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Magnetic hysteresis at the domain scale of a multi-scale material model for magneto-elastic behaviour
Abstract
This paper proposes a multi-scale energy-based material model for poly-crystalline materials. Describing the behaviour of poly-crystalline materials at three spatial scales of dominating physical mechanisms allows accounting for the heterogeneity and multi-axiality of the material behaviour. The three spatial scales are the poly-crystalline, grain and domain scale. Together with appropriate scale transitions rules and models for local magnetic behaviour at each scale, the model is able to describe the magneto-elastic behaviour (magnetostriction and hysteresis) at the macroscale, although the data input is merely based on a set of physical constants. Introducing a new energy density function that describes the demagnetisation field, the anhysteretic multi-scale energy-based material model is extended to the hysteretic case. The hysteresis behaviour is included at the domain scale according to the micro-magnetic domain theory while preserving a valid description for the magneto-elastic coupling. The model is verified using existing measurement data for different mechanical stress levels.
... Various factors such as coercive field, easy axis of the material, and direction of the applied field play a decisive role in determining the hysteretic behavior. The physical explanation of the cause of the hysteretic behavior as a function of these factors was appropriately depicted by an energy landscape proposed by Vanoost et al. [262] shown in Fig. 6. The figure implies that under the absence of the magnetic field, the domains are aligned in their respective easy axis orientation occupying their minimum energy states. ...
... Vanoost et al. [262] proposed a different approach to include the hysteretic behavior in the multiscale model. The irreversible behavior at the domain scale was accounted by the introduction of the hysteresis energy density function. ...
... The energy landscape showing the local minima explaining the remnant magnetization and coercivity. Source:Figure reproducedfrom[262]. ...
An extensive growth in the application of ferromagnetic materials require a firm theoretical understanding of the material behavior to accomplish accurate model prediction. The aim of this review article is to capture the evolutionary journey of the nonlinear magnetoelastic constitutive laws, spanning since the mid-twentieth century. This review discusses the prominent proposed constitutive models based either on physical or phenomenological considerations, by classifying them into two categories, the anhysteretic and the hysteretic, which further incorporates the effect of magnetic field, stress, temperature, and plastic deformation on the ferromagnetic material behavior. The respective advantages and limitations offered by the various classes of proposed approaches in the form of Jiles-Atherton model, Armstrong model, Zheng-Liu model, Preisach model, Stoner-Wohlfarth model, multiscale model, Play model, Plasticity based model, Continuum based model have been summarised. Finally, a holistic outlook is presented portraying the state of the art and avenues for improvement that future research might hold regarding the refinement of the available nonlinear magnetoelastic constitutive laws.
... Two models originate from the same research group and the last model is our own variation on this multiscale model. 17 The paper is organized as follows. In Section 2, the energy density function of a cubic crystal is recapitulated, as well as the new energy function 17 to include hysteresis effect. ...
... At the domain scale, the energy density function describing the ferromagnetic behavior of a single crystal is valid. As described in the previous studies, [16][17][18][19][20] some assumptions are made. As an example, a uniform strain and a uniform magnetic field are considered at this scale so the exchange energy can be neglected. ...
... The domain scale is the smallest scale leading to the "constitutive law." Depending on the used material model, the anhysteretic approach for the magneto-elastic coupling 6,21 is used, or as in our previous work, 17,22,23 the hysteresis effect is also introduced at this scale. First, the anhysteretic description of the reversible magneto-elastic behavior is recapitulated. ...
This paper compares different energy-based magneto-mechanical models, which describe the magnetization changes that a magnetostrictive and anisotropic material undergoes when subjected to a quasi-static H-field excitation and tensile or compressive external stress. The magnetic behavior is either characterized by considering the phenomenological energy-based Hauser hysteresis model or by the recently introduced hysteresis energy. The effect of mechanical stress is included naturally in the energy summation of the multiscale models. Properties of the different models, such as accuracy and parameter identification, are illustrated by comparison with experimental data for a nonoriented FeSi3% electrical steel grade.
... No matter how fine the spatial and temporal scales are resolved, the accuracy of the overall field simulation may heavily depend on the provided material data. Only in rare cases, ab-initio material models are available, not to mention the exuberant computational effort they require, hampering their application within field models [3,11]. More often, sets of material data are given. ...
... The functional is extended to include Ampère's law, similarly to (11). Then, the variations according to H • a and H • b provide the relations ...
This paper develops a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points are minimized while enforcing Maxwell’s equations. The minimization problem is solved by employing the Lagrange multiplier approach. The procedure wraps the FE method within an outer data-driven iteration. The method is capable of considering anisotropic materials and is adapted to deal with models featuring a combination of exact material knowledge and measured material data. Thereto, three approaches with an increasing level of intrusivity according to the FE formulation are proposed. The numerical results for a quadrupole-magnet model show that data-driven field simulation is feasible and affordable and overcomes the need of modeling the material law.
... No matter how fine the spatial and temporal scales are resolved, the accuracy of the overall field simulation may heavily depend on the provided material data. Only in rare cases, ab-initio material models are available, not to mention the exuberant computational effort they require, hampering their application within field models [3], [11]. More often, sets of material data are given. ...
... The functional is extended to include Ampère's law, similarly to (11). Then, the variations according to H • a and H • b provide the relations ...
This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points are minimized while enforcing Maxwell's equations. The minimization problem is solved by employing the Lagrange multiplier approach. The procedure wraps the FE method within an outer data-driven iteration. The method is capable of considering anisotropic materials and is adapted to deal with models featuring a combination of exact material knowledge and measured material data. Thereto, three approaches with an increasing level of intrusivity according to the FE formulation are proposed. The numerical results for a quadrupole-magnet model show that data-driven field simulation is feasible and affordable and overcomes the need of modeling the material law.
... The problem that some existing models might not be adequate for description of hysteresis curves in the whole region of magnetic field variation was noticed in several recent papers, to mention as representative examples Refs. [33,34]. ...
... STEEL GRADES EXAMINED BY V. PROCOP[33] For the examined grain-oriented steels, the maximum relative deviation between the modeled and the measured H c values is below 36.5%. The average modeling deviation for the H c = H c dependence was equal to 7.6% for GO1 and 13.1% for GO2. ...
... These approaches can handle full 3D configurations, but the number of parameters required for the modelling can be high and their identification can be tedious. Some others are based on a multiscale description of magneto-elastic couplings [21][22][23][24][25][26][27]. These models provides a very useful insight into magneto-elastic coupling effects, but they are usually too complex to be directly implemented into numerical analysis tools. ...
... Regarding the modelling results, the definition of the magnetostriction curve (Eq. (27)) incorporates naturally the DE effect, which is the magnetostriction strain as a function of stress under no applied field. In order to be consistent with the representation of experimental results, this initial strain has been removed in the representation of modelling results. ...
Magnetostriction is the magnetisation-induced strain in ferromagnetic materials. It highly depends on mechanical stress. Stress state in electromagnetic devices is usually multiaxial and its effect on magnetostrictive properties is not easily predicted. In this paper, an original three-parameter analytical model for the stress-dependent magnetostriction strain of ferromagnetic materials is proposed. It is based on a simplified energetic description of magneto-elastic behaviour. It follows a similar method previously adopted for the description of the effect of stress on the magnetic permeability of magnetic materials. It is applied for the first time to the magnetostriction behaviour and results in a simple formula to express the effect of multiaxial magneto-mechanical loadings on the magnetostriction strain. The approach also naturally includes the description of the so-called and Delta;E effect. The analytical formula is derived in the paper. It shows very satisfying agreement with experimental results on iron-cobalt alloy and pure iron specimen.
... As this method only serves to describe the anhysteretic part, the influence of couplings on hysteresis can be introduced by adding a dependence on the parameters H c and χ 1 to the different physics. This is a hybrid approach that differs from the fully multi-scale approach proposed by Vanoost et al. in [28]. In this paper, we only consider the use of (17). ...
A novel thermodynamically consistent macroscopic magnetic hysteresis model is presented. Magnetization is calculated from the reversible part of the magnetic field, while the evolution law of the irreversible part involves physically meaningful material constants: the coercive field and the initial susceptibilities of the hysteretic and anhysteretic curves. It is possible to invert the model through an iterative procedure, allowing either the magnetic field or the flux density as an input to the model. The model is tested on both soft and hard magnetic materials for major and minor loops.
... In this model, the change of magnetization state occurs only when the applied field is outside the equipotential surface [12]. Besides, some literature analyzes energy from the micromagnetics field and establishes macroscopic models to characterize the heterogeneity and multi-axiality of the material behaviour, called multi-scale models [13], [14]. As for purely numerical modeling of anisotropic hysteresis, the model proposed by Enokizono and Soda is a typical one, whereas it contains many parameters and requires large amounts of experimental data during the identification process [15]. ...
In this paper a model that describes the anisotropic behavior and core loss of electrical steel sheets over a wide range of rotational excitation is developed. Based on the definition of the effective field, the macro-scopic anisotropy field is deduced from a weighted average of the magnetocrystalline energy of a single crystal. An anisotropic vector hysteresis model is then proposed by applying the effective field to the energy-based model. Experimental measurements are used to fit and validate the model. Either alternating or rotational measurements with a maximum magnetic flux density 1.55 T under 10 Hz are employed to fit the model parameters and the remaining set of measurements is used for validating the model accuracy. The results show that the model can naturally account for the drop in the rotational losses at high flux densities regardless of whether it is identified from alternating or rotational measurement data. The generality of the model is demonstrated through continuous angle results and mod-eling of another material.
... Originally proposed to model the anhysteretic magneto-mechanical behavior [20], the approach shows good prediction capabilities with a clear protocol for parameter identification. A multiscale model with hysteresis is proposed in [21] with the inclusion of a hysteresis energy term in the domain free energy definition that depends on the previous state of magnetization. As pointed out in [22], the localization process in multiscale approaches can result in time-consuming finite element simulation of electromagnetic devices. ...
The influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach, and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.
... Originally proposed to model the anhysteretic magneto-mechanical behavior [20], the approach shows good prediction capabilities with a clear protocol for parameter identification. A multiscale model with hysteresis is proposed in [21] with the inclusion of a hysteresis energy term in the domain free energy definition that depends on the previous state of magnetization. As pointed out in [22], the localization process in multiscale approaches can result in time-consuming finite element simulation of electromagnetic devices. ...
... Magneto-elastic approaches have for instance been developed as extensions of Jiles-Atherton [11][12][13][14] or Preisach [15,16] models. Thermodynamic [17][18][19] and multiscale [20][21][22][23][24][25][26][27][28][29] approaches have been specifically developed to describe the combined effects of magnetic field and multiaxial stress on ferromagnetic materials. These multiscale approaches can be simplified [30][31][32][33] and under very strong assumptions, can provide analytical formulas for the description of magneto-elastic couplings [34][35][36]. ...
Giant magnetostrictive materials such as Terfenol-D and Galfenol are used to design actuators and sensors, converting magnetic input into a mechanical response, or conversely, mechanical input into a magnetic signal. Under standard operating conditions, these materials are subjected to stress. It is therefore important to be able to measure, understand and describe their magneto-mechanical behaviour under stress. In this paper, a comprehensive characterisation of the anhysteretic magneto-mechanical behaviour of Terfenol-D was performed. An energy-based multiscale approach was applied to model this behaviour. Finally, it was shown that the strain behaviour of Terfenol-D can be satisfactorily described using an analytical model derived from the full multiscale approach.
... Magneto-elastic approaches have for instance been developed as extensions of Jiles-Atherton [11][12][13][14] or Preisach [15,16] models. Thermodynamic [17][18][19] and multiscale [20][21][22][23][24][25][26][27][28][29] approaches have been specifically developed to describe the combined effects of magnetic field and multiaxial stress on ferromagnetic materials. These multiscale approaches can be simplified [30][31][32][33] and under very strong assumptions, can provide analytical formulas for the description of magneto-elastic couplings [34][35][36]. ...
Giant Magnetostrictive Materials (GMM), such as Terfenol-D or Galfenol, are used to design actuators and sensors converting
magnetic input into a mechanical response, or conversely, mechanical input into a magnetic signal. Under standard operating
conditions, these materials are subjected to stress. It is therefore important to describe their magneto-mechanical behaviour under
stress. In this paper, an analytical model for the stress-dependent magneto-elastic behaviour of ferromagnetic materials is proposed.
This model is based on a simplification of energetic multiscale approaches for magneto-elastic behaviour. It is applied to Terfenol-D
and compared to experimental results with very satisfactory agreement.
... The borders between the adjacent domains, ie domain walls, move in such a way that domains with a magnetisation in a favourable direction grow at the cost of domains with a magnetisation in a less favourable direction. In the presence of lattice strains, the mobility of the 180° domain walls is higher than that of the 90° domain walls [15][16][17] . ...
Management of the residual stress state is vital for the design and production stages of carburised components in order to satisfy the technical requirements related to performance, fatigue behaviour and useful lifetime. This enforces the use of practical, reliable and time- and cost-effective stress measurement methods by manufacturers. This study aims to investigate the efficiency of the magnetic Barkhausen noise (MBN) method in rapid non-destructive determination of surface residual stresses in carburised steels. A series of AISI 8620 steel specimens with different residual stress states was prepared by altering the carburising and subsequent tempering parameters. The specimens were characterised through scanning electron microscopy (SEM) investigations and hardness measurements, and the surface residual stresses were determined using both the MBN and X-ray diffraction (XRD) methods. The results show that a good correlation exists between surface residual stress and the parameters derived from the MBN signals.
... It is very difficult to span the full range by a few curves based on measurement results, especially when the measurement data do not span the full operation range. As a way out, there is a tendency to employ micro-magnetic models in combination with multiscale techniques [96]. This combination is still challenging but will become a realistic option within nearby future when better computational homogenization techniques and more computational resources become available. ...
This lecture note describes how to set up and what is behind a magnetodynamic field simulation for an accelerator magnet. The relevant formulation of Maxwell's equations is derived. The formulation is discretized in space by the finite-element method and in time by a standard time integration method. The steps for setting up the accelerator-magnet model are described. An exemplary simulation of the GSI SIS-100 magnet is given as illustration. Finally, some extensions to the standard FE method, dedicated to accelerator magnets, are discussed.
... Generally, low-frequency measurements are preferred in cases where the sub-surface properties are more important than the variations in surface. Details on the fundamentals of the MBN method can be found elsewhere [1,2]. In literature it has been reported that microstructural parameters of steels such as average grain size, phases (ferrite, pearlite, martensite, tempered martensite, spheroidized cementite) affect the MBN signals [3][4][5][6][7][8]. ...
... In particular, magneto-elastic properties (permeability, hysteresis losses, magnetostriction) drastically change between uniaxial [16] and multiaxial [17][18][19] field/stress configurations. Possible ways to model the magneto-elastic macroscopic behaviour, in a multiaxial context, are know as energetic [20,21] and multiscale approaches [22][23][24][25][26]. These approaches are based on the material energy balance and give robust predictive models. ...
Magnetoelastic couplings in ferromagnetic materials can be modelled using multiscale approaches. Various degrees of sophistication are accessible depending on the foreseen material and application. Here, we present a set of models, built on this approach, which can be used for devices magnetic field analysis. The representation of combined crystal anisotropy and texture effects is analysed through the introduction of a simplified fiber texture. A method is also proposed for the computation of magnetostriction hysteresis together with magnetization by association with a Jiles-Atherton model. All the models are detailed with their main physical and numerical characteristics, and the whole set of features that are needed for their use in device simulation tools. A test structure is finally simulated using the finite element method in order to illustrate the possibilities offered by these multiscale approaches.
... If measurements of the sample magnetization are to be made in-situ, then the effect of the applied stress on the magnetic properties must be taken into account since it has been shown that even modest loads can have a non-negligible impact on magnetization [88]. This can be clearly seen in Figure 4.22 where magnetization data obtained during unloading of a sample annealed at 760 • C is shown. ...
Cette thèse caractérise un acier Moyen Mn à 0.2C-5Mn-2.5Al qui montre un écrouissage très fort au cours de la déformation plastique dû à l’effet TRIP. Pendant TRIP, l’austénite résiduelle paramagnétique se transforme en martensite ferromagnétique sous déformation plastique, ce qui conduit à un fort écrouissage. Le taux de cet écrouissage dépend des paramètres de fabrication et surtout la température de recuit intercritique. Ces aciers ont aussi des fois le tendance de se déformer de façon hétérogène par des bandes de Lüders ou PLC.Dans cette thèse, une méthode de caractérisation de la cinétique de transformation de phase est développée sur la base des mesures de l’aimantation saturée de l’acier. La méthode magnétique est unique dans son implémentation in-situ sans aucun effet sur l’essai de traction. Une correction pour les effets de la contrainte appliquée sur l’aimantation est aussi introduite pour la première fois avec une base physique. Les résultats des mesures magnétiques ont été comparés contre des caractérisations des bandes de déformation pour montrer que la transformation de phase coïncide avec le passage des bandes de déformation. La sensibilité à la vitesse de déformation est analysée et une caractérisation de la présence et type de bande PLC est présentée en fonction de la cinétique de transformation de phase.
... In electrical machines, mechanical stress appears with static and periodic or cyclic behaviour. Particularly the consequences of static mechanical stress on the iron losses of electrical machines are in the focus of current research [4] as well as the modelling of the magnetomechanical effect [5]. ...
The purpose of this paper is to study the variation of the magnetic properties of non-oriented electrical steel sheets with the fatigue state during cyclic mechanical loading. The obtained results are central to the design of variable drives such as traction drives in electric vehicles in which varying mechanical loads, e.g. in the rotor core (centrifugal forces), alter the magnetic properties. Specimens of non-oriented electrical steel are subject to a cyclically varying mechanical tensile stress with different stress amplitudes and number of cycles. The specimens are characterised magnetically at different fatigue states for different magnetic flux densities and magnetising frequencies. The measurements show a variation in magnetic properties depending on the number of cycles and stress magnitude which can be explained by changes in the material structure due to a beginning mechanical fatigue process. The studied effect is critical for the estimation of the impact of mechanical material fatigue on the operational behaviour of electrical machines. Particularly in electrical machines with a higher speed where the rotor is stressed by high centrifugal forces, material fatigue occurs and can lead to deterioration of the rotor’s stack lamination.
The field of soft intelligent robots has rapidly developed, revealing extensive potential of these robots for real-world applications. By mimicking the dexterities of organisms, robots can handle delicate objects, access remote areas, and provide valuable feedback on their interactions with different environments. For autonomous manipulation of soft robots, which exhibit nonlinear behaviors and infinite degrees of freedom in transformation, innovative control systems integrating flexible and highly compliant sensors should be developed. Accordingly, sensor-actuator feedback systems are a key strategy for precisely controlling robotic motions. The introduction of material magnetism into soft robotics offers significant advantages in the remote manipulation of robotic operations, including touch or touchless detection of dynamically changing shapes and positions resulting from the actuations of robots. Notably, the anisotropies in the magnetic nanomaterials facilitate the perception and response with highly selective, directional, and efficient ways used for both sensors and actuators. Accordingly, this review provides a comprehensive understanding of the origins of magnetic anisotropy from both intrinsic and extrinsic factors and summarizes diverse magnetic materials with enhanced anisotropy. Recent developments in the design of flexible sensors and soft actuators based on the principle of magnetic anisotropy are outlined, specifically focusing on their applicabilities in soft robotic systems. Finally, this review addresses current challenges in the integration of sensors and actuators into soft robots and offers promising solutions that will enable the advancement of intelligent soft robots capable of efficiently executing complex tasks relevant to our daily lives.
This paper proposed an improved magnetostriction model for correlation of anisotropy in non-oriented (NO) silicon steel based on the free energy, which considers stress-induced and magnetocrystalline anisotropy. Firstly, the free energy model, which includes stress-induced anisotropy energy, the energy of magnetic field, and the anisotropic energy of magnetic crystals, is incorporated into the anhysteretic magnetization parameter M an . Then, to obtain the magnetic field and proposed model parameters related to stress-induced and magnetocrystalline anisotropy, the magnetostrictive strain loops at different magnetization directions of NO silicon steel are measured. Finally, based on the parameters obtained from experimental data of the proposed model, magnetostrictive strain loops under varying magnetization directions are simulated. This improved magnetostriction model can be applied to the calculation of the vector magnetostriction of the motor core.
An anisotropic vector play model was developed by the superposition of scalar play models. An analytical identification method was derived for a uniaxially anisotropic term. Computed
BH
loops accurately reconstructed the measured anisotropic hysteretic characteristics of non-oriented silicon steel sheet. Its application to magnetization analysis by a physical magnetization model using multi-domain particles enhanced the prediction accuracy of the stress-dependent loss property.
Purpose
The purpose of this paper is to improve the modeling accuracy of the magnetostrictive hysteretic characteristics by introducing hysteresis energy instead of pinning energy in the assembled domain structure model (ADSM).
Design/methodology/approach
First, the magnetostrictive characteristics and the domain movement process in an electrical steel sheet are measured and observed. The reasons for the influence of stress on magnetostriction are discussed on the mesoscopic level. Second, the ADSM model using the hysteresis energy is investigated to estimate the influence of external stress. Finally, the simulation results of the modified ADSM model are compared with the experimental data under the same calculation conditions.
Findings
The results show that the improved model not only explains the cause of hysteresis clearly from the perspective of the magnetic moment but also improves the modeling ability of magnetostrictive hysteretic.
Originality/value
The magnetostriction in electrical steel lags behind the external magnetic field, and it is significant for reducing core vibration to estimate the magnetostrictive hysteretic property accurately. This paper proposes an effective approach to model the hysteretic characterization of magnetostriction.
Stress concentration and microscopic defects inside a component can cause the failure of equipment and mechanical structures, and traditional non-destructive testing (NDT) methods are not able to completely solve this problem. The magnetomechanical effect organically combines the magnetic field and stress, making it an important approach for detecting stress concentration and microscopic defects in a component. The magnetomechanical model proposed by Jiles can explain the non-linear relationship between stress and magnetic induction, but it fails to explain the asymmetry in the change of magnetisation under the conditions of tensile and compressive stress. A general nonlinear magnetomechanical model proposed by Shi can more precisely explain the magnetomechanical effect, but with complex equations. Using a more precise equation for magnetostrictive strain and taking into account the effects of the demagnetising field and a linear stress-dependent term on the magnetomechanical effect, this paper proposes a concise and accurate model based on the merits of the two methods. This theoretical model can demonstrate the magnetomechanical effect more accurately than Jiles' model and is easier to solve and apply than Shi's model. This model offers the possibility of quantitative measurement of stress concentration by magnetic measurements.
In this paper, an estimation method for the ageing factor of permanent magnets is proposed. It is based on a multi-scale model, which allows estimating the magnetic properties of permanent magnets, combined with the magnetic viscosity theory. Usingof this method, the necessary measurements can be drastically reduced. The results obtained are compared with measurements, with a satisfactory agreement.
The domain rotation process during magnetostriction in Fe-Ga rolled sheet has been clarified. The magnetic domain pattern variation with magnetic field of rolling surface was observed by magneto-optic Kerr Microscopy in-situ. According to the sample information and magnetostriction, different magnetic domain structures were constructed for different magnetization stage. In the demagnetized state, the magnetic domain structure of Fe-Ga rolled sheet was closure domain with lancet domain as supplementary domain, and when the magnetic field is larger than 8.3 kA/m the magnetic domains is lancet domains, which well explains the domain rotation process at the stage of slow magnetostriction growth. Using an equivalent stress, the magnetostriction of Fe-Ga polycrystal was simulated by an energy-based domain rotation model. The result fits well with the measured magnetostriction in rapid growth stage and saturation stage. These two models work as a complement to each other and clearly show the domain rotation process during magnetostriction.
Medium Mn transformation-induced plasticity (TRIP) steels, a subgroup of third generation advanced high-strength steels (AHSS), often present a combination of both dynamic strain aging (DSA) and TRIP. It has been previously shown that TRIP coincides with the passage of strain bands due to DSA, but their interdependence has not been well-established. This study seeks to explore the interactions between the two phenomena as well as the commonly-observed negative strain rate sensitivity. Digital image correlation (DIC) and in-situ magnetic measurements of the retained austenite fraction were employed to demonstrate the variations in mechanical behavior with increasing strain rate. Strain rate jump tests provided measurements of the strain rate sensitivity and were combined with either DIC to characterize PLC bands or with magnetic measurements to measure variations in the martensite fraction during the jumps. Finally, the micromechanics defining the peculiar bursts of martensite transformation in response to strain rate jumps are discussed in terms of a competition between dislocation mobility and austenite stability.
This thesis deals with the prediction of the vibration of a multi-layer transformer core made of an assembly of electrical sheets. This magneto-mechanical coupled problem is solved by a stepping finite element method sequential approach: magnetic resolution is followed by mechanical resolution. A 3D Simplified Multi-Scale Model (SMSM) describing both magnetic and magnetostrictive anisotropies is used as the constitutive law of the material. The transformer core structure is modeled in 2D and a homogenization technique is implemented to take the anisotropic behavior of each layer into consideration and define an average behavior at each element of the finite element mesh. Experimental measurements are then carried out, allowing the validation of the material constitutive law, static structural behavior, dynamic structural behavior, and the noise estimation. Different materials geometries are considered for this workStructural optimizations are finally achieved by numerical simulation for lower vibration and noise emission of the transformer cores.
An Fe-0.2C-5Mn-2.5Al medium manganese steel is studied for three different intercritical annealing temperatures TIA to observe the effects of variations of retained austenite stability on the mechanical work hardening in uniaxial tension. Digital image correlation (DIC) showed that both Lüders bands and type A Portevin-le-Châtelier (PLC) bands occurred in samples with a lower TIA, but both disappeared when TIA was increased. In-situ measurements of sample magnetization with a correction for stress effects on the magnetic properties of the sample allowed for continuous measurement of the retained austenite volume fraction. This method provided a complete characterization of the kinetics of transformation-induced plasticity (TRIP) in the sample over the course of tensile testing. It is shown that the martensite transformation was purely strain-induced and coincided with the passage of both Lüders and PLC bands. An Olson-Cohen model was applied to magnetic data to attempt to explain the differences in TRIP kinetics with varying TIA.
The research presented in this thesis is motivated by the design of rotors for high speed rotating machines.
The increased power density of these devices requires a higher rotation speed, leading to higher levels of centrifugal forces and stress in the rotor.
A first point is to ensure good mechanical strength of the materials.
A second point is to take into account changes in the magnetic behavior (and ultimately torque) when they are subjected to a multiaxial stress state.
The present study aims at exploring the influence of biaxial stress states on the magnetic behavior of the materials of the rotor.
The challenge lies in the development of methods for the characterization of the magneto-mechanical dissipative uniaxial and multiaxial behavior of metal sheets developed by Aperam Alloy and used by Thales Avionics for their aeronautical applications (in FeCo-2V and non-oriented Fe-3%Si).
Non conventional experiments are performed on cross-shaped samples in order to apply biaxial stress representative of the loadings experienced by rotors of rotating machines. These experiments are performed on a multiaxial testing machine, Astrée. Stress level is estimated thanks to digital image correlation and X-ray diffraction
Both anhysteretic and dissipative magnetic responses to magneto-mechanical loadings have been recorded.
On the other hand, a multi-scale multiaxial model describing the behavior of a RVE from the energy balance at the microscopic scale is presented. The approach is based on a comparison of the free energy of each domain. A probabilistic comparison is made to determine the volume fraction of domains used as internal variables. Different strategies for modeling the static dissipation are discussed. Then we present the chosen magneto-elastic approach, improving the description of the effect of stress on ferromagnetic materials behavior.
Magnetic and mechanical behaviour are strongly coupled: an applied stress modifies the magnetic behaviour, and on the other hand, magnetic materials undergo a magnetisation-induced strain known as the magnetostriction strain. These coupling effects play a significant role on the overall performance of elec- tromagnetic devices such as magnetostrictive transducers or high-performance electric machines. In order to provide engineers with accurate design tools, magneto-elastic effects must be included into constitutive laws for magnetic materials. The origin of the magneto-elastic coupling lies in the competitive contributions of stress and magnetic field to the definition of magnetic domain configurations in magnetic materials. The magnetic domain scale is then suitable to describe magneto-elastic interactions, and this is the reason why multiscale approaches based on a micro-mechanical description of magnetic domain structures have been developed in the last decades. We propose in this paper an extension of a previous anhysteretic multiscale model in order to consider hysteresis effects. This new irreversible model is fully multiaxial and allows the description of typical hysteresis and butterfly loops and the calculation of magnetic losses as a function of external magneto-mechanical loadings. It is notably shown that the use of a configuration demagnetising effect related to the initial domain configuration enables to capture the non-monotony of the effect of stress on the magnetic susceptibility. This configuration demagnetising effect is also relevant to describe the effects of stress on hysteresis losses and coercive field.
The influence of applied tensile stress on the hysteresis curve and domain structure in conventional (1 1 0)[0 0 1] Fe–3%Si steel, cut parallel to the rolling direction, is studied on samples with different grain sizes. Quasistatic hysteresis loops under tensile stresses up to 70 MPa were measured. The magnetic domains and magnetization processes were observed by longitudinal Kerr microscopy at different levels of stress. It is shown that for stresses exceeding 5–10 MPa the bulk hysteresis loop can be described with good accuracy by the action of an effective field, which is the product of a function of stress and a function of magnetization. The function of stress is approximately linear with a slope of one. Except for the sample with the smallest grains, the function of magnetization is linear in the magnetization range ±1.2–1.5 T, i.e. it has a typical demagnetizing field shape. Domain observation reveals that the effective field is caused by the demagnetizing fields occurring at grain boundaries and at the sheet surface due to the removal of closure domains transverse to the rolling direction by the tensile stress. The closure structure reappears at higher fields. Another indirect indication of demagnetizing fields is the fact that the hysteresis losses drop continuously with stress and changes in the coercive force are small. The effective field of the sample with the smallest grains increases most nonlinearly with stress similar to the behaviour obtained for non-oriented material.
The prediction of the reversible evolution of macroscopic magnetostriction strain and magnetisation in ferromagnetic materials is still an open issue. Progress has been recently made in the description of the magneto-elastic behaviour of single crystals. Herein, we propose to extend this procedure to the prediction of the behaviour of textured soft magnetic polycrystals. This extension implies a magneto-mechanical homogenisation. The model proposed is discussed and the results are compared to experimental data obtained on industrial iron-silicon alloys. Mathematical subject classification: 74F15, 74Q05, 74Q15, 74M05, 78M40.
The effect of interfaces on magnetic activation volumes in single crystal Co2FeSi Heusler alloy thin films Appl. Phys. Lett. 101, 102410 (2012) Pulse voltage-induced dynamic magnetization switching in magnetic tunneling junctions with high resistance-area product Appl. The physical assumptions underlying the static and dynamic Jiles-Atherton (JA) hysteresis models are critically analyzed. It is shown that the energy-balance method used in deriving these models is actually closer to a balance of coenergies, thereby depriving the resulting JA phenomenology of physical meaning. The non-physical basis of its dynamic extension is demonstrated by a sharp contrast between hysteresis loops predicted by the model and those measured for grain-oriented steel under conditions of controlled sinusoidal flux density at frequencies of 50, 100, and 200 Hz. V C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4747915]
Hysteresis, power losses, and the Barkhausen effect are investigated in an Fe-based highly magnetostrictive amorphous material, as a function of applied stress. By means of the static and dynamic Preisach model, and of existing theories of the Barkhausen effect, the results are shown to be compatible with the existence of a characteristic structural length c , playing a role similar to that of grain size in crystalline materials. At low applied stresses, where the magnetization process is dominated by quenched-in stresses i , c is identified with the typical wavelength of i fluctuations. The theoretical analysis leads to the estimate c 70– 100 m and i 3.5 MPa.
The design of electromagnetic devices submitted to high mechanical stress is a growing issue and requires consequently appropriate modeling tools. We propose in this paper to implement a multiscale model for magneto-elastic behavior into a finite-element code. The 2-D magneto-elastic constitutive law is derived from a multiscale model based on a local energetic approach. The method is applied to study the effect of stress on the magnetic behavior of a switched reluctance motor. This work provides a finite-element tool for the modeling of the effect of multiaxial stress on electrotechnical devices.
The influence of tensile and compressive stresses on the magnetic losses in non-oriented Fe–(3 wt%)Si laminations has been investigated. It is shown that, while moderately affected by tensile stresses, the energy losses strongly increase upon compression. This is assumed to derive from a corresponding evolution of the domain distribution among easy axes, leading to an increase of both coercive field and excess losses. A rationale for the correlated dependence of the DC and AC losses on stress can be found in the framework of the statistical theory of losses.
Ferromagnetic materials display a complex microstructure of domains, walls, Bloch lines and singular points on scales ranging from 100 m down to a few nm. Understanding the formation and overall eects of these structures is crucial for key technological applications. At the same time the rich source of experimental data and the simple mathematical formulation makes the analysis of magnetic microstructure an excellent model problem to develop new mathematical tools for the understanding of multiscale problems, which are ubiquitous in science. In this paper we describe some basic mathematical problems and report on recent analytical progress in three areas: rigorous scaling laws, branching and dimensionally reduced theories for thin lms. 1 Supported by the TMR network FMRX-CT98-0229 (DG 12- BDCN) 2 Supported by NSF 3 Supported by an A. P. Sloan Research Fellowship and NSF grant DMS-9803389 2 DeSimone, Kohn, Muller and Otto Fig. 1. Top: Large domains on the surface of an iron w...
The prediction of the reversible evolution of macroscopic magnetostriction strain and magnetisation in ferromagnetic materials is still an open issue. Progress has been recently made in the description of the magneto-elastic behaviour of single crystals. Herein, we propose to extend this procedure to the prediction of the behaviour of textured soft magnetic polycrystals. This extension implies a magneto-mechanical homogenisation. The model proposed is discussed and the results are compared to experimental data obtained on industrial iron-silicon alloys.
A plastically deformed material, due to its increased content of physical defects, is in a thermodynamically metastable state. On increasing the temperature, the material can lower its free energy by the removal and rearrangement of the lattice defects.
The definition of the eigenstrains is given first. Then the associated general solutions for elastic fields for given eigenstrains are expressed by Fourier integrals and Green’s functions. Some details of calculations for Green’s functions are described for static and dynamic cases.
This paper presents a vector hysteresis model based on micromagnetic theory. In this model, a magnetization state of a magnetic material is described by a collection of single-domain particles, and magnetic reversal processes due to domain-wall motions are treated approximately as a magnetization flip. The present model is applied to calculation of hysteresis properties of grain-oriented silicon steel. The simulation results show that the anisotropic hysteresis properties and iron loss can be reproduced accurately by the present model.
Aiming to better understand and model the different loss mechanisms occurring within electric machines during operation, we present a method to consider the degradation of steel during manufacturing due to punching in finite-element modeling of electric machines. The approach introduces a certain number of boundary layers along the punched edges, with the relative permeability decreasing toward the edge. The method, its implementation, and two example applications are presented and supported with experimental results.
Covering basic physical concepts, experimental methods, and applications, this book is an indispensable text on the fascinating science of magnetism, and an invaluable source of practical reference data. Accessible, authoritative, and assuming undergraduate familiarity with quantum mechanics, electromagnetism and vectors, this textbook can be used on graduate courses. Emphasis is placed on practical calculations and numerical magnitudes - from nanoscale to astronomical scale – with a focus on modern manifestations, including spin electronic devices. Each self-contained chapter begins with a summary, and ends with exercises and further reading. The book is thoroughly illustrated with over 600 figures to help convey concepts and clearly explain ideas. Easily digestible tables and data sheets provide a wealth of useful information on magnetic materials, and 38 principal magnetic materials, and many more related compounds, are treated in detail.
This paper presents an incremental hysteretic magneto-elastic constitutive theory of pseudo-cubic ferro-magnetostrictive alloys, which may be used to predict the magneto-elastic response of these materials under quite general applied magnetic field and stress processes. These processes may include fully saturated major loop, unsaturated minor loop or more general types of magnetic field-stress processes. Comparisons between model results and a set of high quality measurements show that the model is capable of qualitative agreement with the experimental behavior. However, the experimental data shows a strongly decreasing magnetization and magnetostriction hysteresis as the minor loop cyclic applied field amplitude becomes smaller. It appears that irreversible domain wall motion continuously activates as the applied magnetic field is reduced in the range from 79 to 39kA/m. Minor loop processes which do not have a sufficiently low minimum applied magnetic field value do not activate irreversible domain wall translation events and any measured magnetization changes must be due to one or more reversible mechanisms such as domain wall bowing and reversible domain rotation. The present model only includes an irreversible domain wall translation mechanism, therefore the model hysteresis widths remain constant with decreasing minor loop cyclic applied field amplitude.
This paper reports on a method which has been developed to track the location of local energy minima in the orientation of magnetic domains in Tb-Dy-Fe under the action of changing magnetic field and applied stress. The model assumes an array on non-interacting domains. Each domain is initially oriented along one of the axes and aligns with the local minimum energy at each magnetic field strength. The energy surface was calculated from the sum of the magnetocrystalline anisotropy, field and magnetostrictive energies. The evolution of the energy minima are followed by determining the maximum gradient in the energy surface using the appropriate gradient operator.
Magnetic properties of permalloy.-Effect of tension on magnetization and hysteresis. Wires of 5 nickel-iron alloys containing 45, 65, 78.5, 81 and 84 percent Ni, 60 cm long and 0.1 cm in diameter, were studied by a ballistic method, for tensions up to 10,000 lb per in.2 and fields up to saturation (10 to 20 gauss). Permalloy with 81 percent Ni is nearly indifferent to tension in its magnetic behavior; permalloy with less nickel is more easily magnetized and has less hysteresis when under tension, while 84 percent permalloy is more difficulty magnetized and has greater hysteresis when under tension. The saturation values are independent of the tension. In 78.5 percent permalloy, under a tension of 3560 lb per in.2, saturation is reached at only 2 gauss (and is practically complete at 0.2 gauss) and the hysteresis loss is only 80 ergs per cm3 per cycle, so small that it may be regarded as due to slight inhomogeneity rather than to any essential features of the magnetization process. Relation to crystal orientation. X-ray examination proves that this abnormally low loss is not due to any peculiar orientation of the crystal axes as the crystals are found to be oriented at random. Magnetostriction behavior can be deduced from these results. Above 81 percent Ni, permalloy contracts like Ni while below 81 percent Ni, permalloy expands like Fe. Demagnetising factor for a wire with a length 600 times the diameter, was determined experimentally and found to vary from a maximum of 1.6×10-4 to a low value, the changes being like these previously described by Benedicks for iron.
The mathematical description of physical phenomena requires the use of scalars and tensors of various order. Since many of the second-order and fourth-order tensors used in continuum mechanics possess certain symmetries, a compressed vector or matrix representation, respectively, is frequently used in computational applications such as the FEM and BEM. Use of different storage schemes for different tensors lead to an hypothetical nonuniqueness of such matrix representations. The present paper offers a clarification by investigation of the structure of the underlying six-dimensional vector space. It identifies various types of matrix representations as covariant, contravariant or mixed-variant coordinates in that vector space and thus proves consistency of the matrix representation with classical tensor analysis in R3. Furthermore, it is shown that an ortho-normal basis for the underlying tensor representation in R3 does not automatically lead to a normalized space for the compressed matrix representation in R6. Thus, distinction of covariant and contravariant coordinates is necessary even in that case. Theoretical findings are worked out in detail for symmetric second-order and fourth-order tensors in R3. Example applications on commonly used fourth-order tensors as well as a comparison of possible computational implementations close the paper.
The present work reports the magnetic induction, fiber and matrix internal stresses, and magnetostriction of model continuous, [112] oriented, Tb0.3Dy0.7Fe1.9 fiber actuated epoxy matrix composites as functions of fiber actuator volume fraction and applied magnetic field. The analysis indicates that the thermal mismatch strain resulting from cooling the composite from the matrix curing temperature is effective in concentrating magnetization probability about the transverse [11] and [1] directions, which increases the apparent saturation magnetostriction available to a longitudinally applied magnetic field process. The analysis further indicates that the increase in fiber longitudinal compressive stress resulting from the accommodation of an increment of positive fiber magnetostriction increases the fiber magnetoelastic energy in the applied field direction. Therefore, the increased matrix stiffness resulting from a reduction in fiber actuator volume fraction results in a reduced permeability, an increase in the magnetic field strength required for a given level of magnetostriction, and an increase in the magnetic field strength required for saturation.
It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Magnetic non destructive methods are frequently used in the industries of steel since magnetic behavior demonstrates a good sensitivity to the microstructural and/or mechanical changes. Magnetic behavior is especially sensitive to plastic straining that occurs for example with the manufacturing of materials (cutting, punching). Evaluating the state of a material from a measurement requires a modeling of the behaviors of the material (local constitutive laws) involved that must on the other hand demonstrate low computation time. Such magneto-mechanical modeling is proposed, based on the so-called multidomain model.
The study of the energy loss in electrical steels is based on the separation of total losses into hysteresis, classical and excess losses according to the statistical theory. In this article, the stress dependence of the hysteresis loss Wh and of the excess loss parameter V0, both related to the microstructure, is investigated for a nonoriented 3% Si–Fe grade under compressive and tensile stress and at plastic deformation. Parameters Wh and V0 for hysteresis and excess losses modeling increase under compression and high plastic tension and decrease under small elastic tension.
Multiphysics couplings are at the origin of many applications. In order to design devices with optimal coupling effects, advanced modeling tools are necessary. In this paper a generic formalism for the homogenization of coupled magnetoelectrothermoelastic behavior is proposed. It is based on the decomposition in several contributions of the magnetic, electric, thermal, and mechanical fields. This decomposition makes it possible to use the classical homogenization tools developed in the framework of uncoupled behavior. The method is illustrated on the calculation of the effective properties of a magnetoelectric composite made of piezomagnetic and piezoelectric phases.
A hypothesis is presented to explain the mechanism by which externally applied stresses can affect the magnetic properties of ferromagnetic materials. Experiments have revealed coincident points in the second and fourth quadrants on stressed hysteresis loops of mild steel. The results are presented along with an explanation of this effect. An atomic level theory of the origins of the magnetomechanical effect is introduced whereby spin–spin and spin–orbit coupling interact with magnetic moments to alter the magnetocrystalline anisotropy and exchange energies.
The longitudinal stress effect on magnetic properties of Si-Fe sheet materials is considered. Polish sheet materials (grain oriented ET-5 grade and non-oriented EP-20 grade) were tested. Core losses and permeability were determined using a single sheet tester with a device for exerting tensile and compressive stress. Considerable changes of specific core loss, permeability and the shape of hysteresis loop of specimens subjected to stress were observed.
The model is based on considerations of energy balance and statistical domain behavior. The parameters are related to macroscopic hysteresis features such as coercivity, initial susceptibility, saturation, and remanence and identification strategies are presented for static and dynamic magnetization processes. Furthermore, the model parameters are related to spontaneous magnetization, magnetocrystalline anisotropy, magnetostriction, and microstructure geometry which assist in the interpretation of the hysteresis dependence on stress, temperature, and direction of magnetization. Examples and predictions are the magnetization reversal in low dimensional structures, stress demagnetization, temporary decay of magnetization, Barkhausen noise, and the behavior of materials with multiple phases. Finally, the fictitious statistical domains (or unit magnetization reversals) are related to the magnetic spin moments, which enables a quantum-mechanical interpretation of the model.
The theory presented in this article successfully reproduces and explains the experimental magnetostriction and magnetization hysteresis behavior of Tb 0.3 Dy 0.7 Fe 1.9. It is well known that a very large number of individual domain wall translation events combine to produce each measurable domain transformation in a macroscopic sized sample. Each individual domain wall may be expected to suffer some level of domain wall translation inhibition due to the presence of defects in the material, however, the severity of the inhibition will spatially vary. We therefore assume that the presence of defects in the material increases the directional magnetization potential of subsequent domain states within a process, and distributes nontrivial probabilities of occupation of <111> type domain states in a parameter selected, inverse exponential form familiar from the study of statistical thermodynamics. The increased magnetization potential of subsequent high magnetostriction and high magnetization states retards their occupation until higher intensity applied magnetic fields are produced, thus shifting the increasing applied magnetic field curve in a positive field direction and shifting the decreasing applied magnetic field curve in a negative field direction in a form consistent with experiment. © 2002 American Institute of Physics.
A constitutive model is developed for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field. It is envisaged that the polycrystal consists of a set of bonded crystals and that each crystal comprises a set of distinct crystal variants. Within each crystal the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation and to a change in the average linear electromechanical properties. It is further assumed that switching is resisted by the dissipative motion of domain walls. The constitutive model for the progressive switching of each crystal draws upon elastic–plastic crystal plasticity theory, and a prescription is given for the tangent moduli of the crystal, for any assumed set of potentially active transformation systems. A self-consistent analysis is used to estimate the macroscopic response of tetragonal crystals (representative of lead titanate) under a variety of loading paths. Also, the evolution of the switching surface in stress-electric field space is calculated. Many of the qualitative features of ferroelectric switching, such as butterfly hysteresis loops, are predicted by the analysis.
Two stress-magnetization effects, which appear in non-oriented 3% silicon steel sheets, have been investigated, paying attention to the demagnetizing and magnetizing conditions. The two stress effects are proportional, partly due to the tension. The negative sign of the stress effects can be explained in terms of the demagnetizing field and domain structures.
The internal inhomogeneities of stress and strain in an arbitrarily deformed aggregate of elasto-plastic crystals are evaluated theoretically. A tensor constitutive law of a general kind is assumed for the individual crystals. The implied mechanical properties of the aggregate as a whole are estimated by means of a self-consistent model akin to one used by Hershey (1954), Kröner (1958, 1961) and Budiansky and Wu (1962), but differing in significant respects.
Magnetic and mechanical behaviors are strongly coupled. But few models are able to describe magneto-mechanical coupling effects. We propose a multiscale approach for the modeling of the reversible magneto-elastic behavior of ferromagnetic materials. This approach stands between macroscopic phenomenological modeling and micromagnetic simulations. We detail first the definition of the magneto-elastic behavior of a single crystal, deduced from energetic considerations made at the scale of magnetic domains and hypotheses concerning the domains microstructure. This model is then applied to the description of the behavior of polycrystalline media, through a multiscale approach. The heterogeneity of stress and magnetic field is taken into account through a self-consistent localization–homogenization scheme, including crystallographic texture data. Results are discussed and compared to experimental data from the literature.
This paper deals with experimental measurements of the mechanical, magnetic and magnetostrictive behaviours of a non-oriented 3%SiFe alloy. The results show that the low crystallographic texture of the material brings important anisotropic effects and that the coupled magnetomechanical properties are much more sensitive than uncoupled ones.
Magnetic energy losses and hysteresis loops have been determined in FeSi non-oriented laminations as a function of the applied compressive and tensile stress, made to range between − 50 and + 50 MPa. The loss separation analysis has been carried out in association with hysteresis loop calculation by means of the Dynamic Preisach Model. The strong modifications to the hysteresis loop and area introduced in a specific way by compressive stresses can be correctly accounted for by modelling.
A simple variational theory for the macroscopic behavior of materials with high anisotropy is derived rigorously from micromagnetics. The derivation leads to a constrained theory in which the state of strain and magnetization lies very near the ‘energy wells’ on most of the body. When specialized to ellipsoidal specimens and constant applied field and stress, the theory becomes a finite dimensional quadratic programming problem. Streamlined methods for solving this problem are given. The theory is illustrated by a prediction of the magnetoelastic behavior of the giant magnetostrictive material Tb0.3Dy0.7Fe2. The theory embodies precisely the assumptions that have been postulated for ideal ferromagnetic shape memory, in which the magnetization stays rigidly attached to the easy axes of a martensitic material in the martensitic phase. More generally, the framework can be viewed as a prototype for the derivation of constrained theories for materials that change phase, and whose free-energy density grows steeply away from its minima.
It is well known that magnetic properties of Goss-oriented silicon-iron are dependent upon external mechanical stress. This paper describes some of the recent work carried out in the UK on the effects of high compressive stress, combined longitudinal and transverse stresses, and also the effects of elevated temperature on the power loss and magnetostriction of silicon-iron. Results show that,when compressive stress greater than about 15 MPa is applied along the rolling direction the power loss generally is double the zero stress level, the permeability drops linearly, and the B-H loop becomes constricted. The loss does not rise so rapidly in higher permeability material, but the magnetostriction reaches a higher final level. These effects are explained using a simple domain model. Measurements of magnetostriction under combined longitudinal and transverse stress before and after coating removal are shown. At elevated temperature,the effect of stress is found to be more pronounced, and the benefit of the coating on high permeability material is reduced. The extent to which stress may degrade the performance of laminated cores is discussed, and it is hinted that perhaps the effects of stress might only partly account for the building loss in high permeability cores.
It is demonstrated that hysteresis in the magnetostriction k
is coupled to hysteresis in the magnetization M because
of the dependence of the magnetostriction on the magnetization. At the
same time, when stress is present, the magnetization is in turn coupled
to the behavior of the part of the magnetostriction associated with
domain moment rotation. An expression for the magnetostriction is
formulated, and numerical modeling results for magnetostriction
hysteresis are compared to experimental results. Although some features
of the magnetostriction in iron and steel still need additional
explanation, the main features of the magnetostriction are accounted
for. These include liftoff (failure of the magnetostriction to return to
its value in the demagnetized state as the hysteresis loop is cycled)
and a magnetostriction increase after flux density B reaches
its maximum and starts to decrease. A macromagnetic, multidomain
formulation that yields zero magnetostriction in the demagnetized
specimen is used
It is suggested that in many ferromagnetic materials there may occur particles distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector. As the field changes continuously, the resolved magnetization may change discontinuously at critical values of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle and on the orientation of easy axes with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magnetocrystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution, along with a less detailed treatment for the general ellipsoidal form.
Change of magnetization by tension and by electric current
- Villari
Effect of stress on switched reluctance motors
- Bernard
Mechanics and Electrodynamics of Magneto- and Electro-Elastic Materials, CISM International Centre for Mechanical Sciences
- R Ogden
- D Steigmann
Les lois de l'aimantation et de la subdivision en domaines élémentaires d'un monocristal de fer (in French)
- Néel
Influence of material processing steps annealing and cutting on magnetic materials' properties relevant for electrical machine design
- S Steentjes
- K Hameyer
- M Bednarz
- S Vogt
- W Volk
- J Dierdorf
- G Hirt