The equilibrium of a piezoceramic cylindrical body with a parabolic crack

A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 72–80, March, 2000.     

Electroelastic field of a piezoelectric annular finite cylinder

This paper presents a theoretical study of a piezoelectric annular cylinder under axisymmteric electromechanical loading. The piezoelectric material is assumed to be transversely isotropic and the general solutions of the governing equations are obtained in terms of a Fourier–Bessel series containing Bessel functions of the first and second kind. The boundary-value problems for vertical pressure and an electric charge loading applied to the ends of an annular cylinder are solved by expanding the applied loading in terms of a Fourier–Bessel series. Selected numerical results for the electroelastic field of an annular cylinder are presented for different aspect ratios of a cylinder and material properties.     

Modelling and numerical simulation of martensitic transformation in shape memory alloys

We consider the evolution of martensitic fine structures in shape memory alloys which undergo an isothermal phase-transformation. This process is modelled on a microscopical, continuum-mechanical level by partial differential equations. Here a homogeneous degree-1 dissipation potential is involved which can reflect specific energies needed for rate-independent phase transformations. An interface energy is incorporated by a nonlocal term, and hard-device loading is considered. After setting up the model and specifying its energy balance properties, three-dimensional numerical experiments for the cubic-to-tetragonal transformation in an InTl single crystal are presented which demonstrate geometrical/material interactions under tensile and shear loading.Received: 27 June 2002, Accepted: 18 March 2003, Published online: 27 June 2003PACS: 81.30Kf     

The effect of load biaxiality on crack growth in non-linear materials

The influence of load biaxiality on the stress field and fracture behavior of a cracked plate is investigated. Considered is a square plate containing a central through the thickness crack and subjected to a biaxial loading perpendicular and parallel to the crack plane. The stress field of the plate is analyzed by a finite element code based on incremental plasticity and the von Mises yield condition. A method based on the strain energy density theory is used to determine the critical stress for crack initiation. It was found that the equi-biaxial loading mode induces the smallest plastic zones, while the critical applied stress for crack initiation becomes maximum. Quite the contrary happens for the shear loading system which causes the largest plastic zones and the minimum applied stress values fro crack growth. Results showing the dependence of the above quantities on the biaxiality of the applied stress are presented in graphical form.     

Application of underwater shock wave and laser-induced liquid jet to neurosurgery

Paper deals with applications of underwater shock waves to medicine. A historical development of underwater shock wave generation by using pulsed Ho:YAG laser beam irradiation in water is briefly described and an overview is given regarding potential applications of shock waves to neuro-surgery. The laser beam irradiation in a liquid-filled catheter produces water vapor bubble and shock waves intermittently produces micro-liquid jets in a controlled fashion from the exit of the catheter. Correlations between shock dynamics and bubble dynamics are emphasized. To optimize the jet motion, results of basic parametric studies are briefly presented. The liquid jet discharged from the catheter exit has an impulse high enough to clearly exhibit effectiveness for various medical purposes. In liquid jets we observed reasonably strong shock waves and hence invented a compact shock generator aiming to apply to microsurgery. We applied it to a rat's bone window and developed an effective method of brain protection against shock loading. The insertion of Gore-Tex® sheet is found to attenuate shock waves drastically even for very short stand off distance and its physical mechanism is clarified. The laser-induced liquid jet (LILJ) is successfully applied to soft tissue dissection. Animal experiments were performed and results of histological observations are presented in details. Results of animal experiments revealed that LILJ can sharply dissect soft tissue with a minimum amount of liquid consumption, while blood vessels larger than 0.2 mm in diameter are preserved. Shock waves and LILJ have a potential to be indispensable tools in neuro-surgery.This paper was based on work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, March 1–3, 2005.Communicated by K. Takayama PACS 42.62.Be, 47.40.-x, 42.62.-b     

A crack-mechanics based model for damage and plasticity of brittle materials under dynamic loading

A rate-dependent model for damage and plastic deformation of brittle materials under dynamic loading is presented. The model improves upon a recently developed micromechanical damage model (Zuo et al., 2006) by incorporating plastic deformation of the material. The distribution of the microcracks in the material is assumed to remain isotropic, and the damage evolution is through the growth of the average crack size. Plasticity is considered through an additive decomposition of the total strain rate, and a rate-independent, von Mises model is used. The model was applied to simulate the response of a model material (SiC) under uniaxial strain loading. To further examine the behavior of the model, cyclic loading and large-strain compressive loading were considered. Numerical results of the model predictions are presented, and comparisons with those from a previous model are provided.     

THREE-DIMENSIONAL ANALYSIS OF A MAGNETOELECTROELASTIC HALF-SPACE UNDER AXISYMMETRIC TEMPERATURE LOADING 1)

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.     

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.      

The non-linear,dynamic response of an impulsively loaded circular plate with a central hole

A numerical method, called Direct Analysis, is described and applied to solve the problem of a plate undergoing a large impulsive load. For generality, an expanded, non-linear form of the equations of motion is used and shear correction and rotatory inertia are considered. The wave speeds are calculated from the non-linear equations and appropriate boundary conditions are applied so that reflected waves are included. The results for two types of step loading pulses are presented and compared with previously presented solutions. The response of the plate is discussed and conclusions as to the effects of the non-linearities are given.     

轴向变速运动正交各向异性板的动态稳定性

研究面内载荷作用下轴向变速运动正交各向异性薄板的横向振动及其稳定性。利用Galerkin法与平均法,在激励频率为2倍固有频率或为两阶固有频率之和附近时得到自治的常微分方程组;在参数激励频率和激励振幅平面上,分析由共振引发的失稳区域。数值算例验证了面内载荷、轴向速度、加速度参数对失稳区域的影响。     

Elastic beam on a rigid frictional foundation under monotonic and cyclic loading

An elastic beam resting on a frictional foundation and loaded by the concentrated force or moment applied at its tip is considered. The evolution of slip zones along the beam is discussed for both monotonie and cyclic loading. It is shown that an infinite number of slip zones develop and their propagation satisfies in some cases a self-similarity property. Transient hysteretic effects under cyclic loading are discussed. The closed form analytical solution is presented for the elastic friction model in the case of monotonie loading.     

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

Summary A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape. Received 17 October 1997; accepted for publication 19 March 1998     

有限液体负载下压电平板声板波理论分析

主要推导平板声板波受有限液体负载后能量衰减与波速改变情形, 以部分波传理论分析该受液体负载的压电平板波传行为, 并以一128$^{\circ}Y$向切角的铌酸锂芯片为例,分析前20个声板波受水与甘油负载下 的能量衰减,并固定某一平板板波, 针对不同甘油厚度负载下, 计算其相速度与衰减变化,该理论分析对于液体负载下的平板板波传感器应用具有极大的参 考价值.     

Determination of properties for the calculation of aqueous thin film drying

 This paper deals with the determination of various properties required for the numerical calculation of the thin film drying of a water based varnish applied on paper. Experimental and analytical methods which provide the activity of water in paper and in a water based varnish, and the diffusion coefficient of water in this varnish are presented. Received on 23 March 2001     

The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid

Based on the Stroh-type formalism, we present a concise analytic method to solve the problem of complicated defects in piezoelectric materials. Using this method and the technique of conformal mapping, the problem of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric solid is investigated under remotely uniform in-plane electric loading and anti-plane mechanical loading. The exact solutions of the field intensity factors and the energy release rate are presented in closed-form under the permeable electric boundary condition. With the variation of the geometrical parameters, the present results can be reduced to the well-known results of a mode-III crack in piezoelectric materials. Moreover, new special models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and single edge crack emanating from an elliptical hole or circular hole, T-shaped crack, cross-shaped crack, and semi-infinite plane with an edge crack. Numerical results are then presented to reveal the effects of geometrical parameters and the applied mechanical loading on the field intensity factors and the energy release rate.     

基于真空吸盘的新型振动加载技术研究及应用

传统的振动加载技术,试件通过刚性夹具与振动台台面进行连接,刚性夹具采用螺栓与振动台台面和试件进行连接。一些试验要求振动加载装置的连接不能破坏试件结构,传统的螺栓方式不能满足要求。本文研究了一种基于真空吸盘的新型振动加载技术,振动加载杆通过真空吸盘吸附在试件表面。该项技术已在垂尾结构的动态疲劳试验中得到应用。应用实践证明,这种基于真空吸盘的振动加载技术方便、可靠、安全,弥补了传统加载方式的不足。     

Effect of pure mode I,II or III loading or mode mixity on crack growth in a homogeneous solid

Crack growth is analyzed numerically under combined mode I, II and III loading, or under loading in one of these modes alone. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyses are carried out for conditions of small-scale yielding, with the elastic mixed mode solution applied as boundary conditions on the outer edge of the region analyzed. For pure mode I loading crack growth continued far beyond the maximum fracture toughness shows that the predicted subsequent steady-state toughness is well below the maximum. The reason for this is discussed in terms of the local stress and strain fields around the tip. For pure mode II or mode III loading it is shown that there is no maximum before the steady-state. Also results for different mixed mode conditions are presented and discussed in relation to the results for loading in only one mode. Most of the results are based on assuming that the peak tractions for tangential separation are equal to that for normal separation, but it is shown that a relatively smaller peak traction for tangential separation may significantly affect the predictions.     

A General Formulation of Stress Distribution in Cylinders Subjected to Non-Uniform External Pressure

This work presents a two-dimensional stress analysis for elastic solid cylinders subjected to combined loading. The loading is generally formed with a number of concentrated and partially distributed forces all applied radially on the outer surface. The distributed forces cause pressures with non-uniform intensity along the circumferential direction. The cylinder is assumed to be long so that a state of plane-strain is valid. To obtain the stress distribution for the problem of partially distributed forces a new approach is followed first introduced in this paper. It is based on the expressions formed after using the theory of simple radial stress distribution when point-forces are applied on the cylinder and leads to the solution after direct integration. The total stresses due to both concentrated and distributed forces are obtained using the method of superposition. Apart from its simplified formulation, this general solution is always preferable since it proved to have a great advantage. As a result of not containing Fourier series, it eliminates some problems of convergence of the series at the boundaries that appear due to the Gibbs phenomena when the boundary conditions are a discontinuous function. Numerical results are presented for some interesting cases of loading conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Opening and contact zones of an interface crack in a piezoelectric bimaterial under combined compressive-shear loading

A plane problem for a tunnel electrically permeable interface crack between two semi-infinite piezoelectric spaces is studied. A remote mechanical and electrical loading is applied. Elastic displacements and potential jumps as well as stresses and electrical displacement along the interface are presented using a sectionally holomorphic vector function. It is assumed that the interface crack includes zones of crack opening and frictionless contact. The problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved analytically. From the obtained solution, simple analytical expressions are derived for all mechanical and electrical characteristics at the interface. A quite simple transcendental equation, which determines the point of separation of open and close sections of the crack, is found. For the analysis of the obtained results, the main attention is devoted to the case of compressive-shear loading. The analytical analysis and numerical results show that, even if the applied normal stress is compressive, a certain crack opening zone exists for all considered loading values provided the shear field is present. It is found that the shear stress intensity factor at the closed crack tip and the energy release rates at the both crack tips depend very slightly on the magnitude of compressive loading.     

Electrically permeable crack with contact zones between two piezoelectric materials

The paper addresses a plane problem for an infinite plane consisting of two different piezoceramic half-planes with an interfacial crack with smooth contact zones and subjected to the uniformly distributed electromechanical loading applied at infinity. Methods of complex-variable theory are used to reduce the problem to a Dirichlet-Riemann mixed homogeneous boundary-value problem. Its solution is found in closed form. A system with one crack that has one or two contact zones is calculated. Expressions for stresses, electric-flux density, and displacement discontinuities at the interface are written. Equations for the determination of the length of the contact zones and expressions for the stress intensity factors at the crack tips are derived __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 66–74, March 2008.