Crack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method

Several simple formulas have been developed to predict the variations of stress intensity factors for mode I crack induced by the stiffness and geometry of the near crack-tip inclusion. The derivation of the fundamental formula is based on the transformation toughening theory. The unconstrained mismatch strains between matrix and inclusion, which induce the variation of the near crack-tip field, are estimated based on the Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formulas have satisfactory accuracy for a wide range of the modulus ratio between inclusion and matrix as long as the inclusion is located in the K ₀-controlled field.     

Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics

A numerical approach predicting the behavior of ferroelectric ceramics under electric field and mechanical loading is proposed in this paper. In the model, macroscopic properties of ferroelectric ceramics are determined by microscopic structures. Ferroelectric ceramics are seen to be composed of many domains with different orientations, and domain switching is the source of the nonlinear constitutive behavior of the ferroelectric ceramics. Numerical calculations based on the model were carried out, and the computational results are compared with the experimental results, which shows the two sets of results consist with each other. The calculation approach can provide a guidance for the ceramics component design.     

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed-mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite-element analysis. The J-integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack-face loading. In mixed-mode crack problems the total J-integral is split into J_I, J_II, and J_III, representing the severity of the crack front in three modes of deformation. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed-mode fracture problems in isotropic materials. Several pure and mixed-mode fracture problems were analyzed and results found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite-element program.     

An extended equivalent domain integral method for mixed mode fracture problems by the p-version of FEM

A new path-independent contour integral formula is presented to estimate the crack-tip integral parameter, J-value, for two-dimensional cracked elastic bodies which may quantify the severity of the crack-tip stress fields. The conventional J-integral method based on a line integral has been converted to an equivalent area or domain integral (EDI) by the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of domain integrals are readily available in a finite element analysis. The details and its implementation are extended to the p-version FE model with hierarchic elements using integrals of Legendre polynomials. By decomposing the displacement field obtained from the p-version finite element analysis into symmetric and antisymmetric displacement fields with respect to the crack line, the Mode-I and Mode-II non-dimensional stress intensity factors can be determined by using the decomposition method. The example problems for validating the proposed techniques are centrally oblique cracked plates under tensile loading. The numerical results associated with the variation of oblique angles show very good agreement with the existing solutions. Also, the selective distribution of polynomial orders and the corner elements for automatic mesh generation are applied to improve the numerical solution in this paper. © 1998 John Wiley & Sons, Ltd.     

Time domain analysis by the point-matched finite element method

The solution of Maxwell's equations using the point-matched finite-element time-domain approach is presented. The solution scheme is explicit and does not require the solution of any matrix equations. The solution is carried out over a finite domain terminated using appropriate absorbing boundary conditions. Far-field quantities are obtained from the near-field solution by first computing the frequency-domain solutions from the time-domain solution using the fast Fourier transform and then using a near-field to far-field transformation algorithm.<>     

基于原子力显微技术的PZT微阵列图形铁电性能

应用基于原子力显微镜与铁电分析仪联用的方法,在无顶电极的情况下,直接测试了PZT微阵列格点的电滞回线.结果表明,应用铁电分析仪与原子力显微镜联用的测试技术能够表征铁电电容的电滞回线,并且可以定性地评价薄膜微电容的铁电特性.     

Piezoelectric properties and equivalent circuits of ferroelectric relaxor single crystals

Temperature dependent piezoelectric properties of ferroelectric relaxor single crystals, particularly the cerium-doped strontium barium niobate compositions (SBN60: Ce), were investigated by resonance and anti-resonance technique. Characteristic resonant frequencies (f_r−f_a, f_s−f_p, and f_m−f_n) were studied using equivalent circuit simulation. Piezoelectric resonance in a relaxor resonator persists into temperatures much higher than Tm (the temperature at which dielectric constant, κ, has a maximum at 1 kHz) in comparison with the normal ferroelectrics such as TGS. The parameters in an equivalent circuit, however, are phenomenally different from a normal resonator like a TGS, near and above the transition temperature region. The significance and understanding of the piezoelectric resonance characteristics in ferroelectric relaxor are discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Large electric-field-induced strain in ferroelectric crystals by point-defect-mediated reversible domain switching

Ferroelectric crystals are characterized by their asymmetric or polar structures. In an electric field, ions undergo asymmetric displacement and result in a small change in crystal dimension, which is proportional to the applied field. Such electric-field-induced strain (or piezoelectricity) has found extensive applications in actuators and sensors. However, the effect is generally very small and thus limits its usefulness. Here I show that with a different mechanism, an aged BaTiO(3) single crystal can generate a large recoverable nonlinear strain of 0.75% at a low field of 200 V mm(-1). At the same field this value is about 40 times higher than piezoelectric Pb(Zr, Ti)O(3) (PZT) ceramics and more than 10 times higher than the high-strain Pb(Zn(1/3)Nb(2/3))O(3)-PbTiO(3) (PZN-PT) single crystals. This large electro-strain stems from an unusual reversible domain switching (most importantly the switching of non-180 degrees domains) in which the restoring force is provided by a general symmetry-conforming property of point defects. This mechanism provides a general method to achieve large electro-strain effect in a wide range of ferroelectric systems and the effect may lead to novel applications in ultra-large stroke and nonlinear actuators.     

粗大晶粒PZT陶瓷中电畴的结构

应用扫描力显微镜(SFM)的压电响应模式观测未经抛光处理的PZT陶瓷片的电畴结构,用纵向压电响应信号和侧向压电响应信号获得PZT陶瓷材料三维电畴结构.结果表明,将样品晶粒的微形貌与SFM的纵向和侧向压电响应信号相结合,能准确表征粗大晶粒样品的三维电畴结构.用SFM可观测表面不经任何处理的陶瓷样品的电畴,不会引入表面应力等影响因素,能得到样品的原生畴结构.对原生畴结构的观察表明,对于受应力较大的晶粒,成畴的主要原因是降低应变能,而受应力较小的晶粒成畴的主要原因是降低退极化能.     

Determining parameters of ferroelectric crystals by method of optimization

We propose a method based on the switching current variation for determining the physical parameters of ferroelectric crystals. Algorithms providing for the separate and joint determination of parameters such as the surface tension σ and the kinetic coefficient β₀ are presented.     

铁电陶瓷的电畴及畴变观测研究进展

铁电陶瓷材料，特别是锆钛酸铅(PZT)在众多领域具有广泛的应用前景，影响其推广应用的主要因素是使用过程中外电、力场引起的材料性能的退化。观测铁电电畴及畴变的方法对研究其在外场下性能破坏机理、提高其使用的可靠性和预防其失效具有重要的理论和实际意义。本文比较了不同实验方法和测试技术的优缺点，对铁电陶瓷的电畴观测进行了综述，并简要总结了铁电陶瓷的畴变观测技术研究现状，指出了目前该领域研究中存在的问题。     

Homogenization modeling of domain switching in ferroelectric materials

We presented a multiscale nonlinear finite element simulation to analyze domain switching behaviors in ferroelectric materials. We utilized an incremental form of fundamental constitutive law to consider changes in the material properties caused by domain switching. A multiscale nonlinear problem was formulated by employing the asymptotic homogenization theory based on the perturbation method and implemented using finite element analysis. The developed simulation was applied to barium titanate with a Perovskite-type tetragonal crystal structure. The 90° and 180° domain switching behaviors of a single crystal were computed for verification. The nonlinear behaviors of a bulk polycrystal with virtual microstructure were analyzed as a case study. The variation of the crystal orientation distribution in the polycrystalline microstructure was analyzed to reveal its influence on macroscopic hysteresis and butterfly curves.     

Variations in predicting domain switching of ferroelectric ceramics

In this article, a set of equivalent variational formulations for computing the driving forces for domain switching in ferroelectric materials is presented. It is proven that these formulations allow the free adoption of any couple of mechanical and electric fields as independent variables while obtaining consistent results. In addition, explicit expressions are provided for each formulation which allows for the study of the phase transformation process under different constraints.     

Sol-Gel法制备PLZT系铁电薄膜

介绍了Sol-Gel法，并对近年来Sol-Gel法制备PLZT系铁电薄膜材料的有关研究进行了分析和总结，详细介绍了Sol-Gel法制备PLZT系铁电薄膜材料的各种原料及工艺流程。     

改进的两步法制备PZN-PT-BT铁电陶瓷

基于SwartzandShrout的二次合成法,采用改进的两步法,部分原料预合成,一次烧结合成具有完全钙钛矿结构的75Pb(Zn1/3Nb2/3)O310PbTiO315BaTiO3固溶体陶瓷。首先按75∶10∶15一次性称量PbO(并且PbO过量5mol%),然后与ZnNb2O6在660℃预反应1h。粉碎后再加入TiO2和BaCO3,充分混合后,在1060～1140℃保温2h烧结成陶瓷试样。XRD结果表明660℃预合成的中间相中没有钙钛矿相,不同于传统的预合成和烧结,改进的两步法工艺在烧结阶段陶瓷的成瓷和致密化同时进行,完成了中间相向钙钛矿相的完全转变。与二次合成法相比,本方法简化了工艺,降低了预合成温度,拓宽了烧结温度,所获得的陶瓷试样介电性能优良。对陶瓷试样进行相同条件的退火,在1100℃烧结的陶瓷试样,介电常数ε获得95%的增幅;在1140℃烧结的陶瓷试样介电常数ε则获得16%的降幅。     

Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach

A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to have continuous spatial variations through the functionally graded medium. Developed methodology is integrated into a fracture mechanics research finite element code FRAC2D using graded finite elements that possess cubic interpolation. Steady-state and transient temperature distribution profiles in orthotropic FGMs are computed using the finite elements based heat transfer analysis software HEAT2D. EDI method is validated and domain independence is demonstrated by comparing the numerical results obtained using EDI to those calculated by an enriched finite element method and to those available in the literature. Single and periodic edge crack problems in orthotropic FGMs are examined in order to study the influences of principal thermal expansion coefficient and thermal conductivity components, relative crack length and crack periodicity on the thermal stress intensity factors. Numerical results show that among the three principal thermal expansion coefficient components, the in-plane component perpendicular to the crack axis has the most significant influence on the mode I stress intensity factor. Gradation profile of the thermal expansion coefficient parallel to the crack axis is shown to have no effect on the outcome of the fracture analysis.     

An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture

The crack-tip parameters, such asJ; T^*, ΔT^* etc, which quantify the severity of the stress/strain fields near the crack-tip in elastic-plastic materials subject to thermo-mechanical loading, are often expressed as integrals over a path that is infinitesimally close to the crack-tip (front). The integrand in such integrals involves the stress-working density, stress, strain and displacement fields arbitrarily close to the crack-tip. In a numerical analysis, such data near the crack-tip are not expected to be very accurate. This paper describes simple approaches and attendant computational algorithms, wherein, the “crack-tip integral” parameters may be evaluated through “equivalent domain integrals” (EDI) alone. It is also seen that the present (EDI) approaches form the generic basis for the popular “virtual crack extension” (VCE) methods. Several examples of thermo-mechanical fracture, including: (i) thermal loading of an elastic material, (ii) arbitrary loading/unloading/reloading of an elastic-plastic material, containing a single dominant crack, are presented to illustrate the present approach and its accuracy.     

Time analysis of structural concrete elements using the equivalent displacement method

This paper presents a modelling technique referred to as the equivalent displacement method (EDM) which describes the behaviour in time of structural concrete elements, such as reinforced concrete beams and composite beams with full shear interaction, accounting for time effects, such as creep, of the concrete component. The time-dependent behaviour of the concrete is modelled using the algebraic representations, such as the age-adjusted effective modulus method (AEMM), while the steel joist and reinforcement are assumed to behave in a linear-elastic fashion. The main advantage of the EDM method is that it requires only one analysis to obtain the deformation state of the structural system at one step in time based on the AEMM methods, instead of the two required by available modelling techniques (i. e. one performed at timet ₀ and one performed one step in timet). The EDM method is then applied to the analysis of structural concrete elements using the stiffness analysis and the results obtained based on this modelling technique are validated against other modelling methods. The advantages of using the EDM method in design applications are also illustrated.

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Résumé Cet article présente une méthode appelée méthode de déplacement équivalent (EDM), qui décrit le comportement temporel des éléments de béton, par example les poutres en béton armé et les poutres mixtes à interaction complète, tenant compte des effets temporaux, tel que le fluage du béton. Le comportement temporel du béton est modelé par représentation algébrique, tel que la méthode age ajusté du module effectif (AEMM), tandis que la poutre d'acier et les renforts sont supposés linéaire et élastique. L'avantage majeur de la méthode EDM est qu'elle n'exige qu'une seule analyse pour obtenir l'état de déformation du système à un point temporel (méthode EDM), au lieu des deux points exigés par les méthodes courantes, en temps t₀ et l'autre à t. La méthode EDM est ensuite appliquée à l'analyse des éléments structurels en béton, utilisant l'analyse de raideur, et les résultats obtenus par cette méthode sont vérifiés par d'autres méthodes. Les avantages de l'utilisation de la méthode EDM dans les applications du dessein sont aussi illustrés.

     

Frequency domain analysis by the exponential window method and SGBEM for elastodynamics

Dynamic analysis of a system can be carried out either in the time or frequency domain. Time responses/ histories of this system may be directly obtained using time-domain analysis. In case of frequency domain analysis in the Fourier space, the inverse fast Fourier transform (inverse FFT) would naturally be an appropriate choice for converting frequency solutions to the desired time responses. However, the standard FFT can not be applied to undamped systems as the free-vibration terms of these systems never decay which violates the periodic nature of the standard FFT algorithm. In addition, the FFT may be computationally expensive for lightly damped systems. An alternative to overcome the above limitations is the so-called exponential window method (EWM) commonly used in digital signal processing. This paper presents a combination of the EWM and the symmetric-Galerkin boundary element method for 2-D elastodynamic analysis in the frequency domain of undamped and lightly damped systems. Several numerical examples, including fracture problems, are given to illustrate the efficiency and accuracy of the proposed frequency domain analysis.     

Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by the boundary integral equation method

The boundary integral equation (BIE) method is applied for the thermal analysis of fiber-reinforced composites, particularly the carbon-nanotube (CNT) composites, based on a rigid-line inclusion model. The steady state heat conduction equation is solved using the BIE in a two-dimensional infinite domain containing line inclusions which are assumed to have a much higher thermal conductivity (like CNTs) than that of the host medium. Thus the temperature along the length of a line inclusion can be assumed constant. In this way, each inclusion can be regarded as a rigid line (the opposite of a crack) in the medium. It is shown that, like the crack case, the hypersingular (derivative) BIE can be applied to model these rigid lines. The boundary element method (BEM), accelerated with the fast multipole method, is used to solve the established hypersingular BIE. Numerical examples with up to 10,000 rigid lines (with 1,000,000 equations), are successfully solved by the BEM code on a laptop computer. Effective thermal conductivity of fiber-reinforced composites are evaluated using the computed temperature and heat flux fields. These numerical results are compared with the analytical solution for a single inclusion case and with the experimental one reported in the literature for carbon-nanotube composites for multiple inclusion cases. Good agreements are observed in both situations, which clearly demonstrates the potential of the developed approach in large-scale modeling of fiber-reinforced composites, particularly that of the emerging carbon-nanotube composites.