Keywords: MR fluid, Magnetorheology, Shear modulus, Compression Modulus
RH162
Abstract
Magnetorheological (MR) fluids are suspensions of micron-sized particles of magnetizable materials. These suspensions are characterized by the tunability of their rheological properties by means of magnetic field application, a phenomenon known as the MR effect.
In addition to a commercially available MR fluid, a non-commercially available MR fluid was characterized by having carbonyl iron particle content close to the maximum-packing fraction. The magnetorheological properties of both MR fluids were measured at several magnetic field intensities in shear and compression, allowing a comprehensive characterization of their mechanical properties. Both MR fluids show dominantly elastic behavior, characterized by much larger values of the storage modulus than the loss modulus. The results show that when the magnetic flux density varied from 0 mT to 1000 mT, the maximum value of the storage compression modulus is about 10 times larger than the maximum value of the storage shear modulus for the commercial sample. However, the magnetic field-induced change in the storage compression modulus is approximately one order of magnitude smaller than the change in storage shear modulus. For the highly concentrated suspension, the values of the storage shear modulus and the storage compression modulus are of the same order of magnitude. Furthermore, this concentrated MR fluid shows a weaker MR response as compared with the commercial sample. For the concentrated suspension of carbonyl iron powder, saturation is not reached even at 1000 mT, according to both the viscoelastic characterization and the measured yield stress. The results suggest that higher magnetic fields would produce a higher magnetorheological response. On the other hand, the commercial sample reaches saturation at magnetic fiux density values smaller than 1000 mT.
Magnetorheological (MR) fluids are intelligent materials capable of reversibly transitioning from a liquid-like to a solid-like behavior under the application of an external magnetic field. Conventional MR fluids are comprised of micron-sized, highly magnetizable particles suspended in a carrier fluid. In the absence of applied magnetic field, MR fluids exhibit thixotropic behavior akin to colloidal suspensions. When subjected to an external magnetic field, the particles are magnetized and attract one another, forming flocculated aggregates or networks along the applied field direction within milliseconds. This response to magnetic field application, known as the MR effect, ultimately changes the bulk rheological properties, providing a means to tailor fluid characteristics such as yield stress and viscosity by controlling the strength of the magnetic field.
The rheological properties of MR fluids have been characterized for years, and a biannual conference is devoted to the subject of MR fluids. The controllability of the mechanical properties of MR fluids by applied magnetic fields is the base of many technological applications such as MR clutches and dampers. For these applications, rheological parameters such as viscosity, viscoelastic moduli, and yield stress are of extraordinary interest. In addition, many MR devices work in modes that produce tension, compression, squeeze, and bending deformations.
Currently, a plethora of research is focused on characterizing the bulk rheological behavior of MR fluids in the shear direction [1-3]. However, despite the importance of other modes of operation such as compression, the literature on these topics is scarce. A comparative study of the properties of MR fluids under compression and shear deformation is still lacking. To fully understand the behavior of MR fluids under these experimental conditions, the ability to perform rheological analysis and dynamic mechanical analysis (DMA) in the compression direction while also controlling the magnitude of the applied magnetic field is required. This work presents a comprehensive characterization of the compression and shear mechanical properties of MR fluids under applied magnetic fields.
The rheometer used in the characterization of the magnetic properties is a TA Instruments™ Discovery™ HR 30 equipped with a magnetorheological accessory able to reach a magnetic flux density of 1 T with a very high homogeneity. Due to the presence of a second magnetic bearing generation, the instrument is also able to perform axial oscillation movement, allowing the characterization of the viscoelastic properties both in compression and shear modes.
HR DMA mode provides a true linear testing mode and is only possible because of the unique force/torque rebalancer transducer (FRT) normal force transducer. The HR DMA mode can perform oscillation measurements in the axial direction to test solids in bending, tension, and compression modes, turning the rheometer into a Dynamic Mechanical Analyzer. In DMA mode, the HR operates like a single head dynamic mechanical analyzer, controlling the oscillation amplitude and recording the force required to displace the sample. The FRT induction sensor is used to control displacement.
Two MR fluids have been used in the present work. One of them is a commercially available suspension is composed of carbonyl iron particles (1 to 10 microns size) at a concentration in volume of 20%. The material was successfully used in squeeze-film dampers previously, which constituted the main reason for its choice for the present study of behavior under shear and compression deformation.
The other MR fluid is a highly concentrated MR fluid, consisting of carbonyl iron powder (Fe-CC, from BASF, Germany) as solid phase and mineral oil (from Sigma Aldrich, Germany) as carrier liquid. Fe-CC particles have a silica coating and are spherical in shape with a median diameter of 5 microns. The MR fluids were prepared with 50 vol.% approximate concentration. This fluid was selected because of its very high particle content and comprehensive previous characterization under shear mode [1, 2].
In both MR fluids, the tests performed were oscillatory frequency sweeps in shear and in compression at a strain within the linear viscoelastic range. The frequency range was from 0.01 to 10 Hz. Each frequency sweep was made at several magnetic flux densities, B: 0, 2, 5, 10, 20, 50, 70, 80, 100, 200, 300, 500, 800, and 1000 mT.
For the DMA/axial/compression experiments, the amplitude used was 1 micron. Because the gap used was around 300 microns, there is no relevant change in the gap and, therefore, in the magnetic field profile during the oscillatory compression measurements.
For the commercial MR sample, the shear complex modulus (G*), as well as the shear storage (G’) and loss (G’’) moduli, are shown in Figures 2a and 2b.
Figures 2a and 2b show the typical frequency sweep profile of a moderately concentrated MR fluid. Even at 0 mT, the sample shows a “gel-like” behavior. As soon as the magnetic field is increased, G’ also increases and the slope of G’ vs f decreases, showing a lower dependence on frequency, typical of gels and cross-linked systems. The magnetic field produces a mostly 2D network (strands) that increases the sample stiffness.
Figure 3 shows the compression complex modulus (E*), as well as the compression storage (E’) and loss (E’’) moduli, at the same magnetic flux densities as in Figure 2 for the commercial MR fluid.
The trends of E* and E’ versus frequency are like those of G* and G’. In both cases, the MR fluid shows predominant elastic behavior, with E’>>E’’ and G’>>G’’. To compare behavior under compressive and shear stress, the complex modulus data at a frequency of 0.01 Hz were obtained, and a plot of G* and E* as a function of magnetic flux density was constructed. Figure 4 shows the results in log-log scale.
It is possible to observe a tendency toward saturation, but not complete saturation in Figure 4 for both shear and compression modulus. In addition, the values of Figure 4 were normalized 1 to get a better comparative plot (Figure 5).
It can be observed in Figure 5 that the increase in the relative storage compression modulus starts at lower magnetic fields. Table 1 compares both the moduli and the saturation magnetic fields (defined as the magnetic field where the modulus reaches 95% of its maximum plateau value).
Table 1. Data obtained from Figures 4 and 5
| B (in Shear Data) | B (in Compression Data) | |
|---|---|---|
| Magnetic field at the 50% of Modulus Change | 123 mT | 52 mT |
| Magnetic field at the 95% of Modulus Change (saturation) | 511 mT | 480 mT |
| Shear | Compression | |
|---|---|---|
| Storage modulus (at 1000 mT)/Storage modulus (at 0 mT) | 3401 | 228 |
Non-Commercial Carbonyl Sample Results
Once the linear viscoelastic range of the carbonyl suspension was known, a frequency sweep was performed between 0.01 rad/s and 100 rad/s without any magnetic field applied. The experimental results are shown in Figure 6.
Figure 6 shows the typical profile of a highly concentrated suspension. As observed, G’ is completely independent of the frequency. G’’ shows a minimum between two main relaxations, which corresponds to the behavior of a gel. In the presence of applied magnetic field, the situation is much more pronounced with the values of the loss modulus being completely negligible as compared with the values of the storage modulus.
The complex shear and compressive modulus versus the magnetic field are shown in Figure 7 on a linear-log scale. For the MR fluid with 50 vol.% concentration, there is a clear plateau from 0 mT to 70 mT where the complex moduli are independent on B. This behavior seems to be an indication of colloidal forces other than magnetostatic forces being dominant. For magnetic flux densities higher than approximately 70 mT, there is an increase of both moduli, indicating the dominance of the magnetic field over contact forces. The values of the complex modulus for the concentrated MR fluid are much higher (about 3 orders of magnitude) than those of the commercial sample at low field. At the highest field, they are a little bit smaller than the commercial sample, meaning the noncommercial MR fluid has much lower tunability.
The values of Figure 7 have been normalized to 1 to get a better comparative plot, shown in Figure 8.
The profile of Figure 8 and the results in Table 2 show that both moduli increase versus B in a similar trend. The change in the moduli from 0 mT to 1000 mT is similar. The high concentration avoids a larger magnetorheological effect. In comparison with data in Table 1 for the commercial MR fluid, the increase of the moduli with the applied field takes place at higher values of the field. In addition, the tunability of the rheological properties is much smaller for the highly concentrated, non-commercial MR fluid.
Finally, for all the magnetic flux densities applied and for both samples, we obtain the yield stresses from the strain sweep experiments. The results are shown in Figure 9.
Table 2. Data obtained from Figures 7 and 8
| B (in Shear Data) | B (in Compression Data) | |
|---|---|---|
| Magnetic field at the 50% of Modulus Change | 340 mT | 370 mT |
| Magnetic field at the 95% of Modulus Change (saturation) | 770 mT | 778 mT |
| Shear | Compression | |
|---|---|---|
| Storage modulus (at 1000 mT)/Storage modulus (at 0 mT) | 1.46 | 1.76 |
In Figure 9, it can be observed that the yield stress of the carbonyl iron suspension is between 10 and 100 times larger in magnitude than the commercial sample. This is due to the concentrated nature of the carbonyl iron suspension. However, the magnetic field dependence of the carbonyl iron suspension is lower, and the saturation is not reached.
In general, when comparing the magnetorheological properties of the fluids, the highly concentrated carbonyl iron suspension has a weaker tunability on the applied magnetic field. The yield stress and the viscoelastic moduli are already much higher for the concentrated carbonyl iron suspension than for the commercial sample without any magnetic field applied. The high concentration produces a high stiffness and avoids a strong magnetic field response until 1000 mT. Furthermore, the concentrated carbonyl suspension does not reach the saturation point even at fields as high as 1000 mT, contrary to the commercial sample that saturates at smaller values of the applied field.
The magnetorheological properties of two MR fluids, a highly concentrated carbonyl iron suspension and a commercial sample were measured at several values of the intensity of the magnetic field, both in shear and compression, allowing a comprehensive investigation of these MR fluids.
Regarding the commercial sample, the results demonstrate that when the magnetic flux density was ranged from 0 mT to 1000 mT, the maximum value attained for the storage compression modulus was about 10 times larger than the corresponding value for the storage shear modulus. However, the tunability of the viscoelastic moduli was about 1 order of magnitude higher for shear than for compression mode. For this sample, saturation was reached at values of the magnetic field smaller than 1000 mT.
For the highly concentrated carbonyl iron suspension, the values of the viscoelastic moduli (shear and compression) were similar within the range of magnetic flux densities from 0 mT to 1000 mT, with the compression modulus being slightly higher. The high concentration avoids a large magnetorheological effect and, in fact, only a weak tunability of about 50% was obtained for the shear measurements. Furthermore, the carbonyl iron suspension did not reach saturation even at 1000 mT.
Finally, both fluids showed high values of the yield stress, much higher for the highly concentrated MR fluid. However, the magnetorheological response of the commercial sample was considerably larger than that of the concentrated MR fluid, very likely because of the hindering of particle movements under an applied magnetic field due to its very high concentration.
References
- M. T. Lopez-Lopez, and L Rodriguez-Arco et al.: N-Like rheograms of concentrated suspensions of magnetic particles, J. Rheol. 60(2) (2016) 267-274.
- M. T. López-López et al.: Yield Stress in magnetorheological suspensions near the limit of maximum-packing fraction, J. Rheol. 56(2) (2012) 1209-1224.
- C. Carmignani, P. Forte and E. Rustighi: Design of a novel magneto-rheological squeeze-film damper, Smart Mater. Struct. 15 (2006) 164-170.
Acknowledgement
For more information or to request a product quote, please visit www.tainstruments.com to locate your local sales office information.
This paper was written by Carlos Gracia Fernández, Principal Applications Scientist.
TA Instruments and Discovery are trademarks of Waters Corporation or its affiliates.
Click here to download the printable version of this application note.