磁记忆检测中的力-磁关系及其实验观察

从微磁化基本理论出发,依据能量原理,建立了铁磁材料的能量状态方程;采用最小能量原理和拉格朗日乘数法得出了在外力作用下铁磁体内应力与磁化率改变量之间的线性关系式.进一步讨论了在应力方向改变时应力与相应方向磁化率改变量间的对应关系,证明在不同方向上二者之间的线性关系依然成立.根据变压器原理,设计出铁磁材料磁化率检测装置,以45#钢试件为例,测量了不同方向上应力与磁化率变化量间的对应关系,并与理论值做了比较.实验结果表明文中得出的应力-磁化率变化量表达式与实验测定结果符合得较好.以上工作为明确磁记忆检测技术的检测对象和机理,建立磁记忆检测技术的力-磁本构关系在一个新的视角上做了有意义的探索.     

铁磁矩形简支板的磁弹塑性弯曲行为分析

基于广义变分原理得到的磁力计算公式,采用塑性增量理论,Mises屈服准则和有效的增量有限元计算方法,研究了线性强化材料铁磁矩形板的磁弹塑性弯曲行为。在文中定量模拟了铁磁简支矩形板在外加磁场作用下的挠度特征曲线,铁磁板发生塑性变形时的构型图和不同外加磁场下的中截面构型,以及铁磁板在卸载后的残余挠度特征曲线等力学特征,分析了塑性区域随磁场增加而扩展的情况。数值结果表明:当铁磁矩形板上的部分区域发生塑性屈服后,其变形明显大于相同磁场条件下铁磁板发生的弹性变形值;且随着外加磁场倾角的增大(0°<α≤45°),铁磁板进入塑性屈服状态的临界屈服磁场值减小;铁磁板的中截面构形为双半波型,其塑性区域由铁磁板两侧挠度最大的区域向板的中心区域扩展,板的中心最后进入塑性区域等。     

带铁磁薄膜悬臂板的磁场微感应器磁弹性特征研究

对于在可变形非磁材料悬臂梁式板单表面粘贴可磁化材料薄膜所构成的磁场微传感器件结构,研究了其处在磁场环境中的磁弹性弯曲变形的磁场-力学特征。为此,建立了由有限元方法分析磁场与有限差分法计算挠曲变形相结合来计算其结构在磁场中产生磁弹性变形的定量分析程序。在此基础上,对于这一微传感结构的算例给出了其结构变形随外加磁场环境变化的磁场-挠度特征关系等定量结果。结果表明：微传感器件不仅可以测量出磁场的大小,而且给出了测量磁场矢量方向的可能性。     

弹塑性损伤本构关系的显式积分算法研究

首先引入弹塑性损伤本构关系,分别从材料软化与残余应变两个方面,描述伪脆性材料的非线性行为.针对结构动力分析中的强非线性问题,给出了弹塑性损伤本构关系的显式积分算法.算法中引入算子分解的思想,将弹塑性本构关系分成塑性与损伤两个模块.首先求解塑性模块,根据有效应空间塑性演化公式,采用前进欧拉算法,直接构造塑性演化的预测值,并且根据屈服函数的漂移构造了误差限公式,作为衡量显式算法精度的指标.将塑性模块求解的结果代入损伤模块,可以方便地求得损伤变量的演化,并最终得到更新后的应力.整个求解过程不需要迭代,可最大程度的算法稳定性.将论文建立的本构关系显式算法与结构分析显式算法结合,构造了结构显式分析方法,并模拟了两个经典算例,算例结果验证了论文方法的有效性.     

铁磁梁式板磁弹性初始后屈曲及缺陷敏感性分析

从铁磁板的磁弹性广义变分原理出发，通过对铁磁板内外的磁场和板变形 场的摄动技术以及采用经典Koiter理论，对横向磁场中铁磁悬臂、简支、固支梁式薄 板磁弹性稳定性的初始后屈曲行为及缺陷敏感性进行了定性研究. 解析地给出了悬臂板对初 始缺陷敏感，简支和固支板对初始缺陷不敏感等结果，对悬臂梁式板理论预测的临界磁场值 往往大于实验观测结果的现象从定性上给予了合理解释.     

软磁材料的力磁耦合本构的实验研究

磁性材料已经在新技术中起着重要的作用,研究这些磁性材料的力学规律对于磁性材料的应用和发展至关重要.软磁材料在工作状态时,一般受到机械应力场和电磁场双重耦合场的作用,其本构关系本质上是非线性的.这给理论模拟带来了很大困难.目前无论是从实验方面或者是理论模型方面,对软磁材料的力磁耦合本构关系的研究都很不成熟.本文用实验方法,研究了高纯度镍和锰锌复合铁氧体这两种传统软磁材料的力磁耦合本构关系.研制了力磁耦合加载设备,测量设备和监控设备.采用铁氧体粉末烧结方法,烧制了实验所需的圆柱状实验试件.实验结果表明,外加应力对镍和锰锌铁氧体材料的磁致应变具有重要影响,较大预加应力对镍的磁化强度产生较明显的影响.而外应力对锰锌铁氧体材料的磁化曲线影响很小.     

低碳钢塑性变形量磁评定法研究

针对塑性变形量评定的局限问题,基于铁磁材料塑性变形致位错在不同方向分布不同的现象,研究了磁测法在定量评定低碳钢塑性变形量方面的应用前景。实验以工程中常用的低碳钢Q195钢板为测试材料,制作了形状尺寸一致的一批试件,并对其进行了不同程度的塑性变形量加载。通过搭建的磁化检测系统,采用相同强度及频率的正弦波激励,对所有样品进行了不同方向的磁化;同时经线圈及隧道磁敏电阻(TMR)采集了每次磁化的磁化曲线,提取了磁化曲线特征参数,对比了其与塑性变形量的定量关系。结果表明:随着塑性变形量的增加,铁磁钢材在同一磁场强度下产生的磁感应强度也会变大;沿主塑性变形方向磁化时,磁滞消耗能量最少,沿主塑性变形垂直方向磁化时,磁滞消耗的能量最多;磁路内磁场在主塑性变形方向上对塑变量的变化最敏感,而磁路外磁场在主塑变垂直方向上对塑变量的变化最敏感。实现了铁磁材料磁特征参数与塑性变形量的定量关联。本研究为开发简捷的铁磁材料塑性变形量无损评定磁方法奠定了基础。     

铁磁梁式板的磁弹塑性动力特征分析

针对典型的矩形磁脉冲,研究了横向磁脉冲作用下线性强化材料铁磁梁式板的磁弹塑性动力响应及其动力失稳特征,给出了线性强化铁磁梁式板的弹塑性动力失稳特征曲线;探讨了塑性应变强化系数对铁磁梁式板的动力响应特征曲线、最终平衡位置、残余构形等的影响.数值结果表明:在同等条件下,塑性应变强化系数越大,其相应铁磁梁式板的动力失稳磁场值越大,其相应的残余构形越小.     

斜磁场中矩形铁磁薄板的几何非线性磁弹性行为分析

基于复杂磁场中铁磁介质磁弹性广义变分原理,给出了包含磁场、铁磁薄板几何非线性的一组基本方程,并对斜磁场中铁磁薄板的磁弹性弯曲问题进行了分析．根据铁磁板内磁场分布特点定性分析了铁磁薄板所受磁力的特征,建立了考虑铁磁板磁场端部效应以及耦合非线性、几何非线性的磁弹性有限元模型,数值模拟了铁磁薄板的磁弹性耦合弯曲特性并给出铁磁悬臂、简支薄板随磁场倾角变化的磁弹性弯曲变形特征等,数值结果与定性分析结果吻合良好．     

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。     

磁性形状记忆合金力磁耦合行为的唯象模型研究

本文基于热力学及耗散概念,推导了一种磁性形状记忆合金（MSMA）的力磁耦合三维唯象本构关系。采用内变量模拟微观相结构及磁结构的演化,考虑了马氏体相变过程及马氏体重定向过程。同时,本文摒弃了传统的单畴假设,运用双畴模型来模拟循环加载下的磁畴结构演化。根据文献中的二维加载情况的实验数据确定本模型的参数。数值模拟结果表明：本文的模型可以很好的捕捉磁性形状记忆合金的形状记忆效应、应变及磁化响应的滞后性。应变及磁化响应模拟结果明显比文献中的理论模型更加吻合实验数据,尤其是低磁场时尤为明显。     

A small-scale magnetic-yielding model for an infinite magnetostrictive plane with a crack-like flaw

The effect of an external magnetic field on the fracture toughness of magnetostrictive materials has been investigated by determining the local stress fields around the tip of a very slender elliptical flaw embedded in an infinite magnetostrictive plane subjected to magnetic loading, based on the assumption of linear magnetization. In this paper, the above-mentioned analytical approach is extended to develop a small-scale magnetic-yielding model. The magnetic saturation zone is constructed and the distributions of magnetic field and magnetization are obtained around the tip of a slender elliptical crack. Based on the complex potential theory, the stress field is obtained in the vicinity of the tip of the slender elliptical crack by implementing the continuity conditions of displacement and resultant force at the interface between the magnetic saturation and magnetoelastic zones. The stress fields near the tip of the slender elliptical crack are obtained for two kinds of soft ferromagnetic materials each with a small induction magnetostrictive modulus. The theoretical results obtained show that the stresses in the neighborhood of a crack-tip are finite even when the elliptical crack reduces to a sharp crack, and are much smaller than the yield stress or the nominal fracture stress of the material. This suggests that, generally, the magnetic field has no obvious effects on the apparent fracture toughness of soft ferromagnetic materials, which is in agreement with the existing experimental results published in the existing literature. In addition, the theoretical analysis illustrates that no crack is magnetically impermeable, and the corresponding boundary conditions are inappropriate for fracture analysis of soft ferromagnetic materials.     

Magnetoelastic interactions in a soft ferromagnetic body with a nonlinear law of magnetization: Some applications

Linearized equations and boundary conditions of a magnetoelastic ferromagnetic body are obtained with the nonlinear law of magnetization. Magnetoelastic interactions in a multi-domain ferromagnetic materials are considered for magneto soft materials, i.e. the case when the magnetic field intensity vector and magnetization vector are parallel. As a special case, the following two problems are considered: (1) the magnetoelastic stability of a ferromagnetic plate-strip in a homogeneous transverse magnetic field; (2) the stress–strain state of a ferromagnetic plane with a moving crack in a transverse magnetic field. It is shown that the modeling of magnetoelastic equations with a nonlinear law of magnetization provides qualitative and quantitative predictions on physical quantities including critical loads and stresses. In particular, it is shown that the critical magnetic field in plate stability problems found with the nonlinear law of magnetization is in better agreement with the experimental finding than the one found with a linear law. Furthermore, it is also shown that the stress concentration factor around a crack predicted with the nonlinear law of magnetization is more accurate than the one obtained with a linear counterpart. Numerical results are presented for above mentioned two problems and for various forms of nonlinear laws of magnetization.     

铁磁纳米结构磁化状态及其磁-力耦合效应的相场模拟

基于随时间变化的Ginzburg-Landau(TDGL)方程,建立了模拟铁磁材料磁-力耦合效应的相场模型。从弱解形式出发,推导出了相关控制方程的有限元格式,然后编制程序进行数值求解。由于有限元对复杂边界有良好的适用性,该模型可用于不同形状铁磁材料的畴结构模拟。通过相场模拟,发现铁磁纳米结构中的磁化会形成涡旋结构,与实验观察到的磁化涡旋结构符合较好。由非均匀磁化引起的结构的变形、应力等力学参量都可以通过模拟一并得到。本文结果表明,改变结构形状可以有效控制磁畴结构的形态,适当的外应力可以改变磁畴结构及其对外磁性的大小。     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

Magneto-elastic stress in a thin infinite plate with an elliptical hole under uniform magnetic field

Two-dimensional magnetic field and magneto-elastic stress solutions are presented for a magnetic material of a thin infinite plate with an elliptical hole under uniform magnetic field. The linear constitutive equation is used for the magnetic field and the stress analyses. The magneto-elastic stress is analyzed using Maxwell stress since only Maxwell stress is caused as a body force according to the electro magneto theory. Except the approximation of the plane stress state in which the plate is thin, no further assumption is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress for soft ferromagnetic material is analyzed and then those for paramagnetic and diamagnetic materials are analyzed. It is stated that the stress components are the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields are different each other in the plates. If the analysis of magnetic field of paramagnetic materials is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material. Shear deflection as well as stress in the direction of the plate thickness arises and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived.     

A real-space phase field model for the domain evolution of ferromagnetic materials

A real-space phase field model based on the time-dependent Ginzburg–Landau (TDGL) equation is developed to predict the domain evolution of ferromagnetic materials. The phase field model stems from a thermodynamic theory of ferromagnetic materials which employs the strain and magnetization as independent variables. The phase field equations are shown to reduce to the common micromagnetic model when the magnetostriction is absent and the magnitude of magnetization is constant. The strain and magnetization in the equilibrium state are obtained simultaneously by solving the phase field equations via a nonlinear finite element method. The finite-element based phase field model is applicable for the domain evolution of ferromagnetic materials with arbitrary geometries and boundary conditions. The evolution of magnetization domains in ferromagnetic thin film subjected to external stresses and magnetic fields are simulated and the magnetoelastic coupling behavior is investigated. Phase field simulations show that the magnetization vectors form a single magnetic vortex in ferromagnetic disks and rings. The configuration and size of the simulated magnetization vortex are in agreement with the experimental observation, suggesting that the phase field model is a powerful tool for the domain evolution of ferromagnetic materials.