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.

FEM Simulations and Optimization about Residual Stresses in Coating Structures with Functionally Graded Materials Layer

An elasto-plastic finite element method is developed to predict the residual stresses of thermal spraying coatings with functionally graded material layer. In numerical simulations, temperature sensitivity of various material constants is included and mix

Optimal design of Functionally Graded Materials using a procedural model and Particle Swarm Optimization

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples. © 2011 Elsevier Ltd. All rights reserved.

Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfee method

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 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.

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable in influence on the stress intensity factors. The influence for embedded cracks is quite different from that for external cracks.

Friction and wear properties of functionally graded aluminum matrix composites

Aluminum matrix composites are currently considered as promising materials for tribological applications in the automotive, aircraft and aerospace industries due to their great advantage of a high strength-to-weight ratio. A superior combination of surface and bulk mechanical properties can be attained if these composites are processed as functionally graded materials (FGM's). In this work, homogeneous aluminum based matrix composite, cast by gravity, and aluminum composites with functionally graded properties, obtained by centrifugal cast, are tested against nodular cast iron in a pin-on-disc tribometer. Three different volume fractions of SiC reinforcing particles in each FGM were considered in order to evaluate their friction and wear properties. The sliding experiments were conducted without lubrication, at room temperature, under a normal load of 5 N and constant sliding speed of 0.5 ms-1. The worn surfaces as well as the wear debris were characterized by SEM/EDS and by atomic force microscopy (AFM). The friction coefficient revealed a slightly decrease (from 0.60 to 0.50) when FGM's are involved in the contact instead of the homogeneous composite. Relatively low values of the wear coefficient were obtained for functionally graded aluminum matrix composites (≈10-6 mm3N-1 m-1), which exhibited superior wear resistance than the homogeneous composite and the opposing cast iron surface. Characterization of worn surfaces indicated that the combined effect of reinforcing particles as load bearing elements and the formation of protective adherent iron-rich tribolayers has a decisive role on the friction and wear properties of aluminum matrix composites.

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.

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