Showing papers on "Functionally graded material published in 2001"
TL;DR: In this paper, a finite element formulation based on the classical laminated plate theory is presented for the shape and vibration control of the functionally graded material (FGM) plates with integrated piezoelectric sensors and actuators.
407 citations
TL;DR: In this article, an analytic solution for the coupled large deflection of plates and shallow shells made of functionally graded materials (FGMs) under transverse mechanical loads and a temperature field is provided.
342 citations
TL;DR: In this paper, three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method, and the locally effective material properties are estimated by the Mori-Tanaka scheme.
Abstract: Three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method. The locally effective material properties are estimated by the Mori–Tanaka scheme. The temperature, displacements and stresses of the plate are computed for different volume fractions of the ceramic and metallic constituents, and they could serve as benchmark results to assess two-dimensional approximate plate theories.
289 citations
TL;DR: ZrO2-NiCr functionally graded material (FGM) was developed by powder metallurgical process as discussed by the authors, and the suitable fabrication procedure of FGM was determined.
247 citations
TL;DR: In this article, an edge crack in a strip of a functionally graded material (FGM) was studied under transient thermal loading conditions, where the FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip.
Abstract: An edge crack in a strip of a functionally graded material (FGM) is studied under transient thermal loading conditions. The FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip. Thus the material is elastically homogeneous but thermally nonhomogeneous. This kind of FGMs include some ceramic/ceramic FGMs such as TiC/SiC, MoSi2/Al2O3 and MoSi2/SiC, and also some ceramic/metal FGMs such as zirconia/nickel and zirconia/steel. A multi-layered material model is used to solve the temperature field. By using the Laplace transform and an asymptotic analysis, an analytical first order temperature solution for short times is obtained. Thermal stress intensity factors (TSIFs) are calculated for a TiC/SiC FGM with various volume fraction profiles of the constituent materials. It is found that the TSIF could be reduced if the thermally shocked cracked edge of the FGM strip is pure TiC, whereas the TSIF is increased if the thermally shocked edge is pure SiC.
191 citations
TL;DR: This work focuses on basic research into a P/M processed, porous-surfaced and functionally graded material (FGM) destined for a permanent skeletal replacement implant with improved structural compatibility based on a perpendicular gradient in porosity.
Abstract: This work focuses on basic research into a P/M processed, porous-surfaced and functionally graded material (FGM) destined for a permanent skeletal replacement implant with improved structural compatibility. Based on a perpendicular gradient in porosity the Young's modulus of the material is adapted to the elastic properties of bone in order to prevent stress shielding effects and to provide better long-term performance of the implant-bone system. Using coarse Ti particle fractions the sintering process was accelerated by silicon-assisted liquid-phase sintering (LPS) resulting in a substantial improvement of the neck geometry. A novel evaluation for the strength of the sinter contacts was proposed. The Young's modulus of uniform non-graded stacks ranged from 5 to 80 GPa as determined by ultrasound velocity measurements. Thus, the typical range for cortical bone (10-29 GPa) was covered. The magnitude of the Poisson's ratio proved to be distinctly dependent on the porosity. Specimens with porosity gradients were successfully fabricated and characterized using quantitative description of the microstructural geometry and acoustic microscopy.
148 citations
TL;DR: In this article, a modified classical lamination theory (CLT) was developed to account for piezoelectric coupling terms under applied electric field, which is capable of predicting the stress field and out-of-plane displacement of laminated PDE layers.
136 citations
TL;DR: In this article, the authors discussed the fracture behavior of a cracked smart actuator on a substrate under thermal load, where the actuator is made of piezoelectric material with functionally graded material properties.
131 citations
TL;DR: In this paper, a hybrid numerical method (HNM) is presented for analyzing transient waves in a cylinder made of functionally graded material (FGM), where the FGM cylinder is divided into N cylindrical elements with three-nodal line in the wall thickness.
130 citations
TL;DR: In this article, the fracture behavior of compositionally graded glass-filled epoxy is studied relative to homogeneous counterparts made of identical constituents and the apparent stress intensity factors prior to crack initiation are determined using dynamic equivalent of the stationary fields for FGMs while crack tip fields for steadily growing cracks in FGMs are used for post-initiation situations.
108 citations
TL;DR: In this article, a numerical method is proposed for analysing transient waves in plates of functionally graded material (FGM) excited by impact loads, and the displacement response is determined by employing the Fourier transformation and the modal analysis.
Abstract: A numerical method is proposed for analysing transient waves in plates of functionally graded material (FGM) excited by impact loads. The material properties of the FGM plate have a gradient in the thickness direction and are anisotropic in the plane of the plate. In the present method, the FGM plate is divided into layer elements in the thickness direction. For an accurate modelling of the variation of the material property of FGM plates, it is expressed by second-order polynomials in the thickness direction within an element. This can further reduce the number of elements to obtain more accurate results effectively. The principle of virtual work is used to develop approximate dynamic equilibrium equations. The displacement response is determined by employing the Fourier transformation and the modal analysis. As examples, the displacement response of FGM plates excited by line, point and distributed loads is calculated. The computations have shown the efficiency of the present method. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, the compositional responses of compositionally graded piezoelectric layers are analyzed for uniform mechanical loads, including stretch, bending and twisting, and numerical results to show the effects of different compositional gradients are presented.
TL;DR: In this paper, a procedure is suggested for characterizing the material properties of functionally graded material (FGM) plate by using a modified hybrid numerical method (HNM) and a neural network (NN).
TL;DR: In this article, a numerical technique for analyzing one-dimensional transient temperature distributions in a circular hollow cylinder that was composed of functionally graded ceramic-metal-based materials, without considering the temperature-dependent material properties was presented.
Abstract: We have presented a numerical technique for analyzing one-dimensional transient temperature distributions in a circular hollow cylinder that was composed of functionally graded ceramic-metal-based materials, without considering the temperature-dependent material properties The functionally graded material (FGM) cylinder was assumed to be initially in a steady state of gradient temperature; the ceramic inner surface was exposed to high temperature, and the metallic outer surface, which was associated with its in-service performance, was exposed to low temperature Then, the FGM cylinder was cooled rapidly on the ceramic surface of the cylinder, using a cold medium The transient temperature and related thermal stresses in the FGM cylinder were analyzed numerically for a model of the mullite-molybdenum FGM system The technique for analyzing the temperature distribution is quite simple and widely applicable for various boundary conditions of FGMs, in comparison with methods that have been proposed recently by other researchers
TL;DR: In this article, a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered.
TL;DR: In this paper, a multi-layered barium/strontium titanate functionally graded material was fabricated and optical/scanning electron microscopy, energy dispersive spectrocsopy, and X-ray diffractometer were used for microstructural, chemical, and phase analysis, respectively.
Abstract: A functionally graded perovskite material with varying Ba/Sr ratio was known to have a broad transition temperature and as a result it shows a low temperature coefficient and high dielectric constant in a wide temperature range. A multi-layered barium/ strontium titanate functionally graded material was fabricated. Optical/scanning electron microscopy, energy dispersive spectrocsopy, and X-ray diffractometer were used for microstructural, chemical, and phase analysis, respectively. An impedance/gain-phase analyzer was used for dielectric constant measurement. The microstructure and dielectric property of BaTiO 3 -SrTiO 3 system display various gradient distributions corresponding to constitutional change. The average grain size of Ba 1-x Sr x TiO 3 phase was reduced as increasing the volume fraction of strontium. The dielectric properties of BaTiO 3 SrTiO 3 functionally graded materials were discussed in terms of microstructure and chemical composition.
TL;DR: A computational inverse procedure for characterization of the material properties of functionally graded materials (FGMs) using the surface displacement response of the plate was presented in this article, where the authors used the inverse procedure to characterize the surface displacements of the FMs.
Abstract: A computational inverse procedure is presented for characterization of the material properties of functionally graded materials (FGMs) using the surface displacement response of the plate. Amodifie...
TL;DR: In this paper, the steady-state creep response in a particle-reinforced isotropic functionally graded material (FGM) disc with linear variation of particle distribution along the radial distance has been investigated and compared with that of a disc containing the same amount of particle distributed uniformly.
Abstract: Steady-state creep response in a particle-reinforced isotropic functionally graded material (FGM) disc with linear variation of particle distribution along the radial distance has been investigated and compared with that of a disc containing the same amount of particle distributed uniformly. In view of the application of rotating discs in friction drives, turbines, and a number of other machine components, which are often exposed to elevated temperatures, weight saving without impairing the creep response may be a desirable goal. The disc under investigation is made of a composite containing silicon carbide particles in a matrix of 6061 aluminum alloy, and the steady-state creep response of the composite is described by Norton’s law. The material parameters of creep vary along the radial distance in the disc due to varying composition, and this variation has been estimated by regression fit of the available experimental data. The present analysis indicates that the tangetial stress increases due to increased density caused by a higher particle content in the region near the inner radius of the FGM disc. But it is more than compensated by the lowering of creep parameters due to increased particle content, and consequently, the steady-state creep rate decreases compared to those estimated in a disc with the same average particle content distributed uniformly. In the region near the outer radius, the tangential stress decreases and the creep parameters increase, both due to relatively lower particle content. But the resulting lower tangential stress is able to decrease the creep rate in this region overcoming the effect of increased creep parameters. Thus, for the assumed linear particle distributions in an isotropic rotating disc, the steady-state tangential and radial creep rates are smaller by almost an order of magnitude compared to those in an isotropic disc with uniform particle distribution.
TL;DR: In this article, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions, where the shear relaxation function of the material is assumed as μ = μ 0 exp (βy/h)f(t), where h is a length scale and f(t) is a nondimensional function of time t having either the form f (t) = μ∞/μ 0 + (1 - μ α /μ 0 )exp(-t/t 0 ) for a linear standard solid, or f( t)=(
Abstract: In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions, The shear relaxation function of the material is assumed as μ = μ 0 exp (βy/h)f(t), where h is a length scale and f(t) is a nondimensional function of time t having either the form f(t) = μ∞/μ 0 + (1 - μ α /μ 0 )exp(-t/t 0 ) for a linear standard solid, or f(t)=(t 0 /t) q for a power-law material model. We also consider the shear relaxation function μ = μ 0 exp (βy/h)[t 0 exp (δy/h)/t] q in which the relaxation time depends on the Cartesian coordinate y exponentially, Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, μ 0 , μ∞, t 0 ; δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.
TL;DR: In this paper, the theoretical analysis of a control of the transient thermoelastic displacement is developed for a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heat supply.
Abstract: In this study, the theoretical analysis of a control of the transient thermoelastic displacement is developed for a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heat supply. Assuming that the functionally graded plate has nonhomogeneous thermal and mechanical material properties in the thickness direction, the three-dimensional temperature in a transient state and the three-dimensional transient thermal stresses of a simply supported plate for a functionally graded material are analyzed by introducing the theory of laminated composites as a theoretical approximation. By using the solution for a functionally graded plate and the exact solution for a piezoelectric plate of crystal class mm2, the theoretical analysis of three-dimensional transient piezothermoelasticity is developed for a simply supported combined plate. the analysis of a piezothermoelastic problem leads to an appropriate electric potential applied to the piezoelectric plate which suppresses the induced thermoelastic displacement in the thickness direction at the midpoint on the free surface of the functionally graded plate. As an example, numerical calculations are carried out for a functionally graded rectangular plate made of zirconium oxide and titanium alloy, bonded to a piezoelectric plate of a cadmium selenide solid. Some numerical results when the transient thermoelastic displacements are controlled are shown in figures.
TL;DR: In this paper, a numerical integral technique is proposed for evaluating confluent hypergeometric functions (CHFs), which arise from a wave propagation problem in functionally graded material (FGM), where a part of the integrand in the integral representation of the CHFs is approximated by piecewise polynomials.
TL;DR: In this article, the authors studied the dynamic response of a finite crack in an unbounded FGM subjected to an antiplane shear loading and derived the dynamic stress intensity factor from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane.
Abstract: The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.
TL;DR: In this article, an analysis of a crack in a substrate overlaid with a functionally graded material subjected to frictional contact loading is performed, within the linear plane elasticity framework.
TL;DR: In this paper, the inverse problem of evaluating optimum material distributions intending to realize prescribed apparent fracture toughness in thick-walled functionally graded material (FGM) circular pipes was treated, and an approximation method of finding stress intensity factors for a crack in the FGM pipes was introduced in which the nonhomogeneous material properties were simulated by a distribution of equivalent eigenstrain.
TL;DR: In this paper, the authors considered a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material).
Abstract: We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated.
TL;DR: In this article, a non-linear thermomechanical finite element analysis (FEA) is used as an integral part of an overall research program that is being conducted to develop a nonsticking, oxidation and wear-resistant coating system for glass-molding dies and forming tools.
Abstract: Finite element analysis (FEA) is being used as an integral part of an overall research program that is being conducted to develop a non-sticking, oxidation- and wear-resistant coating system for glass-molding dies and forming tools. This non-linear thermomechanical FEA consists of two parts: (1) a global analysis using a coupled thermomechanical model of the complete die to predict the locations where the die experiences extreme stress/strain condition during molding cycles; and (2) a local analysis of the die coating used to protect the die at those positions where extreme conditions were predicted by the global analysis, to analyze the stresses generated in the coating system during a simulated glass-molding process. This paper outlines the methodology developed in this work, which can be used to explore the effects of die geometry, die material, and coating materials on the integrity, reliability and performance of a coated die. This methodology may also be helpful for investigation of the mechanisms relating to the thermal fatigue problem. The preliminary results presented here demonstrate that it is possible to find an optimized coating architecture with optimal stress transition from the substrate to the outmost working layer by selecting appropriate coating materials and engineering the compositional gradients of the functionally graded material (FGM) intermediate layer.
TL;DR: In this paper, the transient temperature solution for a functionally graded material (FGM) is formulated by Green's function based on the Galerkin method and an approximate solution that satisfies the homogeneous boundary condition is substituted into the governing equation to yield an eigenvalue problem.
Abstract: The transient temperature solution for a functionally graded material (FGM) is formulated by Green’s function based on the Galerkin method. An approximate solution that satisfies the homogeneous boundary condition is substituted into the governing equation to yield an eigenvalue problem. To solve the eigenvalue problem, the eigenfunctions are approximated by a series of polynomials satisfying the homogeneous boundary condition. The Galerkin method is used to determine the coefficients of eigenfunctions. The transient temperature solution for a general heat conduction equation with a source and nonhomogeneous boundary conditions is obtained by using Green’s function, which is expressed by eigenvalues and corresponding eigenfunctions. Transient thermal stresses in a FGM plate and a FGM hollow circular cylinder are discussed.
TL;DR: In this paper, a crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous visco-elastic layers was studied under antiplane shear conditions.
Abstract: A crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous viscoelastic layers is studied under antiplane shear conditions. The shear relaxation modulus of the FGM layer follows the power law of viscoelasticity, i.e., μ = μ0exp (βy/h) [t0exp (δy/h) /t]q, where h is a scale length, and μ0,t0,β,δ and q are material constants. Note that the FGM layer has position-dependent modulus and relaxation time. The shear relaxation functions of the two homogeneous viscoelastic layers are μ=μ1(t1/t)q for the bottom layer and μ=μ2(t2/t)q for the top layer, where μ1 and μ2 are material constants, and t1 and t2 are relaxation times. An elastic crack problem of the composite structure is first solved and the `correspondence principle' is used to obtain stress intensity factors (SIFs) for the viscoelastic system. Formulae for SIFs and crack displacement profiles are derived. Several examples are given which include interface cracking between a viscoelastic functionally graded interlayer and a viscoelastic homogeneous material coating. Moreover, a parametric study is conducted considering various material and geometric parameters and loading conditions.
30 Sep 2001-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this article, the authors investigated the thermo-elastic behavior of a bi-material and a functionally graded material using a special hybrid finite element analysis, which evolves from the natural discretization of the domain into basic structural elements, Voronoi elements, by Dirichlet tesselation.
Abstract: In this study, the thermo-elastic behavior of a bi-material and a functionally graded material is investigated using a special hybrid finite element analysis. The algorithm evolves from the natural discretization of the domain into basic structural elements, Voronoi elements, by Dirichlet tesselation. For heterogeneous microstructures, the Voronoi elements contain a second phase of which the effects on the displacement and temperature fields are accurately accounted for. The accuracy and the efficiency of the algorithm are verified by comparing the solutions with results obtained from a standard finite element analysis. The advantages of the algorithm for studying the micromechanistic behavior of heterogeneous solids, such as functionally graded materials, are elucidated.
TL;DR: In this article, a set of nonlinear equations in the sense of the von Karman large deflection is presented and reformulated by use of displacement and stress potential functions, which are then solved for a rectangular inhomogeneous plate by using the mixed Fourier series technique.