Functionally Graded Materials Structures Research Articles

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.

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.

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.

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

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

Introducing ANN-GP algorithm to estimate transient bending of the functionally graded graphene origami-enabled auxetic metamaterial structures

This article presents a new method called the artificial neural networks-genetic programming (ANNs-GP) algorithm, which effectively predicts the bending behavior of functionally graded graphene origami-enabled auxetic metamaterial (FG-GORAM) structures under transient conditions. Functionally graded materials (FGMs) display spatial heterogeneity in their composition and microstructure, resulting in distinctive mechanical characteristics that make them well-suited for a wide range of engineering applications. The objective of this study is to create a prediction model that can accurately capture the intricate transient bending behavior of FGM structures. To do this, the researchers have used the ANN-GP technique, which combines ANNs with GP. The ANN component acquires knowledge from a dataset including actual or simulated bending data, while the GP component fine-tunes the structure and parameters of the neural network to improve its ability to make accurate predictions. The proposed algorithm combines the strengths of ANNs and GP to accurately predict the bending behavior of FG-GORAM structures. This algorithm is robust and efficient, allowing designers and engineers to optimize the performance and reliability of these structures in various applications. The effectiveness of the ANN-GP method is proved by comparing it to experimental or simulated data. This shows that the algorithm has the potential to be a useful tool for designing and analyzing sophisticated materials and structures.

Fabrication of a tri-layer scaffold with dual release of heparin and PRP for tissue engineering of small‐diameter blood vessels

A tri-layer scaffold was fabricated according to functionally graded materials (FGM) theory from poly(glycerol sebcate)/poly(L-lactic acid) blend by the increasing polylactic acid ratio from the inner to the outer layer. Heparin and platelet-rich plasma were loaded in separate layers to achieve proper remodeling and patency. The scaffold showed a linear degradation trend. The elastic modulus was 13.8 ± 1.11 Mpa that was in the favorable range for constructing artificial vessels. The integrity of the layers was preserved due to its FGM structure. The scaffold showed full blood compatibility by minimal platelet adhesion and hemolysis due to relatively slow release of Heparin.

Synthesis and Characterization of a Titanium-Based Functionally Graded Material-Structured Biocomposite using Powder Metallurgy.

This investigation aims at synthesizing and characterizing a biocomposite of hydroxyapatite (HA) and titanium (Ti) as a functionally graded material (FGM) via an economical powder metallurgy route. Ti particles were produced through drilling and chipping, followed by compaction and sintering. Ti foams, so obtained, were then infused with varying volume fractions of HA. The pure Ti foam control sample and the FGM composite samples were then subjected to various characterizations to validate their biocompatibility, structural strength, and integrity. The interface development between the load-bearing Ti implant and living tissue was resolved through an FGM structure, where the base of the implant consisted of load-bearing Ti and the outer periphery changed to HA gradually. HA/Ti specimens of different volume fractions were tested for density measurements, microstructure, hardness, and bioactivity. The bioactive behavior was investigated using the potentiodynamic polarization technique to measure the corrosion rate of the pure Ti foam (0/100 HA/Ti) and the FGM composite (10/90 HA/Ti) samples in a simulated body fluid (SBF). The results showed that the hardness of FGM composites, despite being less than that of 0/100 HA/Ti, was still within safe limits. The corrosion rate, however, was found to be decreased by a significant value of almost 40% for the 10/90 HA/Ti FGM composite sample compared to the pure Ti foam control sample. It was concluded that the optimum composition 10/90 HA/Ti sample offers improved corrosion resistance while maintaining a sufficient allowable hardness level.

Thermal fatigue failure enhancement for FGM coolant pipes subject to high-temperature and hydrostatic lateral pressure

This paper intends to enhance the corrosion resistance of coolant pipes in thermal fatigue conditions and lateral hydrostatic pressure in critical engineering environments. This research applies to circular coolant pipes under hydrostatic pressure of the LBE (lead-bismuth eutectic) boundary in nuclear power plants. The resistance against corrosion caused by liquid LBE is mainly formed by Fe12Cr2Si solid solutions coatings on the pipe. The silicon concentration in Fe12Cr2Si can interact with LBE as an effective oxidized compound such as SiO2 and Fe2SiO4 when the silicon concentration is above 1.25 wt%. The oxide film formed on the coating can resist the LBE corroding in the Fe12Cr2Si structure. The primary material for constructing a coolant pipe is T91 ferritic-martensitic alloys, and the surface anti-corrosion coating is Fe12Cr2Si solid solution. With a high-strength structure, FGC (functionally graded composite material) ensures that the pipe resists the corrosion from Liquid LBE. This study evaluates the thermal fatigue failure of coolant pipes and the silicon concentration when the pipe model is under thermal shock testing by a CO2 laser. The research result indicates that the FGM (functionally graded material) structure performs better in effectively raising the margin of safety and reserving the silicon concentration on the inner surface higher than 1.25 wt% as compared to the FGC structure.

Cellular Automata Approach to Topology Optimization of Graded Multi-Material Structures

Despite decades of progress, structural topology optimization is still one of the most important areas of engineering optimal design. The intensive research within this area has been stimulated by the development of efficient methods and algorithms on one side and the needs and demands of contemporary engineering on the other. Over the years, the practical aspect of topology optimization has become one of the most significant issues within the design community. Simultaneously, the range of design applications has been broadening. Among many research areas where topology optimization is present, attention has been paid to the design of multi-material structures. The gradation of the material properties has a significant influence on the final layout of the structure, so this problem can be treated as an extension of the classical task of the topology optimization of structures made of a material with uniform distributions of properties. While working with multi-material structures, the important role plays an interface between parts made of materials with different properties. In this paper, the implementation of interfaces made of functionally graded materials (FGM) is proposed. A functionally graded interface means that continuous and smooth changes of properties are assigned to a particular direction from one material surface to another. This paper presents the idea of topology optimization of graded multi-material structures using a simple, fast convergent technique based on the Cellular Automata approach. The proposal is to take the advantage of the versatility of efficient professional finite element-based structural analysis software and the simplicity of the original heuristic topology generator, to build a tool for the optimization of FGM structures as well as multi-material structures including the FGM interface.

Advancement in total hip implant: a comprehensive review of mechanics and performance parameters across diverse novelties.

The UK's National Joint Registry (NJR) and the American Joint Replacement Registry (AJRR) of 2022 revealed that total hip replacement (THR) is the most common orthopaedic joint procedure. The NJR also noted that 10-20% of hip implants require revision within 1 to 10 years. Most of these revisions are a result of aseptic loosening, dislocation, implant wear, implant fracture, and joint incompatibility, which are all caused by implant geometry disparity. The primary purpose of this review article is to analyze and evaluate the mechanics and performance factors of advancement in hip implants with novel geometries. The existing hip implants can be categorized based on two parts: the hip stem and the joint of the implant. Insufficient stress distribution from implants to the femur can cause stress shielding, bone loss, excessive micromotion, and ultimately, implant aseptic loosening due to inflammation. Researchers are designing hip implants with a porous lattice and functionally graded material (FGM) stems, femur resurfacing, short-stem, and collared stems, all aimed at achieving uniform stress distribution and promoting adequate bone remodeling. Designing hip implants with a porous lattice FGM structure requires maintaining stiffness, strength, isotropy, and bone development potential. Mechanical stability is still an issue with hip implants, femur resurfacing, collared stems, and short stems. Hip implants are being developed with a variety of joint geometries to decrease wear, improve an angular range of motion, and strengthen mechanical stability at the joint interface. Dual mobility and reverse femoral head-liner hip implants reduce the hip joint's dislocation limits. In addition, researchers reveal that femoral headliner joints with unidirectional motion have a lower wear rate than traditional ball-and-socket joints. Based on research findings and gaps, a hypothesis is formulated by the authors proposing a hip implant with a collared stem and porous lattice FGM structure to address stress shielding and micromotion issues. A hypothesis is also formulated by the authors suggesting that the utilization of a spiral or gear-shaped thread with a matched contact point at the tapered joint of a hip implant could be a viable option for reducing wear and enhancing stability. The literature analysis underscores substantial research opportunities in developing a hip implant joint that addresses both dislocation and increased wear rates. Finally, this review explores potential solutions to existing obstacles in developing a better hip implant system.

Multiscale framework for prediction of residual stress in additively manufactured functionally graded material

Additive manufacturing (AM) of functionally graded material (FGM) is of great interest for alleviating the abrupt material discontinuity and steep gradient of physical properties across the interface between dissimilar materials. This study proposes a multiscale framework based on the inherent strain method to accurately predict residual stress distribution in FGMs processed via AM using directed energy deposition (DED). First, mesoscale representative volume elements for different chemical compositions of austenitic and ferritic steels were modeled with actual process parameters and individual material properties to calculate the inherent strains. Subsequently, the corresponding inherent strains of each chemical composition were continuously mapped to a macroscale model using the lumping layer method to obtain the residual stress distribution. Five types of specimens with different interlayers and scanning strategies were prepared using DED. The contour method, neutron diffraction, and deep hole drilling were used to determine the residual stress distribution. The results indicate that the residual stress distribution in the FGM predicted by the proposed multiscale model is consistent with the experimental measurements. Based on the proposed model, the effects of the interlayers and scanning strategies on the residual stress and distortion of the FGM were investigated. The proposed model allows for a better understanding of the effect of the composition gradient on the residual stress and enables accurate prediction of residual stresses in FGM structures.

Fabrication and characterization of functionally graded material (FGM) structure containing two dissimilar steels (ER70S-6 and 308LSi) by wire arc additive manufacturing (WAAM)

Functionally graded materials (FGM) are components that can provide different material properties in a single structure. It is sometimes required to exhibit locally different material behaviours from parts used for various purposes in the industry. In such requirements, the use of FGM structures emerges as a solution. The fabrication of FGM structures with traditional manufacturing methods is generally complicated and sometimes not possible. However, the additive manufacturing (AM) technique, which is the topic of many applications and research today, has emerged as a superior manufacturing method compared to traditional methods in fabrication FGM structures, thanks to its advantages. Fabrication in the form of layers with the AM allows the fabrication of layers with varying material properties. This study was carried out on the fabrication of FGM structures by the wire arc additive manufacturing (WAAM) method, which is one of the metal AM techniques. Low alloy steel (ER70S-6) and austenitic stainless steel (308LSi) metal wires are used in FGM structures. The FGM structure was successfully fabricated by the WAAM method. Hardness, tensile, and fatigue tests were applied to determine the mechanical properties of the part. In addition, XRD analysis and microstructure studies were carried out to understand the metallurgical properties. As a result of the mechanical tests, no defects were observed in the FGM interfaces, and an increase of up to 46% was observed in the tensile strength compared to the single-material fabrication. In hardness measurements and microstructure studies, it has been observed that the FGM structure exhibits different properties according to the changing layers. It has been concluded that the fatigue limit of the FGM part in the horizontal direction is 25% higher than in the vertical direction.

Buckling of Composite Structures with Delaminations—Laminates and Functionally Graded Materials

In the present paper, buckling problems of constructions with single delamination are examined. Structures were made of unidirectional laminates and functionally graded materials (FGM). Two types of delaminations (closed and opened) were both investigated in experiments both in rectangular plates and axi-symmetric shells. The first part of the work is devoted to the formulation of contact problems (embedded, closed delaminations) with the aid of various functional inequalities. Then, computational models are discussed. To study the influence of the variable material configuration of FGMs, the fourth-order plate/shell relations were adopted. Finally, three particular problems examined are the buckling of flat rectangular plates, spherical shells, and compressed rectangular plates with elliptical delaminations. The experiments were conducted using imperfection sensitivity analysis and post-buckling non-linear analysis. The results demonstrate that the unsymmetric configurations of FGM structures lead to the reduction of buckling loads for structures with delaminations. For FG structures, those effects are described by the simple coefficient. Linear fracture mechanics were employed to distinguish the form of unilateral boundary problems (closed or opened). In the first case, the stable variations of the strain energy release rate GI with the delamination length variations were observed, whereas in the second case the unstable variations were observed.

Computational and Variational Formulations of Unilateral Problems for Structures Made of Composite Materials (Laminates, Functionally Graded Materials)

In the present paper buckling problems of constructions with a single delamination are conducted. Structures are made of laminates and functionally graded materials (FGM). The first part of the work is devoted to the formulation of contact problems with the aid of various functional inequalities. Then computational models are discussed. Finally two particular problems dealing with buckling of spherical shells and compressed rectangular plates. The results demonstrate that the unsymmetric configurations of FGM structures leads to the reduction of buckling loads for structures with delamination.

Thermo-elastic solid shell formulation with phase field fracture for thin-walled FGMs

Thermo-elastic fracture is a matter of important concern for thin-walled structures made of functionally graded materials (FGMs). Based on this practical relevance, a thermodynamically consistent framework is herein proposed to solve the coupled thermo-mechanical phase-field fracture problem in thin-walled structures made of FGMs. The formulation of the current model is constructed via the evaluation of the phase-field in the Clausius–Duhem inequality leading in to first-order stability conditions in order to ensure thermodynamic consistency. The three-dimensional Kirchhoff–Saint–Venant constitutive model is modified to accommodate the functional grading in the material properties. The computational model is combined with Enhanced Assumed Strain (EAS) and Assumed Natural Strains (ANS) to alleviate locking pathologies concerning the solid shell formulation, leading to a coupled non-linear variational formulation. Several benchmark examples (straight and curved shells) are examined to assess the model capabilities. Moreover, crack deflection, and temperature distributions in the FGM structures are compared with their homogeneous surrogates, to show the importance of the technological solutions with two or even three FGM phases.

Corrosion Enhancement for FGM Coolant Pipes Subjected to High-Temperature and Hydrostatic Pressure

The objective of this paper is to enhance the corrosion resistance of coolant pipes in high temperature and lateral hydrostatic pressure in critical engineering environment, especially for circular coolant pipes under hydrostatic pressure of LBE (lead-bismuth eutectic) applications in nuclear power plants. The resistance against corrosion caused by LBE liquid is mainly formed by Fe-12Cr-2Si solid solutions coatings on the pipe. The silicon concentration in Fe-12Cr-2Si can interact with LBE as an effective oxidized compound such as SiO2 and Fe2SiO4 when the silicon concentration is higher than 1.25 wt.%. The oxide film formed on the coating can resist the LBE corroding in the Fe-12Cr-2Si structure. The primary material of a constructing coolant pipe is T91 ferritic-martensitic alloys, and the surface anti-corrosion coating is Fe-12Cr-2Si solid solution. With a high strength structure, FGC (functionally graded composite material), ensures that the pipe resists the corrosion from LBE liquid. In this study, both the steady-state stress values and silicon concentration are evaluated at 700, 1000, and 1200 °C to know the fatigue problems. The research result indicates the FGM (functionally graded material) structure performs better in promoting the margin of safety on stress distribution and reserving the silicon concentration on the inner surface higher than 1.25 wt.% over 60 years as compared to the FGC structure with 34 μm thickness of Fe-12Cr-2Si coating in a high temperature environment.

Investigating the graded-index influence on elastic responses of axisymmetric pressurized and heated thick-walled functionally graded material of cylindrical vessel

This article presents the influence of a graded-index on the elastic responses of an axisymmetric pressurized and heated thick-walled functionally graded material (FGM) cylindrical vessel under plane strain conditions. It is assumed that the inside surface/outside surface of a cylinder is made up of ceramic /metal. The temperature-independent thermo-mechanical parameters of an FGM cylinder are described by using the rule-of-mixture with the function of radius. The profiles of thermo-mechanical material characteristics are assumed to vary continuously and gradually along the thickness direction of a cylinder. The numerical solutions of the thick-walled FGM cylinder governing differential equations are examined by using the non-linear shooting and fourth-order Runge-Kutta approaches. The thermo-elastic solutions of the thick-walled FGM cylinder over the radial direction are computed using Jupiter, Python open-access software, and graphically reported. The analytical solutions (AS) of a ceramic cylinder are compared with numerical solutions (NS) of an FGM cylinder (n = 0) to validate the proposed method. The results reveal that the graded-index n has a higher influence on the profiles of dimensionless hoop stress, dimensionless axial stress, dimensionless radial displacement, hoop strain, radial strain, and thermo-mechanical material properties in the dimensionless radial direction of an FGM cylinder. Nevertheless, the graded-index has an insignificant impact on dimensionless radial stress across the dimensionless radial direction of an FGM cylinder. Based on these findings, it is recommended that graded-index is an important parameter which can be used to regulate the responses of FGM structures under thermal and mechanical loading conditions.

Fracture parameter investigations of functionally graded materials by using ordinary state based peridynamics

Static and dynamic fracture parameter analyses of functionally graded materials (FGMs) are conducted by using the ordinary state based peridynamic theory (OSPD). As a meshfree method, OSPD applies an integral equation to describe the motion of objects, avoiding the geometrical singularity in conventional fracture analysis measures. Domain integral method by introducing material gradient terms is employed in evaluating the static and dynamic stress intensity factors (SIFs). Meanwhile, peridynamic differential operator (PDDO) is also applied for the calculation of physical components derivatives. Different FGM modeling schemes are also examined in the OSPD framework. Cracked FGM structures with mode-I and mixed-mode crack scenarios are under investigation and results are validated by reference solutions. Accuracy and reliability of the proposed method will be examined and discussed.

Investigation of the fracture problem of functionally graded materials with an inclined crack under strong transient thermal loading

In this paper, a special method for solving transient thermal stress intensity factors (TSIFs) in functionally graded materials (FGMs) with inclined cracks under strong, transient thermal shock loading is established based on the hyperbolic heat conduction equation. First, the Newmark method is employed to obtain the strong transient temperature field of FGMs containing inclined cracks. Then, the transient interaction energy integral method (IEIM) is used to solve the TSIFs for inclined cracks. In addition, the influences of the distribution patterns of the thermal relaxation parameter, the crack length and the crack angle on the TSIFs, and the crack growth angle are investigated. Moreover, we discuss the difference between using the hyperbolic heat conduction theory and the classical, Fourier heat conduction theory in calculating the TSIFs of FGMs with inclined cracks. The results show that the present, combined IEIM-Newmark method can be used to solve strong transient thermal shock crack problems with high efficiency. This work can be used for the thermal design, evaluation, and engineering applications of FGM structures.

Analytical Solution for Forced Vibration Characteristics of Rotating Functionally Graded Blades under Rub-Impact and Base Excitation.

This paper presents an analytical investigation on the forced vibration characteristics of a rotating functionally graded material (FGM) blade subjected to rub-impact and base excitation. Based on the Kirchhoff plate theory, the rotating blade is modelled theoretically. The material properties of the FGM blade are considered to vary continuously and smoothly along the thickness direction according to a volume fraction power-law distribution. By employing Hamilton’s principle, the equations of motion are derived. Then, the Galerkin method and the small parameter perturbation method are utilized to obtain the analytical solution for the composite blade under a combined action of radial force, tangential force and displacement load. Finally, special attention is given to the effects of power-law index, rub-impact location, friction coefficient, base excitation amplitude and blade aspect ratio on the vibration characteristics of the FGM structure. The obtained results can play a role in the design of rotating FGM blades to achieve significantly improved structural performance.