Functionally Graded Materials Research Articles

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters.

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

Transition zone parameter development in multi-material powder bed fusion: a general approach

AbstractPower bed fusion of metals using a laser beam (PBF-LB/M) offers unique possibilities to manufacture functionally graded materials (FGM) consisting of different alloys. These so-called multi-material parts enable their material properties to be tailored to local material requirements. In this paper, a new methodical approach for the production of metal FGM with transition zones oriented in different directions and manufacturing sequences of the different materials is investigated. Existing approaches for the manufacturing of these transition zones were enhanced with graded parameter variations, spatial laser movement modulation techniques (wobbling), and geometric approximations using a step structure. For the validation of the approach and the characterization of the transition zones, the manufactured samples were investigated and characterized using optical microscopy and hardness profile measurements. Furthermore, the density of the transition zones was analyzed by image data processing. The feasibility of the presented methods is shown and the production of defect-free transition zones with controlled expansions for functionally graded materials via PBF-LB/M achieved

A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder

The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.

A Receding Contact Problem of Two Layers one of Functionally Graded, Loaded by Circular Rigid Block and Resting on a Pasternak Foundation

In this study, frictionless receding contact problem of two elastic layers which one is functionally graded material (FGM) resting on a Pasternak foundation is considered. The external load is applied to the homogeneous elastic layer by means of a circular rigid block and the functionally graded layer rests on a Pasternak foundation. The effect of gravity forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. Displacement and stress expressions for the layers are obtained using the theory of elasticity and integral transformation technique. By applying the boundary conditions for the problem, reduced to two integral equations in which the contact stresses and contact lengths are unknown. The system of integral equations is numerically solved by making use of appropriate Gauss Chebyshev integration formulas. The equilibrium conditions are satisfied in the solution and the contact stresses and contact distances related to the problem are obtained for various dimensionless quantities.

Finite element analysis of the thermal and thermo-mechanical coupling problems in the dry friction clutches using functionally graded material

Abstract The friction clutch is an important machine part in the torque transmission system, where it is responsible for gently transmitting the power from the engine to the gearbox and damping the tensional vibration. At the beginning of the engagement between the clutch’s elements, a large amount of heat is released due to frictional sliding between the elements of the clutch system, generating very high temperatures. In this work, the two- and three-dimensional finite element models were developed from scratch to explore the clutch disk’s temperature and contact pressure behaviors using an alternative frictional material such as functionally graded material (FGM). The two assumptions for the thermal loads were considered: uniform wear and uniform pressure assumptions. The thermal–structural problem for the new frictional material was solved numerically and then presented as the temperature distributions and the contact pressure at any instant of sliding time. Also, a comparison was made between the clutch system behaviors when using FGM with different frictional materials. The results showed that the FGM has superior results to the other available frictional materials.

Localized heat treatment and XFEM-based investigation of damage mechanisms in reinforced notched plates under uniaxial tensile stress

This study delves into mechanical engineering by investigating damage mechanisms and reinforcement strategies in notched structures. Our research centers on enhancing structural integrity through a localized heat treatment technique applied at the notch before uniaxial tensile stress testing. Central to our approach is Functionally Graded Material (FGM), defined by volume fractions that specific exponents modulate. The innovation lies in treating the interface between the base metal and the heat-affected zone (HAZ). We introduce a novel meshing-based grading technique that facilitates elastoplastic behavior and allows for the gradation of damage properties. This technique is particularly noteworthy as it obviates the need for complex subroutines or FORTRAN compilation. Our methodology employs a mesh model with independent elements, each characterized by a volume fraction gradient to accurately represent the graded material’s behavior. The behavioral model is anchored in the Von Mises equivalent stress flow theory, and tensile tests inform the material properties of steel and the HAZ. The results of our investigation are presented through force-displacement curves, which critically evaluate our reinforcement technique. Moreover, using the eXtended Finite Element Method (XFEM) in our meshing approach has proven particularly effective in delineating structural behavior post-fissure initiation, showcasing its superiority in capturing the nuances of crack propagation and structural separation.

Thermal Vibration of Thick FGM Conical Shells by Using Third-Order Shear Deformation Theory.

A time-dependent third-order shear deformation theory (TSDT) approach on the displacements of thick functionally graded material (FGM) conical shells under dynamic thermal vibration is studied. Dynamic equations of motion with TSDT for thick FGM conical shells are applied directly with the partial derivative of variable R*θ in the curve coordinates (x, θ, z) instead of y in the Cartesian coordinates (x, y, z) for thick FGM plates, where R* is the middle-surface radius at any point on conical shells. The generalized differential quadrature (GDQ) numerical method is used to solve the dynamic differential equations in equilibrium matrix forms under thermal loads. It is the novelty of the current study to identify the parametric effects of shear correction coefficient, environment temperature, TSDT model, and FGM power law index on the displacements and stresses in the thick conical shells only subjected to sinusoidal heating loads. The physical parts with values on the length-to-thickness ratio equals 5, and 10 FGMs can be used in an area of an airplane engine that usually operates near more than 1000 K of temperatures when the thermal stress is considered and affected. The important findings of the presented study are listed as follows. The values of normal stress are in decreasing tendencies with time in cases when the coefficient c1 equals 0.925925/mm2 in TSDT and length-to-thickness ratio equals 5. The shear stress values in x plane z direction on the minor middle-surface radius (r) equals the major middle-surface radius (R) over 8 and length-to-thickness ratio equals to 5 can withstand T = 1000 K of pressure.

Analysis to the dynamic response of a functionally graded spherical microshell in consideration of fractional-order dual-phase-lag heat conduction and nonlocal effect

Functionally graded materials (FGMs) stand as one of the most representative composite materials due to the superior thermal resistance in non-isothermal environment. On another front, the applicability of integer-order heat conduction models is increasingly questionable because the heat transfer shares the history-dependent property at time microscale. It is noted that the small-scale effect of elastic deformation has become significant due to the development of micro-devices. To capture the small-scale effect of elastic deformation and the memory-dependent effect of heat conduction in the FGM microstructures, as a first attempt, the present study focuses on developing a thermoelastic model by incorporating the fractional-order dual-phase-lag (FODPL) heat conduction model and the Eringen’s nonlocal model. Moreover, the extension of the Caputo definition, i.e., the Tempered-Caputo (TC) definition of fractional derivative ruling out singular kernel is adopted to depict the memory-dependent effect of the heat conduction. Then, the modified model is used to investigating the dynamic response of a FGM spherical microshell subjected to a sinusoidal thermal-mechanical loading. The corresponding governing equations are formulated and then solved by Laplace transform techniques. Some parametric results are demonstrated to display the influences of the fractional-order parameter, the nonlocal parameter and the power-law index on the considered physical quantities.

Thermal buckling analysis of a new type of rectangular FG sandwich plates using a new higher-order shear deformation theory

This article presents a novel higher-order shear deformation Theory to investigate the thermal buckling behavior of a new type of functionally graded material (FGM) sandwich structure. The study focuses on a specific configuration of rectangular FGM sandwich plate, consisting of FGM face layers and FGM core layer subjected to temperature gradients varying linearly and non-linearly across the thickness. By employing the principle of virtual work, the governing equations are derived, involving only four unknown functions. The Navier procedure is then utilized to obtain closed-form solutions. In this study, the material properties and thermal expansion coefficient of the two face layers of the sandwich plate are assumed to vary in the thickness direction according to a simple power-law distribution. In contrast, the core layer is assumed to have an exponential variation along the thickness direction. The critical thermal buckling is influenced by various factors, including the thickness, and aspect ratios of the sandwich plate, the gradient index, the type of loading, and the type of sandwich plate. The effects of these variables on the critical buckling temperature are thoroughly examined and analyzed.

Comparative analysis of thermal behaviour in functionally graded material fin under convective-radiative heat transfer: Homotopy perturbation method

In this study, the thermal characteristics of a fully wet, moving longitudinal fin made from linear Functionally Graded Material (FGM) is explored. The fin response to convective-radiative heat transfer is examined through three distinct FGM scenarios namely, a Homogeneous material (HM), Functionally Graded Material I (FGM I) having greater thermal grading near the base, and Functionally Graded Material II (FGM II) having increased thermal grading towards the tip. The derived energy equation is a second-order nonlinear ordinary differential equation is solved using the Homotopy Perturbation Method (HPM) compared with results found in the existing literature. The fin thermal profile has been graphically analysed for the thermal conductivity grading parameter (β), Peclet number (Pe) and other pertinent parameters. It is found that the temperature distribution along the fin is highest for the FGM II fin and lowest for the HM fin, with the FGM I fin displaying intermediate values. Efficiency of the fin (η) is discovered to be lowest in the case of HM fin structures followed by FGM I and FGM II fin structures at the base and vice versa at the tip. The results show significant potential of HPM which benefits the manufacture and design of FGM fin structures.

Nonlinear vibration analysis of geometrically imperfect FGM Timoshenko beams with porosity and elastically restrained ends in thermal environments

This paper aims to analyze the combined influences of pore imperfection, initial geometric imperfection, elasticity of tangential constraints of ends, elastic foundations and elevated temperature on the nonlinear vibration of functionally graded material (FGM) beams. The pores are assumed to distribute into FGM according to even and uneven patterns and effective properties of porous FGM are estimated using a modified rule of mixture. Motion equations of geometrically imperfect beams are established within the framework of Timoshenko beam theory incorporating von Kármán nonlinearity and foundation interaction. Analytical solutions are assumed to satisfy simply supported and clamped conditions of beam ends and Galerkin method is applied to derive a nonlinear time ordinary differential equation. The frequencies of nonlinear free vibration are determined employing fourth-order Runge-Kutta numerical integration scheme. Parametric studies are carried out to assess numerous effects on both linear and nonlinear frequencies. The results reveal that frequency nonlinearity is more significant for beams with tangentially restrained ends, especially at elevated temperatures. It is also found that geometric imperfection increases the linear frequency and lowers ratio of nonlinear-to-linear frequencies.

Vibration characteristics of a cylindrical sandwich shell with an FG auxetic honeycomb core and nanocomposite face layers subjected to supersonic fluid flow

In this paper, the flutter analysis is studied for a cylindrical sandwich shell subjected to external supersonic fluid flow. The sandwich shell consists of a re-entrant auxetic honeycomb (AH) core made of functionally graded materials (FGMs) which is covered with two polymeric face layers enriched with either carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), or graphene oxide powders (GOPs). The volume fraction (percentage) of the ceramic phase in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on either power-law function (P-FGM), exponential function (E-FGM), or sigmoid function (S-FGM). It is assumed that the nanofillers are distributed uniformly inside the face layers. The first-order shear deformation theory (FSDT) and the piston theory are employed to provide the mathematical models of the shell and the aerodynamic pressure, respectively. The governing equations and boundary conditions are derived via Hamilton’s principle. An exact solution is performed in the circumferential direction via harmonic trigonometric functions (sine and cosine) and an approximate solution is performed in the axial direction utilizing the differential quadrature method (DQM). The natural frequencies and corresponding damping ratios are attained through the presented semi-analytical solution and the impacts of several factors on the natural frequencies and the critical aerodynamic pressure of the shell are examined. These factors the type of the FGM, the material index, and inclined angle of the cells in the FGAH core, the thickness of the FGAH core, the type and mass fraction of the nanofillers in the nanocomposite face layers, and boundary conditions.

Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

Hygrothermal buckling analysis of thin rectangular FGM plate with variable thickness

PurposeThis paper aims to contribute novel insights into the analysis of thin functionally graded material (FGM) plates with variable thickness, considering both temperature-dependent and independent material properties, focusing on critical linear buckling temperature rise and the effect of critical linear moisture for various moisture concentrations.Design/methodology/approachThe study derives stability and equilibrium equations for thin rectangular FGM plates under hygrothermal loading, employing classical plate theory (CPT). Buckling behavior is examined using Galerkin’s method to obtain pre-buckling force resultants.FindingsThe findings highlight significant increases in critical buckling temperature with aspect ratio, distinct temperature sensitivity between materials and increasing moisture susceptibility with larger aspect ratios. These insights inform material selection and design optimization for FGM plates under hygrothermal loading, enhancing engineering applications.Research limitations/implicationsThis research primarily focuses on hypothetical scenarios and mathematical model development and analysis.Originality/valueThis paper presents original contributions in the field by addressing the hygrothermal buckling analysis of thin FGM rectangular plates with variable thickness, utilizing CPT, thereby enriching the understanding of structural behavior in varying environmental conditions.

Printable functionally graded tibial implant for TAR: FE study comparing implant materials, FGM properties, and implant designs

Tibial implants with functionally graded material (FGM) for total ankle replacement (TAR) can provide stiffness similar to the host tibia bone. The FGM implants with low stiffness reduce stress shielding but may increase implant-bone micromotion. A trade-off between stress shielding and implant-bone micromotion is required if FGMs are to substitute traditionally used Ti and CoCr metal implants. The FGM properties such as material gradation law and volume fraction index may influence the performance of FGM implants. Along with the FGM properties, the design of FGM implants may also have a role to play. The objective of this study was to examine FGM tibial implants for TAR, by comparing implant materials, FGM properties, and implant designs. For this purpose, finite element analysis (FEA) was conducted on 3D FE models of the intact and the implanted tibia bone. The tibial implants were composed of CoCr and Ti, besides them, the FGM of Ti and HA was developed. The FGM implants were modelled using exponential, power, and sigmoid laws. Additionally, for power and sigmoid laws, different volume fraction indices were taken. The effect of implant design was observed by using keel type and stem type TAR fixation designs. The results indicated that FGM implants are better than traditional metal implants. The power law is most suitable for developing FGM implants because it reduces stress shielding. For both power law and sigmoid law, low values of the volume fraction index are preferrable. Therefore, FGM implant developed using power law with 0.1 volume fraction index is ideal with the lowest stress shielding and marginally increased implant-bone micromotion. FGM implants are more useful for keel type fixation design than stem type design. To conclude, with FGMs the major complication of stress shielding can be solved and the longevity and durability of TAR implants can be enhanced.

A numerical investigation for the development of functionally graded Ti/HA tibial implant for total ankle replacement: Influence of material gradation law and volume fraction index.

Stress shielding is one of the major concerns for total ankle replacement implants nowadays, because it is responsible for implant-induced bone resorption. The bone resorption contributes to the aseptic loosening and failure of ankle implants in later stages. To reduce the stress shielding, improvements can be made in the implant material by decreasing the elastic mismatch between the implant and the tibia bone. This study proposes a new functionally graded material (FGM) based tibial implant for minimizing the problem of stress shielding. Three-dimensional finite element (FE) models of the intact tibia and the implanted tibiae were created to study the influence of material gradation law and volume fraction index on stress shielding and implant-bone micromotion. Different implant materials were considered that is, cobalt-chromium, titanium (Ti), and FGM with Ti at the bottom and hydroxyapatite (HA) at the top. The FE models of FGM implants were generated by using different volume fractions and the rule of mixtures. The rule of mixtures was used to calculate the FGM properties based on the local volume fraction. The volume fraction was defined by using exponential, power, and sigmoid laws. For the power and sigmoid law varying volume fraction indices (0.1, 0.2, 0.5, 1, 2, and 5) were considered. The geometry resembling STAR® ankle system tibial implant was considered for the present study. The results indicate that FGMs lower stress shielding but also marginally increase implant-bone micromotion; however, the values were within the acceptable limit for bone ingrowth. It is observed that the material gradation law and volume fraction index influence the performance of FGM tibial implants. The tibial implant composed of FGM using power law with a volume fraction index of 0.1 was the preferred option because it showed the least stress shielding.

Peridynamic Differential Operator for Stress Analysis of Imperfect Functionally Graded Porous Sandwich Beams Based on Refined Zigzag Theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the even type porosity distribution pattern.

The effect of Al2O3 content on the microstructure and properties of Al/Al2O3 functionally graded material

This study aims to survey effect of Al2O3 content on the microstructure and also the physical and mechanical properties of Al/Al2O3 which functionally graded material (FGM) that are manufactured by the powder metallurgy technique. For this purpose, five-layer Al/Al2O3 green part samples with Al:Al2O3 different weight ratios were fabricated by cold pressed under 620 MPa. After compaction, the samples were sintered for 1 hour in a nitrogen atmosphere at a temperature range between 600 °C and 640 °C. An optical microscope and a field emission scanning electron microscope (FESEM) were used to evaluate the Microstructural characterization. The Archimedes density, Vickers hardness and flexural strength of sintered samples were measured. The highest relative density of 95% was achieved at a sintering temperature of 640 °C on lower Al:Al2O3 weight ration variation on Al/Al2O3 FGM sample. The hardness values gradually changed in cross section of different FGM samples from 31 HV to 65 HV which depend on the sequence of Al2O3 content in different layers. However, the highest flexural bending strength of 70 MPa was obtained at the sample on Al/Al2O3 FGM included the compositions of 35, 25, 15, 5, 0 wt.% Al2O3. By decreasing Al2O3 content along Al/Al2O3 FGM, the changing semi-brittle or brittle to ductile failure mechanism was observed. In some fabricated FGM samples observed a few cracks in the interfacial region between layers with high Al2O3 content.

Recent developments in modeling and analysis of rotating functionally graded panels: A review

This article presents a comprehensive review on recent developments in the techniques for modeling and exploration of rotating functionally graded material (FGM) panels carried out between periods 2000 to 2023. Special attention is given on literature pertaining to analysis of rotating FGM panels subjected to thermo-mechanical loading. This study scrutinizes the advancements made in analysis of panels such as beam, plate, shell and blades that includes effects like porosity, thermal stress, and piezo-electric in the mathematical model. The present article also highlights the importance and ease in implementation of rule of mixture for calculation of different temperature dependent material properties used in the analysis of rotating FGM panels. An in-depth review of literature clearly indicates the importance of taking thermal effect in the estimation of elastic properties for accurate analysis of rotating FGM panels. Further, a detailed analysis of temperature profile viz., linear/non-linear, is carried out. Finally, the article concludes with the future areas that need to be explored for the analysis of rotating FGM panels.

Investigating the effect of select alloying elements in additively manufactured Co-Cr alloy for dental prosthetics

Despite the significant advancements in additive manufacturing and its exploration of functionally graded materials (FGMs), the specific roles of W and Mo in enhancing the tribological and corrosion properties of Co-Cr alloys have remained largely underexplored, particularly in the context of dental applications. To address this, CoCrW and CoCrMo alloys were fabricated using the Laser Powder Directed Energy Deposition (LP-DED) process and subjected to a comprehensive suite of microstructural analyses, and tribological behavior followed by corrosion resistance characteristics in an artificial saliva environment. Results revealed that the inclusion of Mo contributes to finer grain sizes, increased hardness and HCP phase stabilization, thus enhancing the wear resistance. Conversely, W's presence in CoCr alloys was found to bolster corrosion resistance which confirms that a synergistic approach of novel alloy development combining W and Mo can be impactful to enhance the overall performance of Co-Cr alloy-based parts. Based on author’s knowledge, this is the first time the effect of W and Mo on additively manufactured Co-Cr alloy has been presented in a comprehensive way combining manufacturing, materials characterization and performance analyses in a context of application in dental prosthetics.