A magnetoelectroelastic medium with an elliptical cavity under combined mechanical–electric–magnetic loading

The solution for an elliptical cavity in an infinite two-dimensional magnetoelectroelastic medium subject to remotely uniformly applied combined mechanical–electric–magnetic loadings is obtained by using the Stroh formalism and the exact boundary conditions along the surface of the cavity. By letting the minor-axis of the cavity to zero the solution for a crack is deduced. A self-consistent method is proposed to calculate the real crack opening under the combined mechanical–electric–magnetic loadings. The method requires that the crack opening is the minor-axis of the elliptical opening profile. Beside the real crack solution, four different extreme models, i.e., the impermeable crack, permeable crack, electrically impermeable and magnetically permeable crack and electrically permeable and magnetically impermeable crack, are discussed. An expression of the strain energy density factor is derived. Numerical results of the strain energy density at the crack tip are given for a BaTiO₃–CoFe₂O₄ composite with the piezoelectric BaTiO₃ material being the inclusion and the magnetostrictive CoFe₂O₄ material being the matrix. The effects of the proportion of the two phases, permeability of the crack to electric and magnetic fields, the electric and magnetic loadings on the strain energy density factor are discussed.     

Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation

The three-dimensional field equations can in general be regarded as the sum of in-plane and out-of-plane deformation. The method for the general solution is the same for both although the boundary conditions could make a difference. If a particular solution in exact form may be found for the out-of-plane case, the same may not hold for the in-plane case. Hence, there may be a good reason for discussing the out-of-plane crack problem in certain situations that should be emphasized. Otherwise, the reason may lie in the exploration of possible application to the in-plane problem, a direct solution of which would have required a considerable effort. The contribution of this work rests on the new findings for the case of poling parallel to the crack in a magnetoelectroelastic composite made of BaTiO₃–CoFe₂O₄. The inclusions are BaTiO₃ and the matrix is CoFe₂O₄. Several new features of the solution were not expected before hand.Unlike in-plane deformation with poling normal to the crack plane, maximum crack growth enhancement is found to occur in the BaTiO₃–CoFe₂O₄ composite for a volume fraction of about 50%. Crack retardation increases as the volume fraction of the inclusions either increase or decrease. The occurrence of this same phenomenon in Mode I and II remain to be investigated. Poling direction of magnetic and electric field for line defects can have a significant effect on crack growth for magnetoelectroelastic materials. The foregoing conclusions are based on predictions made from the strain energy density criterion.     

Magnetic and electric poling effects associated with crack growth in BaTiO3–CoFe2O4 composite

Magnetoelectroelastic composite possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. The poling directions introduced magnetically and electrically can be different in addition to those for the applied magnetic and electric field. Their choices can influence the character of crack growth which could be enhanced or retarded. The details of how the directions of poling and applied field would affect crack initiation and growth are discussed in relation to the volume fraction of inclusions for a BaTiO₃–CoFe₂O₄ two phase composite. The multi-functional aspects of magnetoelectroelastic materials are involved since they entail multi-scaling features. Failure criteria that applies to isotropic elastic materials may not hold for composites exhibiting piezomagnetic and piezoelectric properties. For instance, a negative energy release rate has been obtained for cracks in piezoelectric materials.In view of what has been said with reference to the energy release rate approach, it is desirable to use the strain energy density function as a failure criterion, even if it is only for its positive definiteness character. Physically speaking, it is attractive to have a function that could rank the proportion of energy related to volume and shape change. They determine the proportion of the hard and soft phase of the composite and hence the volume fraction of the constituent. Strength and toughness parameters used for ranking isotropic and homogeneous materials will not apply for anisotropic and/or nonhomogeneous materials if these microstructure effects could not be suppressed to a lower scale and represented as an average at the macroscopic scale. Too much emphases cannot be placed on the need to clarify the multi-scaling aspects of piezoelectric and piezomagnetic materials. Their behavior as affected by the presence of crack-like defects should be understood prior to deciding whether the material characterization approach would be suitable. That is whether simplicity could justify at the expense of conceptual rigor. Much of this would depend on scaling the time and size related to loading and material structure interaction. The magnetoelectroelastic crack model selected in the work to follow perhaps will provide an insight into the complexicity of the state of affairs for treating the finer details of material behavior with rigor.The proposed test model shows that crack growth in the magnetoelectroelastic materials can be suppressed by increasing the magnitude of the piezomagnetic constants in relation to those for piezoelectricity. A more rational means of evaluating the resistance of materials against fracture is thus proposed, particularly when anisotropy and inhomogeneity might be present.     

Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials

The ferrite and ferroelectric phase of magnetoelectroelastic (MEE) material can be selected and processed to control the macroscopic behavior of electron devices using continuum mechanics models. Once macro- and/or microdefects appear, the highly intensified magnetic and electric energy localization could alter the response significantly to change the design performance. Alignment of poling directions of piezomagnetic and piezoelectric materials can add to the complexity of the MEE material behavior to which this study will be concerned with.Appropriate balance of distortional and dilatational energy density is no longer obvious when a material possesses anisotropy and/or nonhomogeneity. An excess of the former could result in unwanted geometric change while the latter may lead to unexpected fracture initiation. Such information can be evaluated quantitatively from the stationary values of the energy density function dW/dV. The maxima and minima have been known to coincide, respectively, with possible locations of permanent shape change and crack initiation regardless of material and loading type. The direction of poling with respect to a line crack and the material microstructure described by the constitutive coefficients will be specified explicitly with reference to the applied magnetic field, electric field and mechanical stress, both normal and shear. The crack initiation load and direction could be predicted by finding the direction for which the volume change is the largest. In contrast to intuition, change in poling directions can influence the cracking behavior of MEE dramatically. This will be demonstrated by the numerical results for the BaTiO₃–CoFe₂O₄ composite having different volume fractions where BaTiO₃ and CoFe₂O₄ are, respectively, the inclusion and matrix.To be emphasized is that mode I and II crack behavior will not have the same definition as that in classical fracture mechanics where load and crack extension symmetry would coincide. A striking result is found for a mode II crack. By keeping the magnetic poling fixed, a reversal of electric poling changed the crack initiation angle from θ₀=+80° to θ₀=−80° using the line extending ahead of the crack as the reference. This effect is also sensitive to the distance from the crack tip. Displayed and discussed are results for r/a=10⁻⁴ and 10⁻¹. Because the theory of magnetoelectroelasticity used in the analysis is based on the assumption of equilibrium where the influence of material microstructure is homogenized, the local space and temporal effects must be interpreted accordingly. Among them are the maximum values of (dW/dV)_max and (dW/dV)_min which refer to as possible sites of yielding and fracture. Since time and size are homogenized, it is implicitly understood that there is more time for yielding as compared to fracture being a more sudden process. This renders a higher dW/dV in contrast to that for fracture. Put it differently, a lower dW/dV with a shorter time for release could be more detrimental.     

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x ₂ co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x ₁, x ₃)-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet–Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO₃–CoFe₂O₄ with different volume fractions of BaTiO₃ has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.     

Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

In this paper, the elastic wave propagation in phononic crystals with piezoelectric and piezomagnetic inclusions is investigated taking the magneto-electro-elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band structures of three kinds of piezoelectric/piezomagnetic phononic crystals—CoFe₂O₄/quartz, BaTiO₃/CoFe₂O₄ and BaTiO₃–CoFe₂O₄/polymer periodic composites are calculated using the plane-wave expansion method. The piezoelectric and piezomagnetic effects on the band structures are analyzed. The numerical results show that in CoFe₂O₄/quartz structures, only one narrow band gap exists along the Γ–X direction for the coupling of xy-mode and z-mode for the filling fraction f being 0.4; while in BaTiO₃/CoFe₂O₄ composites, only one narrow band gap exists along the Γ–X direction forxy-mode and no band gap exists for z-mode as the filling friction f is 0.5. Moreover, for the new type of magneto-electro-elastic phononic crystal—BaTiO₃–CoFe₂O₄/polymer periodic composite, the band gap characteristics are more superior in the whole considered frequency regions due to the big contrast of the material properties in the two constituents and the effects of the piezoelectricity and piezomagneticity on the band gap structures are remarkable.     

Dynamic analysis of a penny-shaped dielectric crack in a magnetoelectroelastic solid under impacts

The transient response of a magneto-electro-elastic material with a penny-shaped dielectric crack subjected to in-plane magneto-electro-mechanical impacts is made. To simulate an opening crack with a dielectric interior, the crack-face electromagnetic boundary conditions are supposed to depend on the crack opening displacement and the jumps of electric and magnetic potentials across the crack. Four ideal crack-face electromagnetic boundary conditions involving a combination of electrically permeable or impermeable and magnetically permeable or impermeable assumptions can be reduced. The Laplace and Hankel transform techniques are further utilized to solve the mixed initial-boundary-value problem. Three coupling Fredholm integral equations are obtained and solved by the composite Simpson's rule. Dynamic field intensity factors of stress, electric displacement, magnetic induction, crack opening displacement (COD), electric potential and magnetic potential are given in the Laplace transform domain. By means of a numerical inversion of the Laplace transform, numerical results are calculated to show the variations of the physical parameters of concern versus the normalized time in graphics. The effects of applied electric and magnetic loads on the dynamic intensity factors of stress and COD, and the dynamic energy release rate for a BaTiO₃-CoFe₂O₄ composite with a penny-shaped vacuum crack are discussed in detail.     

High-frequency dielectric properties of BSTO ceramic prepared with hydrothermal synthesized SrTiO3 and BaTiO3 powders

BSTO dielectric ceramic was prepared from SrTi03 and BaTi03 powders synthesized by hydrothermal method, as well as from Bao.sSro.4TiO3 powder synthesized by conventional solid-state reaction. The former can be sintered at a relatively low temperature of 1120 ℃. Characterization by SEM showed that the grain shapes of both ceramics are cubical, though the grain size of the former is much smaller. Dielectric constants measured at 20℃ were shown to vary with frequency in the range from I kHz to 2 MHz and dc bias field, and further that the dielectric loss of the former to be less than 2 × 10^- 3 in the frequency range of 20 kHz to 1 MHz, much smaller than that of the latter sample. For the former, temperature dependence of dielectric constant is much flatter and there exists an extended phase transition diffusion covering a wide temperature range of Curie temperature To. The smaller grain size of the former depresses the dc bias electrical field dependence of dielectric constant. The tunability is 7% under a bias field of 0.6 kV/mm dc.     

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.     

Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials

A permeable interface crack between elastic dielectric material and piezoelectric material is studied based on the extended Stroh’s formalism. Motivated by strong engineering demands to design new composite materials, the authors perform numerical analysis of interface crack tip singularities and the crack tip energy release rates for 35 types of dissimilar bimaterials, respectively, which are constructed by five kinds of elastic dielectric materials: Epoxy, Polymer, Al₂O₃, SiC, and Si₃N₄ and seven kinds of practical piezoelectric ceramics: PZT-4, BaTiO₃, PZT-5H, PZT-6B, PZT-7A, P-7, and PZT-PIC 151, respectively. The elastic dielectric material with much smaller permittivity than commercial piezoelectric ceramics is treated as a special transversely isotropic piezoelectric material with extremely small piezoelectricity. The present investigation shows that the structure of the singular field near the permeable interface crack tip consists of three singularities: and , which is quite different from that in the impermeable interface crack. It can be concluded that different far field loading cases have significant influence on the near-tip fracture behaviors of the permeable interface crack. Based on the present theoretical treatment and numerical analysis, the electric field induced crack growth is well explained, which provides a better understanding of the failure mechanism induced from interface crack growth in elastic dielectric/piezoelectric bimaterials. The project supported by the National Natural Science Foundation of China (10572110), Doctor Foundation of the Chinese Education Ministry and Doctorate Foundation of Xi’an Jiaotong University. The English text was polished by Yunming Chen.     

Line-integral representations for extended displacements,stresses, and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials （e.g., BaTiO3）, piezomagnetic materials （e.g., CoFe2O4）, and multiferroic com-posite materials （e.g., BaTiO3-CoFe2O4 composites） also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional （3D） dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic （MEE） bimaterials （i.e., joined half-spaces）. The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.     

Reflection and transmission of plane waves at an imperfectly bonded interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and transmission of plane waves at an imperfect interface between piezoelectric (PE) and piezomagnetic (PM) media. The materials are assumed to be transversely isotropic. The linear spring model is used to describe the imperfection of bonding behavior at the interface. According to this model, the properties of the interface can be characterized by the normal and tangential interfacial stiffnesses. Numerial examples are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, a perfect, slip, normal weak bonding and unbonding interfaces for the coupled quasi-pressure (QP) wave incidence from BaTiO₃ medium are compared in detail. Numerical results of the reflection and transmission coefficients (RTCs) varying with incident angle for different interfacial stiffnesses are presented. Results show that the transmitted QP/reflected QSV waves are the strongest in the perfect/unbonded cases, respectively. The scattered waves in the slip and normal weak bonding cases are between those of the perfect and unbonded cases generally. Critial angles have noticeable effect on the RTCs and energy coefficients for the coupled scattered waves of the perfect and slip cases but have a little/no effect on those of the normal weak bonding/unbonded cases. It is found that the sum of the energy carried by the transmitted/reflected QP and QSV waves is less than unit for the imperfect bonding between BaTiO₃/CoFe₂O₄ solids. These results may provide some useful reference datum for the imperfection measurment at the PE and PM interface.     

Heat transfer enhancement using Al2O3/water nanofluid in a two-phase closed thermosyphon

A two-phase closed thermosyphon (TPCT) is a device for heat transmission. It consists of an evacuated-close tube filled with a certain amount of working fluid. Fluids with nanoparticles (particles smaller than 100 nm) suspended in them are called nanofluids that they have a great potential in heat transfer enhancement. In the present study, we combined two mentioned techniques for heat transfer enhancement. Nanofluids of aqueous Al₂O₃ nanoparticles suspensions were prepared in various volume concentration of 1–3% and used in a TPCT as working media. Experimental results showed that for different input powers, the efficiency of the TPCT increases up to 14.7% when Al₂O₃/water nanofluid was used instead of pure water. Temperature distributions on TPCT confirm these results too.     

Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory

This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic (MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate (SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO₃/CoFe₂O₄. The refined zigzag theory (RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton’s principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.     

Ti_3SiC_2的加入对Ag-MoS_2-graphite复合材料力学及摩擦磨损性能的影响

采用热压烧结技术制备了Ag-Mo S2-graphite和Ag-Mo S2-graphite-Ti3Si C2两种银基自润滑复合材料,考察了两种材料的致密度、硬度、弯曲强度及其在不同环境(大气和低真空)中的摩擦磨损性能.结果表明:低润湿性使得Ti3Si C2与基体界面处的孔隙增多,降低了致密度和弯曲强度,但对硬度影响不明显;摩擦过程中Ti3Si C2颗粒易于从基体材料表面剥落,阻碍了润滑膜的形成,造成Ag-Mo S2-graphite-Ti3Si C2复合材料的摩擦系数高于Ag-Mo S2-graphite复合材料;但Ti3Si C2的添加能够明显提高复合材料在大气中的耐磨性能,这主要与摩擦过程中的材料转移和摩擦化学反应有关.     

Fe_3Al/WS_2复合材料的真空摩擦学性能研究

采用热压烧结的方法制备了添加WS2质量百分数为10%、20%和30%的Fe-28Al-5Cr基复合材料,通过XRD和SEM等手段分析了样品的相组成和组织结构.利用自制的真空摩擦试验机测试了样品在4×10-4Pa真空下的摩擦学性能.研究结果显示:通过与WS2的复合能够显著降低Fe3Al基金属间化合物在真空条件下的摩擦系数,但三种不同WS2含量复合材料的摩擦系数差别不大.随着WS2含量增加,复合材料的磨损率逐渐降低,特别是30%复合材料的磨损率较纯Fe-28Al-5Cr的磨损率低约1个数量级.滑动速度和载荷对三种材料的摩擦系数和磨损率均有一定的影响.纯Fe3Al的磨损表面较为粗糙,出现严重的剥落坑和剥落痕迹,磨损机理为严重的疲劳磨损.添加质量百分数为10%WS2的复合材料的磨损机理为磨粒磨损和疲劳磨损;添加WS2质量百分数为20%和30%的复合材料,其磨损表面相对较为光滑平整,磨损机理为轻微剥落.因此,在复合材料制备中添加WS2能够显著提高Fe3Al金属间化合物的真空摩擦学性能.     

含Fe2O3摩擦层的促进形成对H13和45钢磨损性能的影响

Fe_2O_3是钢材高温或高速干滑动表面摩擦氧化物层的重要构成.本文作者通过在H13钢、45钢/GCr15钢的滑动界面添加Fe_2O_3纳米颗粒,试图促进保护性摩擦氧化物层的快速形成,避免了高温恶化材料的机械性能.研究了Fe_2O_3对H13钢和45钢磨损性能的影响,分析了摩擦氧化物层的形成机理,并探讨了基体硬度对摩擦氧化物层的作用.研究结果表明:无添加时,低硬度45钢的耐磨性明显差于高硬度的H13钢;GCr15钢在与45钢对摩时,磨损率也明显大于与H13钢对摩时.添加Fe_2O_3后,纳米颗粒在H13和GCr15钢表面迅速相互黏着并形成保护性的摩擦氧化物层,导致磨损率急剧下降,且随载荷增加仅轻微波动.而较软45钢基体对摩擦氧化物层的支撑能力较弱,摩擦氧化物层破碎,高载下磨损率明显大于低载下.     

Evaporation heat transfer coefficient in single circular small tubes for flow natural refrigerants of C3H8, NH3, and CO2

An experimental study of evaporation heat transfer coefficients for single circular small tubes was conducted for the flow of C₃H₈, NH₃, and CO₂ under various flow conditions. The test matrix encompasses the entire quality range from 0.0 to 1.0, mass fluxes from 50 to 600 kg m⁻² s⁻¹, heat fluxes from 5 to 70 kW m⁻², and saturation temperatures from 0 to 10 °C. The test section was made of circular stainless steel tubes with inner diameters of 1.5 mm and 3.0 mm, and a length of 2000 mm in a horizontal orientation. The test section was uniformly heated by applying electric power directly to the tubes. The effects of mass flux, heat flux, saturation temperature, and inner tube diameter on the heat transfer coefficient are reported. Among the working refrigerants considered in this study, CO₂ has the highest heat transfer coefficient. Laminar flow was observed in the evaporative small tubes, and was considered in the modification of boiling heat transfer coefficients and pressure drop correlations.     

Near-critical CO2 liquid--vapor flow in a sub-microchannel. Part II: Flow regimes

The mean-field free-energy LBM is used to investigate the liquid--vapor flow regimes in a two-dimensional 200 nm channel with near-critical CO₂ at temperature 25 ^oC and pressure 6.434 MPa as the working fluid. Flow regimes over vapor qualities ranging from 0.01x0.90, Weber numbers O(10⁻²)WeO(10³), and capillary numbers O(10⁻²)CaO(10) are investigated. Three major types of flow regimes are encountered -- dispersed flow, bubble/plug flow, and liquid strip flow, each of which encompasses variations of the basic flow regime. The three major flow regimes with all their variations can be further classified into two major categories – regular and irregular. Irregular flow regimes are characterized by a distorted interface, including distorted bubble/slug flow, intermittent strip flow, wavy strip flow, and wispy-strip flow. Flows in which the interface is ordered and symmetric such as bubble/plug and strip flows are classified as regular flow regimes. It is found that the transition from regular to irregular flow regimes occurs at Weber number between 500 and 1000, independent of the vapor quality. Although no experiments exist at the same conditions, comparison of the predicted transition between regular and irregular regimes shows the same qualitative trends as experiments found in the literature.