Properties Of Functionally Graded Material Research Articles

Comparison of the dielectric properties of functionally graded material dielectrics and layered dielectrics used for electric stress control

Layered dielectric materials are currently in use for electric field stress control, but are limited by charge accumulation at the dielectric–dielectric interfaces. The current work uses micrometric particles to modify the effective permittivity of epoxy resin samples. Two broad kinds of samples are considered: discrete layered material (DLM) samples and functionally graded material (FGM) samples. DLM samples are obtained by bonding layers of epoxy resin with different filler loadings such that abrupt variation in permittivity might occur along the sample thickness. FGM specimens are prepared by hot pressing a comparatively large number of very thin layers of micro-filled epoxy resin with very small differences in permittivity one over the other, thus creating a gradual spatial permittivity gradation. Dielectric properties of FGM and DLM specimens are compared in this study. Space charge accumulation is studied using the pulsed electroacoustic method; the accumulated charge density is seen to be lower in FGM. The uniformity of electric field distribution under applied electric stress is computed, and the field utilisation factor in FGM is seen to have a higher value. Also, the dissipation factor is lower and the short-term breakdown strength is higher in FGM than in DLM samples, providing reason to prefer FGM for insulation to control electric stress.

On the surface elastic-based shear buckling characteristics of functionally graded composite skew nanoplates

Abstract The prime objective of the present investigation is to predict the shear buckling characteristics of skew nanoplates made of a functionally graded material (FGM) in the presence of surface stress effect. For this purpose, the Gurtin-Murdoch surface theory of elasticity is applied to the higher-order shear deformation plate theory within the framework of the oblique coordinate system. Different types of the homogenization scheme including Reuss model, Voigt model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are taken into consideration in order to extract the effective mechanical properties of FGM skew nanoplates. The Ritz method using Gram-Schmidt shape functions is utilized to obtain the surface elastic-based shear buckling loads of FGM skew nanoplates. It is indicated that by increasing the value of the index associated with the material property gradient, the significance of the surface stress type of size effect on the shear buckling behavior of a FGM skew nanoplate improves. Moreover, by changing the boundary conditions from simply supported ones to clamped ones, the influence of the skew angle on the surface elastic-based shear buckling load of a FGM skew nanoplate increases. Also, it is illustrated that by increasing the width to thickness ratio of a skew nanoplate, the free surface area increases which results in to enhance the effect of surface residual stress on its shear buckling characteristics.

Analysis Two Dimension Heat Conduction in Functionally Graded Materials Using Finite Element Methods

Along with the progress of the industrial world, both the aviation industry, the health industry, the chemical industry, the electronics industry, and so on, the need for composite materials is increasing to meet market demand. Functionally Graded Materials (FGMs) are an advanced material class of composite materials that have material properties that vary from one point to another. In this study, two-dimensional heat conduction analysis will be conducted in FGM using the Finite Element Method (FEM). Three models gradation FGMs properties examined in the study, namely polynomial, Trigonometry, and Exponential. The response temperature of FGMs using gradation three models compared and analyzed. The optimum temperature distribution of four models built with the ANSYS software. The result is that heat conduction in trigonometric variations is very good, resulting in low-temperature values when compared to both of them. Then, the performance and efficiency obtained using FEM to analyze two-dimensional heat conductivity in FGMs is also very good.

On the effect of viscoelasticity on behavior of gyroscopes

In the present study, the size- and time-dependent viscoelastic bending analysis of rotating spherical nanostructures made of functionally graded materials (FGMs) is performed. To simulate gyroscopic rotation, the structure is assumed to be rotated around two axes with constant angular accelerations. The nonhomogeneous nanostructure with functionally variable thickness (FVT) is assumed as FGM/FVT structure. Geometrically, the inner side of the structure has a spherical shape and the outer side is considered as an ellipse or any other arbitrary function. The size-dependent governing equations and related boundary conditions are obtained by implementing Hamilton's principle based on Eringen's nonlocal elasticity and first-order shear deformation theories. The resulting equations are solved using the Semi-Analytical Polynomial Method (SAPM). The time-dependent deflection is obtained by applying the boundary and initial time conditions. The effects of a hygro-thermal environment and porosity are also considered for a comprehensive analysis. Since no research has been conducted so far on the nonlocal viscoelastic dynamic analysis of FGM/FVT gyroscopes, the classical results are compared with the previously published works and ABAQUS software as well as the effect of many parameters on the results including nonlocality, FGM properties of the structure, thickness changes, angular velocities and accelerations, hygro-thermal environment, porosity, and viscoelastic properties are thoroughly conducted.

Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory

In this study, a theoretical unification of twenty-one nonlocal beam theories are presented by using a unified nonlocal beam theory. The small-scale effect is considered based on the nonlocal differential constitutive relations of Eringen. The present unified theory satisfies traction free boundary conditions at the top and bottom surface of the nanobeam and hence avoids the need of shearing correction factor. Hamilton’s principle is employed to derive the equations of motion. The present unified nonlocal formulation is applied for the bending, buckling and free vibration analysis of functionally graded (FG) nanobeams. The elastic properties of FG material vary continuously by gradually changing the volume fraction of the constituent materials in the thickness direction. Closed-form analytical solutions are obtained by using Navier’s solution technique. Non-dimensional displacements, stresses, natural frequencies and critical buckling loads for FG nanobeams are presented. The numerical results presented in this study can be served as a benchmark for future research.

Elastoplastic Analysis of a Functionally Graded Material Beam Subjected to Uniformly Distributed Load

ABSTRACTThe elastoplastic behavior of a Functionally Graded Material (FGM) simply supported beam consisting of elastic material A and elastoplastic material B under uniformly distributed load is investigated. A power function is used to describe the volume fractions of the constituent materials, and the average stress of the FGM beam is obtained by using the averaging method. This method can avoid the assumption of the varying properties of the whole material, and can consider the different Possion’s ratios of the different constituent materials. What’s more, only the elastoplastic material B in the FGM beam will yield, and the yield function is determined by the stress of material B only, rather than the average stress of the whole material. The method used in this work is more closer to the real material than the method by assuming the variation of the whole properties of FGM. The theoretical results show a good agreement with the finite element results, which indicates that the method provided in this work is valid. With this method, the variation of the elastic and plastic areas, the stress distribution on the cross section, variation of the curvature and neutral layer, and the residual stress distribution of the FGM beam are discussed through numerical results. This work can provide a new way for the design and in-depth investigation of FGM material.

Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler–Pasternak foundation in various thermal environments

This work presents an analytical approach to investigate the mechanical buckling of functionally graded material (FGM) thin conical panels surrounded by Winkler–Pasternak foundation and exposed to thermal environments. The material properties of FGMs are assumed to be temperature-dependent and graded only in the thickness direction according to the power-law, sigmoid and the exponential distribution of volume fraction. Eight well-known types of micromechanical models, namely Voigt, Reuss, Mori–Tanaka, Hashin–Shtrikman, modified Wakashima–Tsukamoto, Halpin–Tsai, Tamura and LRVE estimations, are studied to determine the effective two-phase FGM material properties as a function of the particles’ volume fraction considering thermal effects. Further, it is been supposed that the FG conical panel is heated uniformly, linearly and nonlinearly through the thickness. The nonlinear temperature distribution is obtained based on Fourier’s law by applying a semi-analytical procedure. The fundamental relations and the basic equations are derived by using Love’s thin shell theory. Finally, the numerical results are provided to reveal the effect of explicit micromechanical model, FGM profile, temperature distribution with various thermal boundary conditions, foundation conditions and the geometric parameters on the stability of these panels. Additionally, the critical buckling load is compared with that of FG truncated conical shells, cylindrical panels and the cylindrical shells.

Thermo-Mechanical Analysis of Functionally Graded Material Plate under Transverse Loading for Varying Volume Gradation

Functionally graded material (FGM) has a unique design in which material properties vary smoothly and continuously which leads to having better thermal and mechanical performance. Functionally graded material has a wide area of application from the pressure vessel to aerospace due to its tailoring properties. The main emphasis has been made here, to present a structural mechanical and steady-state thermal analysis of functionally graded flat plate made up of aluminum and ceramic. The flat plate is subjected to various boundary and loading condition. Material properties of FGM is calculated across the thickness using power law with the help of MATLAB programming. An analysis is performed for various volume gradation using MACROS in ANSYS APDL. The analysis results for functionally graded materials are compared with a composite sandwich plate for the same boundary conditions. It was found that von-Mises stress generated in FGM is 14.6% less than compared to sandwich structure, the stress in x and y-direction is 16.5% less, XY-Shear is 13.5% less and deflection is 33% less than a sandwich plate of aluminum and ceramic.

Multi-directional functionally graded materials for enhancing the durability of shell structures

Uni-directional functionally graded materials (FGMs) providing a relative change in terms of material properties have been implemented in many high-tech engineering applications, including shells and plates. As a new concept, multi-directional FGMs highlight the emergence of modern materials design in the development of multi-functional materials. Pressure vessels made of materials varying in the radial direction have been comprehensively studied. In some practical instances, however, tailored grading of material properties is required in other directions. Shells with bi-dimensional FGM properties can present practical problems arising from excessive temperature gradients and extreme deflections. In this work, asymmetric deformations of two-directional FG pressure vessels under the effect of thermo-mechanical loads are studied numerically, taking advantage of Fourier and polynomial quadrature methods. Unlike most published research on this topic, we assume that the material properties of the shell are graded in the radial and axial directions obeying an exponential formulation, leading to a more accurate simulation of the real work condition. Governing equations are formulated based on three-dimensional elasticity theory, discretised into the series form, and then the resulting equations are solved. To evaluate the accuracy and superiority of this approach, numerical results are obtained and compared with exact solutions for material properties defined by the power law and are found to be in good agreement. In the results section, it is shown that variations of the grading parameter, temperature shock, geometry profile and boundary conditions play important roles in the distribution of stress, displacement and temperature fields. In the context of the thermoelastic theory of shells and plates, the results of this work will provide a reliable database for design engineers to choose a desirable material property function, changing throughout different directions of the geometry, to mitigate thermal stresses, which should be as small and uniform as possible.

Natural frequency of skew FGM plates using finite element method

In the present work aims the free vibration analysis of functionally graded material (FGM) skew plates. Kinematics equations are based on the first order shear deformation theory and a four noded rectangular element is used to mesh the plate geometry. Properties of FGM (Stainless steel and Alumina)material constituents of the plate are considered to be as position and assumed to vary along the thickness direction according to a simple power law. Rectangle plate displacement components are renovated into skew plate geometry by suitable transformation rule. The effects of power law index and boundary condition on natural frequency parameters of FGM skew plates are reported based on FOSD. The related results are discussed briefly. Results are generated for vibration analysis of the FGM skew plate, which may be implemented in the future research involving similar kind of problems.

Thermoelastic Crack Analysis in Functionally Graded Pipelines Conveying Natural Gas by an FEM

Internal cracks are a serious problem in pipelines conveying unsteady pressurized fluids like natural gas. To investigate and overcome this problem, this paper is motivated to highlight and study the response of gas pipes made of functionally graded materials (FGM) instead of the traditional carbon steel material. FGM is proposed as a composite material because of its advantages of minimizing the stress variation in the pipe. Ceramic is applied because of its durability against corrosion and its surface hardness against erosion. FGM properties are radially graded and a finite element model is developed and implemented into ABAQUS package, including FORTRAN subroutines which are adapted for the present case study. Coupled plane strain thermoelastic analysis is used to investigate the stresses and the stress intensity factor (SIF) at various crack depths under the actual thermomechanical loads. Both coupled and uncoupled thermomechanical approaches are introduced and compared to reveal the necessity of the coupled analysis for accurate FGMs’ investigation. The different influences of unsteady thermal and mechanical loads on the crack propagation are discussed.

Application of the FOSDT to the solution of buckling problem of FGM sandwich conical shells under hydrostatic pressure

Abstract In this study, the buckling problem of functionally graded materials (FGMs) sandwich truncated conical shells (STCSs) under hydrostatic pressure was solved using the modified form of first-order shear deformation theory (FOSDT). The FGM properties of the constituents are graded in the thickness direction in accordance with a power-law distribution. The basis equations of FGM sandwich truncated conical shells (FGMSTCSs) are derived from the Donnell kinematics assumptions. Using the Galerkin method to the partial differential governing equations, the formula for the dimensionless hydrostatic buckling pressure (DHBP) in the framework of the FOSDT is obtained to demonstrate the buckling response of FGMSTCSs. A numerical analysis is performed for various types and geometry of FGMSTCSs under FOSDT and the classical shell theory (CST).

Analysis of Functionally Graded Beam

In this paper, static analysis of FGM (functionally graded material) beam is carried out under the framework of Euler–Bernoulli beam theory. Axial stress distribution has been determined for a simply supported FGM beam made of Aluminium and Zirconia. The material properties of FGM are assumed to vary through the thickness, whereas Poisson ratio is held constant. Different material gradation approaches are used to achieve smooth variations of material properties in FGMs. Effect of variation in material properties, on position of neutral axis, is also considered, and stress calculations based on shifted position of neutral axis are performed. Axial stress in bi-material beam made of Aluminium and Zirconia is calculated, and it is found that in the absence of FGM layer, the stress distribution is discontinuous. It is shown that the discontinuity can be removed by introducing a thin FGM layer at the junction of both materials (Aluminium and Zirconia). The results are compared with those available in the literature for the validity of the present methodology.

Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction

Different aspects of thermomechanical fracture of functionally graded materials (FGMs) are considered. Among them are the crack interaction problems in a functionally graded coating on a homogeneous substrate (FGM/H). The interaction between systems of edge cracks is investigated, as well as, how this mutual interaction influences the fracture process and the formation of crack patterns. The problem is formulated with respect to singular integral equations which are referred to the boundary equation methods. The FGM properties are modeled by exponential functions. The main fracture characteristics are calculated, namely, the stress intensity factors, the angles of deviation of the cracks from their initial propagation direction and the critical stresses when the crack starts to propagate. The last two characteristics are calculated using an appropriate fracture criterion. The problem contains different parameters, such as the geometry (location and orientation of cracks, their lengths, and the width of the FGM layer) and material parameters, i.e. the inhomogeneity parameters of elastic and thermal coefficients of the functionally graded material. The influence of these parameters on the thermo-mechanical fracture of FGM/H is investigated. As examples the following real material combinations are discussed: TiC/SiC, Al2O3/MoSi2, MoSi2/SiC, ZrO2/nickel and ZrO2/steel.

Elastic-plastic analysis of functionally graded bars under torsional loading

In this paper a new integral equation solution to the elastic-plastic problem of functionally graded bars under torsional loading is presented. The formulation is general in the sense that it can be applied to an arbitrary cross-section made of any type of elastoplastic material. In material science the Functionally Graded Material (FGM) is a non-homogeneous composite which performs as a single-phase material, by unifying the best properties of its constituent phase material. The nonlinear elastic-plastic behavior is mathematically described by the deformation theory of plasticity. According to this theory, the material constants are assumed variable within the cross section, and are updated through an iterative process so as the equivalent stress and strain at each point coincide with the uniaxial material curve. In this investigation a new straightforward nonlinear procedure is introduced in the deformation theory of plasticity which simplifies the solution method. At each iteration step, the warping function is obtained by solving the torsion problem of a non-homogeneous isotropic bar using the Boundary Element Method (BEM) in conjunction with the Analog Equation Method (AEM). Without restricting the generality, the FGM material is comprised of a ceramic phase and a metal phase. The ceramic is assumed to behave linearly elastic, whereas the metal is modeled as an elastic – linear hardening material. Furthermore, the TTO homogenization scheme for estimating the effective properties of the two-phase FGM was adopted. Several bars with various cross-sections and material types are analyzed, in order to validate the proposed model and exemplify its salient features. Moreover, useful conclusion are drawn from the elastic-plastic behavior of functionally graded bars under torsional loading.

Sample-Based Synthesis of Functionally Graded Material Structures

Spatial variation of material structures is a principal mechanism for creating and controlling spatially varying material properties in nature and engineering. While the spatially varying homogenized properties can be represented by scalar and vector fields on the macroscopic scale, explicit microscopic structures of constituent phases are required to facilitate the visualization, analysis, and manufacturing of functionally graded material (FGM). The challenge of FGM structure modeling lies in the integration of these two scales. We propose to represent and control material properties of FGM at macroscale using the notion of material descriptors, which include common geometric, statistical, and topological measures, such as volume fraction, correlation functions, and Minkowski functionals. At microscale, the material structures are modeled as Markov random fields (MRFs): we formulate the problem of design and (re)construction of FGM structure as a process of selecting neighborhoods from a reference FGM, based on target material descriptors fields. The effectiveness of the proposed method in generating a spatially varying structure of FGM with target properties is demonstrated by two examples: design of a graded bone structure and generating functionally graded lattice structures with target volume fraction fields.

An isogeometric approach for size-dependent buckling analysis of FGM nanoplates

In this paper, a suitable and simple computational formulation based on Isogeometric Analysis (IGA) integrated with higher-order shear deformation theory (HSDT) is introduced for size-dependent buckling analysis of functionally graded material (FGM) nanoplates. The material properties of FGM based on the Mori–Tanaka schemes and the rule of mixture are used. The differential nonlocal equations are utilized to take into account size effects. The nonlocal governing equations are approximated according to IGA based on HSDT, which satisfies naturally the higher-order derivatives continuity requirement in weak form of FGM nanoplates. The effect of nonlocal approach on the behaviors of the FGM nanoplates with several volume fraction exponents is investigated to show the reliability of the proposed method.

The complex variable meshless local Petrov–Galerkin method for elastodynamic analysis of functionally graded materials

As an improvement of the meshless local Petrov–Galerkin (MLPG), the complex variable meshless local Petrov–Galerkin (CVMLPG) method is extended here to dynamic analysis of functionally graded materials (FGMs). In this method, the complex variable moving least-squares (CVMLS) approximation is used instead of the traditional moving least-squares (MLS) to construct the shape functions. The main advantage of the CVMLS approximation over MLS approximation is that the number of the unknown coefficients in the trial function of the CVMLS approximation is less than that of the MLS approximation, thus higher efficiency and accuracy can be achieved under the same node distributions. In implementation of the present method, the variations of the FGMs properties are computed by using material parameters at Gauss points, so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method (FEM) for the FGMs. Several numerical examinations for dynamic analysis of FGMs are carried out to demonstrate the accuracy and efficiency of the CVMLPG.

An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates

Abstract In the present investigation, a suitable and simple computational formulation based on Isogeometric Analysis (IGA) integrated with higher-order shear deformation theory (HSDT) is introduced for size-dependent geometrically nonlinear transient analysis of functionally graded material (FGM) nanoplates. The material properties of FGM based on the Mori–Tanaka schemes and the rule of mixture are used. The nonlinear transient nonlocal governing equations approximated according to IGA based on HSDT, which satisfies naturally the higher-order derivatives continuity requirement in weak form of the FGM nanoplates, are formed using the von Karman strains and solved by Newmark time integration scheme. The effect of nonlocal approach on the behaviors of the FGM nanoplates with several volume fraction exponents is investigated. Several numerical results are presented to demonstrate the reliability of the proposed method.

Crack Tip Fields for Interfacial Crack of FGMs Cylindrical Shell with Reissner’s Effect

The higher order crack-tip fields for the interfacial crack between functionally graded material(FGM) and homogeneous material cylindrical shells are presented. The crack is oriented in circumferential direction. The material properties of FGMs are assumed to be exponential functions with their gradient direction perpendicular to the interface. Base on Reissner theory, the governing equations are derived for weak-discontinuous problems of cylindrical shells. By using the eigen-expansion method, the high order crack tip fields are obtained.