Determination of shear behavior of magneto-rheological elastomers under harmonic loading

Abstract

Magneto-rheological (MR) materials can respond reversibly and quickly under the effect of an external magnetic field. MR materials contain micron-sized iron particles. These iron particles are typically dispersed in an elastomer or a liquid. These materials due to their properties constitute a kind of smart material in terms of engineering material. Such materials are used as isolators in various engineering applications, structures, and sound control subsystems. This study aimed to determine the mechanical properties for shear behavior of MR materials for under harmonic loading. Parameters such as matrix materials with different hardness values, powder types, magnetic field, frequency, and deformation were studied. The parameters related to the MR material itself were analyzed with the obtained data. The present study reveals that considering the sensitivity to magnetic field parameter, composite materials having the most suitable properties were produced with Shore 2 hardness value and SQ magnetic powder. It had been observed on increase about 200% at the rate of Shore A10 and A2 as a result of comparing the hardness scale. Also according to the powder rate while there was an increase on worth effect of relative MR, it is seen that the biggest increase had been in SQ powder with 199% worth. When looked some studies in literature, about comparing different hardness values such as matrix materials powder types etc. there aren’t any studies. The state of magnetic field thinks that features such as MR effect, Storage, and Loss modulus haven’t been examined yet.

Keywords

harmonic loading relative magneto-rheological effect magneto-rheological elastomer shear deformation magnetic field

Introduction

Elastomers are widely used as reliable and cost-effective passive damping behavior for noise and vibration reduction in many engineering applications. Such elastomers are known to be effective within a limited frequency range due to their constant parameters. Magneto-rheological elastomers (MREs) are composite materials that exhibit rapid and reversible changes in dynamic properties under the applications of an external magnetic field. Through the rapid response of MREs, their elastic modulus can be effectively controlled with the help of variable external stimuli.¹ Thus, MREs provide greater potential for actively reducing the vibration in a region over a wide frequency range.^2,3 Furthermore, due to their reversible properties, such materials can be utilized in large-scale engineering applications. When an adaptive response is required, for example, they are used as adaptive-tuned vibration absorbers,⁴ adaptive vibration isolators,⁵ vehicle seat suspension,⁶ and sensing devices.⁷ The production process of rubber-type materials starts with well-mixing of the three main components including ferromagnetic powders, matrix material, and additives. It has been subjected to processes such as holding under vacuum, application of magnetic field during sample production and testing, and vulcanization process in this way they were produced in the isotropic (non-magnetic field) and anisotropic state The MR effect parameter is called the reversible change in the applied magnetic field and module. Parameters such as the increase in the proportion of magnetic particles, the production of soft matrix material, and anisotropic vertical material have increased this value.

Many studies have been conducted considering the parameters such as the material used, test type, magnetic field size, orientation, particle type, particle percentage, and size. These studies are presented chronologically in Table 1.^{8,9,18–20,10–17}

Table 1.

The literature data on the shear behavior of MRE materials.

References	Matrix	Test type	Magnetic flux density	Orientation	Particle type	Particle percentage/size
Demchuk and Kuz’min, 2002¹²	Silicone rubber	Dynamic (vibration and absorbing)	Vulcanized; 0.6 T	During vulcanization	CIP	3.5; 13; 23 μm, 10–25%
Bellan and Bossis, 2002¹³	RTV silicone	Tension, dynamic	Vulcanized 0–200 kA/m; Test 123 kA/m, dynamic 42 kA/m	During vulcanization and test	CIP	2 μm, 5, 15, 25 and 30%
Zhou, 2003¹⁴	RTV silicone rubber	Shear	Test; 0.455 ve 0.8 T	During test	CIP	3 μm, 27%
Gong et al., 2005¹⁰	RTV silicone rubber	Shear (dynamic)	Test; 0.2 T	During test	CIP	3 μm, 20, 40, 60, 70%
Lockette et al., 2006¹⁵	RTV silicone rubber	Compression, dynamic shear	Vulcanized; 2 T	During vulcanization	Iron and Barium ferrite	10–40 μm, 28–32% and 40 nm, 26%
Bose, 2007¹⁶	Silicone rubber	Shear, dynamic test	Vulcanized; 1.3 T Test; 0.7 T	During vulcanization and test	CIP	5 μm, 0, 10, 20%
Lockette et al., 2008¹⁷	Silicone rubber	Dynamic shear	Test; 120 kA/m	During test	Iron	40 and 10 mm, 0–30%
Li et al., 2008⁷	HTV silicone rubber	Dynamic shear	Vulcanized; 0–0.35 T Test; 0-1 T	During vulcanization and test	CIP	6 μm 60%
Guan et al., 2008¹⁸	Silicone rubber	Dynamic	Vulcanized; 40 kA/m Test; 0–636 kA/m	During vulcanization and test	CIP	5 μm, 0, 15, 20, 27%
Wei et al., 2010¹⁹	Silicone rubber natural rubber	Shear	Vulcanized; 0.8 T test; 1 T	During vulcanization and test	CIP	3.5; 6;21 μm, 80%
Ju et al., 2012²⁰	Silicone rubber	Shear	Test; 0–0.6 T	During test	CIP	3.5; 6.5; 14 μm, 60, 70, 80%
Li et al., 2013²³	RTV silicone	Dynamic shear	Vulcanized; 0–0.7 T test; 1 T	During vulcanization and test	CIP	5 μm, 30%
Gao et al., 2017²⁴	Silicone rubber	Dynamic shear	Test; 0–171 kA/m	During test	Iron oxide	2.3 μm, 10%
Wan et al., 2018²⁵	Silicone rubber	Dynamic shear	Vulcanized; 0–0.7 T Test; 0–1 T	During vulcanization and test	CIP	5–9 μm, 23%
Dargahi et al., 2019²⁶	Silicone rubber	Dynamic shear	Test; 0–450 mT	During test	CIP	3.9–5 μm, 40%
Sulatchaneenopdon et al., 2022²⁷	Silicone rubber	Dynamic	Vulcanized; 0.45 T Test; 0-0, 24 T	During vulcanization and test	CIP	3–5 μm, 10%
Qiao et al., 2022²⁸	Silicone rubber	Dynamic shear	Test; 0.75 T	During test	CIP	5 μm, 40,50,60%

RTV: Room-temperature-vulcanizing; HTV: Heat-temperature-vulcanizing.

The studies about MR materials that are made on especially dynamic behavior in recent years have made both iron powder and different powder alloy. It has been analyzed MR that effect helped us for understanding the mechanic features and materials hysteretic behaviors by means of dynamic shear loading. Tahir²¹ calculated the value of MR effect of materials that consist of Fe-Co and Fe-Ni but Khadiret al.²² increased the storage modulus about 260% using foam.

The dynamic response of MREs has been evaluated in some studies taking into account different applications and stimuli.²³ However, experimental and analytical methods for the properties of MREs, standard methods for characterization, and modeling studies of MREs have not been sufficient over the past decade yet. Some studies have commonly focused on different methods and experimental conditions to characterize the mechanical properties of MREs. Generally speaking, we can be classify these studies as tension-compression and shear. The characteristics of materials in the shear mode were studied in two groups. The first group only focused on the identification of MREs^24–26 whereas the second group studied the characteristics of MRE-based instruments such as vibration, absorption, and isolators.² Characterization of MREs is limited by low-frequency stimuli and low-deformation amplitude. The studies exceeding 10% deformation and 5 Hz frequency have not carried out completely so far. Other than the limited rates of loading conditions, the low ferromagnetic powder ratio and the non-linear behavior of MREs that may resemble viscoelastic materials have not been thoroughly investigated. Sometimes when looked into the studies in literature, about comparing different hardness values such as matrix materials powder types etc., there aren’t any studies. The state of magnetic field thinks that features such as MR effect, Storage Module, and Loss module haven’t been examined yet. Here, we aimed to determine the mechanical properties for shear behavior of MRE materials for under harmonic loading. Parameters such as matrix materials with different hardness values, powder types, magnetic field, frequency, and deformation were assessed. The dynamic characterization of the samples was carried out under the magnetic field of 0–0.226 T with the frequency ratio of 5 Hz, and the stroke values of 1, 2, and 3 mm. Loss and storage moduli were measured to determine the dynamic properties of MREs.

Experimental details

Materials

Four different types of MRE materials given in Tables 2 and 3 were used. Matrix material and ferromagnetic powders were mixed at 10, 20, 30, and 40 volume ratios. In this way, it was produced as isotropic and anisotropic in the laboratory situation. The spherical carbonyl iron particles (CIPs) range from 3.8 to 8 μm and the matrix materials from 2 to 59 shore A hardness values. They were provided from BASF and Smooth-on, respectively. The silicone rubber, magnetic particles, and curing materials were mixed well for 10 min with the aid of a blender. Then, we applied vacuum to it for 10 min before casting the mixture in the mold in order to avoid any air bubbles. The mixture obtained was poured into 20 × 20 × 5 mm of aluminum mold, cured at 70°C for 20 min and vulcanized. In this way, isotropic material was manufactured. In addition to these, anisotropic horizontal and vertical materials were produced by applying approximately 0.3 T magnetic fields with the help of Neodymium iron boron (NdFeB) magnets with the dimensions 40 × 20 × 5 mm during material production.

Table 2.

Technical information on matrix materials.

Matrix	Color	Density (g/cm³)	Viscosity (mPas)	Curing time (hours)	Hardness (shore A)	Tensile strength (N/mm²)	Breaking elongation (%)	Tear resistance (N/mm)
Dragon skin FX	Transparent	1.022	18,000	0.67	2	1.985	763	10.68
Vario 40	Translucent	0.98	10,000	6	40	8	450	15
MRTV	Beige	1.29	130,000	16	59	4.5	250	—
Sorta clear	Translucent	1.08	35,000	16	40	5.51	400	—

Table 3.

Technical information on ferromagnetic carbon doped iron powders.

Ferromagnetic powders	Fe min. (%)	C max. (%)	O max. (%)	N max. (%)	Particle size (μm)
BASF SQ	99.5	0.05	0.22	—	3.9–5
BASF SQ-I	98.5	0.03	0.7	—	3.8–5.4
BASF EM	97	0.65-0.85	0.6-0.8	0.1-0.3	4.5–6
BASF CN	99.5	0.03	0.1-0.25	0.01	6.5–8

Experimental setup

Dynamic compression tests of MRE materials were conducted under isotropic and anisotropic conditions with the addition of ferromagnetic powders at 10, 20, 30, and 40% volumetric ratios. Considering the values of 1.2 and 3 mm stroke and 5 Hz frequency, the tests were performed with the help of the LDS V450 shaker shown in Figure 1. The jaws made of aluminum material, which are not affected by the magnetic field, have been designed for the test setup. A maximum magnetic field of 0.226 Tesla was applied to this setup by placing circular NdFeB magnets with a diameter of 100 mm and a thickness of 10 mm. The relationship between the magnetic field and distance is shown in Figure 2. With the help of S type load cell and accelerometer with a capacity of 100 kg, data are obtained. The test results obtained in this process were simultaneously transferred to the computer screen with the help of shaker’s program.

Test method

MRE materials are sensitive to stress softening expressed as Mullins effect. Therefore, there should be no permanent deformation on the material before performing experimental studies. Extensive literature research was conducted by Diani to solve this problem.²⁹ In order to interpret the nonlinear stress-deformation behaviors of MRE materials, tangent modulus (E_T) was calculated with the help of linear slopes at 1% deformations. MR effects are produced by comparing the stress and deformation curves in the situations where the magnetic field is present and absent. Absolute MR effect is defined as the difference between the magnetic field-free (E₀) and field (E_M) elasticity modules

{M R}_{a b s} = E_{M} - E_{0}

(1)

Relative MR effect is defined as the factor between modules

{M R}_{r e l} = \frac{E_{M}}{E_{0}}

(2)

For reproducibility and reliability of the test results, tests should be performed with at least three samples of the same type, and thus, stress-deformation graphics and MR effect parameters should be specified.

Results and discussion

Powder rate

The stress-displacement graphs of Shore 2 matrix material obtained in pure and 10–40% horizontal, vertical, and non-orientational forms are given in Figure 3. When the data in these graphs are examined, it is seen that the test results of each parameter form a hysteresis cycle. Therefore, the cyclic test results of all graphs were compared with each other. The results show that no effect of the magnetic field comes into question in the pure state. In addition, when the test results are examined up to 40% of powder ratio, there was an increase in stress values up to 30% while a decrease occurred at 40%. Schubert and Harrison (2015) reported that pure matrix material is not affected by the magnetic field, but leads to a decrease in stress when the powder ratio is more than 30% by volume.³⁰ Besides, experimental modeling studies by Davis³¹ found that the optimum particle volume ratio is 27% for the largest change in modules. Therefore, the test results were achieved in consideration of 30% of the powder ratio value for all parameters. In Figure 3(a), the maximum increase of stress was found to be 28.6% in the unoriented sample at 30% powder rate and 1 mm deformation. There was no increase in Figure 3(b) and (c). In general, the graphics almost overlapped with each other.

Powder type

Highly saturated magnetic property and high purity powder type should be considered as a distinctive feature in the production of composite materials and in useful situations. There are many studies in relation to that.^{15,16,20,32–35} As the literature reports high-magnetic saturation properties and purity values, carbonyl iron powders are generally used. As shown in Figure 4(a)–(c), the stress-deformation graphics were produced with four different types of powder that is commercially available from BASF supplier. As can be seen from the graphics, increasing stress was obtained with the effect of magnetic field in all three cases with the SQ powder type. These increases were found to be 100% at 0.53 mm displacement and 5.8 kPa strain, 100% at 0.49 mm and 5.82 kPa, and 199% at 0.46 mm and 4.36 kPa. Although EM powder leads to an increase in the stress under the magnetic field effect, the stress values remained the lowest at 1 mm deformation. Contrary to the sensitivity of powders to the magnetic field in Figure 4(a) and (b), the percent increase in stress was found quite high in the vertically oriented MR materials in Figure 4(c). The studies available have shown that vertically oriented materials generally yield better results in terms of strength values due to local orientations in the direction of deformation.^30,34,36

Hardness

The effect of hardness on MR materials is well known now. Static compression tests of different RTV silicon matrix materials with the same hardness value were performed.³⁷ Stress-deformation graphs of dynamic shear tests conducted with three different matrix materials of the same hardness are given in Figure 5. Silicone rubber types with a hardness value of shore A 40 were used in these graphs. The results show that the composite materials produced with these three matrix materials supplemented with SQ powder did not have any stress increase under the magnetic field. Graphs almost overlapped with each other. In order to demonstrate the effect of matrix materials on test results, the tests were done with five different matrix materials given in Figure 6. It is observed that there was an increase about 200% the effects of Shore A2 in Figure 6(c) and (b) Shore A10. This graphics can take different strain values as a result of substitution because they are nonlinear graphics. So Ingraphics that procured with magnetic field and without magnetic field, the value that the biggest exponential increase is used available parameter. On the contrary, overlapping test data are clearly shown on the graphs of the remaining three matrix materials. Therefore, given the sensitivity to powder type, matrix, and magnetic field, it has been concluded that tests are deemed suitable to do using matrix material with Shore A 2 hardness. Although these composite materials have low stress values in terms of strength, they can be used actively in applications where strength increase is needed with the influence of a magnetic field.

Magneto-rheological effect, storage, and loss modulus

The shear-stress-deformation characteristics demonstrate the viscoelastic properties of rubber-type MR elastomers called Fletcher–Gent or Payne effect. This effect is detected under cyclic loading conditions with small deformation amplitudes and depends on the effect of storage module on the applied deformation amplitude. For rubbers, the storage module rapidly decreases with an increase more than 0.1% in deformation amplitude and reaches its lower limit for deformations exceeding 20%. Physically, the Payne effect results from changes dependent on deformation in the microstructure of the material, namely from the breakage and recovery of weak physical bonds linking adjacent filler clusters.^38,39 Increasing the deformation amplitude in MREs leads to higher distances between the ferromagnetic particles, which leads to a reduction of the magnetic force between the polarizable particles and thereby increases the reduction of the shear modulus. Norouzi et al.⁸ studied the effect of the amplitude of the applied dynamic loading on the shear modulus and loss factor of MREs under different intensities of the magnetic field. The reduction in shear modulus is more pronounced under the higher intensity of the magnetic field. Their study also concluded that the loss factor is independent of the deformation level. The hardness value of the matrix material and powder particle type, as well as the characteristics such as magnetic field, frequency, and deformation exert an influence over the storage and loss modulus parameters. Figure 7 shows ShoreA 2 hardness, storage, and loss modulus graphs for different hardness and stroke values of MR elastomer material with ShoreA 2 hardness under non-oriented, horizontal and vertical conditions. Figure 7(a) and (b) shows the storage and loss modulus deformation graphs obtained with 1 mm stroke values. The graph demonstrates that the most increase in the storage and loss module is in the vertically oriented materials due to the magnetic field. The modulus value decreases up to 5% deformation while remaining constant at deformation more than 5%.

Graphs of storage and loss modulus and deformation obtained by using different hardness values are shown in Figure 7(c) and (d). Graphs of storage and loss modulus in materials with Shore 2 and 10 hardness show an exponential decrease up to 5% of deformation while an approximate linear situation is observed after 5% of deformation. As the hardness values increase, the exponential deformation region has receded more. In addition, the magnetic field has affected both parameters. However, there is no effect of magnetic field on the hardness values after Shore 10. The maximum increase was detected in the vertically oriented samples with Shore 2 hardness.

The loss and storage moduli of materials with the Shore 2 hardness were examined according to the hardness and powder type considering the 1 mm stroke. Besides, the loss and storage moduli at different stroke values with SQ powder are presented in Figure 7(e) and (f). When these graphs are examined, the most increase in the modules with the effect of the magnetic field is obtained at 1 mm stroke.

While it is important that comparing with elastomeric polymers in applications, we also need to understand the role of matrix material and powder type in the formation of MR effect. The MR effect was described in the previous section as the effect of the magnetic field applied on some physical properties of the magnetorheological elastomer. MR effect values are the largest in the small deformation values.³⁰ From this point of view, the relative MR effect values of four different types of magnetic powders were tested up to 8% deformation in Figure 8(a). As can be understood from the graph, while the relative MR effect values of all powder types increase, the highest increase is seen in SQ dust with 199% value. Schubert achieved an increase of approximately 119% within the 10% deformation limits. Furthermore, the graph given in Figure 8(b) is drawn to compare the MR effect values of matrix materials with different hardness. This graph shows that while the MR effect values at shore 2 and 10 hardness increased, there are very small variations among the materials with other hardness values. The mechanical properties of the graphs presented in Figure 8 is given in Table 4.

Table 4.

Mechanical properties of different matrix materials and powder types.

Powder type	Deformation (%)	Shear module (0 T) (kPa)	Shear module (0.226 T) (kPa)	Relative MR effect (%)
EM (Shore A 2)	1.31	4.79	8	67
SQ-I (Shore A 2)	0.33	3.22	3.22	99
CN (Shore A 2)	0.45	6.36	6.36	100
SQ
Shore A 2	0.45	1.59	4.77	199
Shore A 10	0.34	3.58	7.16	100
Shore A 25	0.02	6.45	12.89	100
Vario 40	0.21	18.98	25.32	33
Sorta 40	0.66	24.35	32.38	33
Shore A 59	0.05	16.88	25.32	50

The works on the rubber like materials concentrated for enhancing the mechanic features. It is required to be enhancing the features that are both static and dynamics. It is wanted that this materials should be enduring and long durable specially used in automotive industry. So with the work that made considering different parameter, ıt is researched ıf the materials are practical or not ın terms of lots of features.

Conclusions

In this study, parameters such as matrix materials with different hardness values, powder types, magnetic field, frequency, and deformation were evaluated. The analysis results obtained are summarized below:

- Dynamic shear tests were performed with silicon MRE materials using different hardness values and powder types. The test specimens were obtained as isotropic, horizontal, and vertical orientations. Then, the stress, storage, and loss modules and relative MR effect values were found.

- Hardness values directly affect the MR effects. The best MR effect values were found in materials with the Shore 2 hardness values in the graphs drawn with five different hardness values.

- As the hardness values increase, the strength values increase; however, the magnetic property decreases.

- When all the powder rates are considered, the relative MR effect values increase and the highest increase is observed in SQ powder with 199% value.

- The MR material obtained with SQ-I powder was found to be the most resistant, but the best powder ratio in terms of magnetic property was detected as SQ powder.

- Graphs of storage and loss modulus in materials with Shore 2 and 10 hardness show an exponential decrease up to 5% of deformation while an approximate linear situation is observed after 5% of deformation.

- As the hardness values increase, the exponential deformation region has receded more. In addition, the magnetic field influences both parameters. However, there is no effect of magnetic field on the hardness values after Shore 10.

- Hardness pulls the exponential deformation region further back. The magnetic field effect affects both parameters. However, in the article, there is no effect of the magnetic field on the hardness values after Shore 10. It has been determined that the MR material obtained with SQ-I powder is the strongest, but the best powder ratio in terms of magnetic properties is SQ powder.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ilhan Celik

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