Analysis of cracked functionally graded piezoelectric strip

AbstractThe fracture behavior of a cracked strip under antiplane mechanical and inplane electrical loading is studied. A functionally graded piezoelectric strip with exponential material gradation is under consideration. The mechanical and electrical loading is combined via loading coupling factor. The problem of a graded piezoelectric strip containing a screw dislocation is solved. This solution results in stress and electric displacement components with Cauchy singularity. Based on the solution achieved for the dislocation, the distributed dislocation technique (DDT) is utilized to form any geometry of multiple cracks and analyze the behavior of a cracked strip under antiplane mechanical and inplane electrical loading. This technique is capable of the analysis of a strip with a system of interacting cracks. Several examples including strips with single crack, two straight cracks and two curved cracks are presented

The extended finite element method with new crack-tip enrichment functions for an interface crack between two dissimilar piezoelectric materials

This paper studies the static fracture problems of an interface crack in linear piezoelectric bimaterial by means of the extended finite element method (X-FEM) with new crack-tip enrichment functions. In the X-FEM, crack modeling is facilitated by adding a discontinuous function and crack-tip asymptotic functions to the classical finite element approximation within the framework of the partition of unity. In this work, the coupled effects of an elastic field and an electric field in piezoelectricity are considered. Corresponding to the two classes of singularities of the aforementioned interface crack problem, namely, E class and class, two classes of crack-tip enrichment functions are newly derived, and the former that exhibits oscillating feature at the crack tip is numerically investigated. Computation of the fracture parameter, i.e., the J-integral, using the domain form of the contour integral, is presented. Excellent accuracy of the proposed formulation is demonstrated on benchmark interface crack problems through comparisons with analytical solutions and numerical results obtained by the classical FEM. Moreover, it is shown that the geometrical enrichment combining the mesh with local refinement is substantially better in terms of accuracy and efficiency.postprin

Linear interface crack under harmonic shear : Effects of crack's faces closure and friction

Peer reviewedPostprin

Scale-dependent fracture in gradient elastic materials

Micro-electromechanical systems (MEMS) and Nano-electromechanical systems (NEMS) have a wide range of applications in aerospace, power industry, automation & robotics, chemical & medical treatment analysis, information technology and in the infrastructure health monitoring equipments. To ensure the reliability of such small devices, the mechanical and hence fracture behaviour of their common building blocks such as beams, tubes, and plates should be carefully evaluated. However, on a smaller scale, the microstructural effects such as size effects, load-induced and geometrically prompted stress singularities are more noticeable, particularly at the micro/nano scale. Classical continuum elasticity theories are inadequate to accurately describe the situations controlled by the microstructure effects since the influence of these effects are not properly accounted for. On the other hand, the higher order gradient theories such as strain gradient theory may effectively describe the effects of microstructure through the solution of properly formulated boundary value problems. Moreover, when dealing with piezoelectric micro/nano materials, due to the presence of massive strain gradient, the electric field-strain gradient coupling (flexoelectricity) should also be considered. The objective of this research is to evaluate the scale-dependent fracture behaviour of gradient elastic materials using strain gradient theory. In particular, two most widely studied geometrical configurations i.e. double cantilever beam (DCB) and centrally cracked material layer are employed in this work. The findings presented in this thesis are expected to give useful insights to those working in the structural integrity analysis at the micro/nano scale. They are anticipated to help in the design of micro/nano structural components and serve as a benchmark for future theoretical and empirical studies

Embedded Piezoelectric Fiber Composite Sensors for Applications in Composite Structures

Health monitoring of the composite structures is an important issue that must be addressed. Embedded sensors could be an effective way to monitor the health of composite structures continuously and which could also avoid the catastrophic failures of composite structures. Piezoelectric-fiber-composite sensors (PFCS) made from micro-sized Lead Zirconate Titanate (PZT) fibers have great advantages over the traditional bulk PZT sensors for embedded sensor applications. PFCS as an embedded sensor will be an ideal choice to continuously monitor the stress/strain levels and health conditions of composites. This work presents a critical study on using PFCS as an effective embedded sensor within the composite structures. Firstly, a series of carefully planned experiments are conducted to study the sensor performance based on characteristics like transfer function, sensitivity, nonlinearity, resolution, and noise levels. A numerical simulation study is performed to understand the local stress/strain field near the embedded sensor region inside composite specimen. High stress-concentration regions are observed near the embedded sensor corner edge. In-plane tensile, in plane tension-tension fatigue, flexural, and short beam strength tests are performed to evaluate the strengths/behavior of the composites (composite laminates and composite sandwich structures) containing embedded PFCS sensor. Overall PFCS seems to have high compatibility with composites and the reduction in strength values are within the permissible limits. Embedded PFCS’s voltage output response under tension-tension fatigue loading conditions has been recorded simultaneously to study their ability to detect the changes in input loading conditions. A linear relationship has been observed between the changes in the output voltage response of the sensor and changes in the input stress amplitude. This means that by constantly monitoring the output response of the embedded PFCS, one could effectively monitor the magnitude of stress/strain acting on the structure. Experiments are also performed to explore the ability of the embedded PFCS to detect the damages in the structures using modal analysis and impact techniques. PFCS are able to detect defects like delamination and cracks inside the composite structure using these two methods. Hence embedded PFCS could be an effective method to monitor the health of the composite structures’ in-service conditions

Analysis of Dynamic Fracture Parameters in Functionally Graded Material Plates with Cracks by Graded Finite Element Method and Virtual Crack Closure Technique

Based on the finite element software ABAQUS and graded element method, we developed a dummy node fracture element, wrote the user subroutines UMAT and UEL, and solved the energy release rate component of functionally graded material (FGM) plates with cracks. An interface element tailored for the virtual crack closure technique (VCCT) was applied. Fixed cracks and moving cracks under dynamic loads were simulated. The results were compared to other VCCT-based analyses. With the implementation of a crack speed function within the element, it can be easily expanded to the cases of varying crack velocities, without convergence difficulty for all cases. Neither singular element nor collapsed element was required. Therefore, due to its simplicity, the VCCT interface element is a potential tool for engineers to conduct dynamic fracture analysis in conjunction with commercial finite element analysis codes

Aerosol-Jet Printed Nanocomposites for Flexible and Stretchable Thermoelectric Generators

Converting waste heat from the environment into usable electricity, via thermoelectric generators (TEGs) based on thermoelectric (TE) materials, is predicted to be one of the most promising renewable energy solutions of the future. TE materials produce a current when subjected to a temperature gradient as a result of the Seebeck effect, and are characterised by a TE figure of merit, ZT = S2σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the operating temperature, and κ is the thermal conductivity. TEGs can be used as an energy source for ‘small-power’ applications, such as wireless sensors and wearable devices. Nonetheless, traditional inorganic TE materials pose significant challenges owing to their high cost, toxicity, scarcity, and brittleness, particularly when it comes to applications requiring flexibility and/or stretchability. On the other hand, organic TE polymers are less expensive, environmentally friendly, and flexible. However, they typically suffer from poor TE performance due to their comparatively low S and σ. This thesis therefore seeks to explore solutions for high-performance and mechanically conformable TEGs based on organic-inorganic TE nanocomposites, adopting a material engineering approach to enhancing TE properties while ensuring the flexibility and/or stretchability of TEGs. In this work, a flexible and robust TEG based on a novel hybrid nanocomposite structure for harvesting energy from low-grade waste heat, has been successfully fabricated via a customised and scalable aerosol-jet printing (AJP) technique. Firstly, Bi2Te3 nanoparticles and Sb2Te3 nanoflakes were fabricated using a solvothermal synthesis approach, and their resulting morphological and microstructural properties were studied. They were then incorporated into a conducting polymer matrix poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) via the AJP method, resulting in well-dispersed TE nanocomposites on flexible polyimide substrates. These TE nanocomposites comprised Bi2Te3/Sb2Te3 nano-inclusions with higher S and σ embedded within a polymeric PEDOT:PSS matrix having lower κ. The compositions were dynamically tuned and controlled by the in-house developed in situ mixing method to optimise the resulting power factor (PF = S2σ). The AJP technique used in this work allows functional materials to be printed from inks with a wide range of viscosities and constituent particle sizes and shapes. The morphological and TE properties of AJ-printed nanocomposite structures were then evaluated as a function of the composition so that optimum ink formulation and printing conditions could be found to maximise the final TE performance. Importantly, these TE nanocomposites were found to be particularly stable and robust upon repeated flexing. They can be directly integrated into high-performance TEGs with minimal post-possessing treatment, making them particularly suitable for flexible TE applications. Subsequently, multiwall carbon nanotubes (MWCNTs) were introduced to enhance σ of AJ-printed nanocomposites, thereby achieving even higher PF values. A novel in situ mixing method was capable of simultaneously incorporating high-S Sb2Te3 nanoflakes and high-σ MWCNTs that could provide good inter-particle connectivity, to significantly enhance the TE performance of PEDOT:PSS. Rigorous flexing and fatigue tests also confirmed the excellent mechanical robustness and stability of these AJ-printed MWCNTs-based TE nanocomposites. The added MWCNTs have led to not only higher σ, but they also have improved the mechanical flexibility and fatigue robustness of the resulting nanocomposites. Since the ZT and PF of TE materials often have a strong dependence on temperature, a single TE material spanning a given temperature range is unlikely to have an optimal ZT or PF across the entire range, leading to the inefficient TEG performance. The temperature-dependent TE properties of AJ-printed TE nanocomposites were therefore studied as a function of the loading fraction, with a view to enhancing the overall TE performance of a TEG by varying its composition accordingly across a given temperature range. For the first time, compositionally graded thermoelectric composites (CG-TECs) have been developed and shown to improve TE performance over TEGs having a single composition across the same temperature range. The composition of the TE nanocomposite was systematically tuned along the length of the TEG in order to optimise the PF along the temperature gradient between which it operates. Lastly, the AJP technique was used to fabricate free-standing and stretchable TE structures, by printing serpentine patterns of the TE ink onto a sacrificial substrate that was subsequently removed. The TE performance and stretchability under different imposed mechanical conditions were evaluated, including testing for the reliability of prolonged stretching cycles. The CG-TEC concept was also incorporated into the stretchable structure to achieve further improvement of TE performance.China Scholarship Council and Cambridge Commonwealth, European and International Trus

Fracture analysis of piezoelectric composites using scaled boundary finite element method

Piezoelectric materials are widely used as sensors, actuators and transducers owing to the intrinsic mechanical and electrical coupling behavior. In most applications, piezoelectric materials are usually layered with substrates or embedded in a host material. Due to the brittleness and low fracture toughness, they have high tendency to develop cracks, especially under complex mechanical, electrical and thermal loads. In piezoelectric composites, interface cracks and interface debonding may be induced by the high stress concentrations occurring as a result of the mismatch of mechanical and electrical properties between different layers. The increasing use of these materials in modern intelligent material systems emphasizes the importance of the fracture analysis of piezoelectric materials. This thesis develops a novel technique based on the scaled boundary finite element method to analyze fracture problems of piezoelectric composites under static, dynamic and thermal loadings. The scaled boundary finite element equations are derived for piezoelectric materials. In statics, a solution procedure based on matrix functions and the real Schur decomposition is used to solve the scaled boundary finite element equations. The singular stress and electric displacement fields around a crack tip are expressed analytically in the radial direction. Consequently, the generalized stress and electric displacement intensity factors are determined directly from the solution. In dynamics, a continued fraction solution for the scaled boundary finite element equation is presented. The dynamic properties are represented by high order stiffness and mass matrices. This allows the use of efficient time-marching algorithms. Under the thermal loadings, the change in temperature field is obtained using the scaled boundary finite element method. The nodal loads due to the temperature change are treated as a non-homogeneous term in the resulting ordinary differential equations. The particular solution for the non-homogeneous term is expressed as integral in the radial direction. This integral is evaluated analytically leading to a semi-analytical solution for the electromechanical behaviour. Numerical examples are presented to verify the proposed technique with the results from the literature and the numerical results obtained using the commercial software ANSYS. The present results highlight the accuracy, simplicity and efficiency of the proposed technique

Structures Division 1994 Annual Report

The NASA Lewis Research Center Structures Division is an international leader and pioneer in developing new structural analysis, life prediction, and failure analysis related to rotating machinery and more specifically to hot section components in air-breathing aircraft engines and spacecraft propulsion systems. The research consists of both deterministic and probabilistic methodology. Studies include, but are not limited to, high-cycle and low-cycle fatigue as well as material creep. Studies of structural failure are at both the micro- and macrolevels. Nondestructive evaluation methods related to structural reliability are developed, applied, and evaluated. Materials from which structural components are made, studied, and tested are monolithics and metal-matrix, polymer-matrix, and ceramic-matrix composites. Aeroelastic models are developed and used to determine the cyclic loading and life of fan and turbine blades. Life models are developed and tested for bearings, seals, and other mechanical components, such as magnetic suspensions. Results of these studies are published in NASA technical papers and reference publication as well as in technical society journal articles. The results of the work of the Structures Division and the bibliography of its publications for calendar year 1994 are presented

Structural Response Analyses of Piezoelectric Composites using NURBS

Variational method deduced on the basis of the minimum potential energy is an efficient method to find solutions for complex engineering problems. In structural mechanics, the potential energy comprises strain energy, kinetic energy and the work done by external actions. To obtain these, the displacement are required as a priori. This research is concerned with the development of a numerical method based on variational principles to analyze piezoelectric composite plates and solids. A Non-Uniform Rational B-Spline (NURBS) function is used for describing both the geometry and electromechanical displacement fields. Two dimensional plate models are formulated according to the first order shear deformable plate theory for mechanical displacement. The electric potential varies non-linearly through the thickness, this variation is modelled by a discrete layer-wise linear variation. The matrix equations of motion are reported for piezoelectric sensors, actuator, and power harvester. Normal mode summation technique is applied to study the frequency response of displacement, voltage and the power output. A full three dimensional model is also developed to study the dynamics of piezoelectric sandwich structures. Simulations are provided for thick plates using plate theory and three dimensional models to verify the applicability of those theories in their regime. Newmark’s direct integration technique and a fourth order Runge-Kutta method were used to study the transient vibration. The variational method developed in this thesis can be applied to other structural mechanics problem