MAGNETOMECHANICAL BEHAVIORS OF GIANT MAGNETOSTRICTIVE MATERIALS

The Laves phase alloy Tb-Dy-Fe, commercially known as Terfenol-D, exhibits the giant room-temperature magnetostriction at moderate field strength of a few kOe due to its combination of high magnetostriction and low magnetocrystalline anisotropic energy. Thus, this pseudobinary rare earth iron compound has found quite a number of applications such as in magnetomechanical transducers, actuators and adaptive vibration control systems. The simultaneous measurements of magnetostriction and magnetization at various fixed compressive pre-stresses applied in the axial direction for Tb0.3Dy0.7Fe1.95 samples are presented. The results show that the magnetostriction increases with increasing compressive stress until it reaches 1742 ×10^6 under 25 MPa, so does the coercive magnetic field. And the hysteresis loop area for magnetization and magnetostriction also increases with the increment of applied compressive stresses. But the maximum magnetic susceptibility χ（dM/dH） is obtained under zero stress field and the strain derivative dλ/dH increases to the highest amplitude of 0.039×10^-6 A^-1m at a stress level of 5 MPa. In the strain versus magnetization intensity curve, the initial fiat stage mainly consisting of a 180° domain wall motion becomes shorter with increasing stress. It means more initial domains are driven to the transversal direction under the compressive stress before magnetization, which is consistent with the improvement of the magnetostriction.     

MAGNETOMECHANICAL BEHAVIORS OF GIANT MAGNETOSTRICTIVE MATERIALS

The Laves phase alloy Tb-Dy-Fe,commercially known as Terfenol-D,exhibits the giant room-temperature magnetostriction at moderate field strength of a few kOe due to its combination of high magnetostriction and low magnetocrystalline anisotropic energy.Thus,this pseudobinary rare earth iron compound has found quite a number of applications such as in mag- netomechanical transducers,actuators and adaptive vibration control systems.The simultaneous measurements of magnetostriction and magnetization at various fixed compressive pre-stresses applied in the axial direction for Tb_(0.3)Dy_(0.7)Fe(1.95) samples are presented.The results show that the magnetostriction increases with increasing compressive stress until it reaches 1742×10~6 un- der 25 MPa,so does the coercive magnetic field.And the hysteresis loop area for magnetization and magnetostriction also increases with the increment of applied compressive stresses.But the maximum magnetic susceptibilityχ(dM/dH)is obtained under zero stress field and the strain derivative dλ/dH increases to the highest amplitude of 0.039×10~(-6) A~(-1)m at a stress level of 5 MPa.In the strain versus magnetization intensity curve,the initial fiat stage mainly consisting of a 180°domain wall motion becomes shorter with increasing stress.It means more initial domains are driven to the transversal direction under the compressive stress before magnetization,which is consistent with the improvement of the magnetostriction.     

Stability of plane-parallel flow of magnetic fluids under external magnetic fields

In this work,we present a theoretical study on the stability of a two-dimensional plane Poiseuille flow of magnetic fluids in the presence of externally applied magnetic fields.The fluids are assumed to be incompressible,and their magnetization is coupled to the flow through a simple phenomenological equation.Dimensionless parameters are defined,and the equations are perturbed around the base state.The eigenvalues of the linearized system are computed using a finite difference scheme and studied with respect to the dimensionless parameters of the problem.We examine the cases of both the horizontal and vertical magnetic fields.The obtained results indicate that the flow is destabilized in the horizontally applied magnetic field,but stabilized in the vertically applied field.We characterize the stability of the flow by computing the stability diagrams in terms of the dimensionless parameters and determine the variation in the critical Reynolds number in terms of the magnetic parameters.Furthermore,we show that the superparamagnetic limit,in which the magnetization of the fluids decouples from hydrodynamics,recovers the same purely hydrodynamic critical Reynolds number,regardless of the applied field direction and of the values of the other dimensionless magnetic parameters.     

Stability of plane-parallel flow of magnetic fluids under external magnetic fields

In this work,we present a theoretical study on the stability of a two-dimensional plane Poiseuille flow of magnetic fluids in the presence of externally applied magnetic fields.The fluids are assumed to be incompressible,and their magnetization is coupled to the flow through a simple phenomenological equation.Dimensionless parameters are defined,and the equations are perturbed around the base state.The eigenvalues of the linearized system are computed using a finite difference scheme and studied with respect to the dimensionless parameters of the problem.We examine the cases of both the horizontal and vertical magnetic fields.The obtained results indicate that the flow is destabilized in the horizontally applied magnetic field,but stabilized in the vertically applied field.We characterize the stability of the flow by computing the stability diagrams in terms of the dimensionless parameters and determine the variation in the critical Reynolds number in terms of the magnetic parameters.Furthermore,we show that the superparamagnetic limit,in which the magnetization of the fluids decouples from hydrodynamics,recovers the same purely hydrodynamic critical Reynolds number,regardless of the applied field direction and of the values of the other dimensionless magnetic parameters.     

On the stress–strain states of cellular materials under high loading rates

A virtual Taylor impact of cellular materials is analyzed with a wave propagation technique, i.e. the Lagrangian analysis method, of which the main advantage is that no pre-assumed constitutive relationship is required. Time histories of particle velocity, local strain, and stress profiles are calculated to present the local stress–strain history curves, from which the dynamic stress–strain states are obtained.The present results reveal that the dynamic-rigid-plastic hardening(D-R-PH) material model introduced in a previous study of our group is in good agreement with the dynamic stress–strain states under high loading rates obtained by the Lagrangian analysis method. It directly reflects the effectiveness and feasibility of the D-R-PH material model for the cellular materials under high loading rates.     

DYNAMIC MECHANICAL BEHAVIOR OF 6061 AL ALLOY AT ELEVATED TEMPERATURES AND DIFFERENT STRAIN RATES

The compressive stress-strain relationships of 6061Al alloy over wide temperatures and strain rates are investigated. The dynamic impact experiments are performed using an improved high temperature split Hopkinson pressure bar apparatus. The experimental results are compared with those obtained by the modified Johnson-Cook constitutive model. It is found that the dynamic mechanical behavior depends sensitively on temperature under relatively low strain rates or on strain rate at relatively high temperatures. The good agreement indicates that it is valid to adopt the parameter identification method and the constitutive model to describe and predict the mechanical response of materials.     

Investigation on the plastic work-heat conversion coefficient of 7075-T651 aluminum alloy during an impact process based on infrared temperature measurement technology

The plastic work-heat conversion coefficient is one key parameter for studying the work-heat conversion under dynamic deformation of materials. To explore this coefficient of 7075-T651 aluminum alloy under dynamic compression, dynamic compression experiments using the Hopkinson bar under four groups of strain rates were conducted, and the temperature signals were measured by constructing a transient infrared temperature measurement system. According to stress versus strain data as well as the corresponding temperature data obtained through the experiments, the influences of the strain and the strain rate on the coefficient of plastic work converted to heat were analyzed.The experimental results show that the coefficient of plastic work converted to heat of 7075-T651 aluminum alloy is not a constant at the range of 0.85–1 and is closely related to the strain and the strain rate. The change of internal structure of material under high strain rate reduces its energy storage capacity, and makes almost all plastic work convert into heat.     

Influence of stress and high-temperature treatment on the permeability evolution behavior of sandstone

Permeability is an important property of rock in gas and oil exploration engineering, environment temperature and geo-stress have great influence on it. This paper aims to analyze the influence of thermal treatment on the permeability of sandstone under triaxial compression. Based on the gas seepage tests on a sandstone specimen after different thermal treatment temperatures with different gas pressures, hydrostatic stresses and deviatoric stresses, the thermal effect on physical property of sandstone is firstly analyzed. The results show that the mass of the sandstone specimen decreases with the increase of temperature, some spalling damage and tensile crack occur on the lateral surface of the specimen at 400℃. According to the seepage test results with various gas pressures, an exponential relationship has been found between the permeability coefficient and temperature. The permeability coefficient is approximately 100 times as large as the initial value when the temperature increases from 20℃ to 800℃. The permeability evolution of the heated sandstone under hydrostatic and deviatoric compression has also been analyzed. A simplified double pore texture model is proposed which can well describe the permeability evolution of sandstone under compression with hydrostatic stress and deviatoric stress, it can be helpful to estimate the permeability of thermal treated sandstone under elastic triaxial compression.     

MODIFICATION OF ONE-DIMENSION COUPLED HYSTERESIS MODEL FOR GMM WITH THE DOMAIN FLEXING FUNCTION

This paper focuses on eliminating the unphysical negative susceptibility which ap- pears when magnetic field is at unsaturated excitation level and reduces from extremity of the hysteresis loop in one-dimension coupled hysteresis model. The domain flexing function c （H） is used to replace the domain flexing constant c in one-dimension coupled hysteresis model. The fea- sibility and rationality of proposed modification are convinced by comparing the magnetization and magnetostriction curves with experimental data and another typical modification results. The effects of pre-stress and temperature on magnetic-elastic-thermal coupling property and hysteresis behavior are investigated.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.     

EXPONENT MODEL FOR MECHANICAL BEHAVIORS IN A CYLINDRICAL SUPERCONDUCTING COMPOSITE WITH TRANSPORT CURRENT

The mechanical properties of a superconducting composite cylinder with transport current are investigated. By adopting the exponent model, the nonlinear differential equations for flux distributions are derived. The elastic solutions to stress, displacement and magnetostriction are analytically given. Some typical numerical results are displayed. Numerical results show that in the process of transport current reduction, tensile stress generally occurs in the outer region of the composite, and that displacement is always negative in the composite. In addition, as the applied maximal transport current exceeds the outer-cylinder critical current, a hysteresis loop of the magnetostriction exists for the full cycle of the transport current.     

TRANSVERSELY ISOIROPIC BEAM UNDER INITIAL STRESS

Starting from Novozhilov’s nonlinear equations of elasticity by appropriatesimplification and integration over the beam cross-section,a linearized set of equations for atransversely isotropic beam under initial non-uniform state of stress is obtained.In theabsence of initial stress,the obtained equations are reduced to well-known Timoshenkobeam equations.These equations are applied to investigate the vibration and buckling characteristics ofa transversely isotropic beam under uniform initial axial force and bending moment.     

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.     

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE STRESS-STRAIN RELATION FOR MESOSCOPIC HETEROGENEOUS ROCK UNDER UNIAXIAL TENSILE LOADING

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.     

Transversely isoiropic beam under initial stress

Starling from Novozhilov’s nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.     

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.     

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slender,non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam.The material of the cantilever is assumed to be nonlinearly elastic.Different nonlinear relations between stress and strain in tensile and compressive domain are considered.The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.     

Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen's nonlocal elasticity

The size effects on heat conduction and elastic deformation are becoming significant along with the miniaturization of the device and wide application of ultrafast lasers.In this work,to better describe the transient responses of nanostructures,a size-dependent thermoelastic model is established based on nonlocal dual-phase-lag(N-DPL)heat conduction and Eringen's nonlocal elasticity,which is applied to the one-dimensional analysis of a finite bi-layered nanoscale plate under a sudden thermal shock.In the numerical part,a semi-analytical solution is obtained by using the Laplace transform method,upon which the effects of size-dependent characteristic lengths and material properties of each layer on the transient responses are discussed systematically.The results show that the introduction of the elastic nonlocal parameter of Medium 1 reduces the displacement and compressive stress,while the thermal nonlocal parameter of Medium 1 increases the deformation and compressive stress.These findings may be beneficial to the design of nano-sized and multi-layered devices.     

Magnetic field effects on the nonlinear vibration of a rotor

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.