Performance of natural rubber and silicone-based magnetorheological elastomers under large-strain combined axial and shear loading

Abstract

This study presents an experimental investigation on large-strain behavior of natural rubber– and silicone-based magnetorheological elastomers within a larger scope of structural vibration mitigation due to wind, traffic and seismic events. Magnetorheological elastomer samples with different weight percentages of iron particles, additives, and elastomer matrix were fabricated. The microstructures of specimens were examined, and their mechanical properties were investigated by a unique electromagnetic double-lap shear experimental setup capable of applying simultaneous compression and shear loads. The experimental results demonstrated that the isotropic natural rubber–based magnetorheological elastomers exhibit about 30% magnetorheological effect under large strains, while they achieve a higher magnetorheological effect under the combined axial and shear loading. The magnetorheological effect was 92% and 33% for 10% and 100% shear strains when 100 psi axial stress was applied. A natural rubber–based magnetorheological elastomer was further investigated applying dynamic cyclic load with and without compression load for different strains, frequencies, and magnetic field intensities. It was observed that for higher frequency, magnetorheological effect was reduced. Magnetorheological effects were 73% and 29% for 0.1 and 10 Hz frequencies, respectively, under 100 psi axial stress at 150% shear strain. The result of this study suggests that isotropic natural rubber–based magnetorheological elastomers may be suitable for high-demand-force applications, and in particular, in civil structures.

Keywords

Magnetorheological elastomers natural rubber carbon black shear and compression loading

Introduction

Conventional (passive) elastomers, such as natural rubber, have been utilized in structures, vehicles, and other machineries to mitigate shock and vibration. Passive elastomeric layers have limitations in accomodating a wide range of operating conditions. Magnetorheological elastomers (MREs) are a class of materials whose monotonic (shear modulus) and dynamic (storage and loss moduli) properties can be tuned by an external magnetic field. For the fabrication of MREs, magnetically permeable particles are mixed with an elastomeric matrix. When the mixture is cured under a magnetic field, iron particles form chains. On the other hand, when the mixture is cured without a magnetic field, iron particles randomly scatter in elastomer and result in an isotropic MRE. Polyurethane-based anisotropic MRE showed 20% better magnetorheological (MR) effect than anisotropic natural rubber MRE (Shen et al., 2004). Gong et al. (2005) investigated the relation between microstructure and mechanical properties of isotropic MREs and concluded that the isotropic MRE with 70%wt. iron particle showed 51% MR effect. Chen et al. (2007) reported 133% MR effect for the 80%wt. anisotropic natural rubber MRE.

Lokander and Stenberg (2003) demonstrated that natural rubber–based isotropic MR material with irregularly shaped iron particles has a better MR effect than with carbonyl iron. However, MR effect was reduced with a high-viscous matrix than the softer matrix due to less well-dispersed iron particles. The shear modulus of anisotropic MRE increases with increasing strain rate, magnetic field intensity, and pre-compressed loading (Behrooz et al., 2016; Jung et al., 2009). The increase in modulus is significant, if the applied stress is parallel to the particle alignment (Ruddy et al., 2012). A theoretical model based on effective permeability rule and the consideration of normal pressure concluded that the shear modulus of MREs increases with increased normal pressure and the influence of normal pressure is more significant at higher levels of the magnetic field (Dong et al., 2013). Schumann et al. (2017) analyzed magnetic field effect on the particle movement and concluded that magnetic field does have significant effect on rotation and translation of the particles. The addition of carbon black (CB) into the matrix enhances the passive shear modulus of isotropic and anisotropic MREs (Chen et al., 2008; Nayak et al., 2015). Qu et al. (2017) proved that carbon nanotubes can enhance field-dependent conductivity by at least two orders of magnitude. In a previous work by Yarra et al. (2017b), isotropic natural rubber MREs showed better MR effect than anisotropic silicone-based MRE at large strains. The stiffness of anisotropic MREs increases with increased frequency (Behrooz et al., 2016). Stepanov et al. (2007) demonstrated an increase in shear modulus and in loss modulus from three different experimental techniques such as elongation, quasi-static, and dynamic shear tests. Wen et al. (2017) demonstrated that storage modulus of isotropic and anisotropic MREs made of hard magnetic particles can increase with increasing magnetic field and decrease with increasing magnetic field in the opposite orientation. Also, asymmetric storage modulus curves were observed if the magnetizing field was higher than the test magnetic field.

Depending on the application of magnetic field during fabrication of MREs, different iron particle dispersion and different directional mechanical properties can be achieved. Isotropic and anisotropic MREs have been utilized in vibration absorption applications, such as vehicular powertrains (Hoang et al., 2010) and vehicle seat suspension (Du et al., 2011). Popp et al. (2010) built an MRE-based vibration absorber and demonstrated the capabilities in reducing vibrations. Deng et al. (2006) proved that resonance frequency of MRE-based adaptive tuned vibration absorber can be controlled by electrical currents. Also, MREs were used in controllable stiffness and damping devices to evaluate feasibility of adapting in civil engineering applications. MRE-based isolator was tested under shear and compression loading, and experimental results showed 175% increase in stiffness and 216% in damping at 40 Hz when the current was increased from 0 A to 1.5 A (Fu et al., 2013, 2017; Yang et al., 2014, 2015). Li et al. (2013) designed, developed, and tested an MRE-based seismic isolator and concluded that the stiffness and damping can alter up to 37% and 45%, respectively. Li and Li (2014) designed and tested MRE-based isolator and showed an increase of 16 times in lateral stiffness at 8% strain and 0.1 Hz. The optimal design of MRE bearings depends on particle volume fraction (Chen et al., 2016). Lujie et al. (2017) showed that MRE isolator can be used for vibration suppression of bridge-monitoring equipment. Yarra et al. (2017a) have presented a large-scale MRE bridge bearing that showed reduced MR effect of 12%–5% for strain amplitudes of 20%–50%.

Since there have been multiple studies on properties of MRE mainly in a low-strain regime, summary of mechanical properties from previous works is carried out to better compare with the current large-strain results. Based on the data presented in Table 1 and to the best of the our knowledge, the research to date on MREs has been mainly focused on small-strain regimes, loading, and scaled geometry which are not reliable, as MRE materials’ behavior is nonlinear in nature for higher strains. In addition, methods of testing that most of results presented in Table 1 are obtained do not replicate the method used to test isolation bearings for structures. Therefore, large-strains study of MREs is essential in the understanding of structural vibration isolation using MRE isolator, since large strains (up to 150%) are possible in structural events. In this study, test setup was designed such that both shear strain and compression force can be applied and controlled individually or at the same time on American Society for Testing and Materials (ASTM) standard size MRE samples. Electromagnets with extended trapezoidal prism shape were fabricated and used to apply uniform magnetic field focused to surface area of MRE samples. MR effects were studied experimentally using double-lap shear and compression method described in ASTM D5992 for natural rubber and platinum silicone MRE samples for large strains.

Table 1.

A summary of MR effect under different loading conditions.

Reference (year)	IP (%)	Area ofsample (in²)	Thickness(in)	Loading conditions			G_off (psi)	G_on (psi)	ΔG/G₀(%)	Work type
Reference (year)	IP (%)	Area ofsample (in²)	Thickness(in)	Freq. (Hz)	Strain (%)	B (T)	G_off (psi)	G_on (psi)	ΔG/G₀(%)	Work type
Jolly et al. (1996)	30v	0.23	0.04	2	1	0.85	261	342	31	E
Jolly et al. (1996)	30v	0.23	0.04	2	10	0.85	261	290	11	E
Ginder et al. (1999)	27v	NA	NA	2	10	1	319	435	36	E
Ginder et al. (1999)	40v	NA	NA	2	3	1	435	566	30	E
Ginder et al. (1999)	40v	NA	NA	2	6	1	391	471	21	E
Ginder et al. (1999)	40v	NA	NA	2	12	1	290	341	17	E
Davis (1999)	27v	NA	NA	NA	14	>1	109	145	33	FEM
Davis (1999)	27v	NA	NA	NA	19	>1	87	115	32	FEM
Shen et al. (2004)	25v	NA	NA	1^a	11.5	0.4	64	82	27	E
Deng et al. (2006)	70w	NA	NA	10	NA	0.9	87	197	126	E
Deng et al. (2006)	70w	NA	NA	20	NA	0.9	93	210	127	E
Deng et al. (2006)	70w	NA	NA	30	NA	0.9	96	218	126	E
Gong et al. (2007)	80w	NA	NA	5	2	1	49	484	882	E
Chen et al. (2008)	33v	0.16	0.12	1	0.30	0.8	152	286	88	E
Chen et al. (2008)	33v	0.16	0.12	1	0.30	0.8	255	498	95	E
Chen et al. (2008)	33v	0.16	0.12	1	0.30	0.8	561	1146	104	E
Jung et al. (2009)	30v	0.38	1.50	0.1	7.80	0.5	223	325	46	E
Liao et al. (2013)	80w	0.12	0.04	0.06^a	10	1.1	10	50	390	E
Behrooz et al. (2015)	50w	0.44	0.50	0.10	17.50	0.2	52	61	16	E
Schubert andHarrison (2015)	20w	2.32	1.00	50^a	45	0.3	297	467	57	E
Li and Li (2015)	70w	17.53	0.98	0.10	8	3^b	1	20	1629	E
Li and Li (2015)	70w	17.53	0.98	0.10	32	3^b	1	12	881	E
Li and Li (2015)	70w	17.53	0.98	4	8	3^b	2	21	848	E
Li and Li (2015)	70w	17.53	0.98	4	32	3^b	2	13	530	E
Yang et al. (2015)	70w	17.53	0.16	NA	NA	1.5^b	6	28	330	E
Behrooz et al. (2016)	80w	0.99	0.20	0.10	10	0.8	58	88	53	E
Behrooz et al. (2016)	80w	0.99	0.20	0.10	50	0.8	32	45	39	E
Behrooz et al. (2016)	80w	0.99	0.20	0.100	30	0.8	43	56	32	E
Behrooz et al. (2016)	80w	0.99	0.20	5	30	0.8	49	67	39	E
Chen et al. (2016)	5v	1.10	1.18	0.2	6.67	3^b	46	86	87	E
Chen et al. (2016)	11v	1.10	1.18	1	6.67	3^b	49	92	88	E
Chen et al. (2016)	15v	1.10	1.18	2	6.67	3^b	61	120	95	E
Yarra et al. (2017a, 2018)	80w	7.07	1.25	0.10	20	19.5	592	665	12	E
Yarra et al. (2017a, 2018)	80w	7.07	1.25	0.10	50	19.5	513	540	5	E
Yarra et al. (2017b)	80w	1.00	0.20	0.10	30	0.7	137	152	11	E
Yarra et al. (2017b)	76w	1.00	0.20	0.10	30	0.7	33.3	50.2	51	E

E: experimental; FEM: finite element method; NA: not available; IP: iron particles.

mm/min.

Amp.

MRE specimens fabrication process

Isotropic and anisotropic standard size (ASTM, 2011) MREs with silicone and natural rubber matrices, different weight percentages of carbonyl iron particles and additives were fabricated. Elastomer matrix used in the mixture to fabricate anisotropic MRE samples were TAP platinum silicone, which is a bi-component comprised of silicone side A base and silicone side B catalyst with a weight ratio of 1:1, which should be mixed to catalyze the polymer and carbonyl iron particles with an average size of 5 micron (Sigma-Aldrich company, St. Louis, MO). In addition, carbon nanofibers (CNFs), type PR-19-XT-PS (Pyrograf Products, Inc, Cedarville, Ohio) contain less than 14,000 ppm of iron and average diameter of nanofiber is 150 nm (0.15 micron), were included in the mixture to further enhance the magnetic field by linking iron particles together as an additive, and CB, type SR303 (SidRichardson carbon and energy Co, Fort Worth, TX), was used as an additive to increase base passive shear modulus.

In this study, maximum weight percentage of additives was used to achieve highest mechanical and magnetic properties, possible for current samples. Maximum weight percentage of CNFs and CB was determined by mixing different weight percentage of CNF and CB into the base mixture and observing molding capability of the mixture. The different weight percentage of these composites are mixed in a beaker and then placed into a mold designed to produce ASTM (2011) standard size (1.6 in × 0.625 in × 0.2 in) MRE samples. To remove any air bubbles, the mold was kept in a vacuum chamber until the pressure reaches to −70 kPa. Finally, the mold was placed into the electromagnet and cured under 1.2 T magnetic field.

Isotropic natural rubber, type TSR 20 MRE slabs (10 in × 10 in × 0.5 in) comprised different weight percentage of carbonyl iron particles, and CB was fabricated using rubber mills. The natural rubber–based MRE slabs were cut to ASTM standard size to compare with anisotropic silicone-based MRE material properties. Figure 1(a) shows natural rubber–based MRE with carbonyl iron particles and CB. Figure 1(b) and (c) shows silicone-based MREs with added iron particles, CB (Figure 1(b)) and CNF (Figure 1(c)). Reduction in elongation was observed due to carbonyl iron particles and CB presence in natural rubber–based MRE. Silicone-based MRE fabricated with CNF showed smooth surface than made with CB. The material compositions of different tested MRE samples are summarized in Table 2.

Table 2.

The composition of different MRE samples.

Test ID	Polarized particles	Additives		Matrix
	Iron particle (g)	Carbon black (g)	Carbon nanofiber (g)	TAP platinum silicone		Natural rubber
	Iron particle (g)	Carbon black (g)	Carbon nanofiber (g)	Side A: base (g)	Side B: catalyst (g)	TSR 20 (g)
MRE-S-3	80.0	2.0	0.0	9.00	9.00	0.0
MRE-S-4	80.0	1.0	0.2	9.40	9.40	0.0
MRE-S-5	80.0	0.0	0.3	9.85	9.85	0.0
MRE-S-6	75.0	0.0	1.0	12.00	12.00	0.0
NR-S-1	80.0	0.0	0.0	0.0	0.0	20.00
NR-S-4	77.6	3.0	0.0	0.0	0.0	19.40

MRE: magnetorheological elastomer.

A scanning electron microscope (SEM) (HitachiS-4700, Hitachi Ltd., Tokyo) was used to understand the microstructure of silicone- and natural rubber–based MREs. The MRE samples were cut into small pieces by submerging in liquid nitrogen to achieve smooth sectional surface. Subsequently, the surface of the MRE sample was coated with a thin layer of platinum by a turbo sputter coater for SEM microstructure analysis. Figure 2(a) represents silicone MRE with 50%wt. iron particles and 5%wt. CB. As can be seen in Figure 2(a), iron particles were arranged in chain-like forms because MRE was cured under magnetic field. Figure 2(b) shows isotropic microstructure of natural rubber–based MRE sample that was cured without a magnetic field. This sample included 80%wt. iron particles and 5%wt. CB.

Experimental setup

A unique double-lap shear and compression test setup was designed and fabricated as shown in Figure 3. The test setup was used to conduct monotonic and sinusoidal cyclic experiments to characterize quasi-static (shear modulus) and dynamic (storage and loss moduli) properties of MRE samples. The test setup was designed such that the electromagnets generate a closed-loop magnetic field with a strength of 0.6 T at 4 A using TDK-Lambda Corporation’s (Minato-ku, Tokyo, Japan) GEN 300-5 power supplies through the thickness of MRE samples and was verified by ANSYS Maxwell FEA simulation. Rubber pads were used on both sides of electromagnets to apply uniform compression load over an entire surface area of MRE samples. The test setup shown in Figure 3 was used to apply a shear load, compression load, and magnetic field on the ASTM (2011) standard size MRE samples. The actuator was used to apply shear strain, and inbuilt load cell and displacement transducer of the MTS testing machine were used to measure the shear force and associated strain amplitude in the MRE samples during the tests. Pre-compression handle was used to apply compression force and the shear force and associated strain amplitude were measured using external load cell as shown in Figure 3.

Experimental results and discussion

Monotonic experiments

The main objective of monotonic experiments was to identify quasi-static material properties such as shear modulus of silicone-based and natural rubber–based MREs. Experimentally observed shear force–displacement response for the silicone- and natural rubber–based samples due to monotonically applied forces are shown in Figures 4 and 5, respectively.

Specimens were subjected to monotonically increasing shear strains (10%, 30%, 50%, 75%, and 100%) with applied magnetic field intensities of 0, 0.3, 0.5, and 0.6 T. Each test was repeated five times to ensure repeatability, and average results are presented. Based on the experimentally recorded response data, the MR effect (i.e. change in apparent shear modulus with respect to passive mode shear modulus) is quantified by equation (1)

% M R e f f e c t = \frac{G_{o n} - G_{o f f}}{G_{o f f}} * 100

(1)

where $G_{off}$ is the shear modulus obtained with no applied magnetic field, and $G_{on}$ is shear modulus obtained under a magnetic field. As can be seen in Figures 4 and 5, silicone- (MRE-S-5) and natural rubber– (NR-S-4) based MRE samples show various levels of MR effect due to applied magnetic field under pure shear. It was observed that the MR effect can be characteristically different for cases when iron particles are distributed isotropically or anisotropically within the elastomeric compound. The MR effect reduces significantly at large strains (Table 3) for silicone-based anisotropic MRE samples due to increasing distance between iron particles, which are initially aligned in chain-like formations. Furthermore, as these chain-like formations are subjected to shear deformations, the apparent magnetic field intensity diminishes (Table 3). However, silicone MREs can be recommended for low-strain application due to high MR effect. Also, it can be observed from Table 3 that the base passive shear modulus for MRE-S-5 is lower than the MRE-S-4 sample due to the absence of CB in MRE-S-5 sample. MRE-S-5 shows higher MR effect (Table 3) than MRE-S-4 sample due to the higher weight percentage of CNF presence in MRE-S-5 sample. Therefore, it may be concluded that CB and CNFs served their purpose as intended. CB was used to improve base passive shear modulus and CNF was used to link iron particles together and to improve magnetic permeability of MR materials (Luo et al., 2015). Less iron content (75 g) in MRE-S-6 leads to reduced MR effect than MRE-S-5 which has 80 g even though MRE-S-6 has 1 g CNF compared to 0.3 g in MRE-S-5. The iron content influences MR effect more than CNF.

Table 3.

Effective shear modulus values of different silicone MREs under pure shear.

Effective shear modulus (psi)
	MRE-S-3			MRE-S-4			MRE-S-5			MRE-S-6
Shear strain (%)	10	30	50	10	30	50	10	30	50	10	30	50
G_off	74.5	79.2	85.0	86.8	84.2	91.2	79.6	62.8	68.0	72.2	78.0	78.6
G_on	94.1	86.1	86.3	98.9	91.5	93.6	104.3	78.4	76.1	96.0	89.2	83.4
% MR effect	26	9	1	14	9	3	31	25	12	33	14	6

MRE: magnetorheological elastomer; MR: magnetorheological.

In case of natural rubber–based isotropic MRE sample (NR-S-4), it was observed that the MR effect for shear modulus was very stable (Table 4). The MR effect for 0.1 Hz frequency remained nearly constant (approximately 30%) for all strain amplitudes and with no axial force. The constant MR effect on shear modulus is attributed to the nominally isotropic material composition. The random distribution of iron particles allows the formation of alternative and desirable magnetic field paths irrespective of the deformation field within the material.

Table 4.

Effective shear modulus for different natural rubber MREs under pure shear.

Effective shear modulus (psi)
	NR-S-1					NR-S-4
Shear strain (%)	10	30	50	75	100	10	30	50	75	100	150
G_off	202.2	60.9	40.0	33.6	25.5	100.1	50.7	34.7	27.0	23.1	22.0
G_on	217.2	69.9	51.8	41.5	32.5	132.1	64.4	43.7	35.0	30.5	29.4
% MR effect	7	15	29	23	28	32	27	26	30	32	33

MRE: magnetorheological elastomer; MR: magnetorheological.

Figure 6 shows the MR effect of natural rubber–based MRE (NR-S-4) under combined loading. Natural rubber MRE (NR-S-4) demonstrated a better MR effect under axial force; however, the MR effect reduced with increasing strains. It was observed that at 10% and 100% strain with 100 psi axial stress, the MR effects were 92% and 33% (Table 5), respectively. This observation is attributed to the fact that axial force reduces the spacing between iron particles, thus increases forces, thereby enhancing the magnetic field. At constant axial force, increased strain pulls iron particles away from each other thus causes reduced MR effects shown in Table 5. However, at 75% strain, the observed MR effect was 26%, which is less than the MR effect (33%) at 100%. Test conditions, such as temperature of the room, wait time to run the test, timing to switch on power supplies to create magnetic field, distribution of iron particles while fabricating natural rubber–based isotropic MREs, and arrangement of iron particles due to applied magnetic field are possible reasons. The effective shear modulus values for all tested samples are summarized in Table 3 through Table 5.

Table 5.

Effective shear modulus values of NR-S-4 under combined compressive and shear loading.

Effective shear modulus (psi)
	NR-S-4
Shear strain (%)	10	30	50	75	100
G_off	40.9	31.8	27.4	26.3	20.9
G_on	78.7	50.6	39.5	33.1	27.7
% MR effect	92	59	44	26	33

MR: magnetorheological.

Sinusoidal cyclic experiments

Monotonic test results demonstrated that the NR-S-4 was the best candidate for further investigation. A series of sinusoidal cyclic experiments were conducted to study viscoelastic properties and effective stiffness of NR-S-4 sample under varying strain amplitudes (10%, 30%, 50%, 75%, 100%, 125%, and 150%), test frequencies (0.1, 0.5, 1, 3, 5, 7, and 10 Hz), and magnetic field intensities of 0, 0.3, 0.5, and 0.6 T. The loading and unloading cycles were repeated until the load–displacements curve stabilized. The storage and loss moduli were obtained using equations (2) and (3), respectively. The effective stiffness was determined from the second cycle of force–displacement hysteresis by equation 17.8-1 of American Society of Civil Engineers (ASCE-7-16, 2016) as shown in equation (4). The effective damping was determined from the force–displacement loop by using equation 17.8-2 of ASCE-7-16 (2016) as shown in equation (5)

G' = \frac{τ}{γ \cos δ}

(2)

G ″ = \frac{τ}{γ \sin δ}

(3)

k_{eff} = \frac{| F^{+} | + | F^{-} |}{| Δ^{+} | + | Δ^{-} |}

(4)

β_{eff} = \frac{2}{π} [\frac{E_{loop}}{k_{eff} {(| Δ^{+} | + | Δ^{-} |)}^{2}}]

(5)

where δ is the phase lag measured from the shear stress and shear strain responses. $F^{+}$ and $F^{-}$ are the positive and negative forces, at $Δ^{+}$ and $Δ^{-}$ , respectively. $E_{loop}$ is the energy dissipated per cycle, $k_{eff}$ is the effective stiffness, and Δ⁺ and Δ⁻ in equation (5) are the peak displacements in force–displacement hysteresis curve.

The effect of frequency on storage and loss moduli of NR-S-4 is shown in Figure 7. Both moduli increase with increasing test frequency, whereas MR effect reduces with increasing frequencies. As can be seen in Figure 8, the NR-S-4 sample shows an increase in magnetic field results in increase in storage and loss moduli for any given strain amplitude. Unlike silicone MREs, the natural rubber–based MREs show a uniform MR effect with increasing strain amplitudes. For storage modulus, NR-S-4 sample achieved approximately 41%, 47%, 56%, 74%, and 55% MR effect at 10%, 30% 50% 100%, and 125% strain amplitudes, respectively. For the loss modulus, experimentally determined MR effects were 60%, 52%, 50%, 57%, and 50% at 10%, 30%, 50%, 100%, and 125% strain amplitudes, respectively, which implies a constant damping capacity for all strain amplitudes.

Figures 9 and 10 show the shear force–deformation response for different strain amplitudes (10% and 125%), test frequencies (0.1, 3, 7, and 10 Hz), and applied magnetic fields. Accordingly, the effective stiffness and effective damping values show increasing trend with increasing magnetic field intensity. Effective stiffness increases with increased loading rate. However, effective damping values show decreasing trend with increased loading rate. Table 6 summarizes the effective stiffness and damping values with the corresponding MR effect. The MR effect of effective stiffness shows decreasing trend with increasing frequency. Also, it was observed that the effective damping for small strains show increasing trend, while it shows nearly unaffected for large strains. The MR effect on effective stiffness at different strains depend on the formation of magnetic paths and magnetic intensity of those paths due to randomly distributed iron particles.

Table 6.

Summary of effective stiffness and damping values and their corresponding MR effect of NR-S-4.

Effective stiffness (kip/in)					Effective damping
Frequency, Hz	0.1	3	7	10		0.1	3	7	10
10% shear strain
K_off	1795	3587	3822	4166	β_eff _{: off}	0.12	0.09	0.07	0.07
K_on	2772	4544	5159	5167	β_eff _{: on}	0.14	0.12	0.10	0.11
% MR effect	54	27	35	24		17	33	43	57
30% shear strain
K_off	1119	2277	2703	2895	β_eff _{: off}	0.17	0.14	0.12	0.11
K_on	1654	2807	3039	3271	β_eff _{: on}	0.18	0.15	0.15	0.14
% MR effect	48	23	12	13		6	7	25	27
50% shear Strain
K_off	899	1775	2030	2161	β_eff _{: off}	0.19	0.17	0.16	0.15
K_on	1236	2129	2352	2543	β_eff _{: on}	0.20	0.18	0.17	0.16
% MR effect	37	20	16	18		5	6	6	7
75% shear Strain
K_off	892	1609	1833	1922	β_eff _{: off}	0.21	0.17	0.16	0.16
K_on	1004	1555	1753	1956	β_eff _{: on}	0.21	0.21	0.20	0.19
% MR effect	13	3	4	2		0	24	25	19
100% shear strain
K_off	561	1210	1438	1530	β_eff _{: off}	0.22	0.21	0.19	0.19
K_on	932	1498	1664	1735	β_eff _{: on}	0.25	0.22	0.20	0.20
% MR effect	66	24	16	13		14	5	5	5
125% shear strain
K_off	510	1083	1253	1362	β_eff _{: off}	0.24	0.22	0.21	0.20
K_on	775	1289	1461	1540	β_eff _{: on}	0.26	0.23	0.22	0.22
% MR effect	52	19	17	13		8	5	5	10

MR: magnetorheological.

To evaluate the effect of compressive stress on the behavior of natural rubber MRE (NR-S-4), a constant compression force of 100 lb (100 psi) was applied, and the tests were repeated for all strain amplitudes, frequencies, and magnetic fields described previously. Figure 11 shows the effect of frequency on storage and loss moduli under combined loads. As can be seen, both moduli increase with increased frequency. The effect of magnetic field on storage and loss moduli is shown in Figure 12. Increased magnetic field yields increased storage and loss moduli for any given strain amplitude under a compression stress of 100 psi. Storage and loss moduli of natural rubber MRE (NR-S-4) sample showed nearly constant MR effect (65% and 55% for storage and loss, respectively) over a wide range of strain amplitudes from 10% to 150%.

Figures 13 and 14 show the cyclic shear force–deformation relationship for 10% and 150% strain amplitudes and different frequencies (0.1, 3, 7, and 10 Hz) with varying magnetic field intensities (0 and 0.6 T). The effective stiffness increases with increasing magnetic field intensity for any test frequency and strain amplitude. Also, it was observed that the effective stiffness shows increasing trend with increased frequency at any given strain. The MR effect was 29% for the frequency of 10 Hz and strain amplitude of 150%. As shown in Table 7, the MR effect of effective damping shows increasing trend with increasing frequency at 10% strain. However effective damping, equation (5), MR effect was insignificant for large strains (Table 7). Summary of effective stiffness and damping values with their corresponding MR effect are presented in Table 7. The MR effect of effective stiffness reduces with increased frequency. In addition to desirable magnetic field paths due to uniformly dispersed iron particles, the compression force brings iron particles closer to each other and improves the strength of the magnetic field that results improved MR effect.

Table 7.

Summary of effective stiffness and damping values and their corresponding MR effect of NR-S-4.

Compression force (p = 100lb)
Effective stiffness (kip/in)					Effective damping
Frequency, Hz	0.1	3	7	10		0.1	3	7	10
10% shear strain
K_off	1832	3750	4070	4086	β_eff _{: off}	0.17	0.10	0.09	0.08
K_on	2613	4487	5087	5295	β_eff _{: on}	0.17	0.13	0.13	0.13
% MR effect	43	20	25	30		0	30	44	63
30% shear strain
K_off	1007	2261	2728	2903	β_eff _{: off}	0.19	0.16	0.15	0.14
K_on	1539	2793	3189	3281	β_eff _{: on}	0.20	0.17	0.16	0.17
% MR effect	53	24	17	13		5	6	7	21
50% shear strain
K_off	780	1646	2054	2046	β_eff _{: off}	0.22	0.20	0.18	0.19
K_on	1115	2053	2390	2482	β_eff _{: on}	0.22	0.21	0.19	0.19
% MR effect	43	25	16	21		0	5	6	0
75% shear strain
K_off	597	1369	1614	1673	β_eff _{: off}	0.24	0.22	0.21	0.21
K_on	910	1619	1844	1899	β_eff _{: on}	0.26	0.23	0.22	0.23
%MR effect	52	17	14	14		8	5	5	10
100% shear strain
K_off	488	1105	1323	1379	β_eff _{: off}	0.26	0.24	0.22	0.23
K_on	779	1365	1547	1685	β_eff _{: on}	0.27	0.25	0.24	0.23
% MR effect	60	24	17	22		4	4	9	0
150% shear strain
K_off	524	1053	1230	1313	β_eff _{: off}	0.37	0.36	0.35	0.35
K_on	909	1456	1585	1692	β_eff _{: on}	0.41	0.37	0.35	0.36
% MR effect	73	38	29	29		10	3	0	3

MR: magnetorheological.

Summary and conclusion

Different anisotropic silicone-based and isotropic natural rubber–based MREs were fabricated. Monotonic and cyclic experiments were conducted to investigate the static and dynamic properties of MREs. Monotonic experimental results demonstrated that silicone-based MREs are a good choice for lower strain applications due to high MR effect. However, the MR effect reduces with increasing shear deformations due to the increased distance between iron particles that reduces magnetic field flow intensity. CNF improved the performance of silicone-based anisotropic MRE (MRE-S-5) and showed 31% and 12% MR effect at 10% and 50% shear strains, respectively. This is attributed to the magnetic permeability of CNFs, which resulted in higher MR effects.

Natural rubber–based MREs demonstrated constant MR effect (around 30%) at all strain levels due to random dispersion of distributed iron particles that allows the formation of alternative magnetic field paths irrespective of the deformation. For natural rubber MRE (NR-S-4) at 10% and 100% strain with 100 psi axial stress, the achieved MR effects were 92% and 33% (Table 5) compared to 32% and 32% (Table 4) under no axial stress, respectively. This observation is attributed to the fact that axial force; hence, axial deformation, reduces the spacing between iron particles, thereby enhancing the magnetic field.

Furthermore, sinusoidal cyclic experiments ofNR-S-4 for both cases: (1) without compression and (2) with compression for any given strain and/or frequency, the effective stiffness and damping showed increasing trend with increased magnetic field intensity. The MR effect on the effective stiffness reduced with increased frequency. The MR effect on the effective damping for NR-S-4 sample was 57% at 10% shear strain and 10 Hz test frequency. Also, it was observed that the MR effect on the effective damping varied from 2% to 13% for all other shear strains (30%, 50%, 75%, 100%, and 125%) and applied frequencies (0.1, 3, 7, and 10 Hz) without compression load (Table 6). However, 63% MR effect was observed at 10% strain at 10 Hz test frequency under a uniform compression stress of 100 psi. For all other strains and frequencies, MR effect on the effective damping was varied between 3% to 21%.

Footnotes

Acknowledgements

The authors would like to express their gratitude to Advanced Materials and Devices, Inc and to Scougal Rubber Corporation for helping with this effort. The authors also acknowledge employees of Advanced Materials and Devices, Dr Barkan Kavlicoglu and Mr Kyle Willens. The authors also wish to thank Mr Pete Etcheverry of Scougal Rubber Corporation. Finally, the authors would like to thank undergraduate assistants Mr David Mar and Mr Nathan Pinuelas.

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was funded by the Federal Highway Administration under the contract number DTFH61-13-C-00020.

ORCID iD

Faramarz Gordaninejad

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