超磁致伸缩材料的擦除特性和同余特性实验研究

超磁致伸缩材料在力磁耦合作用下具有复杂的迟滞响应。Preisach模型可有效描述物理过程中的滞后现象,它具有两个重要特性,即擦除特性和同余特性。擦除特性是指输入局部极大值擦除了加载过程中小于该值的所有极大值,或输入局部极小值擦除了加载过程中大于该值的所有极小值,同时,与这些历史极值相应的加载历史也被擦除,不再影响之后的输出。同余特性是指输入极大值与极小值相同的所有闭合曲线一致。本文通过实验系统地研究了超磁致伸缩材料在多轴力磁耦合场作用下的磁致伸缩曲线、磁滞回线和应力应变的迟滞行为,发现其在力磁耦合下的非线性滞后行为具有擦除特性和同余特性。这满足了Preisach模型描述滞后现象的两个基本要求,验证了利用Preisach模型描述超磁致伸缩材料迟滞行为的可行性,为超磁致伸缩材料的非线性理论和器件设计提供了依据。     

Numerical simulation on coupling behavior of Terfenol-D rods

Terfenol-D rods, as a kind of giant magnetostrictive materials, are often used as active elements of device for anti-vibration application due to its superior material properties. Their magneto-mechanical responses exhibited in many experiments are nonlinear and coupled. In order to have a good understanding on their coupling characters for accurate control, the numerical simulation on dynamic behavior of a Terfenol-D rod is conducted based on a nonlinear and coupling constitutive model proposed in this paper. The results show that the constitutive model can effectively describe some intrinsic coupling phenomena observed by experiments involving the maximum magnetostrictive strain of a Terfenol-D rod changing with pre-stresses and the corresponding dynamic responses show that the frequency and the amplification of the Terfenol-D rod change with magnetic bias field and pre-stresses, which are also consistent with experimental data and cannot be captured by previous constitutive model.     

Non-linear constitutive relations for magnetostrictive materials

In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.     

EXPERIMENTAL RESEARCHES ON MAGNETO-THERMO-MECHANICAL CHARACTERIZATION OF TERFENOL-D

The coupling effects of axial pre-stress,temperature and magnetic field on magne- tostrictive strain and magnetization as well as Young's modulus of a Terfenol-D (Tb_(0.3)Dy_(0.7)Fe_(1.93)) rod are tested to give a good understanding of magneto-thermal-mecha-nical characteristics of giant magnetostrictive materials.Results show that magneto-thermo-mechanical coupling of gi- ant magnetostrictive materials is very strong;and the influences of pre-stress and temperature on magnetostrictive strain and Young's modulus vary with the intensity of magnetic field.     

磁致伸缩材料的非线性本构关系

给出了磁致伸缩材料的两个非线性本构关系,即标准平方型和双曲正切型。在确定一维问题的本构系数时,基于已有的实验结果,引进一个材料函数,用来描述磁致伸缩材料的压磁系数随预应力变化的关系。将非 线性本构关系的理论模型计算结果与实验曲线对比,结果表明标准平方型本构关系在中低磁场下能精确地模拟实验曲线,而双曲正切型本构关系在高磁场时能反映材料的磁致应变饱和现象。讨论了在标准平方型本构的一般三维情形,给出了确定本构系数的方法。     

超磁致伸缩换能器耦合磁弹性模型与振动特性分析

针对应用于非圆车削加工的超磁致伸缩换能器,建立了其耦合磁弹性动力学模型与复系数动力学微分方程,基于实验建立的激励电流磁致伸缩材料轴向位移-磁场强度三者之间的关系式,得到了换能器磁力-位移关系的磁动方程的解析解,分析了系统的频响特性及不同频率下,激励电流与换能器输出位移之间的滞回关系,对现有磁场-电流公式进行了修正,讨论了偏置磁场对系统的影响,并与数值解进行了对比.结果表明:超磁致伸缩换能器的输出位移与输入激励电流之间的滞回环及其环方位与激励频率有关,且修正公式与实验所得结论完全一致.换能器的频响关系具有明显的共振和反共振特性,且频响曲线的正负向决定了滞回环的方位,换能器输出位移的绝对值决定了滞回环包围面积的大小换能器滞回环的面积、倾斜度随偏置磁场的增大而增大.本文的结果为换能器的控制与优化提供了理论基础.     

A nonlinear constitutive model for magnetostrictive materials

A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function. For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.The project supported by the National Natural Science Foundation of China (10132010 and 90405005)     

稀土超磁致伸缩材料应力与电磁耦合特性的实验研究

讨论了稀土超磁致伸缩棒特性实验的若干应力与电磁耦合问题，利用自己设计制作的实验装置建立了应力电磁耦合系统的物理模型，应用阻抗分析方法得到了相应的等效电路。测定了在电磁场与应力场共同作用下ＴｂｘＤｙ１－ｘＦｅ２－ｚ三元稀土合金超磁致伸缩棒的磁致伸缩系数，机电耦合系数等。针对磁通泄漏问题，专门设计制作了圆柱型硅钢密闭磁路，本的实验结果为稀土眼磁致伸缩材料应用器提供了重要而准确的数据。     

功能铁磁材料的变形与断裂的研究进展

综述了近几十年, 特别是近十几年来铁磁材料的力磁耦合变形与断裂行为的研究概况. 传统铁磁弹性问题的研究已经有较长时间的积累, 文献中已有大量的研究结果发表. 近些年 来, 随着智能材料及结构应用与研究的兴起, 功能铁磁材料如稀土超磁致伸缩材料、铁磁相 变材料以及铁磁复合材料等的力学行为越来越受到重视, 人们在功能铁磁材料的变形与断裂 以及铁磁复合材料的有效性质等方面开展了大量的研究工作. 本文在简单介绍了经典铁磁弹 性和传统铁磁结构的力磁性能的研究背景基础上, 结合作者近年来在铁磁材料变形与断裂方 面所开展的工作, 着重评述了功能软铁磁材料在变形与断裂的实验研究,如实验设备和技术, 以及铁磁复合材料细观力学、软铁磁材料、铁磁功能材料的变形与断裂理论等方面的研究进 展, 并指出了需要进一步研究的方向.     

层状柱壳磁电复合材料的非线性磁电效应研究

本文基于超磁致伸缩材料非线性本构,从基本的控制方程出发,对层状柱壳磁电复合材料的非线性磁电响应进行理论研究,讨论了不同边界下磁场频率以及压电材料厚度比对磁电系数的影响,并得到了不同预压力下磁场大小对于磁电系数的影响。数值计算结果显示,对于Tefernol-D/PZT-5层状磁电复合材料,随着预压力值增大,磁电系数最大值减小,取得最大值时对应的磁场值逐渐增大;不同边界条件、磁场频率和磁场大小下,材料厚度比对磁电系数的也有着不同的影响。特别地当外加磁场频率较大时,相应于压电层厚度比,磁电系数呈现多极值现象。     

岩石化学腐蚀-围压细观损伤本构模型与离散元模拟研究

基于Lemaitre应变等价性假设理论,假定受水化学-力耦合损伤的岩石微元强度服从Weibull分布,考虑化学腐蚀与围压耦合作用对岩石力学参数的影响,通过核磁共振技术与损伤力学理论,引入细观化学损伤变量与力损伤变量,并认为微元破坏符合SMP准则,建立岩石化学腐蚀-力耦合损伤本构模型,并采用理论推导的方法得出所需的模型参数。同时基于颗粒离散元方法,引入参数半径乘子来改变颗粒间的黏结接触尺寸,从而模拟水化学损伤,采用平直节理模型对水化学作用后的岩石进行三轴压缩模拟,得到了水化学作用和不同围压下的岩石三轴应力-应变模拟曲线。通过对比所构建的岩石化学腐蚀-力耦合损伤本构模型理论曲线、离散元模拟曲线和试验曲线,结果表明三者吻合度较好,能够很好地反映岩石在化学腐蚀和围压耦合作用下的力学特性与破坏特征,并通过离散元方法得到了岩石在三轴压缩过程中裂纹的产生与分布情况。     

VIBRATION SUPPRESSION OF CANTILEVER LAMINATED COMPOSITE PLATE WITH NONLINEAR GIANT MAGNETOSTRICTIVE MATERIAL LAYERS

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials(GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions(pre-stress and bias magnetic field).The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method(FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.     

Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal(PC) nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory, in which the surface effect and magneto-elastic coupling are considered. By introducing the nonlinear coupling constitutive relation of magnetostrictive materials, Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect, magn...     

基于唯象相变理论的磁致伸缩材料耦合滞回动力学模拟

本文基于改进的Landau唯象相变理论,构造一个耦合的非线性常微分方程模型来模拟一维磁致伸缩材料的磁滞动态特性。模型的构造通过引入一个非凸的自由能函数来模拟磁致伸缩磁材料中不可逆的磁极化翻转与磁致应变,该自由能函数的每一个局部极小值都对应材料的一个磁化方向。通过热力学平衡条件建立能刻画磁致伸缩效应的非线性本构关系。所构造的模型成功地模拟出了磁场与弹性场之间的磁滞曲线和蝶形曲线,并采用实验结果对模型进行了验证。     

Restrictions on nonlinear constitutive equations for elastic rods

Constitutive equations for the resultant forces and moments applied to a rod-like body necessarily couple the influences of the rod geometry and the constitutive nature of the three-dimensional material from which the rod was constructed. Consequently, even when the nonlinear constitutive equation of the three-dimensional material is known, the influence of the rod geometry on the constitutive response of the rod is not known. The main objective of this paper is to develop restrictions on the constitutive equations of nonlinear elastic rods which ensure that exact solutions of the rod equations are consistent with exact nonlinear solutions of the three-dimensional equations for all homogeneous deformations. Since these restrictions are nonlinear in nature they provide valuable general theoretical guidance for specific constitutive assumptions about the coupling of material and geometric properties of rods. Also, an example of a straight beam clamped at one end and subjected to a shear force at the other end is used to examine the validity of the proposed value for the transverse shear deformation coefficient.     

Nonlinear magneto-electric response of a giant magnetostrictive/piezoelectric composite cylinder

In this study,we investigate the nonlinear coupling magneto-electric(ME) effect of a giant magnetostrictive/piezoelectric composite cylinder.The nonlinear constitutive relations of the ME material are taken into account,and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases,respectively.The influences of different constraint conditions on the ME effect are discussed.In the dynamic case considering nonlinear material properties,the double frequency ME response(The response frequency is twice the applied magnetic frequency) is obtained and discussed,which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2 f in ME laminated structures.Some calculations on nonlinear ME effect are conducted.The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case.     

超磁致伸缩换能器的磁滞非线性动力学仿真

在超磁致伸缩材料输出端位移假设的基础上,建立了以输出顶杆为研究对象、考虑材料内部磁滞非线性及预压弹簧特性的超磁致伸缩换能器非线性动力学模型; 并将Simulink仿真系统应用到超磁致伸缩换能器系统动力学仿真中. 仿真结果表明: 换能器模型系统为稳定周期运动系统,并具有滞回非线性特性;弹簧非线性项中的平方项是影响换能器模型系统的主要因素. 经验证,数值计算结果与文献给出的试验测试结果吻合较好.     

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.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

循环载荷下砂质土的本构模型

提出了一个描述砂质土循环载荷条件下主要特性的本构模型，并且采用不同围压下多种加载途径的土力学实验确定了模型中的待定材料常数，由本构模型的增量工数值积分计算所得到的理论曲线与不同应力路径下实验曲线十分接近，经实验验证这种本构模型能广泛地应用土工问题的弹－塑性有限元分析中。