**1. Introduction**

248 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

pp. 25-35, ISSN 1083-4435.

Zhou, C. & Low, K. H. (2102). Design and Locomotion Control of A Biomimetic Underwater Vehicle with Fin Propulsion. *IEEE/ASME Transactions on Mechatronics*, Vol. 17, No. 1,

> Magnetorheological elastomers (MREs) are smart materials where polarized particles are suspended in a non-magnetic solid or gel-like matrix. Two kinds of MREs, namely anisotropic and isotropic, are fabricated either under a magnetic field or without a field [1,2]. In anisotropic MREs, polarised particles are arranged in chains within a polymer media such as silicon rubber or natural rubber. The shear modulus of MRE can be controlled by the external magnetic field, which has led to many applications, such as tuned vibration absorbers, dampers and sensors [3].

> Additives are used to adjust the mechanical properties or electrical performance of MREs. Silicone oil is an additive which is used to increase the gaps between the matrix molecules and to decrease the gaps between the conglutination of molecules. Apart from increasing the plasticity and fluidity of the matrix, the additives can average the distribution of internal stress in the materials, which makes them ideal for fabricating MRE materials. Graphite powder is a kind of additive which can affect the magnetorheology and electrical conductivity of MREs [4,5]. By introducing graphite microparticles into the elastic matrix, MREs exhibit a lower electrical conductive and a different magnetorheological response.

> When the material in the matrix is magnetic, the polarization of the particles is less effective and the magnetorheological response is therefore smaller. The addition of magnetically active additives (other than MR particles) also decreases the magnetorheology [6, 7]. The overall properties of the elastomer composite are also influenced by the additives, as the filler material causes the volume to increase, so the previous effect also increases. Lokander et al. [7, 8] have shown that the absolute effect of MR (the difference between the zero-field modulus and modulus measured under an external magnetic field) is independent of the matrix material. However, the zero-field modulus can be much higher for hard matrix material

© 2012 Li et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

(for instance, where materials with high volume fraction of iron specifically possess a high zero-field modulus), which means that the relative magnetorheological effect is quite low.

MREs feature viscoelastic properties and magnetorheology [9]. The magnetorheology of MREs is described as a reversible change in modulus in an applied magnetic field. Aligned MREs have mostly been characterized at relatively low frequencies (1 to 20 Hz) to measure the changes in the dynamic shear modulus induced by the external magnetic field [9, 10]. Ginder et al. found a substantial magnetorheology over the entire frequency range studied. The increase in the shear modulus varied initially with the strength of the magnetic field but saturated at higher field strength. When the magnetic field was increased from 0 to 0.56 Tesla the consequent increase in shear modulus was nearly 2 MPa and the frequency of the resonance was shifted upward by over 20% [10]. Zhou et al. [9] stated that the changes of dynamic shear storage modulus can be over 50%, while Gong et al. [11] said that it can be over 100%. Lokander et al. studied the dynamic shear modulus for isotropic MR elastomers with different filler particles and matrix materials. They measured the magnetorheology as a function of the amplitude of strain and found that the magnetorheology decreases rapidly with increasing strain within the measured range, and is not dependent on the frequency of testing. The fact that the absolute magnetorheology is independent of the matrix material means that softer matrix materials will show a greater relative magnetorheology [7, 8].

The effect of additives on the sensing capabilities were studied by a few groups. Kchit and Bossis [7] found that the initial resistivity of metal powder at zero pressure is about 108 Ωcm for pure nickel powder and 106 Ωcm for silver coated nickel particles. The change in resistance with pressure was found to be an order of magnitude larger for a MRE composite than for the same volume fraction of fillers dispersed randomly in the polymer. Wang et al. [8] proposed a phenomenological model to understand the impedance response of MREs under mechanical loads and magnetic fields. Their results showed that MRE samples exhibit significant changes in measured values of impedance and resistance in response to compressive deformation, as well as applied magnetic field. Bica [9] found that MRE with graphite micro particles (~14%) is electroconductive. These MREs possess an electric resistance whose value diminishes with both the increase of the intensity of the magnetic field and with the compression force. Such a variation of resistance with magnetic field intensity is due to the compression of MRE with graphite microparticles. In the approximation of the perfect elastic body, the sums of the main deformations and the compressibility module of MRE with graphite microparticles, depend on the magnetic field intensity. Li et al. [10] introduced graphite into conventional MREs and found that a MRE sample with 55% carbonyl iron, 20% silicon rubber and 25% graphite powder exhibits the best performance. The test result showed that at a normal force of 5 N, the resistance decreases from 4.62 kΩ without a magnetic field to 1.78 kΩ at a magnetic field of 600 mT. The decreasing rate is more than 60%. This result also demonstrated the possibility of using MREs to develop a sensor for measuring magnetic fields. This result indicates that the detection is very sensitive to the normal force. When the normal force is 15N, the field-induced resistance only has less than 28% change from 0.65 kΩ at 0 mT to 0.47 kΩ at 600 mT.

Depending on an elasto-plastic asperity microcontact model for contact between two nominally flat surfaces, Kchit and Bossis developed a model to analyse the contact of two rough surfaces. They used two kinds of magnetic particles: nickel and nickel coated with silver which are dispersed in a silicone polymer as the polarised particles [12]. To understand the complex conductivity of particle embedded composites, quantitative or semi-quantitative models can be used [16]. The Maxwell–Wagner and the Bruggeman symmetric and asymmetric media equations were introduced by McLachlan [17] to model the electrical behaviour of conductor-insulator composites. The microstructures for which these effective media equations apply are considered in simulating the measured impedance and modular spectra of these composites. Woo et al. [18] developed a universal equivalent circuit model in modelling the impedance response of composites with insulating or conductive particles or fibres. Based on the microstructure of MREs, Wang et al. proposed an equivalent circuit model to interpret the impedance measurement results [13].

This chapter is organized as follows. Section 2 describes the fabrication of graphite based MRE samples with various weight fractions. The morphology of the MRE samples and rheological properties of graphite based MREs were presented in Section 3 and 4, respectively. Section 5 presents the theoretical development based on a representative volume for investigating MRE electric properties. The main findings are summarized in Section 6.
