A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys

This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops.     

Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究

研究了不同载荷作用下Tb_0.3Dy_0.7Fe₂合金在压磁和磁弹性效应中磁畴偏转的滞回特性. 基于Stoner-Wolhfarth模型的能量极小原理, 采用绘制自由能-磁畴偏转角度关系曲线的求解方法, 研究了压磁和磁弹性效应中载荷作用下的磁畴角度偏转和磁化过程, 计算分析了不同载荷作用下磁畴偏转的滞回特性. 研究表明, 压磁和磁弹性效应中磁畴偏转均存在明显的滞回、跃迁效应, 其中磁化强度的滞回效应来源于磁畴偏转的角度跃迁; 压磁效应中预加磁场的施加将增大磁化强度的滞回, 同时使滞回曲线向大压应力方向偏移; 磁弹性效应中磁畴偏转的滞回存在两个临界磁场强度, 不同磁场强度下合金具有不同的磁畴偏转路径和磁化滞回曲线, 临界磁场强度的大小取决于预压应力的施加. 理论分析对类磁致伸缩材料磁畴偏转模型的完善和材料器件的设计应用非常有意义.     

离轴磁场退火后Tb0.3Dy0.7Fe1.95〈110〉取向晶体的磁致伸缩"跳跃"效应

将〈110〉取向Tb_0.3Dy_0.7Fe_1.95合金棒放在与轴向成35°夹角的外磁场中退火处理,研究其在0—30 MPa预压应力σpre作用下的磁致伸缩效应.结果表明,σpre=0条件下的饱和磁致伸缩值λs由退火前的1023×10^-6提高到1650×10^-6;σpre 关键词： 磁致伸缩 磁场退火 磁致伸缩"跳跃"效应     

Tb0.3Dy0.7Fe2合金的本构参数辨识方法研究

建立了一种简便的、适用于磁畴模型应用的Tb_0.3Dy_0.7Fe₂ 合金本构参数辨识方法. 针对Tb_0.3Dy_0.7Fe₂合金磁畴模型中本构参数不明确且直接实验测试困难的问题, 提出了一种数值计算与实验测试相结合的参数辨识方法. 采用坐标变换与绘制自由能等势曲线相结合的方法, 简化了载荷作用下Tb_0.3Dy_0.7Fe₂ 合金内磁畴角度偏转的数值计算, 研究了合金磁畴角度偏转模型的参数依赖性. 在此基础上, 结合简单的实验测试, 建立了Tb_0.3Dy_0.7Fe₂合金各向异性常数K₁ 和K₂、能量分布因子ω、晶轴取向分布的辨识及修正方法. 该方法能够简单、快速地完成Tb_0.3Dy_0.7Fe₂ 合金磁畴模型中本构参数的辨识, 对完善磁致伸缩材料磁畴偏转的数值计算模型非常有意义. 理论分析可为类磁致伸缩材料磁机耦合模型的建立、完善, 以及材料本构参数的辨识、获取提供参考.     

On the effect of an elastic shear stress upon the magnetization of ferromagnetic sheets

When an elastic shear stress and a cyclical magnetic field, parallel to each other, are applied in the plane of a ferromagnetic sheet, magnetization changes perpendicular to the field are induced in the sample. “Transverse” hysteresis loops, i.e. transverse magnetization plotted as a function of the longitudinal field, were studied in various materials. The characteristic shape of the loop and the differences in sign and magnitude of the “transverse” magnetization have been qualitatively explained in terms of magnetic domain theory. Work supported by G.N.S.M. (CNR).     

A one-dimension coupled hysteresis model for giant magnetostrictive materials

This paper addresses the development of a one-dimension model for quantifying magnetic-elastic-thermal coupling and hysteresis inherent to giant magnetostrictive materials. Firstly, the anhysteretic law is modeled by considering the Gibbs free energy function G(σ, M, T), and thermodynamic relations are used to obtain the constitutive expressions. These expressions character the effects of coupling between stress, magnetization, and temperature in the giant magnetostrictive material but hysteresis, i.e. strain and magnetic intensity described by above the constitutive expressions are single-valued function of the magnetization. And then pinning is incorporated to describe hysteresis based on Jiles–Atherton model. The model considered in the paper is demonstrated valid by comparing the predicted results with experimental data. Moreover, the model proposed in the paper is convenient to be used in engineering applications since the parameters referred to the model have definite physical mean and can all be easily determined by experiments.     

Magnetostriction of FM/TbFe (FM=Fe, Py-permalloy, FeCo) coupled bilayer

Choosing TbFe as the magnetostrictive layer and using soft ferromagnetic materials (FM=Fe, Py-permalloy, FeCo) as the inductive layer, we report the magnetization and magnetostriction of the S/FM(10 nm)/TbFe(10 nm) coupled bilayer (S-glass substrate). The magnetization of the coupled bilayer is attributed to the soft ferromagnetic layer and there is no contribution from the TbFe layer. Interfacial exchange interaction plays an important role in determining the magnetostriction of the coupled bilayer. The effect coming from the deposition Argon pressure on the magnetostriction of the coupled bilayer was also investigated.     

A new ferromagnetic hysteresis model for soft magnetic composite materials

A new ferromagnetic hysteresis model for soft magnetic composite materials based on their specific properties is presented. The model relies on definition of new anhysteretic magnetization based on the Cauchy-Lorentz distribution describing the maximum energy state of magnetic moments in material. Specific properties of soft magnetic composite materials (SMC) such as the presence of the bonding material, different sizes and shapes of the Fe particles, level of homogeneity of the Fe particles at the end of the SMC product treatment, and achieved overall material density during compression, are incorporated in both the anhysteretic differential magnetization susceptibility and the irreversible differential magnetization susceptibility. Together they form the total differential magnetization susceptibility that defines the new ferromagnetic hysteresis model. Genetic algorithms are used to determine the optimal values of the proposed model parameters. The simulated results show good agreement with the measured results.     

Dynamic Tensile Behavior and Fracture Mechanism of Polymer Composites Embedded with Tetraneedle-Shaped ZnO Nanowhiskers

Dynamic tensile properties of glass-fiber polymer composites embedded with ZnO nanowhiskers are investigated by a split Hopkinson tensile bar. The stress-strain curves, ultimate strength, failure strain and elastic modulus are obtained and the failure mechanism of the composites is investigated by the macroscopic and microscopic observation of fractured specimens. The strain rate effect on the mechanical behavior is discussed and a constitutive model is derived by simulating the experimental data. The experimental results show that the materials have an obvious non-linear constitutive relation and strain rate strengthening effect. The composites with ZnO nanowhiskers under dynamic loading have various failure modes and better mechanical properties.     

Numerical simulation of nonlinear magnetic-mechanical-electric coupling effect in laminated magnetoelectric composites

Considering the significant nonlinear magnetoelectric (ME) characteristics in laminated ME composites, we build a numerical model of magnetic-mechanical-electric coupling effect based on the nonlinear magnetostrictive constitutive relation. The change of the ME field coefficients with bias magnetic field predicted by this model shows good agreement with the experimental result, both qualitatively and quantitatively. Furthermore, this paper considers and predicts the magnetoelectric conversion charateristics of laminated ME composites, calculates and analyzes the influence of the thickness ratio of magnetostrictive layer, the geometrical size of laminated composites, the saturation magnetization, and the types of piezoelectric materials on the ME conversion coefficient of ME laminated composites. We believe that this research provides a theoretical basis for the production of magnetoelectric devices with good magnetoelectric conversion characteristics.     

Combined effect of demagnetizing field and induced magnetic anisotropy on the magnetic properties of manganese-zinc ferrite composites

This work is devoted to the analysis of factors responsible for the high-frequency shift of the complex permeability (μ^?) dispersion region in polymer composites of manganese-zinc (MnZn) ferrite, as well as to the increase in their thermomagnetic stability. The magnetic spectra of the ferrite and its composites with polyurethane (MnZn-PU) and polyaniline (MnZn-PANI) are measured in the frequency range from 1 MHz to 3 GHz in a longitudinal magnetization field of up to 700 Ое and in the temperature interval from −20 °С to +150 °С. The approximation of the magnetic spectra by a model, which takes into account the role of domain wall motion and magnetization rotation, allows one to determine the specific contribution of resonance processes associated with domain wall motion and the natural ferromagnetic resonance to the μ^?. It is established that, at high frequencies, the μ^? of the MnZn ferrite is determined solely by magnetization rotation, which occurs in the region of natural ferromagnetic resonance when the ferrite is in the “single domain” state. In the polymer composites of the MnZn ferrite, the high-frequency permeability is also determined mainly by the magnetization rotation; however, up to high values of magnetizing fields, there is a contribution of domain wall motion, thus the “single domain” state in ferrite is not reached. The frequency and temperature dependence of μ^? in polymer composites are governed by demagnetizing field and the induced magnetic anisotropy. The contribution of the induced magnetic anisotropy is crucial for MnZn-PANI. It is attributed to the elastic stresses that arise due to the domain wall pinning by a polyaniline film adsorbed on the surface of the ferrite during in-situ polymerization.     

Study of the magnetic interaction in nanocrystalline Pr-Fe-Co-Nb-B permanent magnets

The magnetic properties of an isotropic, epoxy resin bonded magnets made from Pr-Fe-Co-Nb-B powder were investigated. The magnetization reversal process and magnetic parameters were examined by measurements of the initial magnetization curve, major and minor hysteresis loops and sets of recoil curves. From the initial magnetization curve and the field dependencies of the reversible and irreversible magnetization components derived from the recoil loops it was found that the magnetization reversal process is the combination of the nucleation of reversed domains and pinning of domain walls at the grain boundaries and the reversible rotation of magnetization vector in single domain grains. The interactions between grains were studied by means of δM plots. The nonlinear behavior of δM curve approve that the short range intergrain exchange coupling interactions are dominant in a field up to the sample coercivity.The interaction domains and fine magnetic structure were revealed as the evidence of exchange coupling between soft α-Fe and hard magnetic Nd₂Fe₁₄B grains.     

Mechanically driven domain wall movement in magnetoelastic nanomagnets

Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current- and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.     

Soft Magnetic Materials in a Bulk Form Prepared by Powder Compaction

The amorphous, nanocrystalline and polycrystalline ferromagnetic alloys are known as materials with excellent soft magnetic properties. These attractive magnetic properties are challenge for researchers to extend investigation of these materials with the aim to broaden their technical exploitation. The shape in which amorphous, nanocrystalline and polycrystalline materials are usually prepared, is in many cases not suitable shape for application, therefore it is logical to attempt to prepare such material in a more “bulk” form, for example in the form of a cylinder or a ring, that would be more convenient for industrial applications. One of the ways to prepare material in bulk form is to compact the powder. There is rational assumption that the non-magnetostrictive alloys (amorphous Co-Fe-Si-B, nanocrystalline Fe-Nb-Cu-Si-B, and polycrystalline Ni-Fe) may be suitable for the preparation of bulk samples by high-pressure compression, because mechanical stress does not induce magnetic anisotropy in ferromagnetic material during preparation process.We observed that milling of ribbons prepared by rapid quenching method leads to the increase of coercivity, which is caused by the increase of the fraction of magnetization vector rotation in the magnetization processes (the fraction of domain wall motion decreases). After long milling the powder particles become single-domain and can be magnetized by the magnetization vector rotation only, exhibiting maximum value of coercivity.Consolidation of powder with high value of coercivity leads to the “magnetic contact” between powder particles resulting in the decrease of coercivity to the value comparable with that for as-spun ribbons.     

The influence of spatially random magnetostatic,magnetocrystalline, magnetostrictive and exchange fluctuations on the law of approach to ferromagnetic saturation of amorphous ferromagnets

Within the framework of the micromagnetic theory developed by Kronmüller and Ulner we have calculated the influence of spacially random dipolar, magnetocrystalline, magnetostrictive and exchange fluctuations on the law of approach to ferromagnetic saturation of amorphous ferromagnetic materials. The effect of fluctuations of dipolar and exchange interactions turns out to be negligibly small in most materials. The magnetocrystalline and magnetostrictive fluctuations, however, may give rise to a 1/?H-term in the saturation magnetization in materials (such as TbFe₂) with huge local magnetocrystalline fields. In materials with non-vanishing volume averages of the magnetocrystalline energy or the magnetostriction the H-dependence of the saturation magnetization reflects the nature of the strained arrangement of atoms.     

Magnetization reversal of ferromagnetic nanoparticles under inhomogeneous magnetic field

We investigated remagnetization processes in ferromagnetic nanoparticles under inhomogeneous magnetic field induced by the tip of magnetic force microscope (MFM) in both theoretical and empirical ways. Systematic MFM observations were carried out on arrays of submicron-sized elliptical ferromagnetic particles of Co and FeCr with different sizes and periods. It clearly reveals the distribution of remanent magnetization and processes of local remagnetization of individual ferromagnetic particles. Modeling of remagnetization processes in ferromagnetic nanoparticles under magnetic field induced by MFM probe was performed on the base of Landau–Lifshitz–Gilbert equation for magnetization. MFM-induced inhomogeneous magnetic field is very effective to control the magnetic state of individual ferromagnetic nanoparticles as well as to create different distribution of magnetic field in array of ferromagnetic nanoparticles.     

Effect of magnetic annealing on magnetostrictive performance of a 〈1 1 0〉 oriented crystal Tb0.3Dy0.7Fe1.95

A 〈1 1 0〉 oriented rod of the alloy Tb_0.3Dy_0.7Fe_1.95 was subjected to a magnetic heat treatment, cooling through its Curie temperature under 240 kA/m. Besides the improved magnetostriction under free conditions, the magnetically annealed rod still exhibited an obvious magnetostriction “jump” effect when subjected to a uniaxial compressive pre-stress. A giant magnetostriction of 2680×10⁻⁶ was achieved under 640 kA/m and 30 MPa, which became 67% larger than before magnetic annealing. The optimum magnetostrictive strain coefficient d₃₃ was also dramatically enhanced. Magnetic force microscopy images show magnetic domain configurations that contribute to the improved magnetostrictive performance. The effect of induced additional anisotropy by magnetic annealing on the improvement of the magnetostriction is also discussed.     

Structural approach to the permeability aftereffect in zero- magnetostrictive amorphous alloys

Magnetic aftereffects are a general feature of both magnetostrictive and zero-magnetostriction amorphous ferromagnetic materials. It is shown, that the existence of magnetic relaxation effects in zeromagnetostrictive amorphous ferromagnets can be explained within a recently proposed structural approach, by taking into account the nonisotropic character of the local magnetostrictive strain.     

Phase domain structures in cylindrical magnets under conditions of a first-order magnetic phase transition

The magnetic and resonance properties of cylindrical magnets at first-order phase transition from paramagnetic to ferromagnetic state were theoretically studied. It has been shown that in the external magnetic field directed perpendicularly to the rotation axis, formation of a specific domain structure of paramagnetic and ferromagnetic layers can be energetically favorable. The parameters of cylindrical phase domains as well as their dependences on temperature, magnetic field and material characteristics have been calculated. Peculiarities of the magnetic resonance spectra appearing as a result of the phase domain formation have been considered. Dependence of the resonance field of the system of ferromagnetic domains on magnetization and temperature has been obtained.