TOWARDS A NOVEL COMPOSITE MATERIAL WITH MAGNETORHEOLOGICAL SWITCHABLE STIFFNESS NEUARTIGE MEHRKOMPONENTENWERKSTOFFE MIT MAGNETORHEOLOGISCH SCHALTBAREN STEIFIGKEITEN E. Dohmen1, M. Obst2, Ch. Lux2, F. Adam3, M. Kästner2, M.S. Khan4, D. Borin3, W. Hufenbach1, M. Gude1, V. Ulbricht2, G. Heinrich4, S. Odenbach3 Institut für Leichtbau und Kunststofftechnik, TU Dresden Institut für Festkörpermechanik, TU Dresden 3 Institut für Strömungsmechanik, TU Dresden 4 Leibniz-Institut für Polymerforschung Dresden

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Introduction The aim of the ECEMP subproject SwitchComp (B4) is to design, manufacture and analyze a lightweight component with magnetic switchable stiffness and damping properties. The main idea of the work is the combination of a polymer matrix, e.g. polypropylene tubes or foams and a material with magnetically controllable rheological properties, e.g. a magnetorheological (MR) fluid [1]. The simplest MR fluid is a mixture of ferromagnetic particles and a carrier liquid. An applied magnetic field dramatically changes the rheological properties of MR fluids and therefore will change the mechanical properties of the composite. In the current stage of the project we synthesized and characterized MR fluids, developed a model for the uniaxial behavior of the MR fluid and considered the coupled magnetostatic-structural field problem. Furthermore, first attempts to combine MR fluids with lightweight polymers have been performed and the preparation of magnetorheological elastomeres (MREs) [2] as reference material has been undertaken. 174

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Preparation and Rheological Charakterisation of MR Fluids MR fluids have been first reported in 1948 by Rabinow [3]. Since then many compositions which can be used for the fluid preparation have been described. The most common magnetic powder used in MR fluids are iron particles of high purity, which can be coated with a surfactant to provide colloidal stability. Due to the unknown composition of the commercial MR fluids they can not be used for the design of novel composite materials with known properties.

Figure 1:

Flow curves of the prepared MR fluid for different magnetic flux densities.

Figure 2: Storage modulus G’ of the MR fluid for different magnetic flux densities as a function of the oscillation frequency for the sweep amplitude of 0.01

Figure 3: Loss modulus G” of the MR fluid for different magnetic flux densities as a function of the oscillation frequency for the sweep amplitude of 0.01

For the first tests simple MR fluids have been prepared. The fluid sample is based on a BASF™ iron powder with particles having an average diameter of about 3.2 µm being coated with silicate. This powder was dispersed in Motul 300V oil with 175

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a dynamic viscosity of 33 mPas (T=25 oC). The volume concentration of the magnetic particles in the sample is 39 vol.% and it has been confirmed by magnetic measurements. The rheological experiments were conducted using an Anton Paar 501 rheometer equipped with a magnetorheological measuring device. Results of the quasi-static and dynamic measurements performed for different magnetic flux densities are presented in figures 1,2,3. The obtained data has been used for the modeling of the material behavior presented below.

Preparation and Charakterisation of a Composite Material Validation of Magnetorheological Properties of a Solid-FluidComposite For a proof-of-principle, a test assembly was developed allowing 3-point bending tests under the presence of a magnetic field (figure 4). The setup enables experiments, in which different magneto-elastic-materials are tested at several magnetic field strengths and with different load-to-field orientations. In addition, custom-made hollow cylinders, which act as an envelope body for the MR fluid, were manufactured (figure 5). The measuring marks applied to these specimens can be tracked by a stereoscopic deformation detection system, such as PONTOS by GOM, to monitor contactlessly the spatial deformations. For the 3-point bending experiments these specimens were successfully used.

Figure 4:

Adapted testing device for 3-point bending tests under variable magnetic field orientations.

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Figure 5:

Specially designed test specimen with measuring marks as an envelope body for MRF during 3-point bending tests.

Microstructural Analysis of Different MRF Formulations Inside the Composite One approach to examine the microstructure of different MR fluid formulations inside the composite is, to use fast scanning, high resolution Computer Tomography (CT). First experiments realized at the ILK using a NanoTom® computer tomography with a tungsten target showed the capabilities of this technique with a three dimensional resolution of 2.88 µm. The microscopic investigations carried out were able to record the in-plane orientation of iron particles in the MR fluid under the influence of an external magnetic field, initial tests using the NanoTom® offer the additional benefit of mapping out the spatial formation of iron particle chains (figure 6).

Figure 6:

Images generated with a NanoTom® computer tomography examining a MR fluid specimen: Particle orientation due to the presence of a magnetic field.

Process Development for the Manufacturing of Composites on the Basis of Polymers with Oriented, Tubular Substructures To achieve the desired switchable multi-component-material from the particular materials, it is essential to design a proper interface. This implements a compre177

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hensive process and tool development for the manufacture of polymers with hollow substructures, such as oriented tubes or evenly distributed cavities. The engineered moulding tool for the analysis of the production of polyurethane foams with oriented hollows is shown in figure 7. The design of this setup enables further research on the influence of tube location and tube diameters to the switchable deformation behavior of the moulded structure, significantly exceeding the feasibility of the basic moulding process.

Figure 7:

Moulding tool for the analysis of process parameters for the manufacture of polyurethane foams with oriented cavities.

Preparation of MREs The properties of the new smart composite have to be compared with established MREs [2]. One of our first steps is to produce MRE and to analyse the internal structure of the samples. For a quantitative comparison it is very important to produce MRE with the same magnetic material as MR fluid. Hence we select carbonyl iron particles with a main diameter of 40 m. A second point to keep in mind is to have the same volume concentration of magnetic material inside the MRE as in the new smart composite. Below, the MRE production procedure is briefly described and the first results of internal structure analysis of the MRE samples are presented. Magnetic networks were prepared from a mixture of a two components. Component A contains polymers while component B provides the cross-linking agent. Carbonyl iron particles have been dispersed in component A at room temperature and the solution has been transferred into a mould. After the component B was added an outgassing in vacuum and following polymerization at 90 oC have been performed. The polymerization was done with an applied magnetic field to produce samples with anisotropic structure and without field to produce isotropic ones. 178

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To analyse the internal structure of the prepared samples a NanoTom® computer tomography has been used. In figure 8 the internal structure of isotropic and anisotropic samples is presented.

Figure 8:

Internal structure of the anisotropic (lefts) and isotopic (rights) MREs.

Modelling of the MR Fluid and Coupling of Magnetic and Mechanical Fields To model the material behavior of the composite a homogenization method will be applied. Amongst others this requires the knowledge of the three dimensional material behavior of each constituent. In the following sections the uniaxial material behavior of the MR fluid and the coupling of magnetic and mechanical fields by electromagnetic induced forces acting on the structural part are considered.

Modeling of the Uniaxial Material Behavior of the MR Fluid Basically a MR fluid is a suspension, a mix of a liquid and distributed particles. That is why without an applied magnetic field it behaves like a fluid (liquid phase). In the presence of a magnetic field first a MR fluid behaves like a solid (solid phase) due to the induced attractive forces. After passing a yield stress Ý there is a solid-to-liquid-phase-transition and it behaves like a liquid (liquid phase). So the mechanical behavior of MR fluids can be divided into two parts, the pre- and the postyield, whereat the yield stress is dependent on the strength of the magnetic field. A phenomenological uniaxial model, which is able to express the solid to liquid phase transition, is given by the Bingham-model [4] (figure 9).

Figure 9: 179

Bingham-Model [4].

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The mechanical behavior in the preyield regime, whereat shear stress |τ|< τy and shear rate  vp =0, is determined by

  G (   vp ),

(1)

where G denotes the modulus of shear and γthe shear strain (see figure 9). For shear stress |τ|> τy and shear rate  vp  0 the Bingham-Model has to describe the postyield regime. Its behavior is given by

   y sign( vp )    

 , G

(2)

where ηdenotes the viscosity. To characterize the mechanical behavior of MR fluids both, the storage G′(γˆ ) and loss modulus G′′(γˆ ) (figure 10(a)), i.e. the material answer to an applied shearstrain γ (t ) = γˆ ⋅ sin(ω ⋅ t ) , and the flow curve τ (γ& ) (figure 12), i.e. the material answer to γ (t ) = γ& ⋅ t with γ& = const. , were measured.

Figure 10:

Storage G’ and loss G’’ modulus. 180

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The prediction of the Bingham-Model is shown in figure 10(b). Comparing it with the measurement it is not able to predict the loss-modulus for smaller amplitudes of the shear strain γˆ . To model the loss-modulus also for this part, an additional damper η 4 (γ& ) is set parallel to the Bingham-Model so that one ends up with the Laun-Model which is shown in figure 11 [4]. This approach is applied to the measured flow curve. The modeling result is shown in figure 12 and requires the nonlinear dampers

2 

 0  vp k



 sign ( vp ) cosh( a  vp )

 |  |  1      η~ − η τ 4 = η ∞γ& + 0 ∞ γ&. 1 + λ | γ& | vp

  1~  sign ( m

vp

) y (3)

(4)

The values of the parameters used in equations 4 and 4 are given in figure 12.

Figure 11: Laun-Model [4].

Figure 12: Flow curve.

Coupled Magnetostatic-Structural Field Problem The coupling considered here is a weak one, thus the magnetostatic as well as the mechanical problem can be solved separately. At first the magnetostatic field is computed. Based on this, magnetic forces are calculated and transferred to the structural part. In a last step the mechanical problem has been solved. The numerical solution is performed using the finite element method.

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Magnetic field problem In the static electromagnetic case the Maxwell equations decouple. For magnetostatics these equations yield

∇ × H = J and ∇ ⋅ B = 0 in Ω, (5) where H denotes the magnetic field intensity, J the steady current density, B the

magnetic induction, ∇-nabla operator defined as ∇ = ∂ (•) e and Ω the domain. i

∂xi

The material is assumed to be linear and isotropic characterized by the constitutive relation

B = µ 0 µ r H + B r = µH + B r

,

(6)

where µ0 denotes the permeability of free space, µr the scalar valued relative permeability and Br the remanent induction. By introducing the magnetic vector potential A through

B = ∇ × A

(7)

the second part of (5) is automatically fulfilled. The potential A is not unique and has to be imposed to a gauge condition. Therefore the Coulomb gauge is used. Boundary conditions are formulated in terms of the vector potential. At a material interface, see figure 13, the continuity conditions for vanishing surface current densities

n ⋅ (B2 − B1 ) = 0 and n × (H 2 − H1 ) = 0 onΓ12

(8)

have to be fulfilled. n is the unit vector normal to the interfaceΓ12 . The subscripts belong to the two adjacent materials of the interface, see figure 13. Force calculation In the case of a linear isotropic, homogeneous, non-permanent magnetized nonconducting material the magnetic volume force density disappears. But surface forces exist as the permeability is discontinuous at a material interface (see figure 13) [5, 6]. The surface force density results from the associated change of magnetic induction and magnetic field intensity. For calculating magnetic forces the Maxwell stress tensor

τ=

1  1   B ⊗ B − ( B ⋅ B) I  2 

µ0 

(9)

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is used. I is the second order unity tensor. The resultant magnetic force acting on a body is calculated by the integration over a closed arbitrary surface lying entirely in free space and surrounds the considered body [7].

Figure 13:

Discontinuity interface.

Mechanical field problem The force obtained from magnetic field is transferred to the structural analysis by a distributed surface load. From the local equilibrium in the static case it follows

∇ ⋅ σ + f = 0 and σ = σ T (10) in Ω, where σdenotes the stress tensor and f the vectorial force per unit volume. For small gradients of the displacement vector the strain tensor εis equal to the symmetric part of the displacement gradient. Mechanical boundary conditions ~ are formulated in terms of prescribed displacements u=u~and tractions n ⋅ σ = t . The linear elastic material with the forth order elasticity tensor is described by the Hookes law σ=C : σ.

(11)

Example A permeable plate of linear elastic material is supported next to a permanent magnet, see figure 14 (a). The plate becomes magnetized and deforms under the action of the magnetic force. The maximum displacement of the midpoint is u=0.26 mm. As it is shown in figure 14 (b) the surface force is non-uniform distributed.

Figure 14. 183

Elastic and permeable plate a) arrangement b) computed surface forces.

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Conclusions and Outlook We prepared and experimentally characterized a MR fluid, as one of the most important components of the future novel composite with switchable stiffness. On the basis of the obtained results an uniaxial material model of the MR fluid has been proposed and an approximation for the problem of the coupling of the magnetic and mechanical fields has been made. A special engineered moulding tool and a 3-point bending test tool have been developed to design and characterize a composite with proper parameters. For the microstructural investigations of the composite a high resolution computer tomography has been implemented. Moreover, MREs with different internal structures have been prepared as reference materials for the future composites. The next step towards a novel composite material with MR switchable stiffness is a combination of an interface matrix with the MR fluid and its basic characterization.

References 1. G. Bossis, S. Lacis, A. Meunier, O. Volkova Magnetorheological fluids Journal of Mag- netism and Magnetic Materials 252 (2002) 224–228 2. M. Kalio The elastic and damping properties of magnetorheological elastomers (2005) VVT Publications 565 3. J. Rabinow The Magnetic Fluid Clutch AIEE Transaction (1948) 67 1308–1315 4. H.M. Laun, C. Gabriel, Ch. Kieburg Magnetorheological fluid (MRF) in oscillatory shear and parameterization with regard to MR device properties. Journal of Physics: Conference Series 149 (2009) 012067 5. G. Meunier The Finite Element Method for Electromagnetic Modeling (2008) ISTE Ltd and John Wiley & Sons, Inc 6. Z. Ren Comparison of different force calculation methods in 3D finite element model- ling (1994) IEEE Transactions on Magnetics 30 3471–3474 7. J. Coulomb A methodology for the determination of global electromechanical quanti- ties from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness IEEE Transactions on Magnetics (1983) 19 2514–2519

Dieses Projekt wird finanziert aus Mitteln der Europäischen Union und des Freistaates Sachsen

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