Cyclic Electric Loading Research Articles

Fatigue crack growth mechanism in ferroelectric ceramics under alternating electric field: An investigation by digital image correlation technique

The deformation of crack tip in PZT ceramics under cyclic electric field loading was characterized by Digital Image Correlation (DIC) technique. Two other specimens without speckles were used to observe the physical processes during the crack propagation in-situ. The deformation of the region of interest is elucidated. Near the U-shaped notch, the DIC results directly reveal the existence of incompatible deformation. However, in the front of the newly formed crack, no incompatible deformation was observed. Additionally, in-situ observation reveals that, the crack growth occurs at the stage of crack closure when the crack propagates steadily. The observed pop-in behavior of the crack during the first cycle of electric field loading is rationalized by the interaction between the incompatible domain switching zones with and without U-shaped notch, which is consistent with the explanation of Westram et al. The subsequent crack propagation after the pop-in cannot be rationalized by the model exploited by Zhu and Yang, Westram et al., and Liu and Fang, which is thought to be related to three different factors – arcing, wedging and grain-to-grain interaction. The mechanism for the appearance and the disappearance of the incompatible domain switching zone near the U-shaped notch and around the tip of the newly formed crack is discussed based on the electrical boundary condition (EBC) of the crack surfaces we proposed recently.

Crack propagation induced by incompatible domain switching in BaTiO3 crystal under electric field loading

Using a system composed of a polarized light microscopy and a charge coupled device (CCD), the crack propagation behavior in BaTiO3 (BTO) crystal under electric field was in situ investigated with the field direction parallel or perpendicular to the crack surface. In addition, the growth behavior of Vickers indentation surface cracks under alternating electric field was also in situ investigated. Three crack propagation modes induced by incompatible domain switching were proposed based on our observation. The electrical boundary condition of the crack surface was also characterized by measuring and comparing the hysteresis loop of a perfect BTO crystal without crack and a BTO crystal completely fractured in half. Results demonstrate that the electrical boundary condition of a fresh natural crack is permeable, and evolves from permeable to partial permeable during cyclic electric field loading.

Fracture and electric‐field‐induced crack growth behavior in NBT‐6BT relaxor ferroelectrics

AbstractThe fracture properties of 0.94(Na0.5Bi0.5)TiO3‐0.06BaTiO3 (NBT‐6BT) relaxor ferroelectrics were investigated using the Vickers indentation method and computation of crack tip opening displacement. It was found that an unpoled sample had a fracture toughness of around 1.35 MPa m1/2. In contrast, an electrically poled sample exhibited anisotropy with a lower fracture toughness perpendicular to the poling direction and a higher value in the parallel direction, as compared to the unpoled sample. Upon cyclic electrical loading (with applied electric field amplitudes between 0.73EC and 1.4EC), the indented surface crack was found to propagate. In general, the crack grew rapidly during the initial cycles followed by crack arrest, and the principal driving force for crack growth was proposed to be residual stress around the indentation, as evidenced by the limited field dependence of crack growth. There was also a contribution from the electromechanical strain, which played a role at high cycles (>100 cycles) and high fields (>1.3 EC). Evidence of a saturation threshold of crack propagation is an advantage for the electromechanical reliability of relaxor ferroelectrics in devices.

Reinvestigation on polarization and strain response of electrically poled lead titanate zirconate ceramics under low-to-medium electric field loading

The polarization and strain response of electrically poled lead zirconate titanate ceramics was reinvestigated under low-to-medium electric field loading. A phenomenon that is usually ignored was pointed out and discussed. That is, under low-to-medium cyclic electric field loading, remnant strains measured under a negative electric field loading are larger than those measured under a positive electric field loading. Here, ‘positive’ and ‘negative’ mean that the applied electric field is aligned or antiparallel to the pre-poling direction of the material, respectively. Moreover, a reverse trend was observed for remnant polarizations. Texture-dependent domain switching, defect dipole reorientation, and interactions between them were used to rationalize this phenomenon. In addition, the equation which is used to describe the strain response, was modified by taking the asymmetry of the electric field versus strain curve into consideration. The modified equation can better describe the strain response than the original equation.

Design of twisted conjugated molecular systems towards stable multi-colored electrochromic polymers

Promising advancement of conjugated polymers in electrochromic devices require to design high-performance electrochromic polymers with rich color conversion and long-term stability under cyclic electrical loads. Here we report a new strategy in developing multi-colored electrochromic polymers with good stability via twisted conjugated molecular engineering. A series of twisted hybrid precursors are synthesized by coupling ortho-alkylenedioxybenzenes with EDOT units, and their corresponding polymers are facilely electrosynthesized at relatively low polymerization potentials. The structure-property relationships of such ortho-alkylenedioxybenzene-EDOT hybrid precursors and polymers are systematically elucidated via DFT calculations, spectral, morphological, electrochemical and spectroelectrochemical analysis, etc. We demonstrate that the dihedral angle between ortho-alkylenedioxybenzenes and EDOT moieties can substantially affect the electrochemical and electrochromic properties of polymers. As the dihedral angle and electron cloud density increases, these hybrid polymers display distinct multiple color switching nature and good overall performance including high coloration efficiency (>200 cm2 C−1), decent optical contrast (>45%), fast switching (<1 s), and excellent switching stability (96% of optical contrast after 3500 cycling) under cyclic electrical loads. With these findings, this work will provide novel insights for rational design of stable and highly efficient multi-colored electrochromic polymers.

Electrical fatigue in 0.94Na0.5Bi0.5TiO3–0.06BaTiO3: Influence of the surface layer

Similar to several Pb-based relaxor ferroelectrics, 0.94Na0.5Bi0.5TiO3–0.06BaTiO3 is reported to have a micrometer-sized surface layer. We hypothesize that since this layer has structural properties distinct from the bulk, it would undergo a different property degradation than the bulk during cyclic electrical loading or fatigue. First, we show the existence of a surface layer by comparing X-ray diffraction patterns of the ceramic surface and powders. Then, we show that fatigue damage is mainly localized in the surface layers, and thus, property degradation due to fatigue can be recovered on removing the affected surface layer. We also show that ion migration may be occurring in the surface layer during fatigue experiments using secondary ion mass spectroscopy, where the ion sources may be the sample itself, the electrode layer or the insulating oil in which the experiment is performed. Finally, we show that permanent fatigue damage such as microcracks is dependent on the choice of electrodes. While permanent damage was observed for Pt electrodes, it was not present for oxide electrodes, suggesting that oxygen permeation and accumulation at the electrode/surface interface may play a role in the formation of observed microcracks. In summary, we have shown that fatigue is influenced by the surface layer, and surface layer damage can be controlled using the selection of electrodes.

Deterministic Role of Carbon Nanotube-Substrate Coupling for Ultrahigh Actuation in Bilayer Electrothermal Actuators.

Here, the actuation response of an architectured electrothermal actuator comprising a single layer of carbon nanotube (CNT) film and a relatively thicker film of silk, cellulose, or polydimethylsiloxane is studied. An electric current is passed through the CNT film, which generates heat responsible for electrothermal actuation, in all samples, affixed as per doubly clamped beam configuration. All samples, including pure CNT film, show remarkable actuation such that actuation monotonically increases with the applied voltage. Cyclic pulsed electrical loading shows a lag in the electric current stimulus and the actuation. Remarkably, an ultrahigh actuation of ∼2.8%, which was 72 times more than that shown by pure CNT film, is measured in the CNT-cellulose film, that is, the architectured actuator with the natural polymer having the functional property of hygroexpansion and the structural hierarchy of the CNT film, however, at a significantly larger length scale. Overall, the synergetic contribution of the individual layers in these bilayered actuators enabled achieving ultrahigh electrothermal actuation compared to the homogeneous, synthetic polymer-based devices. A detailed discussion, which also includes examination of the role of the hierarchical substructure and the functional properties of the substrate and numerical analysis using the finite element method, is presented to highlight the actuation mechanism in the fabricated actuators.

A semi-analytical scale bridging approach towards polycrystalline ferroelectrics with mutual nonlinear caloric-electromechanical couplings

Various caloric aspects of polycrystalline ferroelecrics are investigated, based on an efficient modelling approach. In this context, both linear reversible effects, leading to heating or cooling of the material, and nonlinear dissipation heating, being associated with ferroelectric domain switching, are considered. The semi-analytical approach focusses on the constitutive behavior of a polycrystalline representative volume element (RVE) under the impact of combined electromechanical loadings, incorporating mutual interactions of caloric and electromechanical fields within a framework of non-equilibrium thermodynamics. Temperature dependence of material coefficients is further taken into account. The so-called condensed method (CM) is employed to bridge the scales of domain wall motion within grains and grain interaction in the RVE. Results are compared to those of finite element simulations and experiments taken from literature, illustrating hysteresis loops and dissipation heating due to cyclic electrical loading. Additional findings illuminate the role of mechanical compression during electric cycling, behaviors of single vs. polycrystals, and separate the impacts of linear and nonlinear caloric effects.

Tuning optoelectronic performances for 3-methylselenophene-EDOT hybrid polymer

Rational design of novel high-performance conjugated polymers is still central to the field of polymer electrochromics. In this work, a novel 3-methylselenophene-EDOT hybrid polymer is designed and electrosynthesized from the molecular precursor of 3-methylselenophene end-capped with 3,4-ethylenedioxythiophene (EDOT). The structural characterization, physicochemical properties, micromorphology, electrochemical behaviors, and electrochromic performance are systematically explored to reveal the structure-property relationship of both the precursor and the hybrid polymer. The precursor with planar structure exhibits a much lower onset oxidation potential (0.5 V) than that of both 3-methylselenophene (1.17 V) and EDOT (1.23 V). Low-potential electropolymerization yields smooth and compact hybrid polymer film with high conductivity (10−1 S cm−1) and excellent electrochemical stability under cyclic electrical loads. The 3-methylselenophene-EDOT hybrid polymer also exhibits the obvious color changes from brownish yellow in the reduced to transparent sky blue upon oxidization with favorable optical contrast (39%, 990 nm), high coloration efficiency (161 cm2/C) and fast response time (1.3 s) under low switching voltages.

A micro–macro scale approach for thermal effects in ferroelectrics

The influence of thermal fields on the electromechanical behavior of ferroelectric ceramics under cyclic electric loading is presented. To predict the temperature effect, a 3D micromechanical model for tetragonal domain switching is extended by including thermal effects. Numerical simulations were done through the finite element program Abaqus with the help of a user-defined element. Besides external heat sources, a change in temperature is considered by internal heat generated due to domain switching. Material properties are assumed to be linearly dependent on the temperature. The temperature influence on the behavior of ferroelectrics is shown by means of the strain and polarization hysteresis loops. The model shows a good qualitative agreement with the experimental results available in the literature.

Effects of polymeric filler on polarization fatigue of 1-3 0.74Pb(Mg1/3Nb2/3)O3-0.26PbTiO3 single crystal/polymer composites

Polarization fatigue tests have been conducted on both bulk Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) single crystals and two 1-3 PMN-xPT/polymer composites with both “soft” and “hard” epoxy fillers, respectively. The variations of remnant polarization, coercive electric field, and micro-crack morphology under 10 Hz cyclic electric loading were studied. It was found that the magnitude of coercive field for both composites was higher compared to that of single crystals. However, as the number of cycles increases, the degradation ratio of remnant polarization and the increased portion of coercive field for both composites were lower than that of single crystals; the sequence is PMN-0.26PT bulk single crystal &amp;gt; 1-3 PMN-0.26PT/soft epoxy composites &amp;gt; 1-3 PMN-0.26PT/hard epoxy composites. In addition, the observed micro-crack propagation morphology shows that 1-3 PMN-0.26PT/hard epoxy composites can substantially improve fatigue-resistance owing to the lower stretching strain benefiting from the polymeric filler. Our results indicated that 1-3 PMN-0.26PT/polymer composites present much better electric polarization stability.

Analysis of quantum-dot systems under thermal loads based on gradient elasticity

Since quantum-dot (QD) nanostructures in many applications are subjected to cyclic electrical and thermal loads, it is very important to analyze such nanostructures under transient thermal loads that affect the induced strains which in turn affects the response of the QD system. When the dimensions of the QDs are of the same order of magnitude as the material length scale, gradient elasticity theory should be used to account for the size-dependent behavior of such nano-sized QDs. In this work, a new finite element formulation for gradient-based thermo-electro-mechanical three-dimensional model of strained QDs in piezoelectric matrix under both static and dynamic thermal loads is developed. The proposed formulation requires only C0 shape functions since the original fourth order partial differential equation (PDE) is split into two PDEs of lower order. A unit cell of Indium Arsenide QD in a finite sized Gallium Arsenide (GaAs) substrate is analyzed. Results under dynamic loads demonstrate that the magnitude of the strain component in the thermal loading direction increases significantly with the thermal shock time. On the other hand, at a fixed time, the magnitude of the induced field quantities, such as the strain, decreases remarkably with increasing the size effect parameter. Given that large lattice mismatch induced strain fields are located in or near the QD regions, these newly observed features need to be carefully considered when designing such QD nanostructures.

Simulation of fatigue damage in ferroelectric polycrystals under mechanical/electrical loading

The reliability of smart-structures made of ferroelectric ceramics is essentially reduced by the formation of cracks under the action of external electrical and/or mechanical loading. In the current research a numerical model for low-cycle fatigue in ferroelectric mesostructures is proposed. In the finite element simulations a combination of two user element routines is utilized. The first one is used to model a micromechanical ferroelectric domain switching behavior inside the grains. The second one is used to simulate fatigue damage of grain boundaries by a cohesive zone model (EMCCZM) based on an electromechanical cyclic traction–separation law (TSL). For numerical simulations a scanning electron microscope image of the ceramic’s grain structure was digitalized and meshed. The response of this mesostructure to cyclic electrical or mechanical loading is systematically analyzed. As a result of the simulations, the distribution of electric potential, field, displacement and polarization as well as mechanical stresses and deformations inside the grains are obtained. At the grain boundaries, the formation and evolution of damage are analyzed until final failure and induced degradation of electric permittivity. It is found that the proposed model correctly mimics polycrystalline behavior during poling processes and progressive damage under cyclic electromechanical loading.To the authors’ knowledge, it is the first model and numerical analysis of ferroelectric polycrystals taking into account both domain reorientation and cohesive modeling of intergranular fracture. It can help to understand failure mechanisms taking place in ferroelectrics during fatigue processes.

3D printed electrically-driven soft actuators

Soft robotics is an emerging field enabled by advances in the development of soft materials with properties commensurate to their biological counterparts, for the purpose of reproducing locomotion and other distinctive capabilities of active biological organisms. The development of soft actuators is fundamental to the advancement of soft robots and bio-inspired machines. Among the different material systems incorporated in the fabrication of soft devices, ionic hydrogel–elastomer hybrids have recently attracted vast attention due to their favorable characteristics, including their analogy with human skin. Here, we demonstrate that this hybrid material system can be 3D printed as a soft dielectric elastomer actuator (DEA) with a unimorph configuration that is capable of generating high bending motion in response to an applied electrical stimulus. We characterized the device actuation performance via applied (i) ramp-up electrical input, (ii) cyclic electrical loading, and (iii) payload masses. A maximum vertical tip displacement of 9.78 ± 2.52 mm at 5.44 kV was achieved from the tested 3D printed DEAs. Furthermore, the nonlinear actuation behavior of the unimorph DEA was successfully modeled using an analytical energetic formulation and a finite element method (FEM).

Ferroelectric fatigue mechanism under bipolar electrical loading in KNN lead free piezoelectric ceramic

The effect of bipolar cyclic electrical loading on the ferroelectric and piezoelectric properties of KNN ceramics is investigated. The results showed that the bipolar fatigue leads to a decrease in domain switchability and piezoelectric responses of the ceramic. In the early period of cyclic loading, the fatigue mechanism is dominated by the domain wall pinning effect. When the number of fatigue cycles increases, the microstructural damage has a large impact on the fatigue process. From this, a qualitative model based on the relationship between domain pinning mechanism and internal stress is proposed.

Theoretical modeling and experimental characterization of rate and temperature dependent electromechanical behavior of piezocomposites

Abstract The rate-dependent piezoelectric behavior of 1–3 piezocomposite under thermal environment is presented. Thermo-electromechanical effective properties of 1–3 piezocomposites are evaluated based on the Finite Element (FE) resonant model. The experimentally measured vibration modes for Length Extensional (LE) and Thickness Extensional (TE) resonator model are compared with the simulated results for model validation. A 3D finite element model to predict the non-linear rate-dependent behavior of 1–3 piezocomposite under elevated temperature is proposed. In the present work, the internal variables are considered to be the function of loading rate, to simulate the rate-dependent behavior. The predicted thermo-electromechanical effective properties from the resonant model are used as an input to the proposed non-linear model. The simulation is carried out for various combinations of PZT volume fractions, loading rates, temperatures and compressive prestresses under cyclic electrical loading and validated with the experimental measurements.

Fatigue study on the actuation performance of macro fiber composite (MFC): theoretical and experimental approach

Macro fiber composite (MFC) is extensively used in vibration control and actuation applications due to its high flexibility and enhanced coupling coefficients. During these applications, MFCs are subjected to the continuous cyclic electrical loading, which may lead to the degradation in its actuation performance. In order to predict the life cycle of MFCs, an experimental setup has been devised and experiments are performed under cyclic loading condition. Efforts involved in the experiments are huge in terms of time and cost. Hence, an attempt has been made to develop a theoretical model to predict the fatigue behavior of MFCs. A nonlinear finite element method has been formulated based on Kirchhoff plate theory wherein the fatigue failure criterion based on strain energy is embedded. Simulated results based on the proposed model is compared with experimental observation and are in good agreement with each other. Variation in the life cycle of MFCs are also studied for different operating temperatures as well as structural/geometric configurations.

Modeling of nonlinear behavior of polyrcystalline lead-free piezoceramics with a content of tetragonal, rhombohedral and orthorhombic phases under cyclic loading

The micromechanical model proposed by analogy with crystal visco-plasticity and taking into account the volume fraction of tetragonal, rhombohedral and orthorhombic ferroelectric phases is used for the simulation of hysteresis behavior of lead-free piezoceramics. The model parameters identification is considered and discussed. The results of simulation demonstrate a good agreement with the experimental data for a wide range of cyclic electrical loading amplitudes.

A multi-surface model for ferroelectric ceramics - application to cyclic electric loading with changing maximum amplitude

Depending on the maximum amplitude of externally applied cyclic electric fields, ferroelectric ceramics show minor or major hysteresis. The materials also show asymmetric butterfly hysteresis in a prepoled material. Aiming at capturing these behaviour in a phenomenological constitutive model, a multi-surface modelling approach for ferroelectrics is introduced. In this paper, with the note on the motivation for a multi-surface model related to the results of new experimental investigations and also to experimental data reported in the literature, the constitutive relation for a rate dependent multi-surface ferroelectric model is developed. Following this, a brief graphical illustration shows how this model captures the objective phenomena. Consequently, the numerical implementation of the model to capture experimental results is demonstrated. Finally, the performance of this model to represent behaviour of decaying polarisation offset of electrically fatigued specimen is shown.

Polarization fatigue in ferroelectric Pb(Zr0.52Ti0.48)O3-SrBi2Nb2O9 ceramics

Ferroelectric fatigue induced by cyclic electric loading of the (1-x)PZT-xSBN ceramics (0.1 ≤ x ≤ 0.3) have been investigated in comparison with pure PZT and SBN ceramics. The results showed that pure PZT ceramic possessed severe polarization fatigue after long bipolar switching pulses. This was mainly attributed to the appearance of microstructural damage at the near-electrode regions. Whereas, pure SBN ceramic exhibited no fatigue at least up to 1 × 106 switching cycles. The fatigue-free behavior of SBN ceramics was due primarily to weak domain wall pinning. PZT-SBN ceramics showed less polarization fatigue up to 1 × 106 switching cycles than pure PZT. This could be attributed to their low oxygen vacancy concentration. Therefore, this new ceramic PZT-SBN system seems to be an alternative material for replacing PZT in ferroelectric memory applications.