Functionally Graded Materials Research Articles

Metallurgical and mechanical properties of trimetallic functionally graded material fabricated by wire arc additive manufacturing

This study explores the fabrication of a trimetallic functionally graded material (FGM) using stainless steel (ER316L), duplex steel (ER2205), and Inconel 718 (IN718) through a gas metal arc welding (GMAW) based wire arc additive manufacturing (WAAM) process. The metallurgical examination reveals the large columnar austenitic grains and δ-ferrite phase at the grain boundaries along the built direction in the stainless-steel zone. At the interface of ER2205-IN718, a distinct boundary is observed due to the different alloy compositions. Scanning electron microscopy (SEM) shows metal carbide of nickel (Ni), molybdenum (Mo), and niobium (Nb) along the grain boundaries and nodular-shaped Lave phases in the IN718 zone. The energy dispersive spectroscopy (EDS) analysis reveals a gradual variation of Ni and Fe content, indicating the successful fabrication of the FGM. The mechanical characterization reveals that the hardness of the developed FGM steadily increases from bottom to top. However, at the ER2205-IN718 interface, it experiences a sharp decrease, followed by a subsequent increase within the IN718 zone. The tensile test demonstrated an increase in tensile strength along the built direction, accompanied by a reduction in strain. Notably, the minimum strain observed in the developed FGM is approximately equal to that of IN718 alloy.

Additive manufacturing of functionally graded stellite6/17-4 PH fabricated via direct laser deposition

Multi-material structures with variable functionalities can lead to unique solutions for engineering problems compared to single-material structures. Additive manufacturing of Functionally Graded Materials (FGMs) using Direct Laser Deposition for the multi-material deposition of Stellite6 and 17–4 PH stainless steel has been investigated in this study. Process parameter design was successfully applied to achieve FGM structures with expected composition ratio and defect free. Results revealed that clads with insufficient laser power had unmelted 17-4 PH powders, while those with excessive power resulted in micro-cracks and disrupting the expected composition for the previous layer. Energy Dispersive Spectroscopy analysis results showed that the composition was almost as expected, with less than 10% deviation. The Stellite6 composition in FGM exhibits a minimum ratio near the substrate due to the penetration of 17-4 PH elements. Meanwhile, in multi-track clads, the Stellite6% decreases along the transverse direction due to increased heat input, multiple cladding tracks, higher dilution, and slower solidification rate. The results of the micro-hardness tests illustrated the gradual evolution of micro-hardness along the build direction starting from the base metal, which had a hardness of approximately 300 HV for 17-4 PH and for the compositions of 25%, 50%, 75%, and 100% Stellite6 showed increases of 10%, 39%, 43%, and 63% respectively, reaching up to 490 HV for fully Stellite6 at the top of the specimen.

Machine Learning for Additive Manufacturing of Functionally Graded Materials.

Additive Manufacturing (AM) is a transformative manufacturing technology enabling direct fabrication of complex parts layer-by-layer from 3D modeling data. Among AM applications, the fabrication of Functionally Graded Materials (FGMs) has significant importance due to the potential to enhance component performance across several industries. FGMs are manufactured with a gradient composition transition between dissimilar materials, enabling the design of new materials with location-dependent mechanical and physical properties. This study presents a comprehensive review of published literature pertaining to the implementation of Machine Learning (ML) techniques in AM, with an emphasis on ML-based methods for optimizing FGMs fabrication processes. Through an extensive survey of the literature, this review article explores the role of ML in addressing the inherent challenges in FGMs fabrication and encompasses parameter optimization, defect detection, and real-time monitoring. The article also provides a discussion of future research directions and challenges in employing ML-based methods in the AM fabrication of FGMs.

Nonlinear vibration of sandwich beams made of FGM faces and FGP core under multiple moving loads using a quasi-3D theory

This study aims to investigate nonlinear dynamic behavior of sandwich beams constituted by functionally graded material (FGM) faces and functionally graded porous (FGP) core under the action of multiple moving loads. The energy equations based on a quasi-3D beam theory considering several functions of shear deformation were established for producing the nonlinear equations of motion used for describing dynamic responses of beams with various boundary conditions. By using the hybrid processes of the Newton-Raphson iteration procedure, the time-integration approach of Newmark-β, and the Gram-Schmidt-Ritz method, the new results of nonlinear analysis were explored and proposed. Several prime parameters such as the porous coefficient, sandwich thickness ratio, power law index and others that significantly affect the dynamic response of the beams were taken into investigations. It can be concluded that beams under one moving load have larger dynamic deflections compared to that under many moving loads. This is because the distance between the moving loads can produce a bending moment against the beam deformation.

Vibration and Buckling Characteristics of Sandwich FGM Plate with Conventional and Auxetic Honeycomb Core

The vibration and buckling characteristics of the sandwich plate with a honeycomb core and functionally graded material (FGM) face sheet have been evaluated in this paper. The honeycomb core, also known as conventional honeycomb and auxetic honeycomb, is modeled based on positive and negative Poisson’s ratio. Material properties of face sheets varied according to simple power-law functionally graded material (P-FGM). Hamilton’s principle has been employed to derive the equation of motion, and Navier’s method is used to solve the plate problem. Three different plate configurations are used to study the effect of the thickness layer. In addition, the outcome based on span-to-thickness ratio, aspect ratio, geometric parameters, and volume fraction exponent of honeycomb structure on frequency parameter and critical buckling load is examined and exhibited for three different plate configurations. The validation of the present formulation is ascertained by comparing it with other available results. Some novel results are presented for different angles of the unit cell that can be useful as a validation study for the forthcoming research on sandwich honeycomb rectangular plates. It is observed that the thickness of the honeycomb layer plays a significant role in affecting the behavior of the sandwich plate. Besides, the auxetic structure is highly sensitive to high excitation frequency applications compared to the conventional honeycomb structure.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Phase-field modeling of thermal shock fracture in functionally graded materials

In this paper, the thermo-elastic fracture problems of functionally graded materials (FGMs) are thoroughly investigated based on a modified phase field model. In this model, the material constants and fracture toughness vary along a specified direction, the thermal conductivity and stiffness constants in the damaged regions are degraded by the phase-field variable, and the crack evolution is driven by the variation of elastic energy induced by the thermo-mechanical loading. Therefore, the temperature, mechanical and damage fields are coupled with each other. The validation of the present approach has been checked by comparing the present results with the analytical, numerical, and experimental results in literature. The examples of thermo-elastic tensile fracture and thermal shock cracking of FGMs are performed to investigate the influence of material heterogeneity and external thermal loading. Furthermore, the experimental phenomenon of crack deflection in FGMs has been captured by the present simulations. The present study provides a guidance for understanding the fracture mechanism, material design and safety assessment of FGM structures in engineering practice.

Fracture analysis of spatially graded piezoelectric-flexoelectric materials using XIGA

Dielectric Functionally Graded Materials (FGMs) exhibit superior flexoelectric properties. Gradual changes in material properties lead to large strain gradients and excellent flexoelectric responses. Cracks behave in a complex manner inside piezoelectric-flexoelectric FGMs subjected to electromechanical loading. An extended isogeometric analysis (XIGA)-based formulation is developed for flexoelectric FGMs with crack discontinuities. Ceramic-polymer FGMs of barium titanate (BTO) and polyvinylidene fluoride (PVDF) are selected for analysis since this material combination has shown better flexoelectric response solely due to gradation. A higher-order electromechanical J-integral is used to study the behavior of cracks. The fracture behavior of different crack geometries at various grading indices and levels of flexoelectricity is investigated. A crack interaction study is conducted with varying crack parameters. The length-scale effect on the energy release rate is also shown. A significant reduction in the energy release rate is observed in FGMs due to the flexoelectric effect.

DYNAMIC RESPONSE ANALYSIS OF h-FGS PLATES SUBJECTED TO CONSECUTIVE BLAST LOADING

The main aim of this work is to use a finite element method (FEM) based on Shi’s third-order shear deformation plate theory (TSDT) to study the dynamic response of sandwich plates subjected to consecutive blast loading. The sandwich plate has an auxetic honeycomb core and two different functionally graded materials (FGMs) skin layers (so-called h-FGS plates). The honeycomb core helps significantly reduce the weight of the sandwich structures as well as enhance vibration absorption. The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the dynamic response of h-FGS plates is carried out in detail. The obtained results are expected to be useful for calculating and designing h-FGS plates in practical engineering.

Nonlinear resonant responses of a novel FGM sandwich cylindrical shell structure for supersonic flight vehicles based on 1:1 internal resonance between conjugate modes

A new design scheme for the functionally graded material (FGM) sandwich cylindrical shell structure made of ceramic-FGM-carbon fiber composites is proposed, which is geared towards supersonic flight vehicles and has high specific stiffness and high-temperature resistance. We focus on analyzing the nonlinear resonant responses of the novel FGM sandwich cylindrical shell subjected to external excitation and aerodynamic force. Firstly, the mechanical properties of the novel FGM sandwich material are calculated, and then the nonlinear dynamic model of the FGM sandwich cylindrical shell is established based on the first order shear deformation theory (FSDT) and Hamilton's principle. Due to the axisymmetric property of the cylindrical shell, a 1:1 internal resonance between the driven and companion modes always exists in the perfect cylindrical shell. Taking this into consideration, the nonlinear resonant response problems of the FGM sandwich cylindrical shell are numerically simulated by combining the Galerkin method and the pseudo-arc length continuation method. Finally, the effects of complex parameters such as external excitation, aerodynamic force, aspect ratio, gradient index, and skin-core-skin ratio on the nonlinear resonant responses of the FGM sandwich cylindrical shell are investigated.

Predicting Damage in Notched Functionally Graded Materials Plates through extended Finite Element Method based on computational simulations

Presently, Functionally Graded Materials (FGMs) are extensively utilised in several industrial sectors, and the modelling of their mechanical behaviour is consistently advancing. Most studies investigate the impact of layers on the mechanical characteristics, resulting in a discontinuity in the material. In the present study, the extended Finite Element Method (XFEM) technique is used to analyse the damage in a Metal/Ceramic plate (FGM-Al/SiC) with a circular central notch. The plate is subjected to a uniaxial tensile force. The maximum stress criterion was employed for fracture initiation and the energy criterion for its propagation and evolution. The FGM (Al/SiC) structure is graded based on its thickness using a modified power law. The plastic characteristics of the structure were estimated using the Tamura-Tomota-Ozawa (TTO) model in a user-defined field variables (USDFLD) subroutine. Validation of the numerical model in the form of a stress-strain curve with the findings of the experimental tests was established following a mesh sensitivity investigation and demonstrated good convergence. The influence of the notch dimensions and gradation exponent on the structural response and damage development was also explored. Additionally, force-displacement curves were employed to display the data, highlighting the fracture propagation pattern within the FGM structure.

Modelling and Parametric Study for Panel Flutter Problem using Functionally Graded Materials

Abstract In this paper we will demonstrate the possibility of weight optimization of panels under aero-thermal loading in hypersonic flow using functionally graded materials (FGM). The in-plane volume fraction of two constituents (Aluminium and Nickel) is modelled using polynomial distributions. Different material grading layouts are investigated, including cases with Nickel concentrated at corners, sides, midpoints and center. The solution of the problem utilized a higher order element with C1 continuity. The study covers the linear boundaries of the panel flutter problem as well as the non-linear post-buckling deflections. The results indicated Nickel placement strategies are shown to enhance dynamic pressure and vibration performance for a given mass reduction through optimal center and edge localization. Overall, the integrated modelling approach demonstrates the potential to systematically optimize stability, weight and integrity in hypersonic flow to optimize the weight of panels subject to aero-thermal loads.

Effect of Micromechanical Models on Mechanical Behavior of Functionally Graded Plates Based on a Quasi-3D Hyperbolic Shear Deformation Theory

Five alternative micromechanical models (Voigt, Reuss, Tamura, LRVE, Hashin) are used to predict the valid material properties of a simply-supported functionally graded materials (FGM) plate. The free vibration and static behavior are studied based on a quasi-3D hyperbolic shear deformation theory considering the stretching effect. The profile of an FGM plate is assumed by the power-law, Sigmoid and exponential functions. The numerical results of an FGM plate behavior reveal via Navier-type solution. The temperature effects of the micromechanical models on the fundamental frequency and transverse displacement for an FGM plate are also discussed. By analyzing the influence of different micro-models on the mechanical behavior of an FGM plate, researchers can objectively understand the establishment and differences of structural micromechanical models. And considering the actual high temperature situation, the deformation prediction ability of the structure is predicted. This study provides theoretical guidance for the analysis and modeling of FGM structures for the purpose of engineering practice.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

Assessment of structural defects and mechanical characteristics of IN718/St6 functionally graded material produced by direct laser deposition

Functionally graded materials (FGM) do not show special processing in the composite structure due to the combination of mechanical, thermal, magnetic and stress gradient properties. The aim of this study is to produce IN718/St6 FGM samples by direct laser deposition method. The product of this model should enable the development of mechanical products. Best of all, this can be done without significant reduction in texture and case to residual stress that are a consequence of rapid changes in mechanical and thermal properties in non-FGM samples. To fabricate part, direct laser deposition system equipped with a 1 kW continuous fiber laser is used, SEM/EDS analysis and microhardness testing to measure porosity, chemical composition, and quantify gradient mechanical properties is used. In this study, the cladding composition is selected from 100% IN718 to 100% St6 with a 25% change in St6 composition. To prevent the formation of defects, both single-parameter modes and individual layering are examined, considering the diverse nature of the combination. The result shows that using an individual layering structure, reduces 100% Lack of fusion defects in the IN718/St6 structure. EDS analysis confirmed that the St6 content gradually increased from the first to the fifth layer. The substrate hardness gradually increases from 200 Vickers hardness to 550 Vickers hardness, showing an almost linear trend. Moreover, by using individual layering, the coaxial structure is reduced by 55% and the relative orientation of the vertical line is reduced by 18° compared to using the St6 directly (non-FGM).

Version [1.1] - [2D-xtDCR-LTBEM: A Fortran code for numerical solutions to the unsteady anisotropic-DCR equation of spatio-temporal coefficients]

Variable coefficient equations are usually used as governing equations for modeling problems which are associated with Functionally Graded Materials (FGM). Version 1.1 - 2D-xtDCR-LTBEM is a Fortran code that can be used to find numerical solutions of two-dimensional (2D) initial–boundary value problems which are governed by the unsteady anisotropic-diffusion convection reaction (DCR)-type and the anisotropic-diffusion reaction (DR)-type equations with a class of space–time dependent coefficients, by utilizing a combined Laplace Transform-Boundary Element Method (LTBEM). This code may provide valuable help for simulation of problems of FGM.

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Effect of diffusion of elements on microstructural, mechanical, and machining characteristics of Al7075/ZnAl4 functionally graded material with and without Ag and Pb interface

The current experimental work uses die casting, a liquid processing method, to create functionally graded material (FGM). To reduce the production of undesired intermetallic compounds, the FGM samples were created both with and without interfacing foil during the procedure. Mechanical properties including impact strength and microhardness were examined throughout the manufactured sample's cross-section. In addition, the interfacial bonding of FGM samples with and without an interacting foil was determined by estimating the shear strength. Analysis of the samples using X-ray diffraction (XRD) and scanning electron microscopy (SEM) reveals the existence of compounds in the sample as well as the diffusion of Al and Zn particles from one side to the other. Compared to the FGM without foil, it is observed that the diffusion rate at the interface is regulated when the foil is present. In addition, it was found that, in contrast to pb foil, the inclusion of Ag foil limited the rate at which particles could move from one side to the other. Additionally, machining investigations are carried out at varying depths on both sides of the sample in the direction of the interface with the assistance of electric discharge machining.

Free vibration and buckling behavior of porous P-type FGM and S-type FGM circular plates on elastic foundation under non-uniform thermal field

In this paper, in order to satisfied the design and manufacturing requirements of functional materials, an investigation is carried out to study the free vibration and thermal buckling characteristics of porous P- and S-type functionally graded materials (FGM) circular plates in non-uniform thermal fields in the context of first-order shear deformation theory. FGM is formed by gradient changes in metals and ceramics, the thermomechanical properties were characterized by a gradient along the thickness direction of the circular plate by a power-law function containing porosity correction. The differential equations of motion control are derived using the Hamiltonian variational principle, and the dimensionless equations of motion and boundary conditions are solved analytically by the DTM transformation procedure. The problem has been degraded and compared with the results of the existing literature to confirm its validity. In conclusion, the influence of each parameter on the dimensionless natural frequency of the porous FGM circular plate and the influence of relevant parameters on the critical temperature rise are calculated and evaluated. The porosity weakens the overall stiffness and equivalent mass of the structure, and the foundation enhances the stiffness. The DTM calculation iteration speed is fast, and the results are highly consistent. The results can be used to provide model guidance and data support for future studies of porous FGM circular plates as well as follow-up studies.

A systematic model for the mechanical behavior of thin-walled composite FGM pipelines subjected to strike-slip faults in geohazard area

This paper focuses on the mechanical performances of the buried pipelines with functionally graded materials (FGM) subjected to strike-slip faults. A refined displacement function is introduced to derive the fault displacement and the strain distributions. The yield fault displacement is obtained by using the classical beam theory and the first yielding scheme. A finite element model is developed to verify the present derivations, and the verification indicates that the numerical results are in close agreement with the present analytical predictions characterized by the yield displacement and the strains, respectively. Finally, a parametric analysis is carried out to assess the factors that impact the performances of FGM pipelines, such as the diameter-to-thickness ratio of the pipeline, volume fraction exponent, fault inclination angles, the properties of the soil, and so on.