A load simulation method of piezoelectric actuator in FEM for smart structures

More and more piezoelectric materials and structures have been used for structure control in aviation and aerospace industry. More efficient and convenient computation method for large complex structure with piezoelectric actuation devices is required. A load simulation method of piezoelectric actuation is presented in this paper. By this method, the freedom degree of finite element simulation is significantly reduced, the difficulty in defining in-plane voltage for multi-layers piezoelectric composite is overcome and the transfer computation between material main direction and the element main direction is simplified. The concept of simulation load is comprehensible and suitable for engineers of structure strength in shape and vibration control, thereby is valuable for promoting the application of piezoelectric material and structures in practical aviation and aerospace fields.

Experimental Validation of Improving Aircraft Rolling Power Using Piezoelectric Actuators

Piezoelectric actuators are mounted on both sides of a rectangular wing model. Possibility of the improvement of aircraft rolling power is investigated. All experiment projects, including designing the wind tunnel model, checking the material constants, measuring the natural frequencies and checking the effects of actuators, guarantee the correctness and precision of the finite element model. The wind tunnel experiment results show that the calculations coincide with the experiments. The feasibility of fictitious control surface is validated.

Effective properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading

The material response and failure mechanism of unidirectional metal matrix composite under impulsive shear loading are investigated in this paper. Both experimental and analytical studies were performed. The shear strength of unidirectional C-f/A356.0 composite and A356.0 aluminum alloy at high strain rate were measured with a modified split Hopkinson torsional bar technique. The results indicated that the carbon fibers did not improve the shear strength of aluminum matrix if the fiber orientation aligned with the shear loading axis. The microscopic inspection of the fractured surface showed a multi-scale zigzag feature which implied a complicated shear failure mechanism in the composite. In addition to testing, the micromechanical stress field in the composite was analyzed by the generalized Eshelby equivalent method (GEEM). The influence of cracking in matrix on the micromechanical stress field was investigated as well. The results showed that the stress distribution in the composite is quite nonhomogeneous and very high shear stress concentrations are found in some regions in the matrix. The high shear stress concentration in the matrix induces tensile cracking at 45 degrees to the shear direction. This in turn aggravates the stress concentration at the fiber/matrix interface and finally leads to a catastrophic failure in the composite. From the correlation between the analysis and experimental results, the shear failure mechanism of unidirectional C-f/A356.0 composite can be elucidated qualitatively.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

Experimental Studies of the Material Properties of the Forewing of Cicada (Homoptera, Cicadidae)

Detailed investigations on the structural and mechanical properties of the forewing of the cicada were carried out. Measurement of the structures of the wings showed that the thickness of the membrane of each cell and the diameter of each vein were non-uniform in both the longitudinal and transverse directions, and their means were approximately 12.2 and 133.3 mum, respectively. However, the aspect ratios of the wings and the bodies were quite uniform and were approximately equal to 2.98 and 2.13, respectively. Based on the measured thickness, mass and area of the membranes of the cells, the mean density and the mean area density of the wing were approximately 2.3 g cm(-3) and 2.8 x 10(-3) g cm(-2), respectively. In addition, the diameters of the veins of the wings, including the diameters of the holes in the vein of the leading edge, were examined. The mechanical properties of the wing were investigated separately by nanoindentation and tensile testing. The results indicated that the mean Young's modulus, hardness and yield stress of the membranes of the wings were approximately 3.7 Gpa, 0.2 Gpa and 29 Mpa, respectively, and the mean Young's modulus and strength of the veins along the direction of the venation of wings were approximately 1.9 Gpa and 52 Mpa, respectively. Finally, the relevant results were briefly analyzed and discussed, providing a guideline to the biomimetic design of the aerofoil materials of micro air vehicles.

Determination of Proper Processing Conditions of Material Surface Heat Treatment Through Finite Element Method

A two-dimensional model has been developed based on the experimental results of stainless steel remelting with the laminar plasma technology to investigate the transient thermo-physical characteristics of the melt pool liquids. The influence of the temperature field, temperature gradient, solidification rate and cooling rate on the processing conditions has been investigated numerically. Not only have the appropriate processing conditions been determined according to the calculations, but also they have been predicted with a criterion established based on the concept of equivalent temperature area density (ETAD) that is actually a function of the processing parameters and material properties. The comparison between the resulting conditions shows that the ETAD method can better predict the optimum condition.

Improvement of Aircraft Rolling Power by Use of Piezoelectric Actuators

Piezoelectric actuators are distributed on both side of a rectangular wing model,and the possibility of improvement of aircraft rolling power is investigated. The difference between the model with aileron deflection and the model without aileron (fictitious control surface, FCS) is studied. The analytical results show that these two cases are substantial different. In aileron deflection case, the aeroelastic effect is disadvantageous, so the structural stiffness should be high until the electrical voltage is not necessary. But in the case of FCS,the aeroelastic effect is advantageous and it means that lower structural stiffness can lead to lower voltage. Compared with aileron project, the FCS project can save structure weight.

Static shape control of repetitive structures integrated with piezoelectric actuators

In this paper, several simplification methods are presented for shape control of repetitive structures such as symmetrical, rotational periodic, linear periodic, chain and axisymmetrical structures. Some special features in the differential equations governing these repetitive structures are examined by considering the whole structures. Based on the special properties of the governing equations, several methods are presented for simplifying their solution process. Finally, the static shape control of a cantilever symmetrical plate with piezoelectric actuator patches is demonstrated using the present simplification method. The result shows that present methods can effectively be used to find the optimal control voltage for shape control.

Elastic Waves in a Hybrid Multilayered Piezoelectric Plate

An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a hybrid multilayered piezoelectric plate. In this method, the multilayered piezoelectric plate is divided into a number of layered elements with three-nodal-lines in the wall thickness, the coupling between the elastic field and the electric field is considered in each element. The associated frequency dispersion equation is developed and the phase velocity and slowness, as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. Examples provide a full understanding for the complex phenomena of elastic waves in hybrid multilayered piezoelectric media.

Influences of strain rate and temperature variation on material intrinsic length of plasticity strain gradient theory

Cowper-Symonds and Johnson-Cook dynamic constitutive relations are used to study the influence of both strain rate effect and temperature variation on the material intrinsic length scale in strain gradient plasticity. The material intrinsic length scale decreases with increasing strain rates, and this length scale increases with temperature.

Three-Dimensional Modeling of Heat Transfer and Fluid Flow in Laminar-Plasma Material Re-Melting Processing

Modeling study is performed concerning the heat transfer and fluid flow for a laminar argon plasma jet impinging normally upon a flat workpiece exposed to the ambient air. The diffusion of the air into the plasma jet is handled by using the combined-diffusion-coefficient approach. The heat flux density and jet shear stress distributions at the workpiece surface obtained from the plasma jet modeling are then used to study the re-melting process of a carbon steel workpiece. Besides the heat conduction within the workpiece, the effects of the plasma-jet inlet parameters (temperature and velocity), workpiece moving speed, Marangoni convection, natural convection etc. on the re-melting process are considered. The modeling results demonstrate that the shapes and sizes of the molten pool in the workpiece are influenced appreciably by the plasma-jet inlet parameters, workpiece moving speed and Marangoni convection. The jet shear stress manifests its effect at higher plasma-jet inlet velocities, while the natural convection effect can be ignored. The modeling results of the molten pool sizes agree reasonably with available experimental data.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).