Functional Graded Materials Research Articles

Generalized thermoelastic interactions in functional graded materials under laser heat source with a timed pulse

This work aims to find a solution to a problem involving generalized thermoelastic interaction in functionally graded materials when heated by a laser using a timed pulse. Functionally graded materials (FGM) are materials having spatially variable material characteristics. The governing formulations of a generalized thermoelastic theory with one relaxation time are established. The domain of the Laplace transforms is used to express these equations. The eigenvalues techniques yields the analytical solution in the transform domain. Laplace transform inversion is accomplished numerically. The findings are graphically shown to demonstrate the impacts of non-homogeneity, laser pulse length, and laser intensity on temperature, displacement, and stress.

Phase field modeling for fatigue fracture in functional graded materials

Phase field modeling for fatigue fracture in functional graded materials

Evaluating the Effect of Deposition Strategy on Mechanical Characteristics of 316L Parts Produced by Laser Powder Directed Energy Deposition Process

The production of large components, the possibility to repair damaged parts and the ability to produce components of multi-graded or functional-graded materials are the main drivers of the research and the application of the Laser Powder Directed Energy Deposition (LP-DED) process. However, the knowledge of the process and of the relationships among the process parameters and the characteristics of the produced part is currently not completely understood. The aim of this paper is to fill the current gap in the scientific literature related to the effect of the deposition strategy on the part quality. Therefore, the influence of two of the most important parameters, namely the deposition path and the idle time, on the residual stresses and porosity is evaluated on 316L samples produced by the LP-DED process. The obtained results show that both parameters have a high influence on the porosity level and the residual stresses. In particular, it can be seen that a high value of idle time worsens both porosity and residual stresses. Then, it is also observed that the raster deposition path leads to a lower value of stresses.

Integration of space-holder technique and spark plasma sintering: An innovative approach for crafting radially graded porosity implants

Bone resorption and possible fracture of host tissue are some consequences resulting from the mismatch between the Young's Modulus of the constituent materials of implants and bone that compromises the reliability of implants for replacing damaged bone tissue. The use of functional graded porous materials presents an interesting approach that could help decrease the Young's modulus while simultaneously mimicking highly hierarchical porosity of the bone structure. However, these structures are more difficult to fabricate than those with homogenous porosity. The design and distribution of this porosity in the implant must ensure the biomechanical and biofunctional balance of the bone tissue it is intended to replace. In this study, Ti radially graded structures were successfully fabricated using Spark Plasma Sintering combined with Space Holder Technique. The effects of temperature on porosity and mechanical properties were thoroughly examined. The results indicated that this processing route allows to achieve good control of porosity, close to the amount of added spacer. Yield stress of 181 MPa and an elastic modulus of 56 GPa were obtained for samples sintered at 800 °C for 5 min under a pressure of 6.3 MPa. These mechanical properties make the structure a viable candidate for replacing human long bones.

Electrodeposition of Nickel-Tungsten Alloy with Functional Concentration Periodically Graded Material Structure for Low Stress and High Hardness

A nickel-tungsten alloy film was deposited using an electrodeposition process. The tungsten concentration in the nickel-tungsten alloy was controlled by the applied current density. The surface morphology, micro-structure, internal stress, and hardness were characterized as a single-layer structure. Hardness increased as the tungsten content increased, but micro-cracks occurred on the surface. A multi-layered structure was selected to increase the hardness without micro-cracks. The multi-layered nickel-tungsten alloy film was deposited to form two types: functional periodic materials and functional graded materials. These multi-layered structures were deposited by changing the applied current density periodically and gradually, respectively, during the deposition process. The mechanical properties, such as internal stress and hardness of the nickel-tungsten alloy, were characterized as a function of the tungsten concentration of the nickel-tungsten alloy film. As the number of periods increased, the internal stress decreased, and micro-cracks were removed from the surface. However, the gradually varied nickel-tungsten alloy had higher internal stress than the periodically varied alloy. Similar hardness was observed because the concentration of nickel-tungsten film at the top of the multi-layered structure was the same. Overall, we demonstrated enhanced mechanical properties, including low internal stress and high hardness, of concentration periodically graded nickel-tungsten alloy.

Development of Functionally Graded Metal-Ceramic Systems by Directed Energy Deposition: A Review

Ceramics and metals are the two vastly explored classes of materials whose individual characteristics and targeted applications differ significantly. Continuous thrust for space exploration and energy generation demands materials with a wide range of properties. To tackle this demand, ceramic-metal combined structures that club heat, wear, and corrosion resistance of ceramics to the high toughness, good strength, and better machinability of metals are desirable. While various processing routes to combine ceramics and metals have been developed through the years, solutions to address problems associated with the interface, thermal property mismatch, and poor adhesion need to be explored. In this context, Functional Graded Materials (FGMs) have attracted particular attention by virtue of their ability to avoid sharp interfaces and local stress concentrations. Out of all, Additive Manufacturing (AM) routes, particularly the Directed Energy Deposition (DED) technique, is emerging as a productive technique capable of fabricating a wide range of metal-ceramic graded structures. This paper specifically discusses metal-ceramic FGMs ́ capability as a potential high-temperature material with customized multifunctional material properties. It further outlines the primary concerns with the realization of metal-ceramic graded structures and major techniques developed to mitigate problems encountered in processing them. Specific emphasis is laid on the powder-based Laser DED (L-DED) technique of FGM fabrication owing to its control over complex geometries and microstructural engineering.

Nonlinear CZM-based predictive analysis of damage in single-lap composite joints: An exploration of the FGM concept in Fiber–Matrix coupling

This study introduces an innovative numerical approach, validated through experiments, to incorporate functional graded materials (FGMs) volume fractions into mixing laws for fiber–matrix unidirectional composites. Nonlinear techniques address adhesive ductility, with the cohesive zone modelling (CZM) model integrated into finite element analysis using the ABAQUS code. The CZM model encompasses shear and detachment modes, characterized by adhesive stress increase in a trapezoidal shape. Proposed strategies introduce layer-specific fiber presence; concepts like C-1 exhibit denser fibers toward the middle, while C-2 and C-3 position them nearer to the plate edge. Stiffness from attached plates significantly governs overall responses, particularly under mixed loading conditions. The results have shown that the proposed grading concept C-2 provides an over-resistance capacity compared to other concepts. Additionally, using a special mesh in the composite grading, the results indicate that the adhesive formulation used in this analysis and the approach followed are primarily based on experimental results, demonstrating good agreement with the numerical model employed.

Morphological Analyses of W/Cu Functional Graded Materials Obtained by Conventional and Spark Plasma Sintering.

The paper presents the analysis of two compaction methods for obtaining W/Cu Functional Graded Materials (FGMs) consisting of three layers with the following compositions (% weight): first layer 80 W/20 Cu, second layer 75 W/25 Cu, and third layer 65 W/35 Cu. Each layer composition was obtained using powders obtained through mechanical milling. The two compaction methods were Spark Plasma Sintering (SPS) and Conventional Sintering (CS). The samples obtained after the SPS and CS were investigated from morphological (scanning electron microscopy-SEM) and compositional (energy dispersive X-ray spectroscopy-EDX) points of views. Additionally, the porosities and the densities of each layer in both cases were studied. It was found that the densities of the sample's layers obtained through SPS are superior to those obtained through CS. The research emphasizes that, from a morphological point of view, the SPS process is recommended for W/Cu-FGMs, having raw materials as fine-graded powders against the CS process.

Microstructural evolution of graded W-Cu materials under repeated thermal shocks

To investigate the stability of W-Cu functional graded materials (FGMs) under transient-state heat load, continuous W-Cu FGMs from pure W to W-36 Cu(vol%) layer and W/W-30 Cu(vol%) joints were employed for thermal shock tests at temperatures of 1000 °C-RT under different cycles (50, 100, 150, 200). The results show that the thermal shock damage mainly occurs in the forms of Cu exudation to the sample surface, pores, and cracks caused by various thermal stresses, which were induced by the mismatch of coefficients of thermal expansion (CTEs) between W and Cu, temperature gradient and composition gradient inside W-Cu FGMs. For the continuous W-Cu FGMs, Cu exudation to the surfaces and the maximum exudation occurs in the W-22Cu region, and some microcracks appear in this region after 200 times of thermal shocks. However, for the W/W-30 Cu joints, a macrocrack appears through the entire interfaces between W and W-30Cu layer after 50 thermal shock cycles, and the crack width gradually becomes larger with the increase of the times of thermal shocks.

Using Functionally Graduated Materials Concept to Predict the Damage of Heat-Treated Elbows Under Bending and Pressure Loading

Abstract Elbows in pressurized tubular structures are increasingly stressed by loadings with radial and tangential stresses. These stresses are completely different from those of straight tubular structures. Through the finite element method and using the ABAQUS computer code, the damage of a tubular structure in X60 of an elbow attached by straight parts stressed in internal pressure and in the moment of bending in closing is analyzed in this work. As a proposal for reinforcement, this structure is previously heat-treated and partially at the level of the elbow. The formulation of the heat-treated X60 material is based on the concept of functional graded materials (FGM), where the graduation by volume fraction between the metal in its base and that previously heat-affected named heat affected zone (HAZ) is under a power function of a parameter named volume fraction index (n). The graded properties of HAZ in the base metal along the thickness of the tubular structure are introduced by a row of finite elements using a proposed meshing technique. The elastic–plastic behavior of the HAZ-base metal mixture under the Voce model follows the equivalent stress flow theory of Von Mises. The technique of extended finite element technique (XFEM) in the damage and the mesh proposed in the graduation, were used to evaluate the various parameters, such as: the internal pressure and the heat treatment (surface and index n). The latter condition the response of the structure and the level of its damage.

Nonlinear dynamics of an enhanced piezoelectric energy harvester composited of bi-directional functional graded materials

Given the energy harvesters in the engineering are often confronted with the possibility of catastrophic failure due to the multi-directional loads induced by the seismical or wind actions, a novel piezoelectric energy harvester made of bi-directional (2D) functional graded materials (FGMs) undergoing the large deformation is presented to resist the 2D loads so that the reliability of harvesting the vibration energy in the environment is enhanced. Taking the material properties continuously and smoothly varying across the axial and thickness directions of the substrate into account, Hamilton’s principle is used to establish the electromechanical model of distributed parameters based on the geometric nonlinearity. The Galerkin truncation and the harmonic balance method combined with the arc-length tracking continuation are applied to trace the frequency responses, which are compared with numerical solutions and the excellent agreements are obtained. The stability and bifurcation behaviors on the condition of resonance response interaction are predicted by Floquet’s theory. Numerical examples are disclosed that the effects of the excitation amplitude, damping coefficient, load resistance, axial and thickness FGMs indexes on the vibration displacement, output voltage, and power. Notably, the bifurcation behaviors of the proposed energy harvester may be tailored/tuned by multi-directional FGMs to achieve a wider frequency bandwidth and a higher harvesting power.

Using the Equivalent Plate Concept to Calculate Functionally Graded Plates by Numerical Method

Functional graded materials are based on two materials, with very different properties, which vary continuously, according to a material law, on their thickness (a beam or a plate). The concept of equivalent plate involves the replacement of the given plate, a plate made of FGM, with a homogeneous and isotropic plate, with the same geometric characteristics (shape and dimensions), with the same load, which is attributed material properties that lead to the same behavior with the given plate. The aim of the paper is to provide a way to solve a complex problem (mathematical and structural), as in the case of FGM plates, with available means, with known professional calculation programs, with common finite elements, without intervention in the structure of its program. of finite element matrices, in other words without dedicated calculation programs. The finite element method is applied using the Ansys program and one of the best known finite elements, the 3D Solid185 element, both in the common version (structural) and in the multilayer finite element version.

Fatigue crack propagation simulation method using XFEM with variable-node element

The extended finite element method (XFEM) with the local refinement technique using the variable-node element (VNE) is proposed to simulate the fatigue crack propagation under the cyclic loadings, in which the initially generated coarse mesh around the crack tip is refined after the crack propagation and the VNE is used to connect the refined elements and the adjacent elements. The local refine elements are used to improve the accuracy of stress near the crack tip and it is unnecessary to conform the discretization to the crack surfaces. The maximum tangential stress criterion is used to determine the crack propagation angle θc and the fatigue life is estimated by the Paris law. With this method, the condition number of the global stiffness matrix is alleviated by using the only discontinuous branch enrichment function and the crack increment size can be set flexibly and small enough to reproduce true crack path. Because only the refined mesh around crack tip is updated at each increment step during crack propagation, the simulation cost is much less than that of the method in which global fine mesh is required. Numerical examples of the crack propagation under the monotonic and cyclic loadings are given out and it is demonstrated that the proposed method can calculate the stress intensity factors (SIFs) and predict the crack paths more accurately with the local refine elements near the each crack tip. The proposed method is also suitable to simulate the crack propagation of the functional graded materials under the thermal loadings in the future works, in which the material non-homogeneity near the crack tip requires accurate modeling.

Application of Galerkin iterative technique to nonlinear bending response of three-directional functionally graded slender beams subjected to hygro-thermal loads

In the view of some progressive devices such as shuttles in the aerospace field, the vessels in the marine engineering and reaction equipments in the nuclear field are exposed to super-high thermal or hygro-thermal loads simultaneously varied along the three directions in the operation, we propose the three-directional functional graded materials (3D FGMs) to carry out the composition of slender beams to meet the requirements of the hygro-thermal distribution in the multi-directions and improve the endural ability so that catastrophic failure is refrained due to large deflections. Built up on von Kármán geometric nonlinearity, one takes advantages of the principle of minimum total potential energy to derive the nonlinear governing equation of the structures subjected to hygro-thermal loadings of the uniform, linear and sinusoidal distributions. A novel analytical solution for the nonlinear bending response is presented based on the Galerkin iterative technique, which overcomes the shortcoming of finding difficultly the closed-form solution to antisymmetric nonlinear structures such as multi-directional FGMs. The generalized differential quadrature method (GDQM) is performed for validating the effectiveness of the presented methodology. Numerical simulations are implemented to reveal the effects of 3D FGMs indexes, mechanical and hygro-thermal loadings on the nonlinear bending response. Results exhibit the nonlinear behavior is profoundly dependent on the 3D FGMs and hygro-thermal properties, which is applied for optimizing the 3D FGMs structures in multiple physical fields.

Elastic Behavior of Uncemented Hip Prosthesis Made of Composite with Material Property Grading

Functional graded materials (FGMs) are widely used for hip plant component materials because of their specific properties in a specific design to meet the requirements of the hip joint system. Stem is manufactured with the concept of making new FGM using three different composition of Ti, CrCo, and HA. This has led to the development of a suitable design for functional femoral parts that can be used for a long time. The new FGM design has helped to reduce the protection of the stress and the associated stress that exists on the interface. After changing in composition of FGM, the natural frequency and deformation response exhibited by our model were quite satisfactory. The deflection comes out to be 0.33 mm at the frequency of 15 Hz. The equivalent von Mises stress is found to be 19.5 MPa. These values are closely matching with previous studied. Fatigue study was carried based on “Goodman” theory. This gave promising results. The safety factor found is more than one, which indicates that the part is safe under design. The anticipated life of stem model is 0.3284 × 105 cycle.

A dual-phase-lag (DPL) transient non-Fourier heat transfer analysis of functional graded cylindrical material under axial heat flux

A dynamic thermal conduction problem needs a mathematical formulation and solution consisting of cylindrical coordinates of materials for the application of nuclear reactor and/or laser therapeutic when subjected to higher heat fluxes. In this study, dual-phase-lag (DPL) transient non-Fourier heat conduction in a functional graded cylindrical material is analytically solved under axial heat flux condition. Functional Graded Material (FGM) properties are based by exponential low. Governing equations on the model are expressed in 2D cylindrical coordinates and solved by using the separation of variable method. An effect of the heterogeneity coefficient of the material using Fourier method, Cattaneo–Vernote model and the dual phase lag is analyzed. An influence of non-dimensional temperature changes to the Fourier number in the pure and functional material is analyzed. Results showed that DPL model requires less time to meet the steady temperature compared with single-phase-lag (SPL) model. In the FGMs, each model and method tends to have a constant temperature based on the amount of heterogeneity coefficient, and it can be concluded that one of the factors determining the amount of stable temperature is the properties of the material. The current results provide a straightforward multivariate analytical solution of the non-Fourier conduction equation in a finite cylinder, for cylinders with any boundary conditions and, for cylinders with functional graded materials. It was found that negligible issues with the critical points being presented when compared to the Laplace operator method.

Design and finite element analysis of femoral stem prosthesis using functional graded materials

Conventionally biometals were used for design and development of bioimplants. However, the Young’s Modulus (YM) of these bioimplants is higher than that of a natural bone. Asymmetric load transfer from a bone to the bioimplant results in aseptic loosening and stress shielding. Here-in, the use of functionally graded materials (FGM) has been introduced to design the femoral stem prosthesis as a model bioimplant using computational biomechanics. The material properties variations in these FGMs in longitudinal and radial directions are explored to minimize the aseptic loosening and stress-shielding that plays a vital role in defining the performance and longevity of the prosthesis. Three groups of FGM (Ti-HA, SS316L-HA and CoCr alloy-HA) have been explored to design the stem prosthesis and the finite element analysis (FEA) was carried out using computational biomechanics. The stress distribution profile in the designed stem prosthesis demonstrated an increase in the stress values with an increase in the volume fraction exponent. The results corroborated with the stress distribution obtained from the simulation results of a cortico-cancellous bone. The stress distribution in the Ti-HA prosthesis is observed to be more uniform than CoCr-HA and SS316L-HA prosthesis. In addition, the reduced number of stress shielding points were observed for the Ti-HA prosthesis when compared with the CoCr-HA and SS 316 L-HA stem prostheses. Hence, the results suggested that the Ti-HA prosthesis could be considered as a mechanically stable prosthesis and the same could offer safe design for further development of a femoral bioimplant.

Finite element analysis of functionally graded bar under torsional load

The development of new products with robust design requirements and specific functional attributes arises the need for tailored-made materials like Functional Graded Materials (FGM). These materials show different properties with the change in dimensions corresponding to species composition. Industries dealing in automobile, space, and structural components are continuously trying to adopt new materials for their specific functional requirement to enhance the performance and efficiency of their system. In the present work, the shear stresses developed on FGM bars are analyzed by pure torsional loading for a different cross-section of varying thicknesses. Here, circular, square, and triangular cross-section of FGM bars is modeled for Nickel and Aluminum oxide. The modeling of material is made up of four layers. The innermost layer comprises pure metal whereas the outermost layer consists of only ceramic. The intermediate two layers contain metals and ceramics in varying compositions. Initially, the analysis is done to see the effect of the torsional load on bars with the same thickness of the individual constituents. Finite Element Methods (FEM) based ANSYS software has been used for the numerical analysis of the problem as it is one of the most convenient tools to capture the variation in geometry and composition of the material. Computational analysis has been performed to analyses the development of shear stress in FGM bars of different cross sections. It is observed that in all case the developed shear stress is more in triangular cross-section with respect to other and the shear stress bearing capability of the FGM bars shows remarkable increase with the influence of thickness of the intermediate layer of metal-ceramic.

Microstructure and corrosion behaviour of 316 L-IN625 functionally graded materials via laser metal deposition

In this work, the microstructure of gradient regions and the corrosion behaviour of transition interfaces for 316 L-IN625 functional graded materials fabricated using laser metal deposition are investigated. The microstructure in gradient regions along the build direction such as celluar dendrites, columnar grains, coarse dendrites, and nearly equiaxed grains. When the composition of 316 L is less than or equal to 40%, the over passivation zone appears, resulting in the Mixed Cr (III/VI) oxide as the final corrosion products which consists of surviving Cr (III) oxide and generated Cr (VI) oxide. The composition gradient of 316 L-IN625 can effectively improve the corrosion resistance.

Experimental measurement and simulation of mechanical strength and biological behavior of porous bony scaffold coated with alginate-hydroxyapatite for femoral applications

In the present study, the 3D printer method for fabricating porous bone scaffolds with Polylactic Acid (PLA) printed was used by Fused Deposition Modelling (FDM). Then, the prepared 3D scaffold coated with alginate composed with various amounts of Hydroxyapatite (HA) using the freeze-drying technique. After the fabrication of novel functional graded materials scaffold, the mechanical strength and biological behavior were investigated. The Scanning Electron Microscopy (SEM) and X-ray Diffraction (XRD) analysis used to characterize the morphology and phase characterization. The structure of the porous scaffold was simulated using the ABAQUS analysis method and their mechanical and physical properties were extracted. Also, strong antibacterial properties were observed for all samples with increasing HA nanoparticles against gram-positive and gram-negative bacterial suspensions. These bio-nano composites are compatible with the pH of the blood. In general, it was found that the most suitable bio-nano composite is the sample with 10 wt % HA nanoparticles. The elastic modulus increased from 350 MPa to 394 MPa with the addition of HA nanoparticles, while the porosity percentages decreased from 44 % to 36 %. The compressive strength increases from 25.2 MPa to 32.7 MPa with the addition of 30 wt% HA nanoparticles. The obtained results showed that the bio-nano composites prepared in this study were suitable for further development in bone substitutes with desirable mechanical properties. The alginate/HA material properties reported from the numerical approach, have an acceptable agreement with experimental results. Furthermore, the numerical study indicated that the scaffold compressive strength increases from 22.8 MPa (S1) to 31.2 MPa (S4) with the addition of 30 wt % HA nanoparticles. Nanoindentation test explains that the indenter penetration decreases from 82.163 nm to 69.338 nm with the addition of 30 wt% HA nanoparticles. As a consequence, PLA-alginate/20 wt % HA (S3) and, PLA-alginate/30 wt% HA (S4) have the best mechanical properties. Although due to lower biological advantages of S4 concerning S3, PLA-alginate/20 wt % HA (S3) chose as an appropriate bio-nanocomposite for orthopedic application.