Magnetostriction Curves Research Articles

Coupled Magneto-Mechanical Analysis Considering Permeability Variation by Stress Due to Both Magnetostriction and Electromagnetism

A general model for the coupled analysis of magneto-mechanical systems is developed by minimizing the continuum energy functional of the system using the calculus of variation. This approach, which is in contrast with the traditional approach of minimizing after discretization, allows the use of strain and stress tensors, vector identities and the divergence theorem, and results in coupled governing equations of the system with three coupling terms; the magnetic stress tensor, the magnetostriction stress tensor, and the magnetostriction reluctivity. The model uses the information contained in the set of experimental magnetostriction curves dependent on stress to calculate the permeability variation due to stress. The governing equations are then discretized using the Galerkin method resulting in methods for the calculation of nodal magnetic and magnetostriction forces including the coupling effects. Finally the model is applied to a simple 2D problem and the flux density distributions using the proposed method and the traditional method of using experimental magnetization curves are compared.

A new magneto-elastic resonance based technique to determine magneto-mechanical parameters of amorphous ferromagnetic ribbons

Measurement of the magneto-mechanical parameters characteristics of amorphous ribbons often requires complex or limited methods due to their very small thickness. In this paper, it is shown how one can establish and estimate the characteristics of a magnetostrictive resonator from the experimental frequency response free of any kind of mechanical measurement (stress or elongation). This technique which is completely developed with a ribbon exhibiting good resonator properties, is suitable to estimate the magneto-mechanical coupling coefficient k33 and the Young's modulus and also to establish the magnetostriction curves λ(H) of amorphous ribbons. Results obtained from resonators made of 2605SC and 2826 from Metglas(TM) ribbons confirmed the validity of the present technique. However, measurements performed on a thin foil of nickel demonstrate that the present method cannot be extended to semi-soft magnetic materials. The technique which is proposed, has serious advantages upon others as it is non-destructive, low cost and easy to develop compared to common ones.

Magnetic properties and magnetostriction of PrxNd1−xFe1.9 (0 ≤ x ≤ 1.0) alloys at low temperature

The crystal structure, magnetic and magnetostrictive properties of high-pressure synthesized PrxNd1−xFe1.9 (0 ≤ x ≤ 1.0) alloys were studied. The alloys exhibit single cubic Laves phase with MgCu2-type structure. The initial magnetization curve reveals that Pr0.2Nd0.8Fe1.9 has a minimum magnetocrystalline anisotropy at 5 K. The magnetostriction curve at 5 K shows that Pr0.2Nd0.8Fe1.9 has a very good low-field magnetostrictive property, and the magnetostriction of the PrxNd1−xFe1.9 alloy in high magnetic field is attributable mainly to Pr. The temperature dependence of the magnetostriction (λ‖) at the field of 5 kOe shows that the substitution of Nd reduces the K1 remarkably, and the values of λ‖ of Pr0.2Nd0.8Fe1.9 and Pr0.8Nd0.2Fe1.9 alloys are nearly five times larger than that of the PrFe1.9 alloy below 50 K; the λ‖ of Pr0.8Nd0.2Fe1.9 reaches up to 1082 ppm at 100 K, which makes it a potential candidate for application in this temperature range.

Magnetostriction of Fe100−xVx alloys for 5.2 ⩽ x ⩽ 40.7

We investigate the magnetostriction of polycrystalline Fe100−xVx alloys as a function of vanadium content, with values of x varying from 5.2% to 40.7% (at.%V). The lattice parameter curve behavior as a function of vanadium deviates from a linear behavior at x≈10.2 and x≈30.7. Close to x=10.2 is possible to observe a small lattice contraction and close to x=30.7 an expansion. The magnetostriction curve as a function of vanadium content shows two maxima at x=11.8 and 30.7 and has values of 3/2λs of 68.8ppm and 49.3, respectively. The alloys microstructures investigations do not offer enough elements to connect it with magnetostriction. Therefore first-principles calculations were performed and resulted that the lattice contraction at ∼10.2% of V is due to the formation of strengthened Fe–V interactions associated to stronger hybridization between minority spin d subbands, while the lattice expansion observed in the range 25.5–30.7% of V is associated to the weakening of the Fe–V interaction. As for the case of simulating V–V pairs for the alloy Fe12V4, representative of x=25.0, we associated the experimental result of the lattice expansion observed in the range among 25.5–30.7% of V to the weakening of the Fe–V interaction. These calculated electronic properties explain the lattice contraction (at x=10.2) and expansion (x=25.5–30.7) and are expected to be the sources of the magnetostrictive behavior of these Fe–V alloys.

Magnetostrictive Study of High Strength Steels With Respect to Angle From Rolling Direction

Many of the commonly used high strength steels have small amounts of magnetostriction. This magnetostriction can be utilized, for example to measure the torque on a rotating shaft. Previous studies on the magnetostriction in high strength steels have ignored the internal anisotropies due to previous material handling. This paper presents data taken on rods of a high strength steel that have been machined parallel, perpendicular and 45 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$^{\circ}$</tex></formula> to the rolling direction. Magnetization, magnetostriction, susceptibility, and stress-strain curves have been measured under various stresses and fields. In general, the parallel cylinders showed altered <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$B-H$</tex></formula> , susceptibility, and magnetostriction curves compared to the other two orientations. These measurements will be incorporated into a future Vector Preisach model allowing detailed predictions of the magnetic state after stress and field changes.

Anisotropy and Magnetostriction in Non-Stoichiometric Cobalt Ferrite

This study shows the effect of deviation from stoichiometric composition on the anisotropy and magnetostriction of cobalt ferrite Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-x</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> . Deviation from stoichiometric composition caused the magnetocrystalline anisotropy to become higher for x=0.7 and 0.8, but lower for x=0.2. The amplitude, slope and shape of the magnetostriction curves and strain derivatives of the samples were also strongly affected. The present work indicates how variation from stoichiometric composition can be used to tailor magnetic and magnetostrictive properties.

Sensitivity enhancement of magnetoelectric sensors through frequency-conversion

Thin film magnetoelectric (ME) sensors show sensitivity levels as low as 7.1 pT/Hz over narrow bandwidths at bandwidths of some Hz around their mechanical resonance frequency. The high sensitivity is making the sensors – in principle – suitable for biomagnetic measurements like magnetoencephalography (MEG) and magnetocardiography (MCG). Biomagnetic measurements, however, usually require high sensitivity over a wide frequency band of 0.1–100Hz. Unfortunately, at such low frequencies far from resonance the ME coefficient decreases dramatically and the noise level increases; this leads to a significant reduction in sensitivity.This work proposes and demonstrates a novel frequency-conversion-approach, which represents a remedy to the sensitivity decay. It allows wideband measurements at low frequencies by utilizing the nonlinear characteristics of the magnetostriction curve. The new technique offers the possibility to achieve resonance enhanced sensitivities at virtually arbitrary frequencies outside and therefore also far below resonance. Measurements show that sensitivity at 1Hz can be enhanced by a factor of ∼1000 compared to the non-resonant case using the proposed modulation technique. The new technique also offers advantages for the increase of the sensor slew rate, the suppression of mechanical noise and for the operation of such sensors in arrays.

Exchange biasing of magnetoelectric composites

Magnetoelectric composite materials are promising candidates for highly sensitive magnetic-field sensors. However, the composites showing the highest reported magnetoelectric coefficients require the presence of external d.c. magnetic bias fields, which is detrimental to their use as sensitive high-resolution magnetic-field sensors. Here, we report magnetoelectric composite materials that instead rely on intrinsic magnetic fields arising from exchange bias in the device. Thin-film magnetoelectric two-two composites were fabricated by magnetron sputtering on silicon-cantilever substrates. The composites consist of piezoelectric AlN and multilayers with the sequence Ta/Cu/Mn(70)Ir(30)/Fe(50)Co(50) or Ta/Cu/Mn(70)Ir(30)/Fe(70.2)Co(7.8)Si(12)B(10) serving as the magnetostrictive component. The thickness of the ferromagnetic layers and angle dependency of the exchange bias field are used to adjust the shift of the magnetostriction curve in such a way that the maximum piezomagnetic coefficient occurs at zero magnetic bias field. These self-biased composites show high sensitivity to a.c. magnetic fields with a maximum magnetoelectric coefficient of 96 V cm(-1) Oe(-1) at mechanical resonance.

Characterization of Magnetostrictive Losses Using Complex Parameters

Loss characterization in magnetostrictors is one of the key issues for realizing reliable magnetomechanical transducers. Concerning with the hysteresis minor loop within a relatively linear area of magnetostrictive curve, there are three types of losses, elastic loss, magnetic loss and piezomagnetic coupling loss, similar to the loss mechanism of a piezoelectric (elastic, dielectric and piezoelectric losses) that our group has established recent years. By measuring accurately the mechanical quality factors QA for the resonance and QB for the anti-resonance in the admittance/impedance curve, we can derive these three physical losses. By introducing these losses factors we can characterize magnetostrictive losses using complex parameters.

Experiments and modeling of iron-particle-filled magnetorheological elastomers

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. In this work, we present a combined experimental and theoretical study of the macroscopic response of a particular MRE consisting of a rubber matrix phase with spherical carbonyl iron particles. The MRE specimens used in this work are cured in the presence of strong magnetic fields leading to the formation of particle chain structures and thus to an overall transversely isotropic composite. The MRE samples are tested experimentally under uniaxial stresses as well as under simple shear in the absence or in the presence of magnetic fields and for different initial orientations of their particle chains with respect to the mechanical and magnetic loading direction. Using the theoretical framework for finitely strained MREs introduced by Kankanala and Triantafyllidis (2004), we propose a transversely isotropic energy density function that is able to reproduce the experimentally measured magnetization, magnetostriction and simple shear curves under different prestresses, initial particle chain orientations and magnetic fields. Microscopic mechanisms are also proposed to explain (i) the counterintuitive effect of dilation under zero or compressive applied mechanical loads for the magnetostriction experiments and (ii) the importance of a finite strain constitutive formulation even at small magnetostrictive strains. The model gives an excellent agreement with experiments for relatively moderate magnetic fields but has also been satisfactorily extended to include magnetic fields near saturation.

The stress dependence of magnetostriction hysteresis in TbDyFe [110] oriented crystal

The magnetostriction curves and minor loops of the TbDyFe [110] oriented crystal are tested under different compressive pre-stress from 0 to 120 MPa. It is observed that the magnetostriction hysteresis first increases from about 33 Oe under 0 MPa, achieves the maximum of about 70 Oe under 30 MPa, and then decreases to about 16 Oe under 120 MPa (near disappearance) with an increase in the compressive pre-stress. By the theoretical simulation, it is found that upon increasing the compressive pre-stress the dominant energy changes from magnetocrystalline anisotropy energy to magnetoelastic energy. This leads to the domain rotation mode changing from irreversibility to reversibility and consequently results in the decrease of magnetostriction hysteresis, which explains the experimental results very well.

Effects of magnetocrystalline anisotropy constant K2 on magnetization and magnetostriction of Terfenol-D

Magnetocrystalline anisotropy constant K2 is found to produce significant effects on the magnetization and magnetostriction behaviors of Terfenol-D crystals through magnetic domain rotation mechanism. Such effects have often been neglected in previous studies. Considering different values of K2 in the magnetization rotation of ⟨111⟩ easy-direction domains under external magnetic field and compressive uniaxial stress applied along [1¯1¯2] direction, it is shown that a change in K2 causes significant changes in both magnetization and magnetostriction curves. Therefore, K2 is an important parameter that must be considered in magnetoelastic behaviors of Terfenol-D.

The stress-induced anisotropy in the (110) plane of the magnetostrictive TbDyFe [110] oriented crystal

The magnetostriction curve of [110]-oriented Tb0.3Dy0.7Fe1.9 crystal is measured under different compressive prestress. It is observed that the saturation magnetostriction keeps on increasing with the increase in compressive prestress from 0 to 75 MPa. The distribution of the free energy within the (110) plane normal to the stress axis is calculated to clarify the enhancement of saturation magnetostriction under large compressive prestress. It is found that with the increase in the prestress, the lowest energy positions deviate from the initial four ⟨111⟩ easy axes in the (110) plane, approaching the [11¯0] and [1¯10] orientations. The stress-induced anisotropy results in the change in initial domain configuration and further the enhancement of saturation magnetostriction, which well explains the experimental results.

The influence of the magnetoelastic effect on the hysteretic properties of medium-carbon steel during uniaxial loading

Hysteretic magnetic properties and longitudinal magnetostriction of planar specimens of air-hardened 45 steel were measured as functions of elastic tensile stresses along and perpendicular to the applied loading using a closed magnetic circuit and attachable transducers. Parameters that exhibit monotonic variations with increasing elastic tensile stresses, were found. It was shown that the maxima that were observed in the dependences of residual inductance and relative maximum magnetic permeability on applied stresses, as well as the minima that were observed in the dependences of the coercive force and demagnetizing current of an attachable electromagnet as measured with a sensor arranged along the tension axis on applied stresses, are related to the behavior of the magnetostriction curves of the steel under study.

The magnetostriction of Fe–(18− x) at% Ga– x at% Al (3≤ x≤13.5) alloys

The ingot of Fe–(18− x) at% Ga– x at% Al (3≤ x≤13.5) alloys was prepared from high purity elements using a high vacuum arc melting system. The X-ray diffraction patterns indicated that the alloys were disordered bcc A2 structure. The magnetostriction of the alloys was measured and the effect of partial substitution of Ga with Al on the magnetostriction of the alloys was investigated. Fe–9 at% Ga–9 at% Al alloy, the optimizing magnetostrictive alloy was found in Fe–(18− x) at% Ga– x at% Al (3≤ x≤13.5) alloys. The saturated magnetostriction of the directional solidification Fe–9 at% Ga–9 at% Al rod is up to 135 ppm for 0 MPa and 221 ppm for 53 MPa. It was found that the alloy has the high linearity of the magnetostriction curve, the low hysteresis and saturated magnetic field, which suggests the directional solidification Fe–9 at% Ga–9 at% Al alloy is a potential candidate for magnetostrictive actuator and transducer applications.

패치형 자왜 초음파 변환기 성능에 대한 바이어스 자기장의 영향

The effects of biasing magnetic fields on the performances of magnetostrictive ultrasonic transducers are investigated. The transducers are patch-type ones which are used for SHM of plate structures. Various kinds of configurations of biasing magnets are covered experimentally. It is experimentally verified that how the biasing magnetic field deploys is the most significant factors on maximizing the transducer output. From the magnetostriction curve of nickel, it is concluded qualitatively that it is not the absolute values of biasing magnetic field but the slope of magnetostriction curve to be taken account of.

Influence of Co substitution on magnetoelastic properties of Er 2Fe 14− xCo xB ( x = 1, 3 and 5) intermetallic compounds

The magnetostriction and thermal expansion of Er 2Fe 14− x Co x B ( x = 1, 3 and 5) intermetallic compounds were measured, using the strain gauge method in the temperature range 75–450 K under applied magnetic fields up to 1.5 T. For all samples the longitudinal magnetostriction ( λ l) undergoes an anomaly around the spin reorientation temperature ( T SR). It is also observed that λ l decreases with increasing the Co content. All compounds show saturation type behaviour in their anisotropic magnetostriction curves at different temperatures and applied fields. The saturation behaviour of the compound with x = 3 occurs at higher temperatures than with x = 1 and 5. The volume magnetostriction strongly increases below μ 0 H = 0.3 T, then monotonically rises with applied field up to the spin reorientation temperature. An invar type behaviour is observed above 200 K in the compound with x = 1. The results are discussed based on the temperature dependence of magnetocrystalline anisotropy of compounds below and above their T SR.

Saturation magnetostriction of α″-Fe 16N 2 phase

The saturation magnetostriction of α″-Fe 16N 2 phase was evaluated by measuring the magnetostriction curve of Fe 84.8N 7.8B 7.4 ribbon with α″-Fe 16N 2 nanocrystallites embedded in an amorphous matrix. The magnetostriction measurement was carried out at room temperature by means of the three terminal capacitance method. The prepared sample exhibits a saturation magnetostriction of 2.52 × 10 −6. The saturation magnetostriction of α″-Fe 16N 2 phase is evaluated to be −19.1 × 10 −6 according to a simple rule of mixtures.

Elastic Modulus of Ni–Fe Alloys Under Tensile Stress and Magnetic Field

Fe-Ni alloys can have a variety of magnetomechanical properties, depending on their composition. In order to study the magnetoelastic coupling of the alloys, we obtained the stress dependence of the longitudinal and transverse magnetostriction curves and three magnetoacoustic curves, i.e., the speeds of a longitudinal and two transverse waves propagating in a normal direction to the magnetic field. We obtained five curves, each for Ni, B-type Permalloy, and pure iron under tensile stresses from 0 to 40 MPa parallel to the magnetic field. It is known that the magnetoelastic coupling and the acoustoelasticity induce a uniaxial anisotropy in the elastic coefficients of the ferromagnetic materials. We propose a procedure to determine all the elastic coefficients from the above five curves. We also examine the variation of the elastic coefficients with magnetization by taking into account their stress dependence and comparing them with Fe-Ni alloys .

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material.