Functionally Graded Materials Research Articles

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Introduction:: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method. Method:: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively. Result:: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated. Conclusion:: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.

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 uneven type porosity distribution pattern.

Numerical Analysis of Functionally Graded Material (FGM) Axisymmetric Cylinder under Transient Thermal Load and Variable Internal Pressure

Numerical Analysis of Functionally Graded Material (FGM) Axisymmetric Cylinder under Transient Thermal Load and Variable Internal Pressure

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.

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.

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 vol 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 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.

Wave packet enriched finite element for accurate modelling of thermoelectroelastic wave propagation in functionally graded solids

A wave packet enriched finite element (FE) formulation featuring electrothermomechanical coupling is presented for solving two-dimensional wave propagation problems in functionally graded elastic and piezoelectric media. The FE equations for the Lord-Shulman and Green-Lindsay theories of generalized piezothermoelasticity are derived, where the standard Lagrangian interpolation functions of the temperature, electric potential, and displacement field variables are extrinsically enriched with element-domain sinusoidal wave-packet functions and are solved using the Newmark–β direct time integration. The effective properties of the functionally graded material (FGM) are computed using the volume-fraction-based micromechanics models, the Mori-Tanaka model and Voigt's rule of mixture (ROM) model. A variety of wave propagation problems, including the mechanically and electrically excited high-frequency Lamb wave propagation in FGM plates, impact waves in FGM bars, and thermal shock waves in functionally graded piezoelectric cylinders, are solved using the present formulation, and results are validated with available solutions. The efficacy of the current solution in comparison with the conventional FE is evaluated for all the studied problems. The effect of the inhomogeneity parameter on the transient wave behaviour is also presented for all the problems. The results of the Mori–Tanaka model are compared with those of the widely used ROM.

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.

Microstructure and tribological behaviour of dissimilar steel functional structure developed via arc-based DED process

In this work, heterogeneous functionally graded material (FGM) with SS316LSi and ER70S-6 is deposited using twin wire arc additive manufacturing technique. Tribological, mechanical and microstructural characterization were undertaken for the developed FGM structure. Microstructural analysis revealed acicular ferrite and bainite regions near molten pool boundaries, with "lathy ferrite" formations during solidification. Developed FGM structure exhibited appreciable mechanical strength with an average yield strength of 440±6 MPa, ultimate tensile strength of 714±13 MPa, and 43%±1.23 elongation. Worn surfaces revealed an adhesive wear mechanism. Gradation in wear rate and average coefficient of friction, measured as 9.98 × 10−4mm3/N-m and 0.46–0.51, respectively, was observed in the final deposited structure with intermediate values between SS316LSi and ER70S-6. Results reveal that as-deposited FGM exhibits superior wear resistance and mechanical performance compared to SS316LSi and ER70S-6.

Functionally graded Tribaloy™ T800 and austenitic stainless steel by laser additive manufacturing

Laser additive manufacturing (LAM) of Tribaloy™ T800 (T800) is susceptible to developing cracks during manufacturing due to the formation of a high-volume fraction of the intermetallic Laves phase which imparts brittleness to the material. To resolve this problem, AISI 316 L stainless steel (SS316L) has been incorporated to develop a novel functionally graded Tribaloy™ T800 (FG-T800) structure by LAM. By increasing the fraction of SS316L from the surface to the interior we have demonstrated surface hardness and sliding wear resistance similar to T800 while allowing modification of the amount and morphology of the brittle Laves phase across the deposit depth. In this manner, a tougher core with a reduced propensity for cracking is achieved. This new LAM-based manufacturing approach has the potential to deliver functionally graded material (FGM) structures for T800 cladding and solid components, thereby enhancing performance or component life.

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.

Discussion of the paper “M. Askari-sedeh and M. Baghani, On the extension-torsion of short hyperelastic tubes of axially functionally-graded materials” [Eng Struct 301 (2024) 117344]

Discussion of the paper “M. Askari-sedeh and M. Baghani, On the extension-torsion of short hyperelastic tubes of axially functionally-graded materials” [Eng Struct 301 (2024) 117344]

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.

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.

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.