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Elastic modulus of viscoelastic magnetic silicone gel body.


It was recently discovered that flow rate control can be performed by magnetic fluid membranes that are capable of freely changing the cross section of a pipe under a magnetic field (1), (2). However, a magnetic fluid membrane can only sustain a pressure difference within a limited range since it can withstand only small magnetic traction forces. At high pressure differences and high Reynolds numbers, the structure of the membrane will break, adversely affecting its flow control ability. In order to overcome the above drawback (3-7), it is very desirable to develop a new type of viscoelastic magnetic material with a volumetric configuration capable of changing substantially under a magnetic field.

The viscoelastic magnetic material proposed in this study is a mixture of a viscoelastic silicone gel and fairly large sized ferromagnetic particles. In this mixture, evenly dispersed particles with strong magnetization characteristics are only capable of moving finitely in accordance with the deformation of the silicone gel. Under an applied magnetic field, the viscoelastic magnetic mixture is deformed by magnetic traction force, which is a function of the gradient of the applied magnetic field. The focus of this study was to identify the mechanical properties of viscoelastic magnetic silicone gel bodies through tensile tests (8), (9) carried out under varying magnetic field strengths. Particular attention was given to the effects of the size and magnetic properties of the ferromagnetic particles, and combinations of different silicone gels on the moduli of the resultant viscoelastic bodies.


The tensile tests of the viscoelastic magnetic silicone gel bodies were conducted with a tensile testing machine. The tensile load applied to the test piece was measured by a load cell attached to the tensile section of the machine. The accuracy of the load measurement was controlled within [+ or -]0.5%, considering the testing machine accuracy of setting the tensile strain rate. The test piece was fixed in the tensile test section with the load cell attachment, as photographically displayed in Fig. 1.


It should be mentioned that, in the actual experiment, the test piece was fixed after an electromagnet was installed. The tensile test was carried out by setting a constant magnetic field strength for each test and keeping the temperature of the magnet constant by means of an air gun. In order to prevent drift of the magnetic field strength due to changes in the electric resistance of the electromagnet coil caused by rises in temperature, the temperature of the coil was constantly monitored with a thermocouple attached to the coil and cooled by adjusting the air gun. This ensured that no drifting of the magnetic field would occur due to changes in coil temperature within the accuracy of the measurement.

Electromagnet and Magnetic Field Distribution

Figure 2 schematically shows the arrangement of the solenoid coil electromagnet and the test piece. As displayed in Fig. 2, a cylinedrical solenoid coil with an outer diameter of [[empty set].sub.0] = 28 mm was placed coaxially to the outside of the test piece. The solenoid coil was made of polyester-polyamide coated by copper winding wire with a diameter of 0.37 mm. The number of windings of the coil was 1390. The coil was driven by a 24 V DC current capable of generating a maximum magnetic field strength of [H.sub.max] = 0.05 MA/m at the center of the test piece with an applied current of I = 1.7 A.


Figure 3 shows the typical magnetic field distribution H = ([H.sub.r],[H.sub.z]) in 3-D space. This figure shows the distribution of the axial magnetic field [H.sub.z] (a) and a similar distribution of the radial magnetic field [H.sub.r] (b). It should be noted that the coordinates in Fig. 3 were taken from the cylindrical coordinate system based on the original (zero) point lying at the center of the test piece (see Fig. 2). Hereafter, the applied magnetic field (strength) H is nominally represented by the strength of magnetic field at the origin of the coordinates, i.e., H = [H.sub.z] at r = 0 and z = 0. The magnetic field distribution (for example, Fig. 3) generated by the electromagnet is a typical magnetic field of a solenoid coil. The distribution was measured by traversing a Hall probe (Gauss meter) through the inner space of the solenoid coil without the test piece in place. Thus, in this study, the magnetic field was an external held related to the test piece. Each tensile test was performed after imposing a steady and constant magnetic field to the test piece.


Preparation of Viscoelastic Magnetic Silicone Gel Body

This study used a silicone gel including ferromagnetic particles as a test sample of a viscoelastic magnetic silicone gel body. As a result, large deformation under a magnetic field could be expected. Special care was taken to choose a type of viscoelastic silicone gel material in order to meet the conditions of causticity resistance to air and water, and high intermolecular force so that the ferromagnetic particles, which have an arbitrary shape and size, are evenly and stably dispersed at room temperature after the solidification process. To meet these conditions, two types of silicone gels were used in the study: SE1885 (Toray Dow Coming) and TSE3062 (Toshiba GE Corporation). By mixing these two gel bodies in the appropriate ratios (one of the two is a hardening agent), and adding the appropriate ferromagnetic particles, it was possible to produce silicone gel mixtures with different mechanical characteristics at room temperature before injecting into a mold for the solidification process. The typical mechanical properties of the two silicone gels are tabulated in Table 1. Two types of ferromagnetic particles were used in this study: Carbonyl SQ (Fe, C: manufactured by BASF Co., Ltd) and IR-L3 ([Fe.sub.2][O.sub.4], Ni, Cu, Zn: manufactured by TDK Co., Ltd). The mean particle size was approximately 5.4 [micro]m for Carbonyl SQ and approximately 26 [micro]m for IR-L3. Figure 4 shows the size distribution and scanning electron microscope (SEM) images of the two particle types. As seen in Fig. 4, the Carbonyl SQ particles are highly spherical with good globosity while the TR-L3 particles are nonspherical with a fairly wide size distribution, indicating that the particles have very irregular shapes. Table 2 summarizes the mechanical properties of the particles. In preparation of the various kinds of viscoelastic magnetic silicone gel bodies, meticulous attention was paid to degassing the mixtures, which was performed in a vacuum chamber prior to injecting into the mold. Figure 5a and b show images of the cross section area of the test pieces for the Carbonyl SQ-particle and IR-L3-particle dispersed gel bodies, respectively. The images were synthesized with a superdepth 3D microscope by scanning the electrical signal transmitted by the photo multiplier received from laser beam reflection at the rate of 4000 scans in every 0.02 [micro]m view area. As observed from Figs. 5a and b, the particles were distributed very evenly in both cases, even with the IR-L3-particle body gel.


TABLE 1. Properties of silicone gels.

Silicone gel  Type         Density       Elastic     Penetration depth
                       [kg/[m.sup.3]]    modulus

TSE3062       Two            970           0.89              55

SE1885        Two            980           0.46              90

TABLE 2. Properties of ferromagnetic particles.

Ferromagnetic  Shapes             Density        Mean       Magnetic
particles                      [kg/[m.sup.3]    particle  ermeability
                                                 size         [-]

Carbonyl SQ    Globosity           2500           5.4         7.83
IR-L3          Nonspherocytic      5100           26         10.02

The tensile tests were then carried out using the tensile machine at a 5 mm/min tensile rate with a maximum tensile test length of 15 mm. Various viscoelastic magnetic silicone gel bodies can be made for various magnetic field strengths by combining silicone gels and ferromagnetic particles in different volumetric concentrations. However, this paper reports only four cases with a particle concentration of 35 vol% and an applied magnetic field strength of H = 0.05 MA/m as representative data, which show typical trends. Table 3 lists the viscoelastic magnetic silicone gel body test pieces numbered from 1 to 4. The magnetic permeability of the particles and gel bodies are listed in Tables 2 and 3.
TABLE 3. Representative viscoelastic magnetic silicone gel bodies
tested in the present investigation.

No.  Ferromagnetic particles  Silicone gel  Combination    Magnetic
                                               ratio     permeability
                                               [vol%]         [-]

1    Carbonyl SQ              TSE3062          35:65         3.80
2    Carbonyl SQ              SE1885           35:65         3.80
3    IR-L3                    TSE3062          35:65         5.83
4    IR-L3                    SE1885           35:65         5.83


As the results of this study, the relationship between stress and strain is described for each test piece (nos. 1-4) at a constant magnetic field of H = 0.05 MA/m and no magnetic field H = 0. The strain of the test piece is defined by

[epsilon] = [[DELTA]l/[l.sub.o]], (1)

where [DELTA]l is the tensile length and [l.sub.o] is the natural length of the test piece. It should be noted that the stress [tau] is defined by

[tau] = [F/[[DELTA].sub.a]], (2)

where F is the tensile load and [[DELTA].sub.a] is the mean cross sectional area of the test piece, which was measured by a microgauge when the tensile load was applied.

Figures 6a and b present the tensile test results. Each figure compares test piece nos. 1-4 for clarity. Figure 6a shows the experimental results for test piece nos. 1 and 2, which contain Carbonyl SQ particles at 35 vol% with different dispersant gels. No. 1 is a hard type with a high elastic modulus and low penetration depth (TSE3062: 65 vol%), and no. 2 is a soft type with a low elastic modulus and high penetration depth (SE1885: 65 vol%). As observed in Fig. 6a, the elastic modulus E,


E = [[tau]/[epsilon]] (3)

is almost constant, indicating that the gel bodies of test piece nos. 1 and 2 are linear elastic materials when there is no magnetic field. However, it was observed that E increases when the magnetic field was applied, indicating that a hardening effect occurred. The increment of hardening for test piece no. 1 is higher than that for no. 2. Particularly, E was found to be nonlinear with test piece no. 1 when the magnetic field was applied. The average increment rate [E.sub.a] = ([E.sub.1] - [E.sub.10])/[E.sub.10] was approximately 17% for test piece no. 1, while, for no. 2, the average increment rate [E.sub.a] = ([E.sub.20] - [E.sub.20])/[E.sub.20] was approximately 32%. The average strain difference for test piece no. 2, which is the difference of strain at a given stress with and without an applied magnetic field, was greater than that for test piece no. 1 by about [[([DELTA][[epsilon].sub.2] - [DELTA][[epsilon].sub.1])]/[[DELTA][[epsilon].sub.1] = 41%]]. This fact indicates that the soft gel body deformed much more than the hard gel body for a given stress when the magnetic field was applied, although the increase in elasticity of the soft gel was less than that of the hard gel. This phenomenon is quite understandable. The soft gel has a lower modulus and can deform more extensively than the hard gel for the same magnetic traction force, which can be represented as the Kelvin force density (10), M[nabla]H (M is the magnetization). It is also thought that, except for the original stress (without a magnetic field), the magnetic traction force can yield an additional resistive force, so the magnetic field increases the resultant modulus for each gel body. The complicated interactions of the elastic force and the magnetic force cause the nonlinearity of the hard gel (with higher elasticity and penetration depth).

In a similar manner, Fig. 6b displays the results for test piece nos. 3 and 4 with the IR-L3 magnetic particles. Increases in the modulus without the magnetic field were observed, although the average volumetric concentrations of the magnetic particles were the same as in test piece nos. 1 and 2. This is probably due to the wide size distribution band and irregular shape of the IR-L3 magnetic particles, which create a higher contact surface with the dispersant gel. When comparing Fig. 6a with 6b, this was more prominent for the soft gel. A large increase in the elastic modulus for test piece nos. 3 and 4 were observed due to the higher magnetic permeability of the IR-L3 particles. As observed in Fig. 6b, this indicates that IR-L3 particles have a higher magnetic traction force than Car-bonyl SQ particles. The average increment rates were approximately [E.sub.a] = ([E.sub.3] - [E.sub.30])/[E.sub.30] = 43% and [E.sub.a] = ([E.sub.4] - [E.sub.40])/[E.sub.40] = 57% for test piece nos. 3 and 4, respectively. The [tau]-[epsilon] relationship of test piece nos. 3 and 4 was highly nonlinear. As described above, this is probably due to complicated interactions of the elastic force and the magnetic traction force, and particularly the result of the irregular grain shape configuration (see Fig. 4). The average strain difference is greater for test piece no. 4, whose dispersant is the soft gel (SE1885: 65 vol%), than test piece no. 3 by about ([DELTA][[epsilon].sub.4] - [DELTA][[epsilon].sub.3])/[DELTA][[epsilon].sub.3] = 18%.

Finally, Fig. 7 plots the average elastic modulus [bar.E] (the least square fit for test piece nos. 1-4 at each given magnetic field strength H) with respect to the magnetic field strength. As shown in Fig. 7, [bar.E] is an increasing function of H. The hard gel dispersant (TSE3062) combined with particles with higher magnetic permeability (IR-L3), i.e., test piece no. 3, had the highest rate of H increase. The nonlinearity of H for test piece no. 3 was also higher. In contrast, the soft viscoelastic magnetic silicone gel body, i.e., test piece no. 2, had the lowest rate of H increase and higher H linearity. Therefore, with respect to the development of a highly deformable magnetic material, it is thought that a mixture of a soft gel with spherical magnetic particles is more promising for engineering applications since it creates a linear magnetic gel body, while, with respect to the development of a highly elastic magnetic material, a mixture of hard gel with large (irregular) sized magnetic particles is more appropriate, since it creates a highly nonlinear magnetic material.


One of the causes of body deformation is the effect of magnetostatics, which causes the sample to elongate along the applied magnetic field (a uniform field in this case) to minimize the demagnetizing field opposing the applied field. This effect, which is provided by Maxwell stress, depends strongly upon the body shape. Another reason for body strain is the effect of magnetostriction, which causes the sample to change length in the direction of the applied magnetic field to enhance magnetic permeability. This effect polarizes the embedded magnetic grains and the imposed field creates dipolar interaction between the grains, which manifests as internal stress. As a result, in the case of randomly distributed spherical magnetic grains in an initially isotropic elastic matrix, this stress compressible the body along the field and stretches it out in the transverse direction. The third essential mechanism that causes body deformation is the Kelvin force density. This is the body force that deforms the sample depending upon the gradient of the magnetic field. Kelvin force density plays a particularly key role in the case of a nonuniform magnetic field distribution.

Some reports have been published in recent years to create a theoretical explanation for the deformation of viscoelastic magnetic silicone gel bodies (the so-called magnetorheological elastomers) (11), (12). However, to date there is neither a theory capable of satisfactorily describing the relationship of magnetically induced strain and stress, nor is there a convenient formula available to predict the relationship, particularly in the general, nonuniform magnetic field cases described in this study. Nonetheless, in the most recent publication, the deformation of spheroidal magnetorhcological elastomers caused by a uniform magnetic field, in parallel to the strain direction, is reported by Shliomis and coworkers (13) along with their theoretical approach. This is the so-called the Procrustes effect.

In this study, the major cause of the increasing elastic modulus is thought to be magnetostriction applied to the ferromagnetic micrograms, although the magnitude of this effect cannot be predicted by published theoretical insights such as the Procrustes effect. The nonuniform distribution of the magnetic field may cause stress due to Kelvin force density, but, in the present field configuration, the symmetry of the field along the strain direction would cancel the overall effect. Moreover, since the sample is fairly long in the strain direction, the effect of magnetostatics would be minimal.

Volumetric flow control devices (14), (15) and artificial muscles for robots (16) are existing and conceivable ideas for application of this viscoelastic magnetic silicone gel body. This is based either on the large deformation achievable in magnetic fields even of a moderate intensity, or on the inverse effect, where tensile or compressible strains sufficiently charge the magnetic permeability of these materials, hence enabling magnetic stress and strain tensors.


Various viscoelastic magnetic silicone gel bodies were made in the present study by mixing soft- and hard-type silicone gel dispersants with small magnetic spherical particles and large irregular nonspherical particles, respectively. Tensile tests under magnetic fields showed that the imposed magnetic field increased the elasticity of the gel bodies, and that this increase was a function of the magnetic field. The increase in elastic modulus with a hard gel (a material with large and more irregular shaped particles) was shown to be higher than that of a soft gel. This was due mainly to high magnetic traction force. In addition, this study found that large (and more irregular shaped) particles increased the non-linear characteristic of both of the [bar.E] - H and the [tau]-[epsilon] relationships.

[l.sub.o]            natural length of test piece
[[empty set].sub.0]  outer diameter (if cylindrical solenoid coil
[[empty set].sub.d]  test piece diameter
[H.sub.max]          maximum magnetic field strength
I                    applied dc current
[H.sub.r].            intensity of magnetic field in radial direction
[H.sub.z]            intensity of magnetic field in axial direction
H                    applied magnetic field
[epsilon]            strain of test piece
[DELTA]l             tensile length
[tau]                shear stress
F                    tensile load
[[DELTA].sub.a]      mean cross-sectional area of test piece
E                    elastic modulus
[E.sub.a]            average increment rate
M[nabla]H            Kelvin force density
M                    magnetization vector
[bar.E]              average elastic modulus


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Kazuhiko Matsumura, (1) Hiroshi Yamaguchi (2)

(1) Pacific Industrial Co., Ltd., Godo-cho, Anpachi, Gifu, Japan

(2) Faculty of Engineering Doshisha University, 1-3 Tataramiyakodani, Kyo-tanabe-shi, Kyoto, Japan

Correspondence to: K. Matsumura; e-mail:

DOI I0.1002/pen.21611

Published online in Wiley InterScience (

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Author:Matsumura, Kazuhiko; Yamaguchi, Hiroshi
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:9JAPA
Date:May 1, 2010
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