Functionally Graded Materials Research Articles

Multi-objective optimization in EDM of functionally graded Fe-Al using grey relational analysis

Abstract Functionally Graded Materials (FGMs) are multipurpose materials with a specific goal of managing changes in structural, thermal, or functional qualities. They feature a spatial variation in microstructure and/or composition. The current work prepared three layers of sample with different chemical compositions of Fe-Al FGM (50 Al-50 Fe, 45 Al-55 Fe, and 40 Al-60 Fe) at. % produced by powder metallurgy, then studied the machining behavior of these samples. The literature on the machining behavior of FGM was reviewed, and the influence of electrical discharge machine (EDM) process parameters such as voltage (V), current (I), pulse-on time, and pulse-off time on performance characteristics (material removal rate (MRR), tool wear rate (TWR), and surface roughness (Ra)) was investigated. The optimal machining settings for Fe-Al FGM samples will be ascertained by use of Grey Relational Analysis (GRA), which is based on the Taguchi approach, after an experimental investigation of the L18 orthogonal array design of trials. The GRA findings verify that V 140 volts, Ip10 A, Ton 100 μs, and Toff 75 μs is the optimal combination of process parameters. It has been found that the voltage is more significantly affected than the rest of the input parameters to obtain greater material removal rate (MRR) and lower tool wear rate (EWR) and surface roughness (Ra) through the response table. According to the study, choosing the right process parameters can improve the multi-performance feature.

Thermomechanical Nonlinear Vibration of Axially Loaded Functionally Graded Material Cylindrical Panels Including Porosity

For the first time, the combined influences of axial compressive load, porosity, geometric imperfection, elastic edge restraint, and elevated temperature on the nonlinear free vibration of functionally graded material (FGM) cylindrical panels are investigated in this paper. Unlike previous studies, the structural model considered in this paper includes practical situations and conditions arising in the design process and application of FGM cylindrical panels. The properties of material constituents are assumed to be temperature-dependent, and the effective properties of porous FGM are determined using a modified rule of mixture. Governing equations in terms of deflection and stress function are established based on first-order shear deformation theory, taking into account von Kármán–Donnell nonlinearity and initial geometric imperfection. Analytical solutions are assumed to satisfy simply supported boundary conditions, and the Galerkin method is applied to derive a time differential equation containing both quadratic and cubic nonlinear terms. This differential equation is numerically integrated employing the fourth-order Runge–Kutta scheme to determine the frequencies of nonlinear free vibration. Parametric studies are carried out to assess numerous effects on both linear and nonlinear frequencies of porous FGM cylindrical panels. The study reveals that natural frequencies are strongly decreased and that frequency nonlinearity is more significant due to axial compressive loads.

Yielding onset in FGM thick-walled spherical shells under thermo-mechanical loading

Based on von Mises yield criterion, a thermoelasto-plastic analysis of a thick-walled spherical shell composed of functionally graded material (FGM) subjected to internal pressure and thermal gradient is conducted in order to accurately predict the onset radius of yielding within the vessel wall. The modulus of elasticity, thermal conductivity and thermal expansion coefficients, and yield stress of FGM are assumed to follow power-law functions in radius according to Erdogan’s model. The equilibrium differential equation of the shell under thermo-mechanical loading in steady-state conduction heat transfer are derived analytically and then solved to determine through-thickness variations of the radial and circumferential stresses and radial displacement in elastic and perfectly plastic zones in the vessel wall. The presented approach leads to the definition of new formulation to predict the onset radius of yielding. Moreover, a neural network (NN) solution to reliable quantify the influence of all uncertain input parameters with respect to uncertain output parameter is utilized. The numerical results showed that for various FGM parameters and specific thermal gradient, the plastic zone can commence from inside radius, outside radius, simultaneously in both radii, or may be launched in the intermediate radius of the spherical shell wall.

Peculiarities of Lamb Waves Propagating in Functionally Graded Layers

Propagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by the modified Cauchy six-dimensional formalism. For arbitrary transverse inhomogeneity a closed form dispersion equation is derived. Dispersion relations for materials with different kinds of inhomogeneity are obtained and compared.

Transient analysis of functionally graded axisymmetric plates via finite element method in the Laplace domain

The principal goal of this research article is to examine the forced vibration of Functionally Graded Material (FGM) axisymmetric plates with the aid of the finite element method in the Laplace space. The material properties are assumed to be isotropic, linear viscoelastic, or elastic and vary continuously in the direction of the thickness of the plate. The governing equations of motion are transferred to the Laplace domain and solved for a set of Laplace parameters. Then, a modified Durbin’s inverse Laplace method is employed to retransfer the obtained results back to the time domain. A convergence analysis is conducted to optimize the number of Laplace parameters and time steps. An 8-node quadratic quadrilateral element featuring two degrees of freedom per node is employed to generate the model of the axisymmetric plates. Different loads such as step load, square wave, and sawtooth wave loads are used to observe the impact of load type on the transient response of FGM plates. In viscoelastic analysis, the Kelvin damping model is preferred, and the effect of the damping ratio is investigated. The obtained results are validated with the aid of the available literature and the accuracy of the suggested model is confirmed. It is carried out that the material variation significantly affects the dynamic behavior of the plates, for instance as the material coefficient increases, displacement amplitudes decrease, and periods increase. The novelty of this paper is the employment of the finite element method together with Laplace transformation for addressing the present class of problems for the first time.

Cu/AlN composite and functionally graded materials with high strength and high electrical- and thermal-conductivity fabricated by spark plasma sintering

In this study, Cu/AlN composites and functionally graded materials (FGMs) were fabricated with the spark plasma sintering method. It was observed that a two-step sintering process, involving sintering under low pressure as the initial stage to remove adsorbed chemicals on the powder, was an effective method for producing sintering objects with high relative density. The hardness of the composites significantly increased with higher volume fraction of aluminum nitride (AlN) particles, while electrical- and thermal-conductivity decreased. Nevertheless, the advanse impact of AlN on thermal-conductivity was found to be minimal. Additionally during compression test, a crack was noted at the interface between Cu and Cu-5 vol%AlN region in two-layered FGMs after, whereas no such crack was observed in the three-layered FGMs. Therefore, it is confirmed that the concept of FGMs is useful in overcoming the shortcomings of mutually exclusiveness among high strength, high electrical- and high thermal-conductively.

Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches

This study investigates the free vibration and transient dynamic response of functionally graded material (FGM) sandwich plates with stepped face sheets (FGM-SPSFS) supported by viscoelastic foundation under blast loading. The research focuses on the effects of geometric configurations and material property variations across segments. Each plate comprises three layers: a homogeneous hard core and two FGM face sheets, divided horizontally into two segments with differing face sheet thicknesses, which enhance structural stiffness while maintaining a consistent total thickness. The material properties of the sandwich plates follow a power-law distribution. The formulations are based on higher-order shear deformation plate theory and von Kármán geometric nonlinearity, and are solved using Galerkin’s method. Validation is achieved by comparing the results with published literature and finite element analysis (FEA). Artificial neural network (ANN) models are developed to predict natural frequencies without extensive computational runs, employing Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms in MATLAB. A new graphical user interface (GUI) tool facilitates frequency predictions using the proposed ANN model. Key findings indicate that modifications to the stepped face sheets and core layers affect stiffness, natural frequency, and vibration amplitudes. Increasing the core-to-total thickness ratio enhances stiffness, resulting in higher frequencies and reduced displacement amplitudes. The LM algorithm outperforms the BR algorithm, with errors generally below 1%, compared to 2% to 4% for BR with the log-sigmoid function. This study offers valuable insights into the design and analysis of FGM sandwich structures for engineering applications.

Traveling wave vibration characteristics of rotating FGM conical shell

Abstract Conical shell is common structural component in various rotating machinery. The study of traveling wave vibration performance of conical shell is of great significant for the design of rotating machinery. This paper addresses the traveling wave vibration performance of rotating functionally graded material (FGM) conical shells. Artificial springs, uniformly distributed, are employed to simulate the boundary constraints of rotating FGM conical shell. Accounting for the effects of Coriolis and centrifugal forces caused by rotation, the energy equation of rotating FGM conical shell is calculated, and then the dynamical model of the rotating FGM conical shell under elastic supported constraints is established using the Lagrange equation. The influence of key factors on traveling wave frequency and response characteristics of rotating FGM conical shell are investigated including rotational speed, half-cone angle and material components.

Transfer learning-based techniques for efficient 3D-reconstruction of functionally graded materials

The various properties and phenomena in materials significantly depend on the high-quality three-dimensional (3D) microstructure. This paper proposes a novel method for 3D reconstruction of functionally graded materials (FGMs) using transfer learning techniques to overcome the limitations of experimental 3D microscopy. The approach begins by interpolating 2D cross-sectional images of FGM microstructures through a hybrid deep learning method combining StyleGAN and Gatys techniques, generating intermediate images based on style and content. In the next step, transfer learning is applied using convolutional occupancy networks to reconstruct the 3D microstructure from the 2D image depth layers, with the model trained on point clouds obtained from 2D images. To validate the method, the reconstructed microstructures are compared to actual material images at the same depth using various metrics, including lineal path, two-point correlation, and quality of connection functions. The results show a high degree of accuracy, indicating that the reconstructed images closely match the target microstructures. Finally, to show the application of model the approach is implemented to the functionally graded lanthanum strontium manganite (LSM) and 3D microstructure of this FGM has been extracted using the approach

A Novel Preparation Approach of Aluminum-Based Functionally Graded Material: Auxiliary Wire Filling Gas Metal Arc Directed Energy Deposition

The 2319-1100 aluminum-based functionally graded material (FGM) with continuous gradient transition interface was fabricated by auxiliary wire filling gas metal arc directed energy deposition (AWF-GMA-DED) process via changing the feeding speed of the auxiliary wire ER1100. The droplet transfer behavior, deposition morphology, microstructure and mechanical property of the FGM wall were analyzed. Results indicate that with increasing feeding speed of ER1100, the droplet transfer mode of the auxiliary wire changes in the manner of large droplet transfer—bridge transfer—continuous transfer, while the droplet transfer of the main wire ER2319 is always stable. As the filling ratio of ER1100 increases, the area of interlayer equiaxed grain band and equiaxed grain size increases gradually, the continuity of eutectic structure at the grain boundary is weakened, and the eutectic structure is refined. When the ER1100 filling ratio increases from 10% to 35%, the microhardness decreases by 13.4%, the tensile strength 7.8%, whereas the elongation and corrosion resistance of the FGM part both improve.

Numerical Optimization of Functionally Graded Ti-HAP Material for Tibial Bone Fixation System.

Functionally graded materials (FGMs) are heterogeneous composites characterized by outstanding properties. They are built from two or more components with a gradient distribution of chemical composition along a given direction. A promising graded material for biomedical engineering as an implant could be a FGM made of titanium (Ti) and hydroxyapatite (HAP). It would allow us to counteract the difference between the stiffness modulus of pure titanium and bone tissue. Moreover, it can be a good solution to the problem of stress shielding for bone fixation plates made of conventional titanium or steel. The presented paper aims to perform micromechanical modeling and optimization of a functionally Ti-HAP graded plate, followed by numerical analysis of a fractured tibia stabilization system under specific boundary conditions. Finite element analysis was performed using ANSYS Workbench 2021 software. The models of the FGM plate and tibial fixation system were made using the Space Claim tool. The ANSYS software allowed the optimization of the model considered and the selection of the appropriate structural parameters of the FGM Ti-HAP material. In general, the results proved that the osteosynthesis plate built of graded Ti-HAP material resulted in lower bone stress compared to titanium and steel plates. The results obtained confirmed the validity of the design and the possibility to use functionally graded Ti-HAP bone fixation plates.

Formation of Graded TiO2 Layer on Ti Wire by Direct Alternating Current Discharge Plasma at Atmospheric Pressure

Although metallic materials have been used as load-bearing materials in dental and biomedical fields since they have good mechanical properties such as good ductility and strength, their aesthetic properties are inferior to those of ceramic or resin. To obtain aesthetically improved Ti dental devices, the formation of white titanium oxide on pure Ti dental devices was studied. Direct atmospheric pressure plasma (APP) treatment using alternating current was carried out on pure a Ti plate and wire. It was found that a titanium oxide layer with enough whiteness can be obtained on pure Ti wire using direct APP treatment. Although delamination of the titanium oxide layer was found after a bending test, the concept of functionally graded materials (FGMs) can overcome the shortcoming.

A Novel Method for Analyzing Global Bifurcation and Global Hysteresis of FGM Truncated Conical Shell Structure

In the dynamic bifurcation and dynamic hysteresis of a system, our first consideration is the tiny changes in time that can lead to variations in the vector field, potentially causing the occurrence of system dynamic bifurcation and dynamic hysteresis. This paper presents a novel method for analyzing the global bifurcation and hysteresis of Functionally Graded Material (FGM) truncated conical shell structure under aerodynamics and in-plane force along meridian near internal resonances. This method involves introducing the ratio of vector fields as a periodic perturbation parameter in the system’s nonlinear second-order ordinary differential governing equations. This allows for the analysis of the nonlinear ordinary differential equations as algebraic equations, yielding algebraic expressions that only involve parameters and do not contain state variables. Subsequently, the global bifurcation set and global hysteresis set of FGM truncated conical shell structure are obtained, providing the parameters interval ranges for the stability and instability of FGM truncated conical shell structure. By utilizing MAPLE software for numerical simulation, the images of the global bifurcation set and global hysteresis set about the amplitude of in-plane load are first simulated numerically. Subsequently, the amplitude graphs of the equilibrium points are numerically simulated for validation. The results demonstrate a perfect alignment between the images of the global bifurcation set and global hysteresis set and the data from the amplitude graphs of the equilibrium point. Due to the periodicity of the periodic perturbation parameter, it shuttles between different persistent regions as other parameters change, leading to the generation of chaotic solutions in the governing equations. The validity of the obtained results is confirmed through comparisons with existing literature.

Effect of porous defects on mechanical behavior of functionally graded materials

Porous defects in functionally graded materials (FGMs) significantly change their mechanical behavior, in particular, affecting the displacement of the neutral plane and stress distribution. Defects such as porosity reduce material bending strength while enhancing compression strength and can lead to significant transverse effects. The purpose of this study is to clarify the influence of porosity on transverse effects based on new kinematic model. This research consider in detail a particular case of this model, that allows take into account two Poisson`s effects separately. This study examines the influence of porosity on FGM, highlighting the critical role of changes in Poisson’s ratio through thickness. The theory used for analytical solution satisfies the nullity of the shear stresses at the upper and lower surfaces of the plate without using the shear correction factor. The network of pores proposed to be empty or filled with low-pressure air and material properties graded by thickness according to power-law and exponential models. Navier solution method is used to solve the governing differential equations of equilibrium. The concentration of porosity at the center of the plate or in separate layers results in a reduction in normal tensile stresses along the longitudinal coordinate, suggesting that strategic placement of porosity can be used to reduce stress concentrations, potentially enhancing the structural integrity and performance of functionally graded materials under mechanical loading.

Investigation of periodic heat transfer on the transient thermal characteristics of fully wet moving semi-spherical porous fin composed of functionally graded material

This study investigates the thermal behaviour of a fully wet, moving semi-spherical porous fin made of linear Functionally Graded Material (FGM). This investigation examines the fin response to convective-radiative heat transfer under periodic variations in base temperature across three different FGM scenarios: Homogeneous material (HM), Functionally Graded Material I (FGM I) and Functionally Graded Material II (FGM II). The resultant nonlinear partial differential equation is accurately solved using the Finite Difference Method (FDM) and outcomes are benchmarked against existing literature. This research pioneers an investigation into the effects of periodic heat transfer on the detailed thermal profiles of FGM fin, an area not been explored in existing literature. It significantly enhances understanding of the influence of oscillatory base temperatures on thermal management within FGMs, uncovering pivotal insights into the interaction between material grading, amplitude of temperature oscillation and their collective effects on thermal efficiency. Additionally, this research assesses the influence of variables such as the amplitude of input temperature, frequency of oscillation, thermal conductivity grading parameter and others on temperature distribution along the fin length and over dimensionless time. Notably, periodic heat transfer induces a dynamically wavy thermal profile in the fin over time, attributable to oscillating base temperatures. Moreover, the analysis demonstrates that FGM II fin exhibit the most significant temperature distribution, followed by FGM I and HM. The fin heat transfer rate is profoundly influenced by the amplitude of input temperature and the thermal conductivity grading parameter. These insights are pivotal for optimizing fin designs in critical applications, including electronics cooling, HVAC systems, automotive engine cooling and solar energy collection, substantially improving upon traditional designs.

Dynamic insights into thermal shock response of double-layer cylinders with FGM main layer and viscoelastic holder via generalized Green-Naghdi theory

This study investigates the dynamic thermoelastic response of a hollow cylinder composed of two distinct layers: a Functionally Graded Material (FGM) as the primary layer and an isotropic viscoelastic material as the supporting layer. Utilizing a power function, the material properties of the FGM layer are determined, while the viscoelastic layer follows the Kelvin-Voigt model. The research employs the generalized Green-Naghdi theory to formulate the heat transfer equation, capturing the energy dissipation and thermoelastic wave propagation within this novel configuration. Highly coupled equations governing both layers are derived, incorporating appropriate boundary and continuity conditions. The Chebyshev collocation element (CCE) method is utilized for the spatial solution, significantly reducing the computational effort by requiring only two higher-order elements. The Newmark time marching approach is employed to solve the resulting ordinary differential equations (ODEs). The model's accuracy is validated against existing literature, and parametric studies are conducted to evaluate the impact of thermal shock on the FGM layer. It has been observed that the presence of the viscoelastic barrier effectively impedes the full penetration of stress waves, thereby reducing the potential for shock-induced damage.

Multi-material 3D printing of functionally graded soft-hard interfaces for enhancing mandibular kinematics of temporomandibular joint replacement prostheses

Temporomandibular joint (TMJ) replacement prostheses often face limitations in accommodating translational movements, leading to unnatural kinematics and loading conditions, which affect functionality and longevity. Here, we investigate the potential of functionally graded materials (FGMs) in TMJ prostheses to enhance mandibular kinematics and reduce joint reaction forces. We develop a functionally graded artificial cartilage for the TMJ implant and evaluate five FGM designs: hard, hard-soft, and three FGM gradients with gradual transitions from 90% hard material to 0%, 10%, and 20%. These designs are 3D printed, mechanically tested under quasi-static compression, and simulated under physiological conditions. Results from computational modeling and experiments are compared to an intact mandible during incisal clenching and left group biting. The FGM design with a transition from 90% to 0% hard material improves kinematics by 19% and decreases perfomance by 3%, reduces joint reaction forces by 8% and 10%, and increases mandibular movement by 20% and 88% during incisal clenching and left group biting, respectively. These findings provide valuable insights for next-generation TMJ implants.

Isogeometric vibration analysis of functionally graded material pre-twisted blades with three-dimensional theory

In this paper, the free vibration characteristics of a rotating functionally graded material (FGM) pre-twisted blades are investigated by the isogeometric method based on the three-dimensional (3D) theory. The effects of Coriolis force, centrifugal softening, and centrifugal rigidity of the FGM pre-twisted blades are considered in this vibration analysis model. The material properties of the FGM pre-twisted blades are assumed to change continuously along thickness direction. It is easy to satisfy the weak form requirements of the vibration control equation of the FGM pre-twisted blades by using the NURBS functions. Then, the dynamic equation of the pre-twisted rotating blades can be derived by using the Hamilton's variational principle. Finally, a standard eigenvalue equation is obtained through discretizing equations and expanding dimensions. Numerical examples showed that the current formulation has fast convergency and good accuracy. Additionally, the influence of installation angle, pre-twisted angle, variable cross-section, material properties and rotating speed on the vibration characteristics of the FGM pre-twisted blades under rotating conditions is explored in detail. The work can also shed some new lights on the vibration behaviors of pre-twisted blades composite materials.

Dynamic buckling active control of FGM spherical shell with piezoelectric sensor and actuator layers

The mechanical snap-through phenomenon represents one of the buckling modes inherent in shallow shells, exemplifying the shell's reaction to external loads, which can potentially have detrimental effects on structural performance. This article delves into the study of this phenomenon within the context of spherical shells. Leveraging functionally graded material (FGM) in the main layer of this structure proves instrumental in enhancing the shell's performance against rapid mechanical loads. Furthermore, the strategic placement of piezoelectric layers, both symmetrically and asymmetrically, coupled with the implementation of a proportional and derivative control system, facilitates the control of the shell's response. The formulation of displacement field and electric potential is grounded in the first-order shear deformation theory (FSDT) and second-order distribution, respectively. The strong form of nonlinear dynamic and electrostatic equations is derived using Hamilton's principle. Solving these equations is achieved through the implementation of the generalized differential quadrature (GDQ) method in the spatial domain and Newmark in the time domain. Additionally, the Newton-Raphson method is employed to tackle the inherent nonlinearity of the problem. The Budiansky's criterion is employed for the assessment of the load necessary for the buckling of the shell. Following the validation of results against numerical, analytical, and laboratory outcomes, a set of parametric results is presented. These results underscore the remarkable impact of the control system in mitigating shell deformation under time-dependent mechanical loads, as well as in postponing the occurrence of the snap-through phenomenon and damping the vibrations.

Synthesis and characterization of 4-layered functionally graded Al-Al2O3 MMC

Functionally graded materials (FGMs) have a gradient of properties along their dimensions. These materials are resistant to delamination, making them ideal for replacing conventional composites in various fields of engineering. Among FGMs, aluminium-based FGMs are receiving a lot of attention due to their versatility. Al-Al2O3 FGMs, in particular, are widely preferred in the aerospace and automobile sectors. This study involves synthesizing a 4-layered FG Al-Al2O3 MMC through PM. The material is subjected to impact, compression, and hardness tests, to assess its mechanical properties. To understand the characteristics of the material, Optical microscopy, SEM, and XRD are carried out. The powder metallurgy route produces FG MMCs with improved properties. The material exhibited an impressive hardness of 183 HV at the top layer, which is higher than similar FGMs and FGMs fabricated via Centrifugal Casting. The compressive strength of Al-Al2O3 FGM is 138 MPa and the impact strength is 16.25 kJ/m2. Owing to the improved properties and FGMs being resistant to delamination mode of failure the study recommends the material as a replacement for conventional Al-Al2O3.