Hysteresis of the viscoelastic properties and the normal force in magnetically and mechanically soft magnetoactive elastomers: Effects of filler composition, strain amplitude and magnetic field
Graphical abstract
Introduction
Mechanical hysteresis of an elastomer (rubber) specimen is a well-known phenomenon in physics and engineering [1]. It is manifested in the stress–strain curve, where a somewhat different dependence is obtained for the loading of a rubber specimen from that recorded on retraction. Mechanical hysteresis is due to energy expended as internal friction during the loading which cannot be recovered on unloading. The hysteresis losses are represented by the area between the loading and the relaxation curves. Most rubbers contain fillers, particulate solids, which are embedded into the elastic matrix. It is well known that such fillers increase hysteresis losses.
Recently, much attention has been paid to the so-called magneto-active elastomers (MAE) comprising μm-sized ferromagnetic particles dispersed in an elastomer matrix. If an external homogeneous magnetic field is applied to the MAE specimen, the particles are magnetized and rearrange themselves within the elastomer leading to deformation of the specimen [2], [3], [4], [5], [6], [7], i.e. magnetostriction. Whether the specimen shrinks or dilates depends on the composite microstructure, applied mechanical load and sample shape [6], [7]. Usually, a specimen is elongated. The physical reason for the deformation is the forces acting on magnetized particles. In this sense the application of a magnetic field has a similar effect to mechanical loading, therefore it can be expected that there would be hysteresis of sample elongation as a function of the magnetic field. Indeed, considerable hysteresis of longitudinal magnetostriction (∼16%) with the magnetic field applied has been observed in elastically soft MAE [3]. Similar phenomena have been reported for elastic ferromagnetic composites with a porous matrix [4] and for a ferromagnetic composite with a dense elastomer matrix [5]. Importantly, the iron particles used in Refs. [3], [4], [5] were practically free from magnetic hysteresis (negligible loop in the magnetization M versus magnetic field strength H characteristic). Consequently, hysteresis behaviour of longitudinal magnetostriction as a result of the applied magnetic field strength could not be attributed to magnetic moments of the filler particles in the magnetic field. The explanation offered in Ref. [4] is similar to the “Payne” or “Mullins” effect, namely that of slippage of the adsorbed hydrocarbon chains along the filler surface. If a magnetic field was first increased and then retracted back to the initial value, the particles and the chains between them do not immediately resume their original position. The energy which was dissipated by friction between particles during the magnetic field strength increase cannot be recuperated and any return to the original ordering requires further energy. As a result it can be assumed that there is no guarantee of direct correlation between filler particle position and magnetic field strength during increase and decrease of the magnetic field. If the microstructure of filler particles is different, the relevant mechanical characteristics, e.g. the complex shear modulus G = Gʹ + iGʺ, where Gʹ is the shear storage modulus and iGʺ is the imaginary shear loss modulus, can also be different. In the literature, the magnetosweep usually shows one curve for G-components as a function of increasing magnetic flux density B and the possibility of magnetic hysteresis is ignored. We are aware of only one paper [8], where a hysteresis as a function G(B) for one sample of highly compliant MAE is reported.
There is a striking similarity between the structuring of magnetic filler particles at constant strain amplitude γ with the increasing/decreasing B and at the constant B with the increasing/decreasing strain amplitude γ. In both cases the hysteresis of magnetic-field dependent physical quantities can be expected, since the particles do not necessarily resume their original position. Formation and reorganization of magnetic microstructures in magnetic fields have been directly observed in magnetic elastomers and gels by several groups [8], [9], [10], [11], [12], [13]. Recently, it has been recognized that this reorganization can take place under shear force in a magnetic field. Simultaneously applied magnetic field and shear strain promote particle rearrangement in order to form tighter aggregates. This effect leads to pronounced cyclical stress hardening [12], [13], [14]. Such particle rearrangements, namely string formation and breaking, have been directly observed in magnetic gels comprising small fractions of magnetic particles [12]. At high concentrations, the magnetic particles could form a three dimensional network. Similar processes of particle rearrangement could change the structure and the mechanical strength of this network and thus, influence the magnetic response of MAE.
Strain dependence of magnetorheological (MR) characteristics in highly filled MAE of various compositions and anisotropies and their evolution with cyclically increasing and decreasing strain amplitudes have been studied recently [14], where the impact of matrix elasticity and magnetic interactions on filler alignment have been elucidated. It has been shown that the dynamic modulus saturates after several cycles of shear loading. Furthermore, the pronounced hysteresis behaviour with the loading-unloading strain amplitude has been observed.
For non-magnetic particle filled polymer composites, it has been shown that their mechanical properties are influenced by the particle size, the particle content and the particle-matrix interfacial adhesion [15]. For a given particle loading, smaller particles have larger total surface area and could contribute to more efficient stress transfer mechanisms. In the case of magnetic particles their induced magnetization affects the strength of their interactions. Furthermore, a tighter packing of the filler particles in aggregates could be expected when small and large particles are mixed together. Magnetorheological composites consisting of two entirely different magnetic filler particles (micro- and nano-sized particles) at fixed total concentration have been recently studied [16].
The purpose of this paper is to investigate details of the elastic and magnetic hysteresis of viscoelastic (dynamic modulus and loss factor) properties and the normal force of mechanically soft MAEs comprising magnetically soft particles. In particular how the filler composition affects both the MR effect and the hysteresis are investigated. The importance of the latter issue is undoubtedly of significance, both for the fundamental understanding of particle rearrangement processes and for potential applications.
The paper is organized as follows: In the experimental section sample preparation and details of the rheological study are described. In the following section, results regarding the rheological properties and normal force of MAEs in increasing-decreasing magnetic fields and under cyclic increasing-decreasing strain amplitudes are presented and discussed. The conclusions are drawn in the final section.
Section snippets
Materials and sample preparation
The polymer matrices have been fabricated using the silicone compound SIEL produced by the Russian State Institute of Chemistry and Technology of Organoelement Compounds (GNIIChTEOS). The compound SIEL is commercially available and its composition has been described in detail elsewhere [3], [9], [17], [18].
Carbonyl iron particles of two different average sizes (3–5 μm and 50–60 μm diameter) have been used as the magnetic filler. Mass percentage of the filler has been maintained constant
Results and discussion
Initially, standard tests in the absence of a magnetic field are considered. This is followed by investigations of the MR effect. Finally, the analysis of the amplitude cycle tests at different magnetic field strengths is presented.
Conclusions
In this paper several features of hysteresis behaviour and the effect of the magnetic particle size on MR response of MAEs have been investigated for the first time.
The dynamic modulus of all samples demonstrates hysteresis both with ascending/descending magnetic field strength at fixed strain amplitude and ascending/descending strain amplitude at fixed magnetic field strength.
In increasing magnetic field the storage modulus as well as the loss modulus of MAE gradually increases, while ratio
Acknowledgements
Financial support of the Russian Foundation for Basic Research (grants no. 13-03-00914, 13-03-12147) and the German Federal Ministry of Education and Research (BMBF grants no. 01DJ13006, 17PNT021) is gratefully acknowledged.
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