Stress analysis of electrostrictive material with an elliptic defect

It is shown that the constitutive equation and electric body force used to discuss the stress analysis of electrostrictive material in some previous literature are not appropriate. This paper presents the corrected stress solution for the infinite plane with an insulated elliptic hole under an applied electrical field. The numerical result obtained for the PMN material constants show that the stress near the end of the narrow elliptic hole is the tensile stress.     

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack.     

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.     

Design of a Michelson interferometer for the measurement of electrostrictive strains

In the field of quadratic electrostriction of non-ferroelectric materials, efforts to optimize interferometers for the accurate measurement of small strains are being undertaken because the displacements that have to be measured are very small (10⁻¹³m). Here, a design for a Michelson interferometer is proposed that combines a double-face detection scheme with a null method.     

Non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the jumps in displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of crack length, the distance between two collinear cracks and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement or magnetic flux singularities are present at the crack tips in a magnetoelectroelastic composite material plane. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.     

The interaction of two collinear cracks in a rectangular superconductor slab under an electromagnetic force

The interaction of two collinear cracks is obtained for a type-II superconducting under electromagnetic force. Fracture analysis is performed by means of finite element method and the magnetic behavior of superconductor is described by the critical-state Bean model. The stress intensity factors at the crack tips can be obtained and discussed for decreasing field after zero-field cooling. It is revealed that the stress intensity factor decreases as applied field increases. The crack-tip stress intensity factors decrease when the distance between the two collinear cracks increases and the superconductors with smaller crack has more remarkable shielding effect than those with larger cracks.     

Solution of the one-dimensional linear Boltzmann equation for charged Maxwellian particles in an external field

The one-dimensional linear homogeneous Boltzmann equation is solved for a binary mixture of quasi-Maxwellian particles in the presence of a time-dependent external field. It is assumed that the charged particles move in a bath of neutral scatterers. The neutral scatterers are in thermal equilibrium and the concentration of the charged particles is low enough to neglect collisions between them. Two cases are considered in detail, the constant and the periodic external field. The quantities calculated are the equilibrium and the stationary distribution function, respectively, from which any desired property can be derived. The solution of the Boltzmann equation for Maxwellian particles can be reduced to the solution of the so-called cold gas equation by employing the one-dimensional variant of a convolution theorem due to Wannier. The two limiting cases, the Lorentz gas (m _A0) and the Rayleigh gas (m _A) are treated explicitly. Furthermore, by computing the central moments, the deviations from the Gaussian approximation are discussed, and in particular the large-velocity tails are evaluated.     

Characterization of thermal-shock cracks in ceramic bars

Experimental analysis of the cracking in the ceramics subsequent to water quenching have been conducted to clarify the uncertainties of cracking in the ceramics when subjected to thermal shock. The results here indicate that at the critical point of quench temperature, the crack density and the depth reached the minimum and the maximum limits, respectively. On increase of the quench temperature, the crack density increased rapidly before reaching its saturation point, while the crack depth initially decreased rapidly and then increased gradually before reaching its saturation point.     

On the frequency spectrum of an artificial amorphous solid

Summary The frequency spectrum of an amorphous Lennard-Jones solid, as determined by molecular-dynamics methods, is entirely different from that of a crystalline solid of the same nature, although its radial distribution function shows the environment of each atom to be similar in both cases. Such a disparity is interpreted in terms of a preponderance of the effects of the local forces (i.e. those between direct neighbours) which, in the case of the amorphous solid, is supposed to take place because of the absence of long-range co-ordination among individual atomic motions. To give the observed spectrum, this feature combines with a structure in which atomic clusters of different radii seem to coexist.

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Riassunto Lo spettro di frequenza di un solido amorfo costituito da atomi che interagiscono secondo un potenziale di Lennard-Jones risulta, secondo ricerche di dinamica molecolare, del tutto diverso da quello di un solido cristallino della stessa natura. D'altra parte la funzione di distribuzione radiale non mostra, nella regione del picco principale, cioè quella dei vicini diretti, nessuna significativa deviazione dalla normale struttura del solido cristallino. Questa disparità degli effetti di quelle che sono essenzialmente le stesse forze è interpretabile in termini di una quasi indipendenza delle oscillazioni locali che si unisce, per dare il caratteristico spettro osservato, ad una peculiare struttura nella quale coesistono gruppi sferici di atomi vicini aventi raggi, entro certi limiti, diversi.

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Резюме Частотный спектр аморфного твердого тела Леннарда-Джонсона, определяемЫй методами молекулярной динамики, оказЫвается полностью отличнЫм от частотного спектра кристаллического твердого тела той же природЫ; хотя радиальные функции распределения показывают, что окружение каждого атома является сходным в обоих случаях. Таксе несоответствие интерпретируется в терминах преобладания эффектов локальных сил (t.e. сил между соседними атомами), которое, как предполагается, имеет место в случае аморфного твердого тела, t.e. отсутствуют длиннодействуюшие корреляции между движениями отдельных атомов. Чтобы получить наблюдаемый спектр, эта особенность комбинируется со структурой, в которой сосуществуют атомные кластеры различных радиусов.

     

More on the frequency spectrum of an artificial amorphous solid

Summary In a previous paper on the same subject an analysis of the frequency spectrum of an amorphous Lennard-Jones solid, as determined by methods of molecular dynamics by Rahman and collaborators, was given. There the general form of the spectrum was considered. Here we show how the analysis of the spectrum can be refined so as to allow a separation of the contribution of the propagating waves from the contribution of that fraction of atomic oscillations that do not possess propagational character. It is thus possible to bring indirectly into evidence bands of transverse and longitudinal waves, contributing a nonnegligible fraction of atomic motion.     

Coarsening of cracks in a uniaxially strained solid

We discuss the stress relaxation in a uniaxially strained solid due to the coarsening of a system of parallel cracks. We emphasize similarities and differences of this process to Ostwald ripening in a first order phase transition. A conventional mean-field approximation breaks down and several independent length scales have to be taken into account. Strong elastic interactions between the cracks determine the growth behavior. We derive scaling laws for the coarsening of the different length scales involved and the time evolution of stress relaxation, finally leading to the equilibrium state of a fractured body. The characteristic size of the cracks grows linearly in time which is much faster than in usual Ostwald ripening.     

Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole

The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult.     

横向划痕对光场调制的近场模拟

熔石英亚表面划痕对入射激光的近场调制是导致光学元件低阈值损伤的主要因素之一. 用三维时域有限差分方法研究了连续横向划痕的近场分布, 对比了尖锐截面与光滑截面场调制的差异, 着重探讨了光场调制与划痕宽深比R的关系. 研究表明: 酸蚀后的光滑截面有助于减弱近场调制, 这类划痕的R>10.0时调制较弱且相互接近, R<5.0时调制显著增强. 当R取1---3时, 亚表面的调制达最大值, 最大电场幅值为入射波幅值的4.3倍. 当R取1.0---3.5时, 缺陷附近有80%以上取样点的最大电场幅值超过入射波幅值的2倍. 随着深度的增大, 强场区具有明显的"趋肤效应": 位于划痕正下方的强场区首先往左右两侧移动, 然后移向抛物口界面以及水平界面, 同时衍生出的多条增强线诱导整个亚表面层的光场增强.     

Efficiency of collinear acoustooptic interaction in an anisotropic medium

Collinear acoustooptic interaction in crystals with different values of birefringence is theoretically studied. The crystal medium is considered as a system of thin layers where the orientation of optical indicatrix varies from layer to layer due to the presence of an ultrasonic wave. For collinear diffraction in LiNbO₃, α-SiO₂, Te, CaMoO₄, and Tl₃AsSe₃ crystals, expressions for the transmitted and diffracted intensities are obtained by means of acoustooptic methods and a new method based on the Jones calculus.     

不同功率下无工质微波推力器的推力预估

基于经典电动力学理论,从麦克斯韦方程组和麦克斯韦张量出发,推导出无工质微波推力器的推力计算方程. 应用有限元分析软件,计算了特定谐振模式下的特定圆台谐振腔在不同功率条件下的电磁场分布;根据推导出的理论计算公式,计算了不同功率条件下推力器的总推力. 计算结果表明:推力与功率成正比,而且磁场力决定着总推力的大小;圆台谐振腔消耗20–200 W电磁波功率时所产生的推力在20–250 mN范围内. 关键词： 电磁波 麦克斯韦张量     

Influence of residual surface stress on the fracture of nanoscale piezoelectric materials with conducting cracks

In this paper,we analyze the stress and electric field intensity factors affected by residual surface stress for conducting cracks in piezoelectric nanomaterials.The problem is reduced to a system of non-linear singular integral equations,whose solution is determined by iteration technique.Numerical results indicate that the residual surface stress can significantly alter the crack tip fields at nanometer length scales.Due to the residual surface stress,281he electric field can produce stress around crack tip.This suggests a strong electromechanical coupling crack tip field for nanoscale piezoelectric materials.Such a finding is considerably different from the classical fracture mechanics results.A transit electric field to stress load ratio is identified,for which influences of residual surface stresses vanish.The research is useful for the applications of nanoscale piezoelectric devices.     

General Solution for a Class of Static Charged Spheres

We find a class of solutions to the Einstein–Maxwell system for a charged sphere with a particular choice of the electric field intensity by assuming a particular form for the hypersurfaces {t = constant}. In the uncharged limit we regain static stars studied previously. A qualitative analysis of the physical features of the model is performed. The presence of charge allows for more general behaviour than is the case for uncharged spheres. In particular we show that the causal signals are permitted over a wider range of parameters in the presence of charge. Also we show that our solutions satisfy a simple scaling relationship.     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

Propagation of an electromagnetic soliton in an anisotropic biquadratic ferromagnetic medium

Information storage technology based on anisotropic ferromagnets with sufficiently high magneto-optical effects has received much attention in recent years.Magneto-optical recording combines the merits of magnetic and optical techniques.We investigate the magneto-optical effects on a biquadratic ferromagnet and show that the dynamics of the system are governed by a perturbed nonlinear Schro¨dinger equation.The evolutions of amplitude and velocity of the soliton are found to be time independent,thereby admitting the lossless propagation of the electromagnetic soliton in the medium,which may have potential applications in soliton based optical communication systems.We also exploit the role of perturbation,which has a significant impact on the propagation of an electromagnetic soliton.     

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.