Electro-elastic fields of piezoelectric materials with an elliptic hole under uniform internal shearing forces

The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields     

Analytical Solutions of Cracks Emanating from an Elliptic Hole in an Infinite Plate under Tension

It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering.However,the fracture mechanics studies of hole edge crack problems are not sufficient.The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated.Based on the complex variable method,the analytical solutions of stress functions and stress intensity factors are provided.The stress distribution along the axes and the edge of the elliptical hole is given graphically.The numerical results show that there is obvious stress concentration near the hole and cracks,and the stresses tend to applied loads at distances far from the defect,which conform to Saint-Venant’s principle.Hence,the stress functions are proved to be right.Under special conditions,the present configuration becomes the Griffith crack,two symmetrical cracks emanating from an elliptical hole,two cracks of unequal length emanating from a circular hole,a crack at the edge of a circular hole,or a crack emanating from an elliptical hole.Compared with available results,stress intensity factors for these special shapes of ellipses and cracks show good coincidence.The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole.The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.     

I-beam Crack Identification Based on Study of Local Flexibility due to Crack

Local flexibility of crack plays an important role in crack identification of structures.Analytical methods on local flexibility in a cracked beam with simple geometric crossing sections,such as rectangle,circle,have been made,but there are some difficulties in calculating local flexibility in a cracked beam with complex crossing section,such as pipe and I-beam.In this paper,an analytical method to calculate the local flexibility and rotational spring stiffness due to crack in I-beam is proposed.The local flexibility with respect to various crack depths can be calculated by dividing a cracked I-beam into a series of thin rectangles.The forward and inverse problems in crack detection of I-beam are studied.The forward problem comprises the construction of crack model exclusively for crack section and the construction of a numerically I-beam model to gain crack detection database.The inverse problem consists of the measurement of modal parameters and the detection of crack parameters.Two experiments including measurement of rotational spring stiffness and prediction of cracks in I-beam are conducted.Experimental results based on the current methods indicate that relative error of crack location is less than 3%,while the error of crack depth identification is less than 6%.Crack identification of I-beam is expected to contribute to the development of automated crack detection techniques for railway lines and building skeletons.     

DAMAGE TOLERANCE ANALYSIS ON HOLLOW AXLES OF HIGH SPEED MOTOR TRAINS

According to the rules of UIC515-3, the service loads of the axles are defined, which include some different loads cases as follows： the static loads; the impact loads resulted from running through the rail joints and unevenness rails; the loads through curves and from braking. Through the calculating and analysis, the stress distribution of the hollow axles is obtained for 200 km/h high speed motor trains used in China. At the same time, the fatigue crack growth of hollow axles is studied, and the initial surface cracks of 2 mm depth caused by hard objects strike or the other causes are discussed. On the basis of the linear elastic fracture mechanics theory, the stress intensity factor of the crack of the geometry transition outside the wheel seat is also studied. Associated with fatigue crack propagation equation and the corresponding crack propagation threshold, the crack propagation characteristics under different shapes are calculated. Then the running distances are educed with different shapes propagating to the critical length, and the estimation of the residual lives about hollow axles which are the reference values of examine and repair limit of the hollow axle is given.     

Adaptive Shape Control for Thermal Deformation of Membrane Mirror with In-plane PVDF Actuators

Optical membrane mirrors are promising key components for future space telescopes. Due to their ultra-thin and high flexible properties, the surfaces of these membrane mirrors are susceptible to temperature variations. Therefore adaptive shape control of the mirror is essential to maintain the surface precision and to ensure its working performance. However, researches on modeling and control of membrane mirrors under thermal loads are sparse in open literatures. A 0.2 m diameter scale model of a polyimide membrane mirror is developed in this study. Three Polyvinylidene fluoride(PVDF) patches are laminated on the non-reflective side of the membrane mirror to serve as in-plane actuators. A new mathematical model of the piezoelectric actuated membrane mirror in multiple fields,(i.e., thermal,mechanical, and electrical field) is established, with which dynamic and static behaviors of the mirror can be analyzed.A closed-loop membrane mirror shape control system is set up and a surface shape control method based on an influence function matrix of the mirror is then investigated. Several experiments including surface displacement tracking and thermal deformation alleviation are performed. The deviations range from 15 μm to 20 μm are eliminated within 0.1 s and the residual deformation is controlled to micron level, which demonstrates the effectiveness of the proposed membrane shape control strategy and shows a satisfactory real-time performance. The proposed research provides a technological support and instruction for shape control of optical membrane mirrors.     

Unsteady Flow and Structural Behaviors of Centrifugal Pump under Cavitation Conditions

Cavitation has a significant e ect on the flow fields and structural behaviors of a centrifugal pump. In this study, the unsteady flow and structural behaviors of a centrifugal pump are investigated numerically under di erent cavitation conditions. A strong two-way coupling fluid-structure interaction simulation is applied to obtain interior views of the e ects of cavitating bubbles on the flow and structural dynamics of a pump. The renormalization-group k-ε turbulence model and the Zwart–Gerbe–Belamri cavitation model are solved for the fluid side, while a transient structural dynamic analysis is employed for the structure side. The di erent cavitation states are mapped in the head-net positive suction head(H-NPSH) curves and flow field features inside the impeller are fully revealed. Results indicate that cavitating bubbles grow and expand rapidly with decreasing NPSH. In addition, the pressure fluctuations, both in the impeller and volute, are quantitatively analyzed and associated with the cavitation states. It is shown that influence of the cavitation on the flow field is critical, specifically in the super-cavitation state. The e ect of cavitation on the unsteady radial force and blade loads is also discussed. The results indicate that the averaged radial force increased from 8.5 N to 54.4 N in the transition progress from an onset cavitation state to a super-cavitation state. Furthermore, the structural behaviors, including blade deformation, stress, and natural frequencies, corresponding to the cavitation states are discussed. A large volume of cavitating bubbles weakens the fluid forces on the blade and decreases the natural frequencies of the rotor system. This study could enhance the understanding of the e ects of cavitation on pump flow and structural behaviors.     

ANALYSIS AND EXPERIMENT ON YIELD CRITERION FOR SINTERED POWDER MATERIALS

Plastic deformation is an important process to improve properties and obtain final products made of sintered powder materials.Sintered ferrous material is widely used in many engineering departments and its deformation characteristics are typical for most sintered powder materials.Factors such as deformation strengthening,instantaneous and initial relative densities,ete,on the subsequent yield strength are studied,and an approach to determine the plastic stress coefficient and hardening exponent is derived,which is based on the yield criterion and the strengthening laws of plastic deformation of sintered powder materials as well as on a uni-axial compression experiment of a sintered ferrous cylinder specimen.A unified form of the yield criterion function is obtained,in which the initial and the subsequent yields of sintered powder materials are expressed.     

Three-steps-meshing based multiple crack identification for structures and its experimental studies

Multiple crack identification plays an important role in vibration-based crack identification of structures. Traditional crack detection method of single crack is difficult to be used in multiple crack diagnosis. A three-step-meshing method for the multiple cracks identification in structures is presented. Firstly, the changes in natural frequency of a structure with various crack locations and depth are accurately obtained by means of wavelet finite element method, and then the damage coefficient method is used to determine the number and the region of cracks. Secondly, different regions in the cracked structure are divided into meshes with different scales, and then the small unit containing cracks in the damaged area is gradually located by iterative computation. Lastly, by finding the points of intersection of three frequency contour lines in the small unit, the crack location and depth are identified. In order to verify the effectiveness of the presented method, a multiple cracks identification experiment is carried out. The diagnostic tests on a cantilever beam under two working conditions show the accuracy of the proposed method: with a maximum error of crack location identification 2.7% and of depth identification 5.2%. The method is able to detect multiple crack of beam with less subdivision and higher precision, and can be developed as a multiple crack detection approach for complicated structures.     

EXPERIMENTAL RESEARCH ON EVALUATING STRUCTURE DAMAGE WITH PIEZOELECTRIC DYNAMIC IMPEDANCE

A dynamic impedance-based structural health monitoring technique is introduced. According to the direct and the converse piezoelectric property of piezoelectric materials, the piezoceramic ( PZT ) can be used as an actuator and a sensor synchronously. If damages like cracks, holes, debonding or loose connections are presented in the structure, the physical variations of the structure will cause the mechanical impedance modified. On the basis of introducing the principle and the theory, the experiment and the analysis on some damages of the structure are studied by means of the dynamic impedance technique. On the view of experiment, kinds of structural damages are evaluated by the information of dynamic impedance in order to validate the feasibility of the method.     

Review of Determination of Minimum Ignition Energy of Combustible Gases or Dusts

MIE is an important parameter to be used to rank the ignition risk of the combustible materials.Commonly used electric circuits for generating spark have been reviewed and their features are analyzed in detail.Attention to avoiding test errors is stressed.Ranking of ignition risk is suggested based on MIE data.     

Fracture behavior of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric material

Based on the Stroh-type formalism 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, which allowed us to take the electric field inside the hole and cracks into account. The analytical solutions of the field intensity factors and the energy release rate are presented in closed-form, which includes the extreme cases for an impermeable crack and a permeable crack. Numerical results are then presented to reveal the effects of geometrical parameters, crack permeability and combined mechanical and electric loadings on the energy release rate.     

压电材料平面渗透裂纹的机电耦合场

为提高压电传感器和换能器的品质,针对材料缺陷导致的压电元器件失效或不稳定,用复变函数的方法,结合椭圆形夹杂内的电场强度和电位移为常量这一早期研究结果,研究了压电材料平面电渗透裂纹的机电耦合场及其奇异性。解答表明,切向电场强度和法向电位移在裂纹尖端有由机械载荷引起的奇异,而与电载荷无关;应力强度因子与纯弹性材料结果一致。     

Dynamic response of an anti-plane shear crack in a functionally graded piezoelectric strip

The dynamic response of a cracked functionally graded piezoelectric material (FGPM) under transient anti-plane shear mechanical and in-plane electrical loads is investigated in the present paper. It is assumed that the electroelastic material properties of the FGPM vary smoothly in the form of an exponential function along the thickness of the strip. The analysis is conducted on the basis of the unified (or natural) crack boundary condition which is related to the ellipsoidal crack parameters. By using the Laplace and Fourier transforms, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, the electric field, FGPM gradation, crack length, and electromechanical coupling coefficient.     

An electrically saturated anti-plane shear crack in a piezoelectric layer constrained between two elastic layers

Within the framework of linear elasticity and nonlinear electroelasticity, the electrical nonlinear behavior of an anti-plane shear crack in a piezoelectric ceramic layer constrained between two orthotropic layers is examined by using an electrical strip saturation model. The analysis is performed based on the electrical unified crack surface condition, which can describe all of the permeable, the impermeable, and the limited permeable ones. Fourier transforms are used to reduce the problem to the solutions of two pairs of dual integral equations, which are then expressed to two Fredholm integral equations of the second kind. Some numerical results for the energy release rates are presented to show the effects of the electrical crack condition parameter relating with elliptic flaw shape parameters and permittivity inside the crack, the electric field, the crack length, the electromechanical coupling coefficient, the crack position, and the bonded elastic materials.     

压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的干涉效应

运用弹性复势方法,研究纵向剪切和面内电场共同作用下无限半平面压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的电弹干涉效应,得到该问题复势函数的封闭形式解答,并由此导出广义应力场、裂纹尖端的广义应力强度因子以及作用在螺型位错上的位错力.算例结果表明:增大材料压电常数会相应增大位错力、位错对裂纹尖端的屏蔽和反屏蔽效应;增大位错离裂纹尖端的距离,位错力会相应减小;变化φ(偶极子臂与x轴正半轴夹角)值会出现一个改变位错偶极子对应力强度因子作用方向的临界值.     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

Stress and electric potential fields in piezoelectric smart spheres

Piezoelectric materials produce an electric field by deformation, and deform when subjected to an electric field. The coupling nature of piezoelectric materials has acquired wide applications in electric-mechanical and electric devices, including electric-mechanical actuators, sensors and structures. In this paper, a hollow sphere composed of a radially polarized spherically anisotropic piezoelectric material, e.g., PZT_5 or (Pb) (CoW) TiO₃ under internal or external uniform pressure and a constant potential difference between its inner and outer surfaces or combination of these loadings has been studied. Electrodes attached to the inner and outer surfaces of the sphere induce the potential difference. The governing equilibrium equations in radially polarized form are shown to reduce to a coupled system of second-order ordinary differential equations for the radial displacement and electric potential field. These differential equations are solved analytically for seven different sets of boundary conditions. The stress and the electric potential distributions in the sphere are discussed in detail for two piezoceramics, namely PZT_5 and (Pb) (CoW)TiO₃. It is shown that the hoop stresses in hollow sphere composed of these materials can be made virtually uniform across the thickness of the sphere by applying an appropriate set of boundary conditions.     

Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions

A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E_z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

Analysis of three collinear antiplane interfacial cracks in dissimilar piezoelectric materials under non-self equilibrated electromechanical loadings on a center crack

The problem of three collinear interfacial cracks between two dissimilar transversely isotropic piezoelectric materials is considered under electromechanical loadings. The crack surfaces are assumed to be impermeable to the electric field. A single antiplane mechanical and inplane electrical loads are applied at a point on centred crack surface. The problem is formulated by the complex function method, and reduced to the vector Hilbert problem. By solving the problem, a closed form solution for the stress intensity and electric displacement intensity factor is obtained. This solution can be used as a Green’s function for different loading conditions.