Functionally Graded Materials Research Articles

Mandibular bone remodeling around osseointegrated functionally graded biomaterial implant using three dimensional finite element model.

Dental implantation surgery has been progressed as one of the most efficient prosthetic technologies, however, it still fails very often and one of the main causes is the large difference between implant mechanical properties and those in welcoming bony tissues, making it problematical in osseointegration and bone remodeling. Biomaterial and tissue engineering research shows that there is a requirement in developing implants with Functionally Graded Materials (FGM). Indeed, the great potential of FGM lies not only in the field of bone tissue engineering but also in dentistry. To improve the acceptance of dental implants inside the living bone, FGM were proposed to step up the challenge of ensuring a better match of mechanical properties between biologically and mechanically compatible biomaterials. The aim of the present work is to investigate mandibular bone remodeling induced by FGM dental implant. Three-dimensional (3D) mandibular bone structure around an osseointegrated dental implant has been created to analyze the biomechanical behavior of the bone-implant system depending on implant material composition. In order to implement the numerical algorithm into ABAQUS software, UMAT subroutines and user-defined material were employed. Finite element analysis have been conducted to determine the stress distributions in implant and bony system, and to evaluate bone remodeling induced by the use of various FGM and pure titanium dental implants over the period of 48 months.

Experimental analysis on deformation and damage behavior of Al6061/SiC functionally graded plates under low-velocity impact

Due to their promising features provided by ceramic and metal constituents in a single volume, Functionally Graded Materials (FGMs) have received great attention for impact applications. Most of the available studies on the low-velocity impact behavior of FGMs have been carried out by analytical or numerical methods. This study addresses an experimental analysis on the low-velocity impact response of Al6061/SiC FGM plates. The influence of the material composition of the FGM plate (from metal-rich to ceramic-rich) on the energy absorption mechanisms as well as on the deformation and damage behavior was investigated. The ceramic-rich FGM plate exhibits a quasi-brittle response that includes a combination of elastoplastic indentation and brittle failures with increasing impact energy, while the metal-rich and linear FGM plates show elastoplastic behavior. Plastic deformation is the primary energy absorption mechanism for the metal-rich and linear FGM plates, whereas plastic deformation, brittle failures (radial cracks and conoidal crack/fracture), delamination, and pore collapse are effective on the energy absorption of the ceramic-rich FGM plate.

Synthesis of functionally graded aluminium metal matrix composites - a mini review

Functionally graded materials (FGMs) are materials with property gradients along a particular dimension. These are novel and advanced materials that are becoming excellent replacements for composites. Among the FGMs, functionally graded Aluminum metal matrix composites (FG AMMCs) are receiving tremendous attention as they possess versatile properties compared to their counterparts. Out of various synthesizing techniques, the Powder metallurgy (PM) route is the cheapest and easier method of fabricating functionally graded composites (FGCs). This review provides information about the Functionally graded Aluminium metal matrix composites and their synthesis through the PM route. The review analyses important properties including density, hardness, tensile and compressive strength. A study of the microstructure through Scanning Electron Microscopy (SEM) of the synthesized FGMs is presented. The PM route could be conveniently exploited for large-scale production of FG AMMCs. There is scope for the characterization of FG AMMCs reinforced with B4C, TiO2, TiB2, TiC, CNT, and Few layered Graphene (FLG) as only a few studies are reported in the literature. The variation in mechanical and tribological properties of the FGMs could be investigated by varying the processing parameters of the ball milling, compacting, and sintering conditions.

Microstructure and mechanical properties of additively manufactured γ-TiAl with dual microstructure

The latest research on electron beam powder bed fusion (PBF-EB), additive manufacturing (AM) process, reveals the possibility of establishing a dual microstructure and differing mechanical properties inside a complex-shaped component made of titanium aluminides (TiAl). The functionally graded material (FGM) parts are processed with two different, well-adjusted AM process parameter sets leading to a significant change in localized aluminum (Al) loss via evaporation during PBF-EB. By heat treatment, the as-built microstructure, containing two different levels of Al, is transformed into customized microstructures: fully lamellar (FL) and nearly lamellar (NL + γ). This study aims to determine the microstructural and mechanical characteristics of PBF-EB processed 4th generation TiAl alloy TNM. Tensile and creep tests are performed for single (FL or NL + γ) and dual microstructure specimens with two orientations. The element distribution of aluminum is determined, the microstructures are characterized, and the fracture-inducing defects are identified. The presented new FGM processing route is a groundbreaking benefit from the PBF-EB process and is necessary for superior mechanical performance. The stress-strain and the creep properties of the dual microstructure specimens are situated between the single microstructure specimens. The mechanical characterization shows that the interface between FL and NL + γ does not cause any weakening of the specimens. The failure always takes place in the weaker microstructure (tensile: FL; creep: NL + γ). For the first time, AM components such as TiAl turbine blades can consist of creep-resistant airfoil sections and high-strength root sections taking advantage of new microstructural FGM design possibilities.

Traveling Wave Characteristics of a Rotating Functionally Graded Laminated Cylindrical Shell with General Boundary Conditions

The traveling wave modes of rotating functionally graded laminated cylindrical shells with general boundary conditions are studied by using different admissible displacement functions. Firstly, the effective temperature-dependent material properties of the functionally graded materials (FGMs) are described by the Voigt model and the Sigmoid-type volume fraction. Subsequently, considering Love’s thin shell theory, the motion equations of the FGMs shell subjected to the Coriolis force, the centrifugal inertial force, the hoop initial tension and the internal thermal force are derived. Thereafter, the displacement functions are expanded by six different sets of admissible displacement functions. The Rayleigh–Ritz method is utilized to derive the eigenvalue equations of the rotating FGMs laminated shells. In the end, the convergence rate and computational efficiency of the six polynomial functions are compared and parameter study is carried out. Results indicate that the Legendre orthogonal polynomials (LOP) are the best ones in terms of convergence rate and computational efficiency for predicting the traveling wave modes. The patterns of [Formula: see text] expressed by Sigmoid law are more sensitive to the modal frequency of the shell than the ceramic volume fraction exponents. The stiffness of the axial springs plays a more significant role in the traveling wave modes than the stiffness of other springs.

A novel EFG meshless-ANN approach for static analysis of FGM plates based on the higher-order theory

An Element Free Galerkin (EFG) meshless formulation and solutions using higher order shear deformation theory with nine degrees of freedom for the static analysis of Functionally Graded Material (FGM) plates are provided. This technique estimates the shape function using Moving Least Squares (MLS) method. The proposed method is validated by comparing the present findings with those in the literature. A novel Artificial Neural Network (ANN) model is developed to forecast the deflection of FGM plates within less computational time. Detailed parametric and convergent studies reveal that the proposed EFG solution and the ANN technique are more efficient than their conventional counterparts. The validation and comparison of the generated results in the present investigation with the other analysis methods revealed that the EFG method and ANN model give more accurate results than the FEM and other meshless methods. The current EFG-ANN model reduces computing time by 99.94% when compared to the EFG approach. Also, the accuracy is enhanced using the EFG approach with HSDT9 for the FGM plate.

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes.

Effect of elastic foundation and porosity on buckling response of linearly varying functionally graded material plate

This work presents the buckling response of porous plate made of functionally graded materials (FGMs). A tapered FGM plate with uniaxial and biaxial loading under numerous boundary conditions was investigated. Simple power law and sigmoidal law are applied to compute the tailored material properties. Further, the effect of Pasternak foundation on the buckling response for a plate is computed, considering the five types of porosity pattern. The first order-shear deformation theory (FSDT) is used to describe the kinematic field of the plate. The variational principle is used to derive the equation of motions. Subsequently, the solution for buckling analysis is found by applying the Galerkin’s-Vlasov method. It has been seen that the effect of elastic foundation largely influenced the buckling response of FGM plate, especially Pasternak foundation has significant effect when comparing with Winkler’s foundation. Similarly, buckling load, subjected to uniaxial or biaxial compression of plate, decreases greatly for porous material. Numerical examples for computing buckling response are compared for accuracy and verification purpose of the present formulation, with earlier published results. Considering the effect of thickness variation, span ratio, compressive load conditions, foundation stiffness and porosity on buckling analysis are estimated and established as a benchmark result in tabulated form. Moreover, parametric studies have been done, by keeping in view, to explore the utility of FGM tapered plate and the responses represented in the graphically form.

Different build strategies and computer-aided process planning for fabricating a functional component through hybrid-friction stir additive manufacturing

ABSTRACT Hybrid Additive Manufacturing (HAM) technologies leverage the strength of Additive Manufacturing (AM) and Subtractive Manufacturing (SM) in fabricating complex geometries with precision. Friction Stir Welding (FSW) has been acknowledged for joining sheets of similar or dissimilar materials with improved mechanical/metallurgical properties. However, due to the inherent pinhole defect and complicated toolpath planning, this process has not been explored much for fabricating the objects in a layer-by-layer manner. Therefore, this work investigates Computer Aided Process Planning (CAPP) for realizing fully functional metallic parts through a HAM system. This HAM system uses a Sheet Lamination (SL) process, i.e. Friction Stir Additive Manufacturing (FSAM), synergistically coupled with an SM process, i.e. machining. To realize complicated geometries through the proposed HAM system, three different build strategies are developed viz. Near-net block fabrication, Near-net shape fabrication via ‘form-then-bond approach’ and ‘bond-then-form approach.’ Each build strategy consists of a detailed CAPP that includes toolpath planning, tooling aspects, simulated outcome and so on. Further, these build strategies are discussed for realizing the parts with Functionally Graded Materials (FGM) & embedded structures. Finally, a monolithic object of aluminium has been fabricated as a case study to demonstrate one of the aforementioned build strategies.

Bending Analysis of Asymmetric Functionally Graded Material Sandwich Plates in Thermal Environments

This paper investigates the bending of asymmetric functionally graded material (FGM) sandwich plates subjected to thermo-mechanical loads in thermal environments. In this paper, a thermo-mechanical analysis model for asymmetric FGM sandwich plates is proposed, which contains only four control equations and four unknown variables. The governing equation is obtained through refined shear theory and the principle of virtual work, and the Navier method is used to solve it. Numerical examples of simply supported FGM sandwich plates under thermo-mechanical loads are given to verify the accuracy of the model. Finally, detailed studies are conducted on the bending of asymmetric FGM sandwich plates under thermo-mechanical loads, exploring the effects of various parameter changes on their bending behavior, and providing strong guidance for the application of asymmetric FGM sandwich plates in industrial production practice.

Fracture Resistance and Crack Growth Mechanisms in Functionally Graded Ti–TiB

This paper presents the results of fracture tests and crack path observations for a layered functionally graded material (FGM) consisting of Ti and TiB phases. The composition varied in a nearly linear manner from a TiB-rich layer at the bottom to commercially pure (CP) Ti at the top. Elastic properties of the mixed phase interlayers were measured using nanoindentation testing, demonstrating a linear variation with composition. These results differ significantly from approximations calculated in previous studies using a non-linear rule-of-mixtures approach. Fracture tests were conducted on single edge notch bend [SEN(B)] specimens with the notch aligned orthogonal to the direction of the composition gradient. For this crack orientation, "average" R-curve behavior based on the J-integral was investigated to understand the mechanics of crack growth. The value of J was found to be minimal (less than 1 N/mm) below 47 pct volume fraction of TiB compared to a reported value of approximately 150 N/mm for pure Ti. These results indicate that a steeper transition to high concentrations of the metallic phase is necessary to achieve adequate fracture resistance in this metal/ceramic FGM. Observations on the specimen surface indicate crack path toughening mechanisms of this functionally graded material include crack bridging, branching, and deflection.

Effect of in-situ cooling during pressure and frictional deformation on mechanical and metallurgical properties of Ni-based functionally graded material developed by wire arc additive manufacturing

In this article, Ni–Cr–Mo-based functionally graded material with a designed composition is successfully fabricated using the wire arc additive manufacturing process. The effect of the gradual variation of Ni, Cr and Mo concentration and the effect of high-temperature high-pressure deformation (HTHPD) in the different cooling environments on the morphology, microstructure, and mechanical properties along the gradient direction of the manufactured functionally graded materials (FGMs) have been investigated. With increasing Cr and Mo content from the bottom to the top, the FGM exhibits a gradual increase in tensile strength and microhardness. The hardness varies from 114 to 230, 130 to 205 and 164 to 256 HV for as-deposited, HTHPD with air-cooled (HTHPD-A) and HTHPD with water-cooled (HTHPD-W) samples, respectively, from bottom to top. Similarly, the average tensile strength is achieved at 793, 715 and 875 MPa in as-deposited, HTHPD-A and HTHPD-W samples, respectively. The microstructural examination of fabricated samples shows the columnar grain produced in as-deposited samples, deformed during the HTHPD process and recrystallized grains with orientation along the deformation direction has been formed.

Computer simulation of the stress-strain state of thin plates and cylindrical shells with a circular hole reinforced by an inclusion from functionally graded material

Computer simulation and FEM analysis of the stress-strain state of thin plates and thin-walled cylindrical shells, weakened by a circular hole in the presence of an annular inclusion of a functionally graded material (FGM) surrounding it, have been carried out. The influence of the dimensions of the FGM-inclusion and the law of change of its elastic modulus on the concentration of the parameters of the stress-strain state of plates and shells in the vicinity of the hole is studied. The distribution of stress and strain intensities in the zones of local stress concentration is obtained. It has been established that when using a radially inhomogeneous FGM-inclusion with certain mechanical properties, it is possible to reduce the stress concentration factor by more than 35%. The law of change in the modulus of elasticity of the FGM-inclusion and the width of the inclusion have a significant effect not only on the concentration of the parameters of the stress-strain state of the plate and shell, but also on the nature of the stress distribution over their surfaces. The results of a series of large-scale computational experiments show that the use of an FGM annular inclusion makes it possible to reduce the intensity of both stresses and deformations around the hole.

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

This article studies the free vibration responses of functionally graded material (FGM) porous nanoplates exposed to thermal load. The developed mathematical model includes a shear deformation, size-scale, and microstructure influence by a high-order shear deformation (HSDT) and nonlocal strain gradient (NGST) theories. The study considers four different porosity patterns across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The equation of motion of the FGM porous nanoplate, including the effects of thermal load, is derived with Hamilton's principle, and then solved analytically by employing the Navier method. For the free vibration responses of the nanoplate, the effects of nonlocal and strain gradient elasticities, temperature rise, porosity volume fraction and its distribution are analyzed.

On vibrations of functionally graded double wishbone structural systems

In the framework of dynamic finite element methodology, this articleinvestigates the free and forced vibration behaviors of functionally graded double wishbone structural systems considering the deformability of links and joints. Due to the advantages of the functionally graded materials (FGMs), the double wishbone control arms are modeled as a plane functionally graded frame based on the Timoshenko beam theory (TBT). The power law is adopted to model the through-thickness material gradation. Based on the power gradation law, analytical expressions for the equivalent material stiffnesses and the equivalent inertia are derived. On the other hand, joint deformability is modeled using flexible translational and rotational springs. The dynamic equations of motion are derived based on the Hamiltonian principle. Based on the isoparametric Timoshenko plane frame element, a displacement-based dynamic finite element model is developed. The accuracy of the developed numerical procedure is verified for both free and forced vibration behaviors and good agreement is obtained. Numerical results are obtained and discussed. The results show the significant effects of the FGM distributions on the free and forced vibration behaviors. The developed procedure and the obtained results are supportive of the design and manufacturing processes of such structural systems.

Study of the dynamic electro-mechanical and microstructural behaviour on the elastic wave in FGM/FGPM composite structure: WKB asymptotic approach

This paper presents a theoretical investigation of the horizontally polarized shear wave in a composite structure. The assumed composite is composed of Functionally graded piezoelectric material (FGPM) layer constrained between an FGM (Functionally graded material) layer and a couple stress half-space with size-dependent microstructural effect. The variation in rigidities and densities are considered parabolic and linear in the upper and constrained layers, respectively. An analytical WKB (Wentzel–Kramers–Brillouin) asymptotic approach has been adopted for obtaining the dispersion relation. Also, a finite difference scheme (FDS) has been introduced to calculate the phase velocity and group velocity of the SH-wave. If waves travel in the time domain, it is necessary to check the accuracy and stability requirements. So that FDS has been adopted because of its accuracy, reliability, and flexibility. For the purpose of numerical calculation, three sets of FGPMs are considered namely, PZT−4, PZT−5H ceramic, and ceramic. Graphs have been plotted by means of dimensionless phase velocity against dimensionless wave number to show the effect of various parameters on the propagation of SH-wave. Numerical results demonstrated the accuracy and versatility of the phase and group velocity depending on the stability ratio of the FDS.

Analysis of stress shielding reduction in bone fracture fixation implant using functionally graded materials

Bone density reduction occurs when implants are used to arrest fracture propagation. Bones are stress shielded by the implants when enough loads are not placed on the bones. Stress-shielding occurs when stiffness mismatch between the bone and the fracture fixation implant is significant. The aim of this study was to perform an analysis of stress-shielding reduction using functionally graded material (FGM) implants when Young’s modulus vary along the length of the implant. In this study, the finite element method (FEM) was used for the simulation of functionally graded implant mounted on a bone. The effect of FGMs on the reduction of stress-shielding imposed on a bone was studied parametrically by conducting simulations of various two-dimensional (2D) and three-dimensional (3D) computational models. First, a low-fidelity 2D model was created where it was observed that the FGMs were capable of reducing the stress-shielding substantially. Then, high-fidelity models such as single-sided with and without screws as well as double-sided FGM implants with different shapes for consideration of partial cracks were simulated. Several simulations were carried out to investigate the minimum required number of layers in an FGM to avoid stress concentration at the FGM layer interfaces. Furthermore, various material gradations in an FGM were tested to present the FGM gradation index that can reduce the stress shielding. Lastly, it was established convincingly through the finite element simulations that FGMs were able to reduce the stress-shielding on a bone with a crack.

Nonlinear oscillations of a cylindrical shell with a circumferentially discontinuous elastic base

This work investigates the linear and nonlinear vibrations of a functionally graded (FG) transversally excited cylindrical shell and in contact along its length with a circumferentially discontinuous elastic base, a configuration frequently found in practical applications. The elastic medium is modeled as a Winkler foundation. The adopted distribution of the FG material along the thickness is similar to that of a sandwich shell, with one material predominating in the core and the other on both faces. First a finite element analysis (FEA) is performed to obtain the natural frequencies and vibration modes of the FG cylindrical shell and a parametric analysis is conducted to study the influence of the contact region and foundation stiffness on natural frequencies and mode shapes. Even though the problem is a symmetric, the cylindrical shell displays a sequence of symmetric and antisymmetric vibrations modes and these modes may interact due to nonlinear coupling. For much geometry the lowest vibration modes have very close natural frequencies, leading to internal resonances, which influence strongly the nonlinear shell response. To obtain a reliable reduced order model (ROM) for the nonlinear dynamic analysis, Donnell’s nonlinear shallow shell theory is considered. To discretize the nonlinear equations of motion by the Galerkin method, a consistent modal solution is obtained considering nonlinear couplings and interactions. Here, first the displacements are consistently derived from a perturbation procedure proposed in previous papers. To start the perturbation procedure, a seed solution is necessary for the transversal displacement field. For this, first the linear vibration modes obtained from the finite element analysis are expanded in Fourier series in terms of the circumferential coordinate. Then, the essential modes to be used in the ROM are identified using a mathematical procedure that combines Fourier transform and Parseval theorem. The proposed modal solution for the transversal displacements is also used to obtain the modal expansions for the axial and circumferential displacements and their modal amplitudes are determined as a function of the modal amplitudes of the transversal displacements, thus reducing even further the number of unknows. These expansions are finally used to discretize the nonlinear equation of motion in the transversal direction and the resulting equations of motion are solved numerically using continuation software AUTO. A geometry displaying multiple internal resonances is selected and resonance curves, time-responses and phase-portraits are obtained to analyze the nonlinear dynamics of the shell. Depending on the excitation, different bifurcation scenarios are obtained, with important changes in stability and resonant peaks due to modal interaction. Competition between coexisting stable attractors is investigated using basins of attraction, which exhibit a complex topology, often with fractal boundaries.

Dynamic Analysis of Shaft with Variable Mechanical Property under Dynamic Load by FEM Method

The paper introduces the dynamic responses of a circular shaft with variable mechanical properties under dynamic loads. The direct construction of finite element formulation for dynamic problems, which include stiffness matrix, and mass matrix for circular axis. The Functionally Graded Material (FGM) shaft with material properties is assumed to vary continuously in the longitudinal direction investigated. Building a numerical program for the problem based on Bernoulli beam theory, and Newmark numerical algorithm. The obtained numerical results have found the kinematic response of the shaft with the longitudinal variation of mechanical properties under the action of dynamic loads. The results were also compared with the analytical results in some special cases to clarify the reliability of the calculation method.

Free vibration analysis of FGM framed nanostructures using variational-consistent boundary conditions

This paper analyses free vibrations of framed nanostructures made of Functionally Graded Material (FGM) based on the Nonlocal Elastic Theory (NET) and the Dynamic Stiffness Method (DSM). FGM characteristics vary nonlinearly throughout the height of the beam element. The NET considers the nonlocal parameter that perfectly captured the size effect of nanostructures. However, the NET makes nonlocal paradoxes in the bending and vibration behaviour of framed nanostructures with the free ends. To overcome these phenomena, the nanostructure is modelled according to the Euler–Bernoulli beam theory and the variational-consistent nonlocal boundary conditions have been derived. The exact solutions of differential equations of motion and variational-consistent nonlocal boundary conditions are found using the DSM. The influences of the nonlocal, material, geometry parameters and Pasternak’s foundation on the free vibration are then analyzed. It is shown that the study can be applied to other FGMs as well as more complicated framed structures.