Magnetostrictive Composites

Energy Absorption in Axial and Shear Loading of Particulate Magnetostrictive Composites Geoffrey P. McKnight and Greg P. Carman Mechanical & Aerospace Engineering Department, University of California, Los Angeles

ABSTRACT Energy absorption properties of polymer matrix Terfenol-D particulate composites have been experimentally measured. In this work two volume fractions of Terfenol-D were investigated (20% and 40%) and both exhibited peak energy absorption of up to 25 % per cycle. The tests include mechanical loading in both axial and shear (torsion) combined with applied axial magnetic fields. The results show that the energy absorbed in a cycle of loading is a strong function of stress amplitude. The peak energy absorption for the zero magnetic field case in both axial and shear loading occurs near zero amplitude and decreases with increasing stress amplitude. The maximum energy absorption near zero stress amplitude has been observed previously in monolithic Terfenol-D and is a result of the low magnetic anisotropy of Terfenol-D. Combined magneticmechanical loading demonstrated the influence of magnetic field on energy absorption properties. The energy absorption is decreased as the static magnetic field is increased if the cyclic stress amplitude is held constant. If however, we hold a constant magnetic field and vary the cyclic mechanical loading amplitude, it has been observed that the peak energy absorption curve is shifted to higher stress values. This suggests stress tunable dampers are possible. Keywords: magnetostrictive, magnetostrictive composite, particulate, energy absorption, damping, shear

1. INTRODUCTION Structural damping techniques have generally been focused into two areas: passive damping using viscoelastic materials and active systems employing sensor/actuator/controller strategies. A class of materials previously used only in actuator type of applications, magnetostrictive, may provide a bridge between these two areas. Viscoelastic systems can generally be grouped into free layer and constrained layer technologies [1]. The free layer technique simply adds a viscoelastic material to the existing structure. The combined structure has a geometric damping characteristic in bending proportional to the product of the loss factor and modulus of the material [2]. This implies a limitation in the damping capacity of polymers due to their inherent low modulus. In the constrained layer technique, the viscoelastic material is sandwiched between the structure and a high stiffness constraining layer. The effect of the constraining layer is to change the principal deformation in the viscoelastic material from extension to shear. This permits tuning of the damping at a frequency specified by the geometry and material properties. A disadvantage of the constraining layer technique is that the geometry effectively filters out the low frequency damping since the bending energy is exclusively in the structural material and the constraining layer. Thus, at low frequencies, the energy is not put into the damping material where it can be absorbed. These frequency effects, in addition to the frequency dependence of the viscoelastic materials, complicate designing a structural damper. An alternative approach to damping is to use an active system consisting of sensors, actuators, and control systems. This approach can be very effective in reducing structural vibrations if the actuators and sensors are correctly placed on the system. The major drawbacks of this system are the increased complexity of the overall structure and the additional weight added. The structure must now be augmented with a control system and power supplies to drive the actuator components. Additionally the complexity and electrical connections necessary in this system increase its susceptibility to failure and decrease is performance robustness. These drawbacks, in addition to the added cost of an active system, limit implementation to very specific applications.

The use of magnetostrictive materials as damping components has been suggested by Hathaway, Teter and Clark of NSWC [3,4]. The authors indicate that the theoretical upper bound for energy absorption in single crystal Terfenol-D is 80% of the applied energy [3]. In combination with the relatively high stiffness of Terfenol-D (~ 30 GPa), this damping capacity make Terfenol-D attractive for use as a damping material. The energy absorption mechanism in a magnetostrictive material stems from domain motion; a process that also results in magnetic hysteresis. In a magnetostrictive material, the high coupling between elastic and magnetic properties permits an applied mechanical load to alter the magnetic domain configuration. Hathaway et al. describe two principal mechanisms for energy absorption in magnetostrictive materials. The first is the irreversible motion of domain walls due to lattice imperfections and grain boundaries. The second is described by magnetization jumping; a process where the magnetization can quickly change from one stable configuration in the crystal to another when the sum of the magnetic and elastic energies make such a jump favorable. This jumping mechanism is an irreversible process dissipating system energy as heat. Unlike purely magnetic hysteresis, in mechanical hysteresis the magnetization jumping accounts for the majority of energy absorption since the application of stress does not influence 180° domain walls, which account for most of magnetic hysteresis. Initial experimental work has also been performed on Terfenol-D as an energy absorbing material [4]. Homogenous Terfenol-D samples were tested by applying a saturating magnetic field to the specimen followed by a mechanical load. The saturating field was applied to rotate the magnetic domains predominantly parallel to the loading direction. This could have also been achieved by applying a tensile mechanical load. However, the monolithic form of Terfenol-D is brittle and would easily fracture under tensile loading. Results of Hathaway et al. [4] indicate that the material exhibits a large single cycle damping behavior characterized by a maximum Q factor of 0.28 at a stress amplitude of 5 MPa. However, both the brittleness and the single cycle damping limitation significantly reduce the usefulness of the material as a damper. We believe that a composite sample could be used to overcome this limitation. In a composite, the domains could be aligned with a tensile load eliminating the need for an external magnetic field. Work on polymer matrix magnetostrictive composites has focused on improving the high frequency performance of Terfenol-D transducers by eliminating eddy currents losses [5-8]. Researchers report results with frequency performances in excess of 10 kHz [7], representing an order of magnitude improvement over monolithic Terfenol-D. The composite material has been shown to produce high strain levels near that of the monolithic material using only a fraction of the magnetostrictive material. One important aspect of particulate magnetostrictive composites is the ability to structure the geometry of the particulate using applied magnetic fields during manufacturing. An applied field tends to align the particulate within the composite, which produces a material geometry similar to a unidirectional fiber composite. This alignment procedure allows the magnetostrictive material to dominate the mechanical properties such as modulus and strain output. One significant advantage in the context of damping is durability. The composite form permits complex mechanical loads such as tension, shear, and impact loading to be supported, rather than only simple compression as in the monolithic material. This supports the proposition that magnetostrictive composites could be used in damping applications where the loading is generally a complex state of bending or shear. Other composite properties that support this hypothesis include tailored stiffness properties produced by changing the volume fraction of the constituent materials [6]. Thus, one can impedance match the material for a specific application to maximize energy transfer into the damping material. An additional advantage of the composite system is that similar performance to the monolithic material can be obtained with a much lower density material [8] resulting in weight reduction.

2. EXPERIMENTAL Magneto-mechanical testing was performed on two aligned particulate Terfenol-D specimens in both uni-axial tension/compression loading and torsion loading. Baseline tests were performed on a sample of neat vinyl ester resin to determine its contribution to overall composite damping properties. The mechanical loading consisted of cyclic loading at a quasi-static frequency of either 0.5 Hz (torsion) or 1.0 Hz (axial) in all tests. In addition to cyclic mechanical loading at zero magnetic field, cyclic mechanical loading at constant magnetic field was also performed. The specimens were prepared using a low viscosity vinyl ester resin system with room temperature cure and a mix viscosity of 100 centipoise. The Terfenol-D magnetostrictive particles consist of a poly-distribution mixture with all particles less than 300 microns in size. The particles were of varying shape due to the ball milling process used to create the particles from the bulk material. In general, the particles were jagged and difficult to wet. To overcome this problem, the particles were coated with a solution of vinyl ester polymer prior to their introduction into the composite. The coated particles and resin were mixed and repeatedly degassed to remove unwanted trapped air. The specimens were placed in a static magnetic field

produced by two large rare earth permanent magnets, and the resin allowed to cure. The static magnetic field aligns the particles into chains (i.e. pseudo continuous fiber) creating an anisotropic particle distribution. For discussion purposes the aligned particles were treated as fibers with a composite connectivity of 1-3. Three specimens containing particle volume fractions of 20 and 40 percent were produced with the particle aligned in the direction of loading (0 degree composite). For other particle alignments the reader is referred to McKnight and Carman [9]. The combined magneto-mechanical loading required a novel sample mounting procedure (Figure 1). The specimens were mounted in an inset butt-joint configuration on the ends of steel rods that could be placed into a solenoid. The sample was mounted in the hydraulic testing machine in-situ to ensure that the loading would be completely in plane and have no bending components. This configuration allowed for approximately 15 MPa of tensile loading before the mount would fail.

Figure 1. Testing configuration for combined magnetic-mechanical loading testing. This specimen is gaged for axial testing; for torsion testing the specimens were machined into cylinders and mounted with 45°biaxial strain gages. The axial loading of each specimen consisted of tension/compression sinusoidal cyclic loading about zero load. The total stress amplitude was varied from 4 MPa to 24 MPa. Lower load levels could not be obtained due to the load sensitivity of the hydraulic machine. The alternation of tensile and compressive loads is important to reset the domain configuration during each loading cycle. The loading was also repeated with applied constant magnetic fields from a minimum of 0 kOe to a maximum of 5 kOe. Torsion loading gives some insight into material damping behavior in shear loading. Shear loading is typical in damping applications especially considering constrained layer damping techniques. The torsion loading was performed on the same specimens as the axial testing. However, each specimen was machined into a cylinder using a lathe to ensure concentric loading and geometric axes. The specimens were then gaged with biaxial rosettes at a 45°angle to loading and then mounted inside of the solenoid in the hydraulic testing machine. The loading tests consisted of applying positive and negative torque to the cylinder while maintaining zero extensional load using axial load control. The samples were tested in sinusoidal loading about the zero torque position with amplitudes from 1 to 16 MPa maximum shear stress at the edge of the cylinder. Assuming that the cross-section of the sample remains plane and rotates without distortion during torsion, the shear stress may be described as follows,

τ =

Tρ J

where τ is the shear stress, T the applied torque, J the moment of inertia about the loading axis, and ρ the radial distance from the center. The variation of stress through the thickness is a concern and future tests may involve a thin walled tube where the stress is approximately constant through the thickness. However, as a gage of damping behavior in shear loading, this test provides good insight. To provide reasonable comparison with the axial loading tests, the shear stress reported in this work is the average stress over the cross section of the material, τavr.

3. RESULTS The tests performed on each specimen and loading configuration produces a hysteresis loop in stress and strain. The typical qualitative shape of the loops varied with loading magnitude and applied field but generally was ellipsoid in the axial loading tests and more s-shaped in the torsional tests (see Figures 2a and 2b). The energy absorption was determined by numerical integration of the data curves. The procedure for the integrations is as follows. For each loading cycle two strain energies were calculated that will be referred to as loading and unloading strain energies. The loading strain energy was calculated by integrating the curve produced from the minimum to the maximum stress level. The unloading curve was calculated by integrating the loading curve produced from the maximum stress value to the minimum stress value. The energy absorbed is calculated as the difference between loading and unloading strain energies divided by the loading strain energy. The results of all tests performed without a magnetic field are presented in Figure 3. This figure provides energy absorption as a function of total stress amplitude for both axial and shear loading (torsion). Since the basis for the energy absorption is linked to the domain-stress interactions, we expect the energy absorption to be dependent on the stress magnitude. We note energy absorption is highly dependent on the stress amplitude in all cases. The highest values of energy absorption are at the lowest measured stress amplitude except for the 40% shear case where the peak occurs at 1.3 MPa total stress amplitude. The peak energy absorption can be linked to the design of Terfenol-D as an actuator material. The composition of TerfenolD (Fe0.3Tb0.7Dy2.0) was formulated to posses a magnetic anisotropy as close to zero as possible so that a minimum magnetic field is necessary to drive the strain response. This low magnetic anisotropy also tends to force stress-domain interactions to be a maximum near zero stress amplitudes. Teter et al. observed a similar behavior in monolithic Terfenol-D [4]. Currently this is the only stoichiometry commercially available of Terfenol, but other ratios may display a different stress amplitude damping behavior due to different magnetic anisotropy. 3.0

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Figure 2a and 2b. (a) Typical ellipsoid hysteresis behavior of axial loading tests. (b) Typical more S-shaped hysteresis behavior of the higher energy absorption torsion specimens. Guide lines have been provided to clarify the differences in behavior between the two curves. The highest energy absorption was founds in shear (torsion) loading. This effect may be a result of the higher load accuracy in the torsion mode of the hydraulic testing machine than in the axial mode. Very low axial stress amplitudes cannot be obtained accurately with the current test setup. If lower axial stress amplitudes were possible, the authors believe that they would reach similar peaks to those obtained in shear loading. An explanation of this follows. The domain interaction to tensile and compressive stresses is shown in Figure 4a. A tensile stress tends to align domains parallel to the loading direction and a compressive stress tends to align domains perpendicular to the loading direction. Shear loading can represented by a biaxial stress state though a rotation of 45 degrees (Figure 4b). In this state, two stresses are acting perpendicular to each other but in opposite directions. From a domain interaction standpoint, these dual stresses tend to have the same effect on the domain state. That is the tensile stress acts to align domains parallel to the tensile load, and the compressive stress also orients domains parallel to the tensile load. Thus, shear loading has very similar effects on domains as axial loading and one should expect similar damping behaviors, but possibly at different stress amplitudes.

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Figure 3. Energy absorption per cycle of loading for shear (torsion) and axial loading versus the total stress amplitude of the stress cycle. Shear stress amplitude is the average stress value through the cross section. Based on the results in Figure 3, the volume fraction did not play a significant role in the energy absorption. This counterintuitive behavior may be a result of the manufacturing process for these composites. The vinyl ester epoxy used for the particle binder possesses a very low room temperature viscosity that is necessary for a quality composite, but also exhibits a large chemical shrinkage during cure. This shrinkage imparts a large residual stress state on the magnetostrictive particles. This residual stress state is most likely a complicated state unique to each particle depending on local geometry and architecture. This residual stress state may considerably alter the particles magneto-mechanical behavior. The fact that damping measure in this study was independent of volume fraction also suggests the exhibited behavior is well below the maximum energy absorption possible. This is supported by the theoretical predictions of Hathaway et al., which predicts single crystal energy absorption of 80% per cycle.

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Figures 3a and 3b. (a) Uniaxial domain-stress interactions for tension and compression. (b) Mohr's circle decomposition of pure shear loading into biaxial tension-compression through a 45° rotation ( 90° Morh rotation) and the domain-stress interaction in this loading.

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Figure 4. Stress-shifting behavior in shear (torsion) loading with an applied static magnetic field. The peak energy absorption is shifted out in stress space as the field is increased. Two types of combined loading experiments were performed. The first experiment was to apply a constant amplitude cyclic mechanical load ( 16 MPa axial ) at different static magnetic fields. The magnetic field was varied from 0 to 5 kOe. In the second type of test a constant magnetic field (0,0.2kOe, and 0.75kOe) was applied and then a series of increasing amplitude cyclic mechanical loadings was performed. The applied mechanical load was cyclic torsion with a maximum shear stress amplitude varying from 1 MPa to 16 MPa. The results of the first test for constant 12 MPa axial loading and varying strength static magnetic fields ( Figure 4 ) shows that the energy absorption decreases until the behavior approaches that of the vinyl ester material for high fields. This result is due to the “locking” of the domain state by the external field. As the magnetic field increases, additional mechanical energy is required to cause magnetization jumping. Since the mechanical energy in this test is constant (i.e. mechanical amplitude constant), the number of domains with sufficient energy to cause magnetization jumping decreases with applied field and eventually becomes zero as the field is raised to a critical value. This is apparent because at high field the behavior approaches that of the vinyl ester. The results of the second test ( constant field – multiple mechanical shear stress amplitudes ) are shown in Figure 5. The energy absorbed for three separate magnetic fields magnitudes ( 0, 0.2, 0.75 kOe ) are plotted against total peak-to-peak stress amplitude for the 20% volume fraction composite. The stress-energy absorption is shifted out in stress space. That is, the peak value occurs at higher stress amplitudes with increasing magnetic field. This behavior can also be explained by considering the relationship between domain level processes and energy absorption. The mechanical energy necessary for magnetization jumping and domain wall motion is higher when an external magnetic field is added. Thus to increase the number of irreversible domain reorientations through magnetization jumping and other mechanisms, the amount of mechanical energy must be increased as the magnetic energy is increased. We believe that a peak also occurs in the zero field case (Figure 5). However due to equipment limitations we are unable to accurately measure energy absorption in this low stress range. This field shifting behavior could be important in damping applications. For instance, by adding a static magnetic field around the magnetostrictive particles, the composite could be made into a stress-activated damper that would only apply significant damping at a threshold stress value.

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Figure 5. Field shifting phenomenon observed during the application of a static magnetic field to cyclic mechanical testing. The peak of energy absorption is moved to higher levels of cyclic stress amplitude with an increase in field energy.

4. SUMMARY Energy absorption behavior of magnetostrictive composites during cyclic mechanical loading has been measured in axial and shear loading. The results of these experiments show the energy absorption of particulate magnetostrictive composites are a strong function of loading amplitude. Under zero applied magnetic field, both the shear and axial loading have peak energy absorption at low stress amplitudes. This behavior is attributed to the formulation of Terfenol-D such that the magnetic anisotropy is near zero at zero field or stress. The application of a static magnetic field in addition to cyclic mechanical loading shifts the energy absorption curve to higher stress levels. Thus as the field increases, the stress amplitude level for peak energy absorption also increases. These effects may be explained by observing that the energy absorption in the magnetostrictive material occurs due to irreversible magnetic domain motion. The energy condition necessary for changing domain structure is a function of magnetic and elastic energies. An increase in the magnetic energy in the system (as a result of an applied H field) will require a subsequent increase in elastic energy to cause the same change in magnetization in the material.

5. ACKNOWLEDGEMENTS The authors of this paper gratefully acknowledge the financial support provided by the Defense Advanced Research Projects Agency/Air Force Research Lab monitored by Keith Denoyer at AFRL.

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2. 3.

Kerwin, E.M., and E.E. Ungar,"Requirements Imposed on Polymeric Materials by Structural Damping Applications," from Sound and Vibration Damping with Polymers, eds. Corsaro, R.D. and L.H. Sperling, American Chemical Society, 1990, pp. 317-345 Ungar, E.E., in Noise and Vibration Control, ed. L.L. Beranek, Mc-Graw Hill, 1971, Ch. 14 Hathaway, K.B., Clark, A.E., and J.P. Teter, "Magnetomechanical Damping in Giant Magnetostrictive Alloys," Metallurgical and Materials Transactions A, Vol. 26A, 1995, pp. 2797-2801

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