Showing papers on "Functionally graded material published in 2022"

Nonlinear transient analysis of porous P-FGM and S-FGM sandwich plates and shell panels under blast loading and thermal environment

Abstract: The present work is an attempt to develop a simple and accurate finite element formulation based on C0 continuity of transverse displacement for obtaining and comparing nonlinear transient response of porous functionally graded material (FGM) sandwich plates and shell panels. The volume fraction for the layers made of FGM is computed according to the power-law (P-FGM) or sigmoid (S-FGM) model. The FGM sandwich panel is subjected to blast loading and thermal environment considering the heat conduction in thickness direction and the material properties are assumed to be temperature-dependent. An eight-noded isoparametric element along with first-order shear deformation theory is used to develop a finite element model. The strain–displacement relation is obtained using Sander’s approximation incorporating von Karman type nonlinear strains. Two configurations, first having the top and the bottom layers made of pure ceramic and pure metal and the core of same composed of FGM, second having the top and the bottom layers made of FGM and the core composed of pure metal are considered for the present investigation. The FGM layers for the two configurations are porous and two types of porosity, viz., evenly spaced and unevenly spaced are considered for the analysis. The results obtained from the present finite element formulation are first validated with several benchmark examples available in the literature. Parametric studies are carried out to investigate the effect of volume fraction index, porosity model, temperature gradient, core to facesheet thickness ratio and blast load on nonlinear transient analysis of porous P-FGM and S-FGM sandwich plate and shell panels. It is observed that by selecting optimum parameters, the amplitude of the nonlinear transient response due to different blast loading is controlled.

Defect of Functionally Graded Material of Inconel 718 and STS 316L Fabricated by Directed Energy Deposition and Its Effect on Mechanical Properties

Abstract: For multi-materials having different compositions, delamination or crack may occur at the interface of two dissimilar materials due to differences in a lattice structure, residual thermal stress, and coefficient of thermal expansion. To solve such problems, functionally graded material (FGM) that gradually changes the properties of the interfacial boundary has been attracting attentions. Since the chemical compositions of FGM materials are gradually changed according to position, inter-layer residual stress between two heterogenic materials can be relieved. In this study, a functionally graded material (FGM) containing Inconel 718 and stainless steel (STS) 316L was fabricated by directed energy deposition (DED), with STS 316L volume fraction changing in the range of 0 wt% to 100 wt%. The fabricated FGM includes depositions of 25% graded (Graded (25)) and 10% graded (Graded (10)) materials. In non-graded samples, cracks were observed at the interface of Inconel 718 and STS 316L. In all three conditions, cracks in the vertical direction were observed in specific regions, and these cracks were caused by precipitation, inclusion, and columnar-to-equiaxial transition (CET). As far as hardness is concerned, a smooth decrease in hardness was observed in the graded-materials, but the hardness decreased rapidly at the interface of the non-graded sample. The highest tensile strength and elongation were obtained in the Graded (25) material. Microstructural and mechanical properties indicated that mechanical properties vary depending on the gradient composition, and it is essential to choose the appropriate gradient composition of FGM fabricated by DED.

Vibration and stability characteristics of functionally graded sandwich plates with/without porosity subjected to localized edge loadings

Abstract: This article investigates the influence of porosity and localized edge loads on the vibration and buckling characteristics of functionally graded material (FGM) plates using the finite element (FE) method. The analysis is carried out by choosing a single-layer FGM and two different types of FGM sandwich plates in such a way that there is no material discontinuity along the thickness direction. The porosity imperfections are accounted for in this study as criteria of stiffness reduction and are incorporated using modified power law distribution. The vibration and buckling responses are studied by considering four types of localized edge loads on plates with different porosity distributions. The application of different types of localized edge loads on the plate leads to the development of nonuniform in-plane stresses. Hence, they are computed first by using a dynamic approach before obtaining the buckling loads. The accuracy of the FE formulation is first validated for FGM plates by comparing the natural frequencies and the critical buckling loads obtained in the present investigation with the solutions already available in the literature. After validating the accuracy, detailed parametric studies have been performed on plates with varying volume fraction exponent, porosity distribution, porosity index, side-to-thickness ratio, load width ratio, aspect ratio, and support condition, and the results are presented with appropriate conclusions. A probabilistic sensitivity analysis is carried out to identify the significant parameter affecting the buckling load and natural frequency of porous FGM plates subjected to localized edge loads, which considerably aids in the design of the FGM plates.

Vibration and Uncertainty Analysis of Functionally Graded Sandwich Plate Using Layerwise Theory

Abstract: In the present study, free vibration analyses of porous functionally graded material (FGM) sandwich plates are carried out in thermal environment. Two types of sandwich plates such as sandwich with FGM face sheets and homogeneous core and sandwich with homogeneous face sheets and FGM core are considered for free vibration analysis with nonlinear temperature variation over the thickness direction. The metal and ceramic components are assumed to be temperature dependent. The higher-order layerwise theory is adopted with an eight-noded rectangular element to build a finite element model for free vibration analysis. A radial basis function network (RBFN) based surrogate model is developed to investigate the stochastic frequency response due to the uncertain material properties. The accuracy and the efficiency of the RBFN model are established by comparing the results with that of Monte Carlo simulation. Further, the developed surrogate model is implemented to perform various parametric studies and sensitivity analyses. The influence of the volume fraction index, types of porosity, and thermal gradient on the stochastic frequency response are analyzed. Though the influence of different stochastic input parameters is strongly dependent on the volume fraction index, the mass density of metal is found to be the most sensitive parameter for the sandwich plate with FGM face sheets and homogeneous core.

Natural Frequencies Optimization of Thin-Walled Circular Cylindrical Shells Using Axially Functionally Graded Materials

Abstract: One method to avoid vibration resonance is shifting natural frequencies far away from excitation frequencies. This study investigates optimizing the natural frequencies of circular cylindrical shells using axially functionally graded materials. The constituents of functionally graded materials (FGMs) vary continuously in the longitudinal direction based on a trigonometric law or using interpolation of volume fractions at control points. The spatial change of material properties alters structural stiffness and mass, which then affects the structure’s natural frequencies. The local material properties at any place in the structure are obtained using Voigt model. First-order shear deformation theory and finite element method are used for estimating natural frequencies, and a genetic algorithm is used for optimizing material volume fractions. To demonstrate the proposed method, two optimization problems are presented. The goal of the first one is to maximize the fundamental frequency of an FGM cylindrical shell by optimizing the material volume fractions. In the second problem, we attempt to find the optimal material distribution that maximizes the distance between two adjoining natural frequencies. The optimization examples show that building cylindrical shells using axially FGM is a useful technique for optimizing their natural frequencies.

Fabrication and characterization of functionally graded material (FGM) structure containing two dissimilar steels (ER70S-6 and 308LSi) by wire arc additive manufacturing (WAAM)

Abstract: Functionally graded materials (FGM) are components that can provide different material properties in a single structure. It is sometimes required to exhibit locally different material behaviours from parts used for various purposes in the industry. In such requirements, the use of FGM structures emerges as a solution. The fabrication of FGM structures with traditional manufacturing methods is generally complicated and sometimes not possible. However, the additive manufacturing (AM) technique, which is the topic of many applications and research today, has emerged as a superior manufacturing method compared to traditional methods in fabrication FGM structures, thanks to its advantages. Fabrication in the form of layers with the AM allows the fabrication of layers with varying material properties. This study was carried out on the fabrication of FGM structures by the wire arc additive manufacturing (WAAM) method, which is one of the metal AM techniques. Low alloy steel (ER70S-6) and austenitic stainless steel (308LSi) metal wires are used in FGM structures. The FGM structure was successfully fabricated by the WAAM method. Hardness, tensile, and fatigue tests were applied to determine the mechanical properties of the part. In addition, XRD analysis and microstructure studies were carried out to understand the metallurgical properties. As a result of the mechanical tests, no defects were observed in the FGM interfaces, and an increase of up to 46% was observed in the tensile strength compared to the single-material fabrication. In hardness measurements and microstructure studies, it has been observed that the FGM structure exhibits different properties according to the changing layers. It has been concluded that the fatigue limit of the FGM part in the horizontal direction is 25% higher than in the vertical direction.

Fabrication, Microstructural Characterization and Finite Element Analysis of Functionally Graded Al-Al2O3 Disk Using Powder Metallurgy Technique

Abstract: In the present work, powder metallurgy technique was employed to fabricate a three-layer functionally graded (FG) disk. The volume fraction of metal-ceramic composition changes radially as layer-1 (100 % Al), layer-2 (95 %Al +5 % Al2O3), and layer-3 (90 %Al +10 % Al2O3). The microstructural investigation was carried out under an optical microscope and SEM (scanning electron microscopy) integrated with EDS, confirming a uniform distribution of reinforcement particles (alumina) in the matrix (aluminum). Interface microstructure indicates a successful fabrication of FGM (functionally graded material) as the transition is uniform in the graded layer without the development of any crack or void at the interface. In comparison to layer-1, the average increase in hardness values was found to be 18 % and 29 % for layer-2 and layer-3 respectively. An increment in hardness was observed in layers where alumina composition is higher. The Archimedes principle was employed to calculate the experimental density of the sample, and the theoretical models were presented to effectively estimate the density of porous FG materials. Furthermore, theoretical models for estimating material properties such as Young's modulus and yield strength of individual layers were proposed on the basis of material composition and particle shapes obtained from the microstructure of FG disk. These material properties were then used in finite element formulation for the application of rotating disk, the validation of which is also proposed. Subsequently, finite element analysis was employed to perform stress analysis on layered FG disk when subjected to centrifugal loading.

Fabrication and Characterization of Cu/SiC‐Based Axially Functionally Graded Beam

Abstract: Metal−ceramic based functionally graded materials (FGMs) are mainly used for thermal and structural applications in industry. A metal matrix‐based axially FGM beam is fabricated using a powder metallurgy manufacturing process. The main objective of this work is to develop a processing method for an axially graded beam made of Cu/SiC by stacking powder in the longitudinal direction. A three‐layered Cu/SiC FGM having a step‐wise gradation along the length is fabricated. The green specimens are prepared by the uniaxial compaction of powder mixture by the universal testing machine (UTM) followed by cold isostatic pressing (CIP). Further, a detailed microstructure analysis of the powders and the sintered specimens is conducted. The Vicker's microhardness test is also performed for each layer of the sintered specimen to analyze the effect of SiC content. A smooth transition of the ceramic content in the specimen along the length is observed. The effect of ball milling on the crystallite size is studied using Scherrer and Williamson−Hall approach. An uniform and consistent distribution of the SiC particles shows a reduction in porosities and increment in the hardness value with increase in SiC wt% is also observed. The present investigation helps to design functionally graded rotor blades, gears, and orthopedic implants.

Thermoelastic wave propagation due to local thermal shock on the functionally graded media

Abstract: Abstract The present study is based on investigating the effect of locally applied thermal shock on the ceramic side of the functionally graded (FG) domain using nonlinear Lord-Shulman generalized thermoelastic theory. The constituent materials and therefore their properties in the two-dimensional FG domain are considered to be graded as a function of horizontal or vertical coordinates according to the power law. The finite element (FE) form of the nonlinear coupled differential equation is solved using the Picard method at each time-step in the framework of the Newmark time-integration scheme. The gradation of the material properties due to FGM is incorporated using graded finite elements in the FE formulation. The numerical results concerned with studying the effect of volume fraction index and orientation of the gradation of material properties across the FG domain are presented. It is observed from the study that both the gradation of material properties, as well as the direction of orientation of material gradation, have a substantial effect on the propagation of the thermal and elastic waves in the domain. Moreover, the thermal waves appear to be more dominant than the elastic waves at the time of application of thermal shock, which may also alter as time progresses.

Modal Study on FGM Elliptical Plate Under Thermal Environment

Abstract: This research article deals with modal study of functionally graded material (FGM) elliptical plate with thermal environment. Material parameters are functions of temperature and are varying in the thickness direction. Power law gradation is adopted for variation of the material constants. Results are provided under different end conditions under thermal effect. The FEM application software COMSOL-5.4 is used for acquiring natural frequencies and their respective mode shapes. The results obtained using FEM are agree well with results published in previous research articles. The effects of temperature rise, material gradient index, aspect ratio and end conditions on the eigenfrequencies of FGM elliptical plate are explored.

Nonlinear Axisymmetric Vibration of Sandwich FGM Shallow Spherical Caps with Lightweight Porous Core

Abstract: This paper presents the axisymmetric vibration responses of sandwich Functionally graded material (FGM) shallow spherical caps with lightweight porous core subjected to uniformly external loads and shell-foundation Pasternak interaction. Based on the first-order shear deformation theory (FSDT) with von Karman geometrical nonlinearity, the governing equations are established. By using the Galerkin method and the Runge–Kutta method, the fundamental frequencies and the nonlinear dynamic responses of the shell are obtained. The effects of porosity coefficient, geometrical parameters, and foundation are considered.

Effect of Porosity on the Thermal Buckling Analysis of Power and Sigmoid Law Functionally Graded Material Sandwich Plates Based on Sinusoidal Shear Deformation Theory

Abstract: This work examines the effect of porosity distributions on thermal buckling analysis of functionally graded material (FGM) sandwich plates. To consider the porosity effect, five different types of distribution models, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven are considered. It is assumed that the FGM faces of the sandwich plate are porous while the ceramic core is nonporous. To investigate the thermal buckling behavior of porous FGM sandwich plates, four different types of thermal loads, such as uniform, linear, nonlinear, and sinusoidal temperature rise along the thickness direction are considered. Effective material properties and thermal expansion coefficients of FGM sandwich plates are evaluated based on Voigt’s micromechanical model considering power law FGM (P-FGM) and sigmoid function FGM (S-FGM). The analytical solution is carried out using Hamilton’s variational principle considering the von Karman nonlinearity. The equilibrium and stability equations are derived based on sinusoidal shear deformation theory (SSDT). Numerical results are obtained to observe the influence of different porosity distributions, porosity coefficients, thermal loadings, and geometrical parameters over critical thermal buckling temperature.

A new higher-order shear deformation theory for frequency analysis of functionally graded porous plates

Abstract: The current investigation aims to account for the influence of porosity modeling while studying the dynamic response of functionally graded material (FGM) plates within the framework of a new, higher-order shear deformation theory for the first time. In the newly developed porosity modeling, the reciprocal effect of mass density and Young’s modulus is considered. Furthermore, silicon carbide in the ceramic phase and nickel in the metallic phase are selected as the constituent materials of the functionally graded plate. Based upon the new higher-order theory, the kinetic and kinematic relations are derived. This theory does not need any shear correction factor. The dynamic form of the principle of virtual work is employed to achieve governing equations of structure. Afterward, Galerkin’s method is implemented to solve obtained governing equations of porous, functionally graded plates. In order to verify the accuracy of the method, the obtained results were compared with the results reported in the literature, and good agreement was found. At last, the influences of some parameters such as porosity coefficient, length to thickness ratio, and aspect ratio of the porous, FGM plate on the dimensionless frequency are studied and the results are illustrated in detail.

Effect of an edge crack on stress concentration around hole surrounded by functionally graded material layer

Abstract: The present work aims to investigate the effect of an edge crack on the stress concentration around the circular hole surrounded by Functionally Graded Material (FGM) in an infinite plate subjected to uniaxial tensile load. The numerical investigation has been carried out using Extended Finite Element Method (XFEM). Two cases have been analysed in this work, i.e. the whole plate made up of radial FGM and homogeneous material plate having radial FGM layer around the hole. Young’s modulus of FGM varies according to exponential and power law function. The relations of stress intensity factor (SIF) and stress concentration factor (SCF) with normalised crack length, Young’s modulus ratio, FGM layer thickness and power law index have been presented. It has been observed that the FGM layer case has low SCF around hole than FGM plate case in presence of an edge crack.

Porosity-dependent free vibration and transient responses of functionally graded composite plates employing higher order thickness stretching model

Abstract: Tailoring the mechanical properties in hybrid materials, like functionally graded materials (FGMs), has become more pragmatic with the recent progress in material manufacturing and design. The porosities in FGMs, which develop during the manufacturing process, may become detrimental to armored plates or bulletproof designs. On the other hand, gradient-porosity distributions may have broad advantages in the design of lightweight and variable-stiffness aircraft components. The present study investigates the free vibration and transient responses of porosity-gradient FGM plates. A higher order theory, which considers the transverse shear and normal deformation, warping of the transverse cross-section, and higher order rotary inertia, is utilized for the first time to model the deformation of the porous FGM plate. The advantages of this model are (i) higher order kinematic terms for membrane and bending deformations due to the coupled membrane-bending behavior of FGMs in addition to the thickness-stretching effects, and (ii) the flexibility of applying external loads at different points along the thickness direction of the FGM plate. An analytical solution technique, popularly known as Navier’s approach, is adopted for the spatial solutions, and Newmark’s average acceleration method is utilized for the temporal solutions. The influence of the geometrical and porosity parameters on the structure’s vibration response is studied. Natural frequencies are affected significantly with uniform porosity distribution, while graded porosities can tweak vibration response in a small range but with better control. In the absence of the elasticity solutions, the present results may be considered the possible benchmark solutions for comparison of the other two-dimensional (2D) kinematic models.