Functionally Graded Materials Research Articles

316L-toughened porous Al2O3-based ceramic functionally graded materials using binder jetting

Al2O3-based ceramic functionally graded materials (FGMs) containing 1 wt% CuO and 4 wt% TiO2 as sintering aids and 0–40 wt% 316L as a toughening phase are fabricated by binder jetting additive manufacturing, and the low-temperature co-sintering toughening mechanism was studied. According to the 3D Stereo Microscope and XRD results, the interfacial microstructure exhibited a noticeable gradient change after being sintered from 1200 °C to 1450 °C for 2 h, and the main phases were Al2O3, γ-austenitie, Fe3C and a small amount of δ-ferrite. The FGMs sintered at 1450 °C had maximum relative density, X–Z-axis dimensional shrinkage and average bending strength values of 70.05%, 4.89%, 10.15%, 17.53% and 26.9 ± 0.87 MPa, respectively. Bending cracks originated from the pure Al2O3-based ceramic layer and gradually propagated to the high-316L side, accompanied by the crack bridging and deflection phenomena. The maximum crack deflection degree was about 90° at 1200 °C and 1400 °C. Obviously, the existence of crack bridging and deflection illustrated that 316L addition effectively improves the toughness of FGMs.

Application of Chebyshev collocation element method to Green-Naghdi thermoelasticity of a bi-layered media consists of FGM and viscoelastic domains

In this study, the generalized coupled thermoelastic wave propagation and temporal evolution in a bi-layered system are analyzed. The main layer is made of functionally graded materials (FGM), while the holder layer is viscoelastic. The constituent volume fractions in the FGM layer are calculated by a power law function. Moreover, the Voigt rule of mixtures is employed to obtain the homogenized material properties. On the other hand, the constitutive law for the viscoelastic environment is considered based on the Kelvin-Voigt model. The heat conduction equation for each layer is represented based on the general form of the Green-Naghdi theory. First, for each layer, two motion and heat conduction coupled equations are derived, as well as the boundary and appropriate continuity conditions. The Chebyshev collocation element (CCE) method is used to solve the spatial-dependent parts of equations and also assemble the governing matrices into a global system. Finally, the Newmark numerical integration method is implemented to solve the ODEs and calculate the system response. The achieved response is verified with limited articles in the literature. Some parametric results are shown to evaluate the performance of FG and viscoelastic characteristics on the FGM layer response which is subjected to a thermal shock.

Modeling of FGM contacts using piecewise linear variation in Young’s modulus

Functionally graded materials (FGM) are used as coatings at contact interfaces to tailor the desired surface properties while avoiding sudden changes in material properties. This work investigates the full-sliding frictional contact between a rigid indenter and FGM-coated half-space under plane-strain conditions. The FGM-coating is divided into a number of sublayers, with Young’s modulus varying linearly in each sublayer, effectively making the overall variation piece-wise linear. This approach overcomes the disadvantage of discontinuity of material properties at the interfaces of sublayers that exists in multi-layered piecewise constant modeling. Series solution approach based on the solution to the singular integral equation that characterizes the 2D contact is considered. In this approach, pressure distribution at the interface is expressed as a series expansion. This approach can be used to analyze any arbitrarily shaped contacts. The results show that the piecewise linear FGM modeling approach with tractions expressed as modified Fourier series is a more accurate and efficient way of representing FGM material property as compared to piecewise constant material properties, which are used in most of the existing literature. The number of layers needed to converge in continuous variation is also very less compared to the piece-wise constant and hence the computational time is less.

Analytical study on bending behaviour of plates made of functionally graded materials using higher-order shear

Functionally Graded Materials (FGM) are the alternate replacement of laminated composites and metallic substances in structural members from daily use to aerospace applications due to their superior characteristics like ability to with stand large temperature gradients, competence to endure to heavy forces and superior sturdy properties, lesser residual and thermal stresses, high capacity to resist surface wear and tear, and an overall increment in strength to weight ratio. As this advanced class of materials are being used as the structural components their ability to with stand various loads considering different boundary conditions under various analytical approaches is very essential even before put into use. The key objective of the current study is to apply higher–order displacement model to determine bending behaviour of plate made of functionally graded material with distinct geometrical constraints, forces and degree of orthotropy under simply supported boundary conditions. An analytical investigation on the behaviour stresses developed in plates made of functionally graded material by applying higher order shear displacement model approach is carried-out by considering the effective material properties according to power law distribution of the volume fraction of the constituents and the equations obtained for simply supported beam made functionally graded materials from closed form using Navier’s empirical equations. A Computer code has been developed using MATHEMATICA 7.0 Software for displacement model to predict deflections and stresses. The accurateness of the current higher-order shear deformation theory has been tested for static bending of functionally graded material plates. The findings are reported in non-dimensional form for various thickness ratios, aspect ratios, degrees of orthotropy, volume fraction index values, and loading circumstances for static bending issues involving mechanical loading of functionally graded material plates. All the solutions derived by the current higher order shear deformation theory agree well with the other plate theory solutions that are documented in the literature.

Microstructure and Mechanical Properties of Functionally Graded AlSi/MWCNT Composite Cylinders

Experimental fabrication of functionally graded Aluminum Silicon-carbon nanotubes (AlSi-MWCNT) reinforcement is significantly less, despite substantial theoretical interest. Many studies focused on axially layered functionally graded material because of ease of fabrication. Full advantage of AlSi-MWCNT functionally graded material only is taken when designed to the various shapes. In this research work, functionally graded cylinders were produced with 2wt% MWCNT at the outer surface to provide a complex and wear-resistant surface. The interior surface is soft with AlSi to provide elasticity. FGM1 sample indicates 112% and 11% increase in maximum tensile strength compared to AlSi and AlSi-MWCNT1wt%. FGM1 sample shows a 37% increase in elongation percentage compared to the AlSi-MWCNT1wt% composite. Test samples showing the typical nature of barrelling. FGM1 sample exhibits compressive strength of 237MPa, exceeding by 245% that of AlSi and by 3.5% that of AlSi-MWCNT1wt%. Three samples consider for each test. Hardness value ranges from 65HV at the core to 115HV at the outer surface. Hardness value Exceeds 56% in the outer layer compared to an inner region of FGM2.There is a proper bond between the layers, and the same demonstrate with properties of tensile, compressive, and hardness. OM with porosity, SEM with EDX evaluates to predict structural gradation in FGM cylinder. KEYWORDS: Aluminum silicon (AlSi) alloy; Functionally graded materials(FGM); Multi wall carbon nano tubes (MWCNT); Nano-composites; Thermo-mechanical processing

Mechanical Response of Thin Composite Beams Made of Functionally Graded Material Using Finite Element Method

Functionally Graded Material (FGM) is a new generation of composite materials, it can be used for different engineering fields according to the loading environment, but the study of its mechanical behavior requires sophisticated numerical and analytical models. Several investigations in these models are available in the literature, however, most of those investigations are based on simplifying assumptions. In this paper, we present a three-dimensional finite element modeling of functionally graded material (FGM) beams subjected to static loading. Material properties are assumed to vary continuously along the beam thickness according to the power-law distribution with linear elastic behavior. The FGM beams are discretized by hexahedral finite elements type C3D20R (continuum stress/displacement, three-dimensional 20-node, reduced integration). We studied several numerical examples of FGM beams and compare the obtained numerical results with those of analytical models in the literature.

Optimization of functionally graded plates under Thermo-elastic free vibration using nature-based algorithms

This article presents the parametric optimization of the free vibration characteristics of a functionally graded material (FGM) plate exposed to nonlinear thermal loading using the finite element method and nature-based algorithms. The one-dimensional (1D) Fourier heat conduction equation is used to calculate temperature distributions over the thickness of the plate. Using Lagrange’s equation, we get the dynamic equation of motion for the plate. An eight-noded iso-parametric plate element with five degrees of freedom per node is used in the finite element formulation based on first-order shear deformation theory. Rectangular plates have temperature-dependent material characteristics; the thickness of the plates is scaled using a straightforward power law distribution. Here, the investigation of the FGM plate is conducted with two different boundary conditions, such as simple support and fully clamped. Additionally, new hybrid optimization approaches, namely RSM-Composite Desirability Optimization (RSM-CDO), Whale Optimization Algorithm (WOA), Corrected Moth Search Optimization (CMSO), Lichtenberg Algorithm Optimization (LAO), Sunflower Optimization Algorithm (SFO), and Forensic-Based Investigation Algorithm (FBI), are utilised to determine the best optimal solution, and the obtained findings are validated using confirmatory tests.

A novel way for vibration control of FGM fluid-conveying pipes via NiTiNOL-steel wire rope

In this study, a coupling model of fluid-conveying pipes made of functionally graded materials (FGMs) with NiTiNOL-steel (NiTi-ST) for vibration absorption is investigated. The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method (GTM) and harmonic balance method (HBM). The harmonic balance solutions and the numerical results are consistent. Also, the linearized stability of the structure is determined. The effects of the structure parameters on the absorption performance are also studied. The results show that the NiTi-ST is an effective means of vibration absorption. Furthermore, in studying the effect of the NiTi-ST, a closed detached response (CDR) is first observed. It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR. This vibration absorption device can be extended to offer more general vibration control in engineering applications.

Unsteady temperature distribution in a cylinder made of functionally graded materials under circumferentially-varying convective heat transfer boundary conditions

Abstract A novel model on 2D unsteady conductive heat transfer in an infinite hollow cylinder is proposed. The cylinder is made of functionally graded material (FGM) that has variable properties both in radial and angular directions. Volumetric heat capacity and thermal conductivity coefficient are changed according to the power function of the radius. In the presence of variable coefficients, the governing equations of unsteady heat transfer in FGMs have caused the complexity. The Laplace transform method is used to transfer the energy equation from time to frequency domain whereas the meromorphic function is used for the inverse Laplace transform to obtain the desired solutions. The closed form solutions have been well validated and the results have been presented for different values of functionally graded indices for thermal conductivity coefficients and volumetric heat capacity. Two different FGM cases with different complicated thermal boundary conditions have been investigated. The first case has a constant temperature in the inner radius and a variable heat flux along with the convection condition in the outer radius. In the second case, the inner radius has a specific harmonic temperature and the outer radius is exposed to the convective conditions. It was observed that in both cases, the temperature value in the cylinder decreases with the increase of the FG index for the conductivity coefficient. The presented analytical solution provides a good tool for validating unsteady numerical solutions presented in the field of heat transfer in FGMs.

Understanding high-temperature corrosion behavior of an AlN/Mo functionally graded material exposed to Li/LiF-LiCl-LiBr vapor

The high-temperature corrosion behavior of an AlN/Mo functionally graded material (FGM) under the Li/LiF-LiCl-LiBr vapor has been investigated. It is suggested that the Li vapor diffuses along the AlN and AlN/Mo grain boundaries and enters the interior of adjacent AlN grains, leading to the disintegration of AlN grains and subsequent failures. The 3D Mo networks are barely corroded, thus preventing cracking that may occur due to the inconsistent deformation inside the FGM. This work unravels the high-temperature corrosion mechanisms for the AlN/Mo FGM. Meanwhile, the operating temperature threshold for the liquid metal batteries employing Mo/AlN/Mo seals is determined to be ∼ 600 °C.

Mechanical and Tribological Properties of Al2024/Al2O3 Functionally Graded Spur Gears Synthesized by Centrifugal Casting Process

The mechanical and tribological properties of spur gears are important because they can affect the efficiency and wear life of these gears. Thus, this study's primary goal is to use functionally graded material (FGM) to enhance the properties of Al2024 aluminium alloy spur gears. The mechanical and tribological properties of aluminium alloy Al2024 with graded Al2O3 reinforcement particles spur gears synthesized by the vertical centrifugal casting (VCC) process were investigated experimentally. Different weight percentages were used for the reinforcement particles, including 0, 2, 5, and 10 wt.% of Al2O3. Microstructural and mechanical properties were determined by SEM, EDS, and hardness tests. The Al2024/Al2O3 FGM spur gears were subjected also to dry sliding wear conditions. It was seen that hardness, strength, and wear resistance values increased by adding Al2O3 reinforcement particles to the Al2024 base material. In addition, the wear rate of FGM gears decreased by increasing the Al2O3 reinforcement particles in Al2024 alloy.

High-Precision Isogeometric Static Bending Analysis of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

A new quasi-three-dimensional (3D) shear deformation theory, called the spectral displacement formulation (SDF), is proposed for high-precision static bending analyses of functionally graded plates. The main idea is to expand unknown displacement fields into Chebyshev series of a unique form in the thickness direction; the truncation numbers are set to be adjustable to meet various application requirements. Specifically, 3D elasticity solutions and traction-free boundary conditions can be approached by increasing the number of Chebyshev bases. The SDF is also an extension of the classical plate theory and naturally avoids the shear locking problem, making it versatile for functionally graded material (FGM) plates of arbitrary thicknesses. The C1 continuity requirement for the discretization of the generalized displacements is conveniently fulfilled by the nonuniform rational B-splines (NURBS)-based isogeometric method. Numerical examples demonstrate the excellent performance of the proposed method for the displacement and stress analyses of functionally graded plates. The high precision and versatility of the present method have manifested its great potential applications in strain-based or stress-based reliability analysis, optimization design, fatigue analysis, and fracture analysis of FGM plates, and other related fields.

Nonlinear dynamic analysis on centrifugal stiffening of rotating cracked tapered functionally graded beam for flap-wise vibrations

Vibration-based condition monitoring for remotely located rotating blades is one of the important aspects to avoid sudden breakdown of the machinery. Vibration analysis of damaged blades provides the information to identify the damage during operation. In this work, dynamic attributes of rotating cracked tapered cantilever functionally graded material (FGM) beams for various tapered configurations are investigated using energy method. The nonlinearity due to in plane stretching as a result of large deformations is taken in to consideration. Nonlinear governing equations for cracked rotating tapered FGM beams are generated by optimizing the energy functional. An iterative algorithm is developed to solve the derived nonlinear equations. The effects corresponding to location of crack and centrifugal stiffening on the various modes has been presented for different tapered configurations, material indices, crack depths and rotational speeds. Crack compensating speeds are studied and reported for different tapered ratios and crack parameters for the first time. The effect of crack location and crack depth on the first two nonlinear frequency ratios is also investigated for different tapered configurations and material indices. The influence of centrifugal stiffening on nonlinear responses of FGM beams is presented for various crack parameters and tapered configurations.

Influences of arbitrary-distributed Kerr foundation on free vibration and nonlinear transient response of functionally graded plate in thermal environment

For the first time, a novel theoretical model is presented for analyzing the effects of the arbitrary-distributed Kerr foundation on the free vibration and transient responses of the functionally graded material (FGM) plate in a thermal environment. According to the power law distribution, the mechanical characteristics of FGM plates are assumed to vary with plate thickness. The three-parameter Kerr model is founded on the independence of the upper and lower elastic layers with respect to the shear layer. The shape and location of the elastic foundation can be determined arbitrarily using mathematical functions. In the area of the FGM plate, the distribution of the elastic foundation is assumed to be either centralized or decentralized. The Reddy’s third-order shear deformation theory is utilized to express the governing equations. Then, the dynamical characteristics of the FGM plate are obtained by using the Galerkin’s method. To validate the accuracy of the current computational model, the achieved results are compared to those derived from published literature. In addition, graphical representations of the effects of stiffness, distributions, and geometrical parameters of elastic foundation, geometrical parameters of plate, material properties, and thermal environment on the vibrational characteristics of the plates are provided.

Warping included mixed finite elements for bending and stresses of functionally graded exact curved beams

This study presents a warping included mixed finite element formulation for the static and stress analyses of functionally graded (FG) exact curved beams. Another distinctive feature of this study is to present the range of geometric and material parameters where the first-order shear deformation theory lacks necessary precision. The constitutive equations are derived from the 3D elasticity theory of an elastic continuum. The couple effects are considered in addition to the variations of FG material constituents through the transverse/axial directions. The mixed finite element formulation is enhanced by the cross-sectional warping deformations over a displacement-type finite element formulation. The two-noded curved mixed finite elements with 12 degrees of freedom at per node are derived over exact curvature and length. Satisfactory results are obtained for the static responses and stresses of axially FG-sandwich and transversely FG exact curved beams with power-law dependence compared to the 3D behavior of brick finite elements. Finally, the influences of ellipticity, width to thickness ratio, FG material constituents, and material gradient index on the static response of FG exact curved beams are investigated.

GDQ computation for thermal vibration of thick FGM plates by using third-order shear deformation theory

The third-order shear deformation theory (TSDT) effects on the thick functionally graded material (FGM) plates under thermal vibration are investigated by using the generalized differential quadrature (GDQ) method. The nonlinear coefficient term of displacement field of TSDT is used to derive the equations of motion for thermal vibration of thick FGM plates. The simpler form stiffness of FGM plates under linear temperature rise is considered in the thermo-elastic stress–strain relations. The dynamic equilibrium differential equations of FGM plates in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads and inertia terms are derived. Two parametric: environment temperature and FGM power law index effects on the thermal stress and center deflection of FGM thick plates are investigated.

Investigation of the mechanical properties triple periodic minimal surfaces lattice structures with functional graded of porosity

In recent years, triple periodic minimal surfaces (TPMS) have attracted attention in many applications such as biomaterials, aerospace, defense industry etc. lightweight components with high strength and functionally graded material (FGM). In particular, the mechanical properties and deformation behavior of these structures under load should be examined. In this study, it was aimed to evaluate the manufacturability and mechanical performance of fixed pore size and functional graded porosity (FGP) lattice structures produced by fused deposition modelling (FDM) method. TPMS primitive and gyroid lattice structures designed in the dimensions of 20 × 20 × 20 mm with fixed 20% pore size and functional graded (FG) from 20% to 40% pore size were used in the experiments. In order to reveal the effects of pore size on mechanical performance, uniaxial compression tests were carried out. In addition, for the validation of the experimental results, compression tests with the finite element method (FEM) were simulated for each sample. In the two different pore size changes tested in the study, the gyroid lattice structure showed the highest mechanical performance compared to the primitive lattice structure. In addition, the FEM results were in good agreement with the experimental results.

Tracking of Marangoni driven motion during laser powder bed fusion

Laser Powder Bed Fusion (LPBF) can be used to create Functionally Graded Materials (FGMs) by selectively distributing property augmenting particles throughout the build matrix. With this method parts can be created with nonhomogeneous properties tuned to spatially varied, pre-determined design constraints. To unlock this capability, the fluid motion that occurs in the molten liquid phase must be thoroughly understood. More importantly, the actual tracking of motion during the LPBF process is needed. A numerical model of heat transfer and fluid flow in LPBF process was created. Using results from the model the motion of particles starting at many different locations was tracked. The average change in position for these particles based on starting location was calculated. The effects of non-dimensional parameters on melt pool size were examined. These results were validated experimentally and compared to what is available in the literature.

Optimization of Neural Network architecture and derivation of closed-form equation to predict ultimate load of functionally graded material plate

Functionally Graded Material (FGM) plate is a complicated structure with complex allocation of spatially changing proportions of ceramic and metal within the matter. Various analytical and numerical methods have been applied with a view to evaluating the critical load of FGM plate. However, these conventional methods struggle when the computational complexity is significant, which represents an obstacle to incorporation with other advanced techniques where computational power is required (e.g. optimization or random simulations). The Neural Network (NNet) model has been successfully applied to resolve this issue. However, the conventional NNet requires proper configuration to take advantage of the model, and thus, careful parameter tuning is required. Furthermore, the NNet is typically a “black box,” where the prediction mechanism is hidden. This paper establishes an optimized architecture for NNet, with parametric study of the model’s hyperparameters. Variance propagation is also applied to observe the variation of the model’s performance on random sub-databases splintered from the database. To this end, the explicit expression of the trained NNet model is provided after mathematically deploying the hidden algebra behind an NNet prediction. The developed model has very promising evaluation metrics: R2, MAE, and RMSE on the test set are 0.999925, 0.067516, and 0.146438, respectively.

Finite-Element Modeling for Static Bending Analysis of Rotating Two-Layer FGM Beams with Shear Connectors Resting on Imperfect Elastic Foundations

The static bending of rotating two-layer functionally graded material (FGM) beams with shear connectors resting on imperfect elastic foundations was performed for the first time in this study. Timoshenko beam theory and the finite-element method are used to derive finite-element formulations. The precision of the current approach and mechanical model is shown by comparing the calculated findings of this study to those of previous precise papers. A wide variety of parameter studies are carried out to capture the impact of geometric and material characteristics on the structure’s static bending behaviors, such as the distance d, rotational speed, volume fraction index, elastic foundation parameters, and boundary conditions. This paper’s theory and mechanical models are fascinating since mechanical systems involving rotational motion are pretty standard in engineering practice. Therefore, the computed results of this work aim to contribute to our understanding of structures of this kind.