Functionally Graded Materials Research Articles

Effect of Three Layered Centrifugal Casting on Tribological and Microstructural Characteristics of Mg Based Functionally Graded Material Alloy

Objectives: The aim of this study is to examine the tribological properties and microstructural of functionally graded material (FGM) composites based on magnesium (Mg) base material. Magnesium alloys are commonly employed in the development of biomaterials for implant applications owing to their favorable corrosion properties. The research objective is to produce Zn/Mo reinforced functionally graded magnesium composites using the centrifugal casting. Methods: A centrifugal process was employed to fabricate a functionally graded material (FGM) consisting of three layers with a cylindrical shape. The base material used for this FGM was Magnesium, which was alloyed with 10% of Zn and 10% of Mo. The developed FGMs have been analyzed for their mechanical and microstructural characteristics. The microstructure of the samples were analyzed via the Optical Microscope (OM). It is identified that denser particle molybdenum (Mo) have influenced the mechanical and microstructural characteristics of the FGM composites. Findings: Results recommend that, all the three layered testing’s, Mg (80%) +Zn (10%) + Mo (10%) composite exhibited favorable mechanical and microstructural properties. It is identified that denser particle of Mo which is influenced the microstructural characteristics. The alteration in micro hardness in the direction of centrifugal force is observed, and it is observed that the minimum wear loss for sliding wear samples A, B & C of Mg based FGM alloy were found to be 0.0018 g, 0.028 g and 0.031 g respectively, while the maximum wear loss for sliding wear samples A, B & C of FGM alloy were found to be 0.0021 g, 0.41 g and 0.31 g respectively. Novelty: In this study, a novel three-layered centrifugal casting technique was devised. Owing to its rapid degradability, the anticipated duration of the implants within the human body would be significantly shorter in comparison to alternative biomaterials such as Titanium and Stainless steel. Furthermore, the findings from the conducted tests strongly advocate for the utilization of this technique in biomedical implantations. Keywords: Functionally graded material (FGM), Centrifugal casting, Tribological characteristics, microstructural behavior, and bio­implants

Machine learning-based prediction of heat transfer performance in annular fins with functionally graded materials

This paper presents a study investigating the performance of functionally graded material (FGM) annular fins in heat transfer applications. An annular fin is a circular or annular structure used to improve heat transfer in various systems such as heat exchangers, electronic cooling systems, and power generation equipment. The main objective of this study is to analyze the efficiency of the ring fin in terms of heat transfer and temperature distribution. The fin surfaces are exposed to convection and radiation to dissipate heat. A supervised machine learning method was used to study the heat transfer characteristics and temperature distribution in the annular fin. In particular, a feedback architecture with the BFGS Quasi-Newton training algorithm (trainbfg) was used to analyze the solutions of the mathematical model governing the problem. This approach allows an in-depth study of the performance of fins, taking into account various physical parameters that affect its performance. To ensure the accuracy of the obtained solutions, a comparative analysis was performed using guided machine learning. The results were compared with those obtained by conventional methods such as the homotopy perturbation method, the finite difference method, and the Runge–Kutta method. In addition, a thorough statistical analysis was performed to confirm the reliability of the solutions. The results of this study provide valuable information on the behavior and performance of annular fins made from functionally graded materials. These findings contribute to the design and optimization of heat transfer systems, enabling better heat management and efficient use of available space.

Active layer damping of bi-directionally tapered functionally graded sandwich plates with 1-3 piezoelectric composites

This article investigates the effect of smart damping on bi-directionally tapered functionally graded sandwich plates. The substrate comprises FG material on both sides of the core of either soft herex or ceramic material. The viscoelastic layer of ALD is restrained, while the compelling layer consists of 1-3PZC. The finite element formulation developed incorporates layer-wise and first-order-shear-deformation theory. The plate’s damping is actively controlled using velocity feedback control incorporating piezoelectric patches. The effects of various parameters of taper ratio and patch positions on vibration control are investigated. The efficacy of the ALD in improving the structural performance of plates is investigated.

Three-dimensional nonlinear stress analysis of functionally graded shells subjected to displacement-dependent loads

The nonlinear geometrically exact (GeX) hybrid-mixed four-node solid-shell element under non-conservative loading, developed in the companion paper, is here extended to the stress analysis of functionally graded material (FGM) shells. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms can be taken exactly at element nodes. The FGM solid-shell element formulation is based on the choice of N sampling surfaces (SaS) parallel to the middle surface and located at Chebyshev polynomial nodes within the shell as well as on the outer surfaces, to introduce the displacements of these surfaces as basic unknowns. The use of Lagrange polynomials of degree N–1 in the distributions of displacements, strains, stresses, and elastic coefficients through the thickness of the shell leads to an efficient 3N-parameter shell formulation. To develop the FGM four-node solid-shell element based on the hybrid-mixed method, in which strains and stresses are utilized as primary variables, the Hu-Washizu variational principle is applied. Due to the analytical integration used to evaluate the tangent stiffness matrix, the developed FGM solid-shell element subjected to displacement-dependent loads shows superior performance in the case of coarse meshes and allows the use of only one load step in most of the considered benchmark problems. It has been established that the difference between the second Piola-Kirchhoff and Cauchy stress tensors in non-conservative problems for FGM shells undergoing moderately large strains can be significant.

Galerkin finite block method with Lagrange multipliers method for cracked solids in functionally graded materials

This paper presents the application of the Galerkin Finite Block Method (GFBM) to address cracked solids associated with Functionally Graded Materials (FGMs), leveraging the foundational principles of the Galerkin method. The equilibrium equations pertinent to FGMs are articulated in their weak form. Employing Chebyshev polynomials as shape functions, the GFBM integrates mapping techniques to accommodate irregular finite or semi-infinite physical domains. Boundary and continuity conditions are enforced through the Lagrange Multiplier Method. The domain integrals are calculated through either analytical or numerical integration. The proposed method can easily solve the edge crack or diagonal crack problem by using the crack opening displacement method. The accuracy and convergence of the proposed method are illustrated through a selection of numerical examples. The obtained numerical solutions are verified with analytical solutions and the results from the Finite Element Method.

Characteristics of 3D Printed Functionally Graded Material for Replacement of Dissimilar Metal Weld in Nuclear Reactor

The dissimilar metal welds in the most of the reactors are connections between low alloy steel parts and stainless steel piping. There is a high possibility of primary water stress corrosion cracking (PWSCC) damage attributed to residual stress caused by the difference in material properties in the dissimilar metal weld joints. A number of accidents such as leakage of radioactive coolant due to PWSCC have been reported around the world, posing a great threat to nuclear safety. The objective of this study is to develop a technology that can fundamentally remove dissimilar metal welds by replacing the existing dissimilar metal parts with the functionally graded material (FGM) manufactured by metal 3D printing consisting of low alloy steel and austenitic stainless steel. A powder production, mixing ratio calculation, and metal 3D printing were performed to fabricate the low alloy steel-stainless steel FGM, and microstructure analysis, mechanical properties, and coefficient of thermal expansion (CTE) measurement of the FGM were performed. As a result, it is observed that CTE tended to increase as the austenite content increased in FGM. The gradual change of coefficient of thermal expansion in a FGM showed that the additive manufacturing using 3D printing was effective for preventing an abrupt change in thermal expansion properties throughout their layers.

Symplectic superposition method for the free-vibrating problem of sigmoid functionally graded material rectangular thin plates clamped at four edges

The symplectic superposition method (SSM) is implemented to investigate the free vibration problem of sigmoid functionally graded material (FGM) rectangular thin plates clamped at four edges. Firstly, the vibration equation of the sigmoid FGM rectangular thin plate is transformed into Hamiltonian canonical equations. Then based on the analysis of boundary conditions of the plate, the vibration problem of the sigmoid FGM rectangular thin plate clamped at four edges is decomposed as two sub-problems simply supported on two opposite edges. And then based on the symplectic elasticity method (SEM), the series expansion solutions for the two sub-vibrating problems are obtained. Afterward, by superposing the series expansion solutions for the two sub-vibrating problems, a symplectic superposition solution of the freely vibrating sigmoid FGM rectangular thin plates clamped at four edges is obtained. Finally, we apply the obtained symplectic superposition solution to research the frequencies and vibration mode functions of some specific sigmoid FGM rectangular thin plates, and the impact of the aspect ratio a/b and material gradient index k on the vibration frequencies of the sigmoid FGM rectangular thin plates is studied.

Thermo-elastic Characteristics of Thermal Barrier Coating in a Gas Turbine Combustion Chamber with an Intermediate FGM Layer

This study is focused on the analysis of thermos-elastic characteristics of a gas turbine combustion chamber, where the inner surface experiences a higher temperature while the outer region of the wall should be thermally conductive to dissipate the heat of combustion. Using a single material is not suitable to ensure the above two requirements simultaneously. Instead of using a single material, a layered combustion chamber with high-temperature material at the inner region and thermally conductive material at the outer region can be a solution. This produces the problem of a sharp interface where disbonding occurs due to high thermal stresses. The problem of sharp interface can be eliminated by using a functionally graded material (FGM) layer in between the inner and outer layers of the combustion chamber. The present study considers a gas turbine combustion chamber consisting of three layers: the inner layer is used as a thermal barrier coating, the intermediate layer is a smooth transition from the inner layer to the outer layer, and the outer layer is a thermally conductive material. ANSYS simulation is used for the analysis of thermos-elastic characteristics of the combustion chamber with homogeneous and FGM intermediate layers. The effect of linear and nonlinear material distributions in the FGM layer on the thermos-elastic characteristics is studied. A comparison of results reveals that thermal stress smoothly changes from the inner layer to the outer layer in the case of the FGM intermediate layer compared to the homogeneous intermediate layer. This suggests that a combustion chamber with an FGM intermediate layer is more reliable than a homogeneous intermediate layer.

Discovery of microsegregation-aided transformation and twinning-induced plasticity in low Mn steel through directed energy deposition of functionally graded materials

Functionally graded materials (FGMs) combining two dissimilar steels, stainless steel 316 L and high-strength low-alloy steel, were additively manufactured using directed energy deposition. High-throughput characterization of the dissimilar steel FGM led to the discovery of a low Manganese (Mn<1 wt.%) TRIP (transformation-induced plasticity) and TWIP (twinning-induced plasticity) steel with a metastable microstructure enabled by additive manufacturing. Microsegregation from non-equilibrium solidification caused phase stability and stacking fault energy heterogeneity, leading to TRIP and TWIP effects in the as-built condition without heat treatment. Tensile testing of the new as-built TRIP and TWIP steel resulted in ultimate tensile strength of 960 MPa, yield strength of 415 MPa, total elongation of 26 %, and a unique strain hardening rate that increases after yielding. We compare experimental measurements of microsegregation with thermodynamic modeling to discuss the impact of microsegregation on phase stability, stacking fault energy, and solidification cracking susceptibility in additively manufactured FGMs. The highlights of this work include the discovery of a novel pathway for achieving TRIP and TWIP effects in additively manufactured steels without heat treatment. This work also shows that the TWIP effect can be introduced without high Manganese content playing a critical role in adjusting stacking fault energy.

Vibration analysis of Timoshenko microbeams made of functionally graded materials on a Winkler-Pasternak elastic foundation

In this work, the free vibration analysis of Timoshenko microbeams made of the Functionally Graded Material (FGM) on the Winkler-Paternak elastic foundation based on the Modified Coupled Stress Theory (MCST) is investigated. Material characteristics of the beam vary throughout the thickness according to the power distribution and are estimated through Mori–Tanaka, Hashin-Shtrikman and Voigt homogenization techniques. The Timoshenko microbeam model considering the length scale parameter is applied. The free vibration differential equations of FGM microbeams are established based on the Finite Element Method (FEM) and Kosmatka’s shape functions. The influences of the size-effect, foundation, material, and geometry parameters on the vibration frequency are then analyzed. It is shown that the study can be applied to other FGMs as well as more complex beam structures.

Advanced frequency of thick FGM cylindrical shells with fully homogeneous equation

The effects of shear deformation theory and improved shear correction factors on the advanced computation of frequencies by using the fully homogeneous equation for thick functionally graded material (FGM) circular cylindrical shells are studied. It is quite reasonable to consider the extra advanced effect of third-order shear deformation theory (TSDT) of displacements on the varied shear correction coefficient. The values of advanced nonlinear shear correction coefficient are usually functions of the nonlinear coefficient term in TSDT, power-law exponent parameter, and environment temperature. The main achievements in the nonlinear case of displacements and with the varied value of shear correction coefficients, the non-dimensional fundamental frequencies are estimated, investigated, and compared with the values in the linear case. This paper aims to study the fundamental frequencies of very thick FGM cylindrical shells under the advanced effects of shear deformation theory and improved shear correction factors.

Energy absorption and mechanical response of Graded face-centered cubic structures

Enhancing the energy absorption capability of lightweight structures, through the use of functionally-graded materials, has recently attracted attention. The thickness grading method of plate lattices in the literature is limited to a discrete layer-by-layer grading, as the thickness in any single layer is uniform but different from the thickness of the other layers. The sudden changes between the layers result in a stress concentration. A continuous thickness grading is achieved in this study, and the effect of employing distinct grading schemes applied to FCC structures has been investigated. Axial continuous thickness grading, lateral continuous thickness grading, and an axial-lateral hybrid continuous thickness grading are examined, alongside discrete layer-by-layer unit cell size grading. Manufactured from Nylon using the material extrusion additive manufacturing method, the samples were benchmarked against uniform structures. To further understand the behavior of these structures, a numerical study, via Abaqus models of the quasi-static compression test, was undertaken and the resulting predictions offered good agreement with the experimental data. The axial thickness grading exhibits significant potential, resulting in a substantial increase of up to 39 % in specific energy absorption due to the layer-by-layer deformation, compared to their uniform counterparts. In contrast, unit cell size grading compromises the energy absorption efficiency, while improving the crushing force efficiency by 35 %. A higher mean crushing force up to 8 % was achieved by the lateral grading method. This investigation highlights the effect of adopting distinct grading approaches on both energy absorption and mechanical response, yielding useful information for the design of advanced protective systems.

Phase change in a one-dimensional functionally graded material

Functionally graded materials (FGMs) are a class of materials with engineered microstructure to achieve spatial variation in properties so as to serve a desired function. While FGMs have been well-researched for their structural properties, there is a lack of investigation of FGMs in solid-liquid phase change heat transfer processes. A well-designed functionally graded phase change material (FG-PCM) may overcome some of the well-known limitations of the phase change process. In order to investigate this possibility, this work presents a theoretical model to predict phase change propagation in a one-dimensional FG-PCM containing an arbitrary spatial variation in thermal conductivity, thermal diffusivity and latent heat. The problem is solved using the method of eigenfunction expansion to determine the temperature distribution, wherein, spatial variation in thermophysical properties listed above is accounted for by deriving a first-order matrix ordinary differential equation in the coefficients of the series solution. Results are found to correctly reduce to the well-known Stefan solution under special conditions. The impact of variation in thermophysical properties is investigated in detail. It is found that while spatial variation in thermal conductivity and latent heat has a significant effect on the rate of phase change, the impact of the thermal diffusivity function is negligible for realistic values of the Stefan number. The effect of the Stefan number governing this problem on the rate of melting is investigated. The nature of phase change under linear (1+aξ), polynomial (1+aξn) and exponential (eaξ) functional forms of thermophysical properties is investigated. It is shown that an appropriate choice of these spatial functions may help overcome the well-known self-limiting nature of phase change and produce a nearly-linear phase change propagation curve. For example, results show 33% increase in phase change propagation for a linear (1+5ξ) variation in thermal conductivity compared to baseline. The theoretical tools developed here may help design and optimize functionally graded PCMs towards improved phase change heat transfer in applications of practical interest.

Multi-Directional Functionally Graded Sandwich Plates: Buckling and Free Vibration Analysis with Refined Plate Models under Various Boundary Conditions

This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton’s principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal–ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors.

Geometrical and material optimization of the functionally graded doubly-curved shell by metaheuristic optimization algorithms

This paper presents the simultaneous geometrical and material optimization of functionally graded doubly-curved shells under static load and free vibration. The weak form of governing equations is derived from third-order shear and normal deformation theory. Bending and free vibration analyses were conducted using the finite element method. The functionally graded material (FGM) is composed of metal and ceramic, and Voigt’s rule of mixtures is applied to capture the characteristics of FGMs throughout the shell thickness direction. In this regard, two multi-objective optimization algorithms (i.e., multi-objective particle swarm optimization and multi-objective cuckoo search optimization algorithms are employed. The objective functions combine minimizing the maximum normalized displacement and mass and maximizing the first dimensionless frequency. The results show that where minimizing the mass of the FG shell structure was considered an objective function, the value of the power index is equal to zero for almost all studied cases.

Heat conduction in multi-component step-wise FGMs

AbstractThis paper provides a thorough investigation of a heat conduction problem that pertains to tolerance modelling in layered materials made up of multiple components. These media are functionally graded materials and thus have varying properties that affect their effectiveness. The proposed equations explain the conduction of heat in layered composites. The formulation involves partial differential equations, which utilise smooth and slowly varying functions. Notably, an extension of the unified tolerance modelling procedure is presented generalising existing models for two-component step-wise functionally graded materials (FGMs). This extension allows for the analysis of specific issues related to heat conduction in multi-component stratified composites with a transversal gradation of effective properties. This is the most important novelty achievement of the present paper because it will contribute to advancing knowledge and allows researchers, engineers, and practitioners to use the method in a broader context, addressing a more extensive set of real-world situations not limited to the number of component materials.

Free vibrational behavior of a conical sandwich shell with a functionally graded auxetic honeycomb core

In the presented paper, the free vibration of a conical sandwich shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM) is analyzed. The percentage (volume fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core changes from zero at the inner surface of the core to one at the outer surface according to a power-law function. The FGAH core is enfolded with a homogenous outer face layer made of ceramic and a homogenous inner one made of metal. The shell is modeled based on the first-order shear deformation theory (FSDT), and Hamilton’s principle is utilized to attain the governing equations and boundary conditions. A trigonometric-based analytical solution is carried out in the circumferential direction, and an approximate solution is presented in the meridional direction via the differential quadrature method (DQM). The impacts of various factors on the natural frequencies are inspected like the thickness of the core-to-thickness of the shell ratio, geometric factors of the cells in the FGAH core, and material gradation in the FGAH core.

Flutter analysis of laminated fiber-reinforced magnetorheological elastomer sandwich plate resting on an elastic foundation using an improved first-order shear deformation theory

Magnetorheological elastomers (MREs) are polymers with viscoelastic properties that can be adjusted by manipulating the magnetic field. When MREs are combined with reinforcing fabrics, a new category of materials known as MRE composites (MRECs) can be created, which not only possess the characteristics of MREs but also enhance their rigidity. This study focuses on investigating the supersonic aeroelastic instability of a rectangular sandwich plate with a laminated MREC core layer and functionally graded materials with porosities as face layers. Additionally, the sandwich plate is supported by an elastic foundation and subjected to supersonic airflow. This investigation presents an improved first-order shear deformation theory, postulating a parabolic distribution of shear stresses. Consequently, the transverse shear stresses are rendered as zero at the surface of every individual layer; thus, the requirement for shear correction in this theory is eliminated. In addition, 8-node elements are implemented to circumvent the necessity for distinct handling of shear-locking. The aeroelastic pressure acting on the structure is considered using first-order piston theory. Micromechanical approaches, such as Halpin‐Tsai and rule of mixture approaches, are employed to determine the effective mechanical properties of the core and face layers. The dynamic equations of the structure are derived using Hamilton’s principle and the finite element method. The study also examines the impact of different magnetic fields, fiber volume fraction, elastic foundation factors, layering angles, geometry, and boundary conditions on flutter frequency.

The nonlinear instability of transverse vibration behavior of functionally graded materials sandwich rectangular plates of under a harmonic loading and subsonic flow

This work is devoted to studying the combined action of periodic in-plane load and tangential subsonic flow on the nonlinear mechanism of the out-plane deformation of the functionally graded composite plate. Three distribution functions are proposed to investigate the distribution of the transverse shear strains and stresses across the thickness of the plates. By using Hamilton’s variational principle, the equations governing the plate instability boundaries are formulated. A nonlinear differential equation describing the first mode of the plate dynamic instability behavior by employing Galerkin’s method. The method of multiple time scales is used to obtain a periodic one-mode solution, which directly leads to the solvability condition. The different resonance cases for the interaction between the frequency of out- plane deformation and the external forces are discussed to discover the extent of the sandwich functionally graded material (FGM) rectangular plate resistance in the presence of external influences. Various bifurcation diagrams for different cases of resonance are obtained versus the basic parameters. In view of this study, we could get a deeper look at the complexity of frequency components in resonance responses of the sandwich FGM rectangular plate. The results could provide some suggestions for the sandwich plate’s vibration reduction design or fault diagnosis field or design fault diagnosis.

Systematic schemes for buckling analyses of a subsea bio-inspired non-circular FGM polyhedral liner with an arch invert

This study develops theoretical frameworks for the buckling failure of a non-circular thin-walled liner encased in a cracked pipeline with an arch invert. The buckling performance of the pipeline-liner system is improved by combining the polyhedral profiles and the Functionally Graded Materials (FGM). The liner is close-fitting to the inner surface of the pipeline. The energy function is obtained by assembling the thin-walled shell principle and the theory of minimum potential energy. Then, the nonlinear equilibrium equations and the buckling equations are derived to predict the buckling performances of the FGM polyhedral pipeline-liner system with an arch invert. Moreover, the present buckling behaviors of the system are compared with other available results, and good agreements are accomplished when the FGM polyhedral liner degenerates into an FGM circular liner or a homogeneous polyhedral liner. In addition, an enhancement coefficient is defined as the ratio of the buckling pressure of a polyhedral liner to a circular one. Finally, several key geometric and material parameters are examined to quantify their effects on the buckling behavior of the FGM polyhedral pipeline-liner system with an arch invert. These parameters are volume fraction exponents, polyhedral shapes, and thickness-to-radius ratios, respectively.