Efficient modeling of smart piezoelectric composite laminates: a review

Current research issues in the development of efficient analysis models and their efficient numerical implementation for smart piezoelectric laminated structures are discussed in this paper. The improved zigzag theories with a layerwise quadratic variation of electric potential have emerged as the best compromise between accuracy and cost for hybrid composite, sandwich and FGM beams and plates. The concept of associating surface potentials to electric nodes and internal potentials to physical nodes is very effective in modeling the equipotential electroded surfaces. Unified formulations for shear and extension mode actuation, and modeling of piezoelectric composite actuators and sensors are discussed. Future challenge lies in developing efficient theories capable of predicting the interlaminar transverse shear stresses in hybrid laminates directly from the constitutive equations.     

Functional composites for sensors,actuators and transducers

Following the trend in structural applications, composite structures are being used more commonly in transducer applications to improve acoustic, mechanical and electrical performance of piezoelectric devices. Functional composite transducers for actuators and sensors generally consist of an active ceramic phase incorporated with a passive polymer phase, each of which has a phase transition associated with it. In this paper, several polymer–piezoelectric ceramic composite transducers, mostly designed for sensing hydrostatic waves, are discussed based on the connectivity of the constituent phases. Also discussed are some recent examples of metal–ceramic composites, and single element ceramic transducers with modified shapes for improved performance. A comparison of these designs is given based on their hydrophone figure of merit (d_h·g_h).     

A gradientless technique for optimal distribution of piezoelectric material for structural control

Application of smart piezoelectric materials in structural control is gaining momentum. Optimum placement and actuation of the smart material is an aspect of paramount importance in such structures. In this paper, we present an iterative technique to optimize the shape of piezoelectric actuators in order to achieve the desired shape of the structure. A C₀‐continuous eight‐node plate finite element with five degrees of freedom is employed. A gradientless shape design procedure based on the residual voltages is developed. It aims at minimizing the quadratic measure of the global displacement residual error between the desired and the current structural configuration. The actuators gradually adapt to a shape that is most efficient in resisting the external excitation. The present technique can be well suited for any static and time‐varying excitation. In vibration control it is often necessary to create modal sensors and actuators in order to observe or excite some specific modes. Such modal sensors and actuators alleviate spillover problems and thus they avoid exhaustive signal processing. Several numerical examples for static as well as dynamic cases are presented to demonstrate the efficacy of the present technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical modelling of piezoelectric actuators exposed to hydrogen

Modern fuel injectors have been developed based on piezoelectric stack actuators. Performance and durability of actuators in a hydrogen environment are important considerations in the development of hydrogen injectors. 2D plane stress and 3D models for analysis of coupled diffusion and thermo-electromechanical response of actuators are presented. Chemical potential, electric field and temperature gradients are taken as driving forces for hydrogen transport. The explicit Euler finite difference method is used to solve the nonlinear diffusion governing equation. The finite element method is used for time-dependent analysis of fully coupled mechanical, electric and thermal fields. The diffusion process and thermo-electromechanical deformations are coupled through the dependence of piezoelectric properties on hydrogen concentration. Experimental results for the piezoelectric coefficient d ₃₃ of PZT ceramics exposed to different hydrogen concentrations are used. A comparison of a fully coupled 2D model with 2D and 3D models with reduced coupling is made to examine the significance of coupling and computational efficiency. Selected numerical results are presented for time histories of hydrogen concentration, temperature and stroke of an idealized actuator unit cell to obtain a preliminary understanding of the performance of actuators exposed to hydrogen.     

Finite element formulation for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems

A finite element algorithm has been developed for the efficient analysis of smart composite structures with piezoelectric polymer sensors or/and actuators based on piezoelectro‐hygro‐thermo‐viscoelasticity. Variational principles for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems have also been proposed in this study. As illustrative studies, dynamic responses in laminated composite beams and plates with PVDF sensors and actuators are obtained as functions of time using the present finite element procedures. The voltage feedback control scheme is utilized. The proposed numerical method can be used for analysing problems in the design of smart structures as well as smart sensors and actuators. Copyright © 1999 John Wiley & Sons, Ltd.     

Hybrid‐stabilized solid‐shell model of laminated composite piezoelectric structures under non‐linear distribution of electric potential through thickness

Eighteen‐node solid‐shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. The explicit hybrid stabilization method is employed to formulate stabilization vectors for the uniformly reduced integrated 18‐node three‐dimensional composite solid element. Unlike conventional piezoelectric elements, the concept of the electric nodes introduced in this paper can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the non‐linear distribution of electric potential in the piezoelectric layer is expressed by introducing internal electric potential, which not only can simplify modelling but also obtains the same as the exact solution. Copyright © 2003 John Wiley & Sons, Ltd.     

Recent progress in bismuth-based high Curie temperature piezo-/ferroelectric perovskites for electromechanical transduction applications

Piezo-/ferroelectric materials with high Curie temperature (T_C) are widely needed in sensors, actuators and transducers which can be used for high-temperature (HT) electromechanical transduction applications. In recent years, remarkable progress has been made in bismuth-based piezo-/ferroelectric perovskite materials (BPPs). In this article, recent progress in high T_C BPPs is reviewed. This review starts with an introduction to HT piezoelectrics and their applications. A detailed survey is then carried out on bismuth-based perovskites (BPs) with high T_C. Material synthesis, doping effects and chemical modifications of the related solid solutions are examined. Based on this analysis, the structure–property relationship of these materials is established. In addition, recent developments of BPPs for HT electromechanical transduction applications are presented and evaluated. Lastly, some main existing issues are analyzed and their possible solutions are proposed. This article provides a comprehensive overview of the research and development of BPPs and offers some prospects towards making these materials a viable resource for the design and fabrication of electromechanical transducers with unique specifications, especially, high temperature, high frequency and high power, for a wide range of technological applications.     

Coupled three‐layered analysis of smart piezoelectric beams with different electric boundary conditions

This paper presents a theoretical and finite element (FE) formulation of a three‐layered smart beam with two piezoelectric layers acting as sensors or actuators. For the definition of the mechanical model a partial layerwise theory is considered for the approximation of the displacement field of the core and piezoelectric face layers. An electrical model for different electric boundary conditions (EBC), namely, electroded layers with either closed‐ or open‐circuit electrodes with electric potential prescribed or layers without electrodes, is considered. Using a variational formulation, the direct piezoelectric effect for the different EBC is physically incorporated into the mechanical model through appropriate approximations of the electric field in the axial and transverse directions. An FE model of a three‐layered smart beam with different EBC is proposed considering a fully coupled electro‐mechanical theory through the use of effective stiffness parameters and a modified static condensation. FE solutions of the quasi‐static electrical and mechanical actuations and natural frequencies are presented. Comparisons with numerical FE and analytical solutions available in the literature demonstrate the representativeness of the developed theory and the effectiveness of the proposed FE model for different EBC. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of active damping in composite laminate cylindrical shells of revolution with skewed PVDF sensors/actuators

Active damping in a FRP composite cylindrical shell with collocated piezoelectric sensors/actuators is studied. The electrode on the sensors/actuators are spatially shaped to reduce spillover between circumferential modes. A three noded, isoparametric, semianalytical finite element is developed and used to model the cylindrical shell. The element is based on a mixed piezoelectric shell theory which makes a single layer assumption for the displacements and a layerwise assumption for the electric potential. The effects of location of patch of collocated piezoelectric sensors/actuators, percentage length of the shell covered with these patches, fiber angle of the laminae in the composite laminate, stacking sequence of laminae in a laminate and skew angle of the sensor/actuator piezoelectric material, on the system damping for various modes is studied.     

Development of PZT powders by wet chemical method and fabrication of multilayered stacks/actuators

Lead zirconate titanate (PZT) compositions near morphotropic phase boundary (MPB) Pb(Zr_xTi_1−x)O₃, 0.48≤ x ≤0.54, were prepared by wet chemical route using water soluble precursors. Compositions were prepared with donor dopants, such as La³⁺, Nd³⁺ or their combinations. The combined hydrous precursors were calcined in the temperature range of 750–900 °C. From the X-ray diffraction (XRD) patterns of calcined PZT powders, a change of tetragonal to rhombohedral phase was noticed with increase in zirconia concentration from 0.48 to 0.54 mol. Both rhombohedral and tetragonal phases were found in the composition range of 0.52–0.54 mol ratios of zirconia, therefore, this range was identified as MPB composition. Calcined PZT powders were compacted and sintered at 1250 °C/2 h in a closed lead rich atmosphere. The sintered compacts were leveled, polished, electroded and the ferroelectric and dielectric properties were measured. After poling, piezo properties were also measured. In case of undoped samples, it was observed that remnant polarization (P_r), dielectric constant (K) and piezoelectric charge constant (d₃₃) increase with zirconia concentration. In general, the above properties increase substantially by addition of dopants at low concentrations. The increase was found more for lanthanum doped samples compared to neodymium. The d₃₃ value for the combined dopants of lanthanum and neodymium was in between the values obtained for individual dopants of the same concentration. A few multilayered (25 layers) stacks were fabricated using thin strips cut from the sintered blocks of the above powders. The strips were electroded and poled in a dc field of 2 kV/mm and were laminated into multilayered stacks. The free strain of the multilayered stacks was measured by applying a dc voltage up to 650 V. The free strain was found to be linear and 0.1% of the height of the stack.     

Estimation of Ct parameter in transversely isotropic materials under transient creep conditions

The crack growth life assessment procedures at high temperature developed for isotropic materials need to be extended for anisotropic creeping materials. In this study, estimation of C_t in transversely isotropic creeping materials is proposed. Equivalent creep coefficient (A_eq) is defined for the transversely isotropic materials and its calculation equation is derived in terms of the ratio between the longitudinal and the transverse creep coefficients. A series of finite element analysis was conducted and values of correction factors required in calculating C_t were determined in tabular form. The newly proposed equation gave the same C_t values as the finite element results under the full range of the creep conditions including the small scale creep.     

Finite element-computation of the electromechanical J-Integral for 2-D and 3-D crack analysis

Piezoelectric ceramics find an application in many fields of technology. They may serve as sensors or actuators, mostly beeing exposed to high electric and mechanical loads. Therefore, fracture mechanics of piezoelectrics is an important field preserving strength and reliability under different conditions of application. This paper deals with the calculation of electromechanical energy release rates for arbitrary cracks in spatial piezoelectric structures applying a generalized J-integral. The crack problem is solved using a commercial FEM-code obtaining electric and mechanical field variables in nodes and integration points. These results serve as input data for the numerical computation of the electromechanical J-integral. The results are compared to findings from analytical and alternative numerical methods.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Microfiber SMPU film affords quicker shape recovery than the bulk one

Comparing to the bulk SMPU (shape memory polyurethane) film, microfiber SMPU film afforded much quicker and sharper shape recovery when heated in water bath. The shape recovery of the microfiber film only took ~ 1/4 time of that needed for the bulk film from R_r (shape recovery ratio) = 10% to R_r = 90%. The final R_r and R_f (shape fix ratio) of the microfiber film was also enhanced. The microfiber film was fabricated by electrospinning with the fiber diameter of 200 nm to 1 μm. DSC and DMA results indicate that the formation of microfiber has very limited effect on the T_trans (switching temperature) of the SMPU. The quick shape recovery of the microfiber SMPU film is considered due to the higher surface area of microfiber film that is favorable for quicker heating/cooling of the sample and quicker diffusion of water. This study offers a possible way to improve the shape recovery speed without changing the chemical composition, which may meet special needs for sensors or actuators of biomedical devices and others.     

Titanium dioxide thin films for high temperature gas sensors

Titanium dioxide (TiO₂) thin film gas sensors were fabricated via the sol-gel method from a starting solution of titanium isopropoxide dissolved in methoxyethanol. Spin coating was used to deposit the sol on electroded aluminum oxide (Al₂O₃) substrates forming a film 1 μm thick. The influence of crystallization temperature and operating temperature on crystalline phase, grain size, electronic conduction activation energy, and gas sensing response toward carbon monoxide (CO) and methane (CH₄) was studied. Pure anatase phase was found with crystallization temperatures up to 800 °C, however, rutile began to form by 900 °C. Grain size increased with increasing calcination temperature. Activation energy was dependent on crystallite size and phase. Sensing response toward CO and CH₄ was dependent on both calcination and operating temperatures. Films crystallized at 650 °C and operated at 450 °C showed the best selectivity toward CO.     

Process-induced strains in RTM processing of polyurethane/carbon composites

The development of residual strains and stresses is critical to manufacture composite structures with the required dimensional stability and mechanical performance. This work uses Fiber Bragg Grating (FBG) sensors to monitor strain build-up in carbon fiber composites with a polyurethane (PU) matrix designed for high production volume applications. The PU matrix presents an initially low viscosity combined with a fast cure reaction, which makes it adequate to very short processing cycles. FBG sensors were incorporated into PU-matrix composites manufactured by vacuum assisted resin transfer molding (VARTM). The measured strains were compared with those obtained with different benchmark epoxy-matrix composites and with those obtained through micromechanical finite element simulations. Results showed that most of the residual strains were built-up during cool-down from the post-curing temperature and that stresses in the PU-matrix composites were comparable to those obtained for epoxies with similar T_g.     

Tailoring Thin‐Film Piezoelectrics for Crash Sensing

Crash sensing and its assessment play a pivotal role in autonomous vehicles for preventing fatal casualties. Existing crash sensors are severely bottlenecked by sluggish response time, rigid mechanical components, and space constraints. Miniaturized sensors embedded with custom‐tailored nanomaterials upholds potential to overcome these limitations. In this article, piezoelectric Zinc‐Oxide thin film as a crash sensing layer is integrated onto a flexible metal‐alloy cantilever. Material characterization studies are conducted to confirm piezoelectric property of sputtered ZnO film. The piezoelectric d ₃₁ coefficient value of ZnO film was 7.2 pm V^–1. The ZnO sensing element is firmly mounted on a scaled car model and used in a crash sensing experimental set‐up. A comprehensive theoretical analysis for two different real scenarios (nearly elastic and nearly inelastic collision) of crash events followed by experimental study is discussed. The crash sensor's output exhibits a linear relationship with magnitude of impact forces experienced at crash events. The response time of ZnO crash sensor is 18.2 ms, and it exhibits a sensitivity of 28.7 mV N^–1. The developed crash sensor has potential to replace bulk material sensors owing to its faster response time, high sensitivity, and compactness as the demand for crash sensors in next‐generation automobile industries is progressively growing.     

Biomimetic electro-active polymer based on sulfonated poly (styrene-b-ethylene-co-butylene-b-styrene)

Based on the sulfonated poly (styrene-b-ethylene-co-butylene-b-styrene) ionic membrane, a novel electro-active polymer, which can be used as sensors and actuators, was developed through the electroless plating procedure. The surface and cross-sectional morphologies of the SSEBS actuator were disclosed by using scanning electron microscope and transmission electron microscopy. The electromechanical results of the SSEBS actuators show high-speed bending actuation under constant voltages and also give excellent harmonic responses under sinusoidal excitation. In the voltage-current test, the electrical current is almost synchronous with the applied voltages, while the mechanical displacement shows high phase shift from the voltage signals. The SSEBS-based ionic polymer-metal composite can be a promising smart material and may possibly be used to implement biomimetic motion.     

Analysis of adaptive shell structures using a refined laminated model

This work presents the development of a shell conical panel finite element model, which has the possibility of having embedded piezoelectric actuators and/or sensors patches. A mixed laminated theory is used, which combines an equivalent single layer higher order shear deformation approach for the mechanical behavior with a layerwise representation in the thickness direction to describe the distribution of the electric potential in each of the piezoelectric layers of the finite element. The electrical potential function is represented through a linear variation across the thickness with two electric potential nodes for each piezoelectric layer. Based in this model an active damping scheme applied to laminated shell structures is presented and discussed.     

Fracture assessment of damaged square hollow section (SHS) K-joint using BS7910:2005

A pre-cracked square hollow section K-joint was tested under static loads up to failure. It is found that the load-displacement curves are in good agreement with the finite element results. Ductile tearing was observed to initiate from the crack front parallel to the chord side wall where fracture toughness is smaller. Using plastic collapse load obtained via twice elastic compliance technique and fracture toughness obtained from crack tip opening displacement, the two fracture parameters K_r and L_r are plotted on the standard failure assessment diagram. It shows a conservative assessment for the cracked K-joint subjected to brace end axial loads.