of MR shell and magnetic field direction.

The experiments were performed by controlling the operating temperature 22°C ± 0.15°C and the temperature was controlled using a cooling system where temperature module connected to the base pate and temperature control hood applied over the magnetic chamber. The cooling system has a coolant tank to store the coolant fluid and coolant fluid flow through the pipes in the temperature control hood, as shown in Figure 1(a). It was observed that by applying 0, 1, and 2 A currents, the increment in temperature was well limited within 0.02°C. While at 3 and 4 A currents, a fluctuation of temperature vary significantly and increases for 0.06°C and 0.14°C, respectively. The operating inputs parameter like a current, shear rate, strain amplitude, and stress levels were controlled by Anton Paar RheoCompass 1.22 software and output data was recorded and processed with a data acquisition board (DAQ) and computer system. The rheological test of the shear stress response of MR fluids was conducted under shear rate sweep mode at the different magnetic fields with shear rate varies from 0 to100 s⁻¹. The dynamic performance of MR fluids measured under amplitude sweep test by ranging the strain amplitude from 0.001% to 100% at a 10 rad/s fixed angular frequency and frequency sweep test by ranging frequency from 0 to 100 rad/s at a fixed strain of 0.1% under different magnetic field.

The surface morphology of CI, Fe₃O_4, and CI/Fe₃O₄ suspension and their particle size distribution was observed using Hitachi S-4800 field emission scanning electron microscope (FESEM). The sample was kept in a dry vacuum system during measurement and specifications of Hitachi S-4800 FESEM are included with 0.5 to 30 kV accelerating voltage, 1 nm resolution at 15 kV, 1.4 nm at 1 kV, and magnification from 30× to 800,000×. For the sample preparation, the Cressington 208 sputter coaters are used to apply a thin gold layer to non-conductive samples earlier to SEM imaging and EDS analysis. Gold sputter coating particles become visible and samples are suitable for imaging at higher magnifications. Elemental analysis of samples was measured with energy-dispersive X-ray spectroscopy (EDS). For elemental measurement, X-ray beam excitation is used in X-ray fluorescence spectrometers and a detector is used to convert X-ray energy into voltage signals; this information is sent to a pulse processor, which measures the signals and passes them onto an analyzer for data display and analysis.

The crystalline structure and phases of CI, Fe₃O₄, and CI/Fe₃O₄ particles were investigated using the Rigaku SmartLab X-ray diffractometer. X-ray diffraction (XRD) is one of the most important non-destructive tools to analyze powders and crystals. Rigaku SmartLab is the newest and most novel high-resolution X-ray diffractometer (XRD) with automatic high-resolution θ-θ multipurpose X-ray diffractometer (XRD) with expert system Guidance software.

The magnetic properties of pure CI, iron oxide (Fe₃O₄), and dry form of CI/Fe₃O₄ mixture were studied using a vibrating sample magnetometer (VSM) at room temperature. VSM was performed using quantum Design’s PPMS VersaLab is a cryogen-free cryocooler-based material characterization platform with a temperature range of 50–400 K without any consumption of helium gas, 3-T magnetic control platform, and equipped with an integrated cryopump and vacuum gauge for controlling the sample environment.

3. Results and discussion

3.1. Particle characterization

Figure 2(a) and (b) showed the morphology characteristics of the pure CI particles and mixture of CI/Fe₃O₄. Figure 2(a) showed that the CI particles exhibited flake shapes with an average particle size of 6–10 µm. The inset figure in Figure 2(b) indicates that Fe₃O₄ nanoparticles exhibit a moderately smooth surface and disc-shaped structure of 50–100 nm average particle size. In the case of the CI/Fe₃O₄ mixture, Fe₃O₄ nanoparticles surround the surface of CI microparticles and occupy the vacancies among the CI particles. A few Fe₃O₄ particles are attached to the surface of CI particles due to magnetic behavior and increase the size of CI particles. The surface structure and size of the magnetic particles influence the magnetorheological response of the MR fluid (Ngatu et al., 2008). In the schematic image of the CI/Fe₃O₄ mixture presented in Figure 2(c), it can be observed that under applied magnetic field CI microparticles formed a chain arrangement along the applied direction of the external magnetic field, and Fe₃O₄ nanoparticles packed the interspace among the CI particles and improved the overall friction. As a result, under the applied magnetic field, magnetic interaction among the CI microparticles and Fe₃O₄ nanoparticles improved and developed a more robust chain structure and improved the MR performances. The water base MR fluid has low viscosity at zero magnetic fields. It can be easily poured into borosil glass cylinder. Figure 2(d) is the picture of prepared CI/Fe₃O₄ with 1 wt% of Fe₃O₄ water-based MR fluid, where we can see that magnetic particles form a chain structure along applied the magnetic field direction.

Figure 2.

SEM image of (a) pure flake-shaped CI, (b) mixture of CI/Fe₃O₄, (c) schematic image of the MR effect of CI/Fe₃O₄ mixture, and (d) picture of prepared CI/Fe₃O₄ water-based MR fluid under magnetic field.

The magnetic properties of pure CI, Fe₃O₄, and CI/Fe₃O₄ with 1 wt% of Fe₃O₄ were investigated with VSM, as shown in Figure 3(a). The magnetization curves present the magnetic moment of each sample as a function of applied magnetic field strength varying from −2387.14 to +2387.14 kA/m (−30 to +30 kOe). All the samples show a typical superparamagnetic material behavior with a minimal coercive field and narrow hysteresis curve. Superparamagnetism can create magnetic particles that quickly scatter in solution with negligible magnetic interactions and avoid magnetic clustering, which is extremely important and helpful in practical applications of MR fluids (Wang et al., 2016). The top inset shows hysteresis loops of samples at very low magnetic field strength, and the bellow inset shows enlarge hysteresis loops at the center of the M-H curve. The magnetization curves of samples indicate a negligible remnant magnetization $(M_{r})$ and coercive force $(H_{c})$ . The saturation magnetization $(M_{s})$ of the CI, Fe₃O₄, and CI/Fe₃O₄ with 1 wt% of Fe₃O₄ were 211.87, 85.6, and 206.7 emu/g, respectively. The $M_{s}$ value of CI/Fe₃O₄ with 1 wt% of Fe₃O₄ was much higher than Fe₃O₄ and close to that of pure CI. The remnant magnetization $(M_{r})$ and coercive force $(H_{c})$ of Fe₃O₄ were approximately 7.9 emu/g and 10 kA/m, respectively. Meanwhile, CI has $M_{r}$ and $H_{c}$ values were 1.3 emu/g and 1.6 kA/m, respectively, and CI/Fe₃O₄ with 1 wt% of Fe₃O₄ has 1.5 emu/g and 3 kA/m, respectively. The above results indicate that CI, Fe₃O₄, and CI/Fe₃O₄ exhibited soft magnetic properties. Soft materials are desirable for MR performance; they are highly reversible and easily magnetized in on-state and demagnetized in off-state (Olabi and Grunwald, 2007; Wang et al., 2014). The magnetic performance of particles is much dependent on the structure size, morphology, and crystallinity of the samples (Yang et al., 2017).

Figure 3.

(a) VSM plot of CI, Fe₃O₄, and CI/Fe₃O₄ mixture. The inset presents the enlarged hysteresis loops at a small magnetic field and (b) XRD pattern of CI, Fe₃O₄, and CI/Fe₃O₄ mixture (inset figure shows the EDS of CI/Fe₃O₄ mixture).

The XRD patterns of CI, Fe₃O₄, and CI/Fe₃O₄ mixture investigated, as shown in Figure 3(b). The patterns of CI and Fe₃O₄ particles display prominent diffraction peaks of CI and Fe₃O₄, which presented that functionalities do not influence the core iron and magnetite, respectively. The positions of peaks matched with the usual XRD information for the cubic spinel structure of iron and magnetite. Diffraction peaks of CI and Fe₃O₄ particles have been indexed with no impurity phase peaks and a sequence of characters as (110), (200) (211), and (111), (220), (311), (400), (422), (511), (440), (533), (731), (800) planes of body-centered cubic (bcc) phase Fe, respectively. The CI/Fe₃O₄ mixture has similar diffraction peaks as CI particles. The inset figure showed the EDS spectral observation of the CI/Fe₃O₄ mixture; it established the CI/Fe₃O₄ microcluster composition with C and O elements with high Fe content.

3.2. Rheological measurement

The shear stress under controlled shear rate was investigated of the MR fluid containing CI/Fe₃O₄ 1 wt% in off-state and on-state and compared with MR fluid containing CI, as shown in Figure 4. In practice, pre-shearing conditions can significantly influence the results of MR fluid response (Shan et al., 2015); thus a fresh state pre-shearing (at zero magnetic fields) test was conducted before the test under magnetic fields to eliminate the shear history effect. The shear rate varies from 0 to100 s⁻¹, and magnetic field density varies from 0 to 0.74 T. The figure shows that the shear stress increased with the increasing magnetic field density due to strong dipole-dipole interaction among the CI and Fe₃O₄ nanoparticles magnetic particles. It was seen that shear stress of the CI-based MR suspension enhances with adding Fe₃O₄ nanoparticles. It is because nanoparticles occupy the voids between CI microparticles, which developed a strong magnetic chain-like formation and decreased the energy losses in the MR suspension because of inter-particle solid frictions. In addition to the wrapping effect on the CI particles, helps in increasing the strength of the columns and reforming the broken chain structure (Kim et al., 2016). The inset figure shows that adding the nanoparticles shear stress little enhanced at zero magnetic fields. The developed shear stress $(τ)$ and shear rate $(\overset{\cdot}{γ})$ flow curve relation can be represented by the widely used Bingham-plastic (BP) model, which is presented as:

τ = τ_{y} + η_{o} \overset{\cdot}{γ} (\overset{\cdot}{γ} > 0)

(1)

Where $τ_{y}$ is the yield stress at a low shear rate range and function of external magnetic field strength and $η_{o}$ is the post-yield plastic viscosity close to the MR suspension viscosity at the high shear rate regime, and $\overset{\cdot}{γ}$ is the shear rate. Furthermore, the flow curves were fitted by the Bingham model, which is showing good quality conformity with the experimental results for both MR fluids, as shown in Figure 4. Table 1 presents the identified optimal fitting Bingham model parameters in the range of 0–100 s⁻¹.

Figure 4.

Shear viscosity plotted as the shear rate function (inset figure presents the magnified view of stress at 0.0 T).

Table 1.

Optimal fitting parameters for pure CI and CI/Fe₃O₄ based MR fluids using Bingham fluid model.

	CI suspension		CI/Fe₃O₄ suspension
	$τ_{y}$ (kPa)	$η_{o}$ (mPa · s)	$τ_{y}$ (kPa)	$η_{o}$ (mPa · s)
0.0 T	0.00087	7.70	0.0045	41.02
0.17 T	2.10	2889.8	6.13	3662.8
0.35 T	5.21	1354.5	17.62	2984.5
0.54 T	6.96	1397.2	23.36	2589.67
0.74 T	8.10	1446.1	34.42	2768.5

Furthermore, when the magnetic flux density was smaller or equal to 0.35 T, the initially taken gap thickness of 0.50 mm between the parallel plates of the rheometer was maintained. So we observed a stable plateau of shear stress as the shear rate increases at the lower magnetic field. While at higher magnetic field strength (above 0.35 T) 0.54 and 0.74 T the gap thickness between the plates changes from 0.50 to 0.69 mm and from 0.50 to 0.78 mm due to the developed maximum initial normal force 16.3 and 27.3 N, respectively. The initial maximum developed normal force increases the gap thickness continuously with time and shear rate to the maximum value at a particular magnetic field between the parallel plates. Therefore, shear stress may show decreasing trends with time (shear rate) at higher applied magnetic field strength due to continuous breakage of chain structure at larger gap thickness.

3.3. Dynamic performance

The amplitude test is a helpful method to examine the dynamic mechanical performance of MR fluid. A strain is forced to the fluid and the elastic and loss energy response measured. The viscoelastic behavior and chain formation can be observed by the elastic/storage modulus $(G^{'})$ that provides energy storage capability and the viscous/loss modulus $(G^{″})$ that offers the dissipation energy within the material (Jahan et al., 2017). The $G^{'}$ and $G^{″}$ as a function of strain amplitude $(γ)$ , swept from 0.001% to 100% at a 10 rad/s fixed angular frequency under applied constant magnetic field B = 0 to 0.74 T, as shown in Figure 5. A critical value of strain $γ_{crt} = 0.1 %$ classified two characteristics region: linear viscoelastic (LVE) region and nonlinear viscoelastic region. Over the small strain area $γ \leq γ_{crt}$ , the storage modulus $(G^{'})$ of the CI/Fe₃O₄ sample showed a plateau region and $G^{'}$ independent of strain amplitude, known as the linear viscoelastic (LVE) region (Maurya and Sarkar, 2021). In LVE region $G^{″}$ indicated nonlinear behavior with an increase in value with the strain amplitude. At higher strain amplitude, $γ \geq γ_{crt}$ both $G^{'}$ and $G^{″}$ decrease with increase in strain rate, known as nonlinear viscoelastic region. In the linear region, $G^{'}$ larger than $G^{″}$ even in off-state (0 T), which suggests the dominance of elastic modulus and confirms solid-like behavior of the MR fluid. Both $G^{'}$ and $G^{″}$ were increased with the increment in magnetic flux density and higher value of $G^{'}$ confirmes the increase in a chain-like configuration in the applied magnetic field direction (Wang et al., 2019a). At a higher magnetic field, differences between $G^{'}$ values become minimal. It was because of the magnetic saturation of magnetic particles. After the LVE region, both $G^{'}$ and $G^{″}$ began to decrease with an increase in strain rate because of the irreversibility in transforming the MR fluid from a solid-like to fluid-like state (Han et al., 2020). After that, at higher strain amplitude, the $G^{'}$ and $G^{″}$ intersect at the cross point $(G^{″} > G^{'})$ , which suggests the dominance of loss modulus and MR fluid chain was generally broken in a nonlinear region.

Figure 5.

Storage modulus $(G^{'})$ and loss modulus $(G^{″})$ of CI/Fe₃O₄ sample as a function of strain amplitude

The viscoelastic behavior of the CI/Fe₃O₄ MR fluid was measured using the frequency sweep at a fixed strain of 0.1%, and frequency ranging from 0 to 100 rad/s under the magnetic field. The storage moduli $(G^{'})$ were exhibited an elastic response and almost constant (stable) plateau region over the whole frequency test range and increased with the increasing applied magnetic flux density, as shown in Figure 6. This behavior confirmed that MR fluid exhibited robust solid-like behavior under the magnetic field (Kwon et al., 2018). Furthermore, $G^{'}$ was larger than $G^{″}$ at applied magnetic flux density even at zero magnetic flux density. Figure 7 shows that $G^{'}$ and $G^{″}$ is a function of the magnetic field and indicates a growing trend with the magnetic field before getting magnetic saturation at the high magnetic field. At the lower magnetic field, the increasing tendency is large, and after some point tendency becomes almost constant.

Figure 6.

Storage modulus $(G^{'})$ and loss modulus $(G^{″})$ of CI/Fe₃O₄ sample as a function of angular frequency.

Figure 7.

$G^{'}$ and $G^{″}$ as a function of magnetic flux density of MR fluid at a constant strain of 0.1% and angular frequency of 10 rad/s.

The loss factor is an essential parameter to analyze the performance of MR fluid as it provides information about storage and loss modulus and considers the damping properties of the material. It is the ratio of loss to storage modulus $(\tan δ = G^{″} / G^{'})$ . The loss factor is dependent on applied external magnetic field density, as shown in Figure 8. It was observed in three different regimes by changing magnetic flux densities. In regime I, the loss factor decreases sharply from its maximum value at low applied magnetic flux density due to robust induced internal structure (Wang et al., 2019b). In regime II, the fluid transition from a liquid to a solid form due to competition between frequency and magnetic force-induced chain structure and loss factor reduces gradually with a high magnetic field. In regime III, MR fluid forms an almost stable solid-like structure at a higher magnetic field, and the loss factor has a small variance (Jahan et al., 2017). Furthermore, the loss factor is correlated to the energy dissipation, which induces by the interaction among various inner structures. Then, energy dissipation and loss factor were decreased with increment in the magnetic field. The loss factor is also dependent on strain amplitude; as the strain was higher, the loss factor was larger, as shown in Figure 8. It has occurred because more energy dissipation takes place at the higher strain rate

Figure 8.

Loss factor is a function of a magnetic flux density of MR fluid at a constant strain of 0.1% and angular frequency of 10 rad/s.

Figure 9 shows the plot of $G_{max}^{'}$ and $G_{max}^{″}$ of CI/Fe₃O₄ MR fluid as a magnetic flux density function. It can be observed that energy storage ability $(G_{max}^{'})$ as well as energy dissipation $(G_{max}^{″})$ values increase with the magnetic field. Figure 10 shows the dynamic efficiency $(η_{e})$ as a function of magnetic flux density of MR fluid using strain sweep test at 10 rad/s constant angular frequency. Dynamic efficiency is defined as:

η_{e} = \frac{G'_{H} - G'_{0}}{G'_{0}}

(2)

Where $G'_{H}$ is the storage modulus with the magnetic field, and $G'_{0}$ is the storage modulus without a magnetic field. Dynamic efficiency of MR fluid is increased with increasing magnetic field. Dynamic efficiency has a larger slope at the low magnetic field and the higher magnetic field slope little decrease because of the magnetic saturation of the particles.

Figure 9.

Dependence of the ${G^{'}}_{max}$ and ${G^{″}}_{max}$ on magnetic flux density.

Figure 10.

Dynamic efficiency of MR fluids as a function of magnetic flux density.

3.4. Creep and recovery behavior

Creep is the changing of strain with time under steadily applied stress $(τ_{o})$ of a viscoelastic material. Creep is a time-dependent mechanical performance that helps realize deformation mechanisms of materials (Xu et al., 2012). If the applied constant stress is removed instantaneously, a little of the time-dependent deformations are recovered with time, and dependence on time is known as the recovery phase. Furthermore, the microstructure development of viscoelastic material can be deducted from creep and recovery tests, which is useful to realize the structural mechanism at the back of the rheological behavior of materials (Xu et al., 2012). Creep and recovery performance of MR fluid at different stress levels is a useful way to evaluate the viscoelastic properties in the presence of the magnetic field. The creep and recovery curve of a nonlinear viscoelastic is shown in Figure 11.

Figure 11.

Schematic diagram of the creep and recovery behavior of a nonlinear viscoelastic material.

3.4.1. Creep phase

Stress $(τ_{o})$ is enforced instantaneously at the time $t = 0$ to the material and controlled at a constant level for a set phase of time $t_{o}$ . As a result, time-dependent creep strain $γ_{c}$ can be represented as follow:

γ_{c} (t) = γ_{ic} + γ_{r} (t) + γ_{v} (t)

(3)

For the viscoelastic materials, $γ_{ic}$ is the instantaneous (creep) strain, $γ_{r} (t)$ is the retarded elastic strain, and $γ_{v} (t)$ is the viscous strain. The instantaneous creep $(γ_{ic})$ strain for nonlinear viscoelastic material comprises of elastic $(γ_{e})$ and plastic $(γ_{p})$ contribution, that is, $γ_{ic} = γ_{e} + γ_{p}$ , and $γ_{p}$ cannot be recovered in the recovery phase. The instantaneous recovered strain is $γ_{ir} = γ_{e}$ . Furthermore, linear viscoelastic materials $γ_{ic}$ represent the elastic behavior of the materials, which is recoverable and disappears after removing the stress level, that is, $γ_{ic} = γ_{e}$ . The $γ_{r} (t)$ is also an elastic strain component, which behaves a steadily diminishing trend and fully recovered with time (Li et al., 2010). The $γ_{v} (t)$ is the viscous flow strain, linearly increases for linear viscoelastic material with time, and irreversible after unloading (Li et al., 2002). For the nonlinear viscoelastic materials, the $γ_{p}$ grow and $γ_{r} (t)$ and $γ_{v} (t)$ decrease $(γ_{ic} 〉 γ_{ir} as γ_{p} 〉 0)$ (Wang et al., 2014). The plastic component of strain is integrated into the residual strain, so it is also an irreversible strain. The plastic strain can be calculated by deducting the viscous flow strain $(γ_{v} (t))$ from the residual strain. However, mechanical behaviors with time are more complicated for the most realistic material than those described in Figure 11.

The three components of strain ( $γ_{ic}$ , $γ_{r} (t)$ and $γ_{v} (t)$ ) are proportional to the applied constant stress $(τ_{o})$ . So a creep compliance function $J_{c} (t)$ can be written as follow:

J_{c} (t) = \frac{γ_{c} (t)}{τ_{o}} = J_{ic} + J_{r} (t) + J_{v} (t)

(4)

From equation (4) and equation (3). The $γ_{c} (t)$ can be written as follow:

γ_{c} (t) = τ_{o} (J_{ic} + J_{r} (t) + J_{v} (t))

(5)

3.4.2. Recovery phase

It can be observed from Figure 11 that after removing the load from the material at $t_{o}$ , the instantaneous elastic strain $(γ_{e})$ recovered instantly, and retarded elastic strain $(γ_{r} (t))$ recover gradually, whereas viscous flow strain $(γ_{v} (t))$ irreversible. So time-dependent recovery strain $γ_{R} (t)$ can be written as follow:

γ_{R} (t) = γ_{e} + γ_{r} (t)

(6)

Correspondingly, a recovery compliance function $J_{R} (t)$ can be represented as follow:

J_{R} (t) = \frac{γ_{R} (t)}{τ_{o}} = J_{e} + J_{r} (t)

(7)

3.4.2.1.The influence of various stresses on creep and recovery performance

Figure 12(a) to (d) show the creep and recovery curves of fluid at different constant stress levels 200, 2000, 6000, and 10,000 Pa, respectively. The creep and recovery performance significantly depends on the applied loads for constant applied magnetic field 0.35 T, as shown in Figure 12. At lower stress $τ_{o} = 200 Pa$ , which is much lesser than the dynamic yield stress, the creep strain consists of the instantaneous creep strain $(γ_{ic})$ , retardation strain $(γ_{r})$ , and viscous strain $(γ_{v})$ . Where viscous strain is an irreversible and instantaneous strain, retardation strain is recoverable after removing the stress in the recovery phase. Here instantaneous strains $(γ_{ic})$ are equal to instantaneous recovery strain $(γ_{ir})$ , that is, $γ_{ic} = γ_{ir} = γ_{e}$ , and MR fluid acts as a linear viscoelastic material. As the level of stress increases to 2000 Pa, the instantaneous creep strain increases to $γ = 0.42$ , and the contribution of $γ_{r}$ and $γ_{v}$ decreases. The MR fluid behaves like nonlinear viscoelastic material, that is, $γ_{ic} > γ_{e}$ .

Figure 12.

Creep and recovery performance of MR fluid at: (a) 200 Pa, (b) 2000 Pa, (c) 6000 Pa, and (d) 10,000 Pa.

Similarly, for the applied stress levels 6000 and 10,000 Pa, the contribution of the instantaneous creep strain greatly increases $γ = 6.1$ and $γ = 33.6$ , respectively. The strain instantaneously reached the equilibrium state. The contribution of retardation strain and viscous strain significantly decreases or becomes negligible compared to creep strain at higher stress levels instantaneously. The MR fluid behaves to an elastic solid. The instantaneous creep strain comprises both elastic $(γ_{e})$ and plastic $(γ_{p})$ components, that is, $γ_{ic} = γ_{e} + γ_{p}$ , and MR fluid acts as a nonlinear viscoelastic material. Furthermore, removing the applied load, there is a very slight recovery of elastic strain, as shown in Figure 12(c) and (d). The elastic strain to residual strain ratio becomes negligible for 6000 and 10,000 Pa, which are 31.8% and 33.6%, respectively. Therefore it can be said that the residual strain is influenced by plastic strain. This plastic strain mostly generated in the primary creep process, and its rate maintains nearly steady after the MR fluid goes into the secondary creep process. The elastic-plastic characteristics of MR fluid can be analyzed by breaking and restructuring the particle chain structures throughout the small gap period of the impulse. The plastic deformation of MR fluid may begin from the slipping between iron particles (Xu et al., 2012).

As discussed in Figure 12(a) to (d), the instantaneous recovery strains $({γ_{i}}_{r})$ are lesser than the instantaneously creep strain $(γ_{ic})$ , excluding case (a) when the applied stress level is deficient. MR fluid particles formed a single-chain-width chain under the magnetic field, as presented in Figure 2(c). At critical strain, the chains distort affinity; they formed chains that break in half and quickly reformed their original state. At low stress 200 Pa, the stress in the direction normal to the magnetic field vector gives to energy storage in the stressed chains. Therefore at 200 Pa, the fluid acted elastically and recovered completely without an enduring strain and behaves like viscoelastic liner material. In the case of a larger stress level, the energy taken for chain stretching was not stored but dissipated completely, and the strain was irreversible in the recovery phase (Li et al., 2002).

3.4.2.2. The influence of magnetic field on creep and recovery performance

Controlibity of magnetic properties of the MR materials is one of the most essential and attractive properties. Being a type of magneto-responsive material, a magnetic field plays a significant character in the creep and recovery performances of MR fluid. When a magnetic field is applied to MR fluid, CI particles formed a rigid chain structure; as a result, movement between the particles is restricted. Creep and recovery performances measured at different magnetic fields for constant stress of 2000 Pa, as presented in Figure 13. The instantaneous creep strain $(γ_{ic})$ decreases with increasing magnetic field. Therefore, the elastic modulus $(G^{'})$ , which is the ratio of constant applied stress $(τ_{o})$ to the developed instantaneous creep strain, $(γ_{ic})$ $(G^{'} = τ_{o} / γ_{ic})$ increases with the increasing magnetic field, as shown in Figure 14. The $G^{'}$ at 0.18, 0.35, and 0.52 T are 2125.4, 4672.9, and 11299.4 Pa. The instantaneous creep strain ratio to residual strain was 2.3, 1.5, and 0.87 at 0.18, 0.35, and 0.52 T magnetic flux density, respectively. It means with increasing the magnetic field, instantaneous creep strain reduces sharply, and elastic recovery strain increases. These results prove that elastic component grows with increment in magnetic flux density, and MR fluid becomes rigid and time-dependent properties show solid behavior under creep and recovery performance.

Figure 13.

The influence of the magnetic field on creep and recovery behaviors.

Figure 14.

The ratio of elastic strain as a function of the magnetic field.

However, the reversible strain $γ_{r}$ will also provide a quantity of energy storage. The ratio of $(γ_{ir} + γ_{d} / γ_{ic})$ was plotted at 2000 and 6000 Pa as dependent on the magnetic field to realize the influence of stress level and magnetic field on the time-dependent mechanical behaviors. It was observed that the ratio of elastic strain increases with the increasing magnetic flux density. It means instantaneous creep strain $(γ_{ic})$ decreases sharply, and reversible strain $(γ_{ir} + γ_{d})$ increases with increasing the magnetic field. Furthermore, total strain reduces with the rising magnetic field, and the energy storage capacity of MR fluid is enhanced. Simultaneously, increment in applied stress levels shows the opposite behavior; with increasing the stress levels, total strain increases, and the elastic strain ratio decreases. The elastic strain ratio plot proves that MR fluid behaves as solid-like material and increases elastic energy storage capacity with increasing magnetic field.

Creep compliance is the total strain per unit applied stress levels before the creep break occurred. Creep compliance is dependent on stress levels and the magnetic field, as presented in Figure 15(a) and (b), respectively (Xu et al., 2012). It was observed that the creep compliance increases with the increment in the stress levels for the creep time range of 500 s at constant magnetic flux density 0.35 T, as shown in Figure 15(a). Results show that the MR fluid behaves like linear materials at small stress levels (200 and 2000 Pa), while at larger stress levels (6000 and 10,000 Pa) behave like complex nonlinear materials. Creep compliance depends on the applied magnetic field and shows a decrease in creep compliance value with increment in magnetic flux density for MR fluid, as presented in Figure 15(b) at a constant stress level of 2000 Pa. It occurred because creep compliance is the total load strain per unit of stress and the yield stress of MR fluid increases significantly with increasing the magnetic field. The creep compliance shows a constant plateau with time at different applied magnetic field except at magnetic field of 0.52 T. It was because, at 0.52 T, the temperatures of the MR sample region increases 22°C–22.08°C after 200 s and increase continuously with time up to 22.14°C, and as a result yield stress of MR fluid decreases with increase in temperature of MR sample. So due to the decrease in yield stress of MR fluid creep compliance shows a significant increase in trend with time after 200 s.

Figure 15.

Creep compliance with time and dependent on (a) applied stress levels and (b) magnetic flux density.

4. Conclusions

This study measured the dynamic and creep and recovery performance of MR fluid under different operating mechanical conditions. The MR fluid contained CI microparticles and Fe₃O₄ nanoparticles mixture with 65 wt% of CI and 1 wt% of Fe₃O₄ and suspended in 35 wt% of water. CI/Fe₃O₄ suspension exhibited soft magnetic properties. Therefore suspension was highly reversible and, as a result, easily magnetized and demagnetized in on-state and off-state, conditions respectively. The rheological properties of CI-based suspension were enhanced with the addition of Fe₃O₄ nanoparticles because nanoparticles occupy the voids between CI microparticles, which make a strong magnetic chain-like structure and reduce the energy losses in the MR suspension due to inter-particle solid frictions. Under oscillatory sweep mode, the critical strain was $γ_{crt} = 0.1 %$ the storage modulus $(G^{'})$ of CI/Fe₃O₄ showed a plateau region over the small strain area $γ \leq γ_{crt}$ and $G^{'}$ independent of the applied strain. Whereas at larger strain, $γ \geq γ_{crt}$ both $G^{'}$ and $G^{″}$ decrease with a rise in strain amplitude. Under frequency sweep mode, the storage modulus $(G^{'})$ was exhibited an elastic response, an almost constant (stable) plateau region over the whole frequency range, and increased with the increasing applied magnetic flux density. Creep and recovery experiments showed that at lower stress $τ_{o} = 200 Pa$ , CI/Fe₃O₄ suspension acts as a linear viscoelastic material because instantaneous strains $(γ_{ic})$ are equal to instantaneous recovery strain, that is, $γ_{ic} = γ_{ir} = γ_{e}$ . As the stress levels increase, the contribution of retardation strain and viscous strain decreases. The MR fluid acts like nonlinear viscoelastic material, that is, $γ_{ic} > γ_{e}$ . The instantaneous creep strain decreases sharply, and elastic recovery strain raises with a rising magnetic field. As a result, MR fluid becomes stiffer with increment in magnetic field, and the elastic energy storage capacity of MR fluid increases.

Footnotes

Acknowledgements

The authors would like to be grateful smart material and machines lab in the Department of Mechanical Engineering at IIT Patna, Patna, for providing a rotational rheometer (Anton Paar MCR102) for experimentation and all other resources used in this research.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Chandra Shekhar Maurya

Chiranjit Sarkar

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