A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

Behavior of Sandwich Beams With Functionally Graded Rubber Core in Three Point Bending

The three-point bending behavior of sandwich beams made up of jute epoxy skins and piecewise linear functionally graded (FG) rubber core reinforced with fly ash filler is investigated. This work studies the influence of the parameters such as weight fraction of fly ash, core to thickness ratio, and orientation of jute on specific bending modulus and strength. The load displacement response of the sandwich is traced to evaluate the specific modulus and strength. FG core samples are prepared by using conventional casting technique and sandwich by hand layup. Presence of gradation is quantified experimentally. Results of bending test indicate that specific modulus and strength are primarily governed by filler content and core to sandwich thickness ratio. FG sandwiches with different gradation configurations (uniform, linear, and piecewise linear) are modeled using finite element analysis (ANSYS 5.4) to evaluate specific strength which is subsequently compared with the experimental results and the best gradation configuration is presented. POLYM. COMPOS., 32:1541-1551, 2011. (C) 2011 Society of Plastics Engineers

Functionally graded hydroxyapatite-alumina-zirconia biocomposite: Synergy of toughness and biocompatibility

Functionally Gradient Materials (FGM) are considered as a novel concept to implement graded functionality that otherwise cannot be achieved by conventional homogeneous materials. For biomedical applications, an ideal combination of bioactivity on the material surface as well as good physical property (strength/toughness/hardness) of the bulk is required in a designed FGM structure. In this perspective, the present work aims at providing a smooth gradation of functionality (enhanced toughening of the bulk, and retained biocompatibility of the surface) in a spark plasma processed hydroxyapatite-alumina-zirconia (HAp-Al2O3-YSZ) FGM bio-composite. In the current work HAp (fracture toughness similar to 1.5 MPa.m(1/2)) and YSZ (fracture toughness similar to 62 MPa.m(1/2)) are coupled with a transition layer of Al2O3 allowing minimum gradient of mechanical properties (especially the fracture toughness similar to 3.5 MPa.m(1/2)).The in vitro cyto-compatibilty of HAp-Al2O3-YSZ FGM was evaluated using L929 fibroblast cells and Saos-2 Osteoblast cells for their adhesion and growth. From analysis of the cell viability data, it is evident that FGM supports good cell proliferation after 2, 3, 4 days culture. The measured variation in hardness, fracture toughness and cellular adhesion across the cross section confirmed the smooth transition achieved for the FGM (HAp-Al2O3-YSZ) nanocomposite, i.e. enhanced bulk toughness combined with unrestricted surface bioactivity. Therefore, such designed biomaterials can serve as potential bone implants. (C) 2012 Elsevier B.V. All rights reserved.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

Ballistic Studies on TiB2-Ti Functionally Graded Armor Ceramics

The objective of this paper is to discuss the results of the ballistic testing of spark plasma sintered TiB2-Ti based functionally graded materials (FGMs) with an aim to assess their performance in defeating small-calibre armor piercing projectiles. We studied the efficacy of FGM design and compared its ballistic properties with those of TiB2-based composites as well as other competing ceramic armors. The ballistic properties are critically analyzed in terms of depth of penetration, ballistic efficiency, fractographs of fractured surfaces as well as quantification of the shattered ceramic fragments. It was found that all the investigated ceramic compositions exhibit ballistic efficiency (eta) of 5.1 -5.9. We also found that by increasing the thickness of FGM from 5 mm to 7.8 mm, the ballistic property of the composite degraded. Also, the strength of the ceramic compositions studied is sufficient to completely fracture the nose of the pointed projectile used. Analysis of the ceramic fragments (2 mu m-10 mm) showed that harder the ceramic, coarser were the fragments formed. On comparing the results with available armor systems, it has been concluded that TiB2 based composites can show better ballistic properties, except B4C. SEM analysis of the fragments obtained after testing with FGM showed formation of cleavage steps as well as presence of intergranular cracks, indicating that the FGM fractured by mixed mode of failure. It can be concluded that the FGM developed has lower ballistic properties compared to its monolith TiB2-20 wt.% Ti.

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition. (C) 2013 Elsevier Masson SAS. All rights reserved.

Compressive and Flexural Properties of Functionally Graded Fly Ash Cenosphere-Epoxy Resin Syntactic Foams

The present study focuses on developing functionally graded syntactic foams (FGSFs) based on a layered co-curing technique. The FGSFs were characterized for compressive and flexural properties and compared with plain syntactic foams. The results showed that the specific compressive modulus was 3-67% higher in FGSFs compared to plain syntactic foams. FGSF exhibited 5-34% and 34-87% higher specific modulus and strength, respectively in flexural mode. The microscopic examinations of comparative responses of the filler and matrix to deformation suggest that the failure is dominated by the matrix. The gradient in the composition of syntactic foams helps in effectively distributing the stress throughout the microstructure and results in improved mechanical performance of syntactic foams. From the microscopy studies, it is evident that, the failure mechanism in the FGSF under flexural loading is governed by a crack that initiated on the tensile side of the specimen and propagated through the thickness to cause complete fracture. The microscopic observations further clearly demonstrate the existence of seamless interfaces between the layers and a clear difference in the cenosphere concentration across the interface, affirming the gradation in the prepared samples. The results show that appropriate compositions of FGSFs can be selected to develop materials with improved mechanical performance. POLYM. COMPOS., 36:685-693, 2015. (c) 2014 Society of Plastics Engineers

Biomechanics of Substrate Boring by Fig Wasps: Role of Zinc in Insect Cuticle

There are many biomechanical challenges that a female insect must meet to successfully oviposit and ensure her evolutionary success. These begin with selection of a suitable substrate through which the ovipositor must penetrate without itself buckling or fracturing. The second phase corresponds to steering and manipulating the ovipositor to deliver eggs at desired locations. Finally, the insect must retract her ovipositor fast to avoid possible predation and repeat this process multiple times during her lifetime. From a materials perspective, insect oviposition is a fascinating problem and poses many questions. Specifically, are there diverse mechanisms that insects use to drill through hard substrates without itself buckling or fracturing? What are the structure-property relationships in the ovipositor material? These are some of the questions we address with a model system consisting of a parasitoid fig wasp - fig substrate system. To characterize the structure of ovipositors, we use scanning electron microscopy with a detector to quantify the presence of transition elements. Our results show that parasitoid ovipositors have teeth like structures on their tips and contain high amounts of zinc as compared to remote regions. Sensillae are present along the ovipositor to aid detection of chemical species and mechanical deformations. To quantify the material properties of parasitoid ovipositors, we use an atomic force microscope and show that tip regions have higher modulus as compared to remote regions. Finally, we use videography to show that ovipositors buckle during oviposition and estimate the forces needed to cause substrate boring based on Euler buckling analysis. Such methods may be useful for the design of functionally graded surgical tools.

Origin of the Enhanced Photoluminescence from Semiconductor CdSeS Nanocrystals

Internal structures of extraordinarily luminescent semiconductor nanoparticles are probed with photoelectron spectroscopy, establishing a gradient alloy structure as an essential ingredient for the observed phenomenon. Comparative photoluminescence lifetime measurements provide direct evidence for a minimization of nonradiative decay channels because of the removal of interfacial defects due to a progressive change in the lattice parameters in such graded structures, exhibiting a nearly single exponential decay Quantum mechanical, calculations suggest a differential extent of spatial collapse of the electron and the hole wave functions in a way that helps to enhance the photoluminescence efficiency, while at the same time increasing the lifetime of the excited state, as observed in the experiments.

Finite element simulation of BAW propagation in inhomogeneous plate due to piezoelectric actuation

A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous material when subjected to mechanical, thermal loading or piezo-electric actuation. Elastic, thermal and electrical properties of the materials axe allowed to vary in length and thickness direction. The elements can act both as sensors and actuators. These elements are used to model wave propagation in functionally graded materials (FGM) and the effect of inhomogeneity in the wave is demonstrated. Further, a surface acoustic wave (SAW) device is modeled and wave propagation due to piezo-electric actuation from interdigital transducers (IDTs) is studied.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.