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Mechanical responses of solid materials are governed by their material properties. The solutions for estimating and predicting the mechanical responses are extremely difficult, in particular for non-homogeneous materials. Among these, there is a special type of materials whose properties are variable only along one direction, defined as graded materials or functionally graded materials (FGMs). Examples are plant stems and bones. Artificial graded materials are widely used in mechanical engineering, chemical engineering, biological engineering, and electronic engineering. This work covers and develops boundary element methods (BEM) to investigate the properties of realistic graded materials. It is a must have for practitioners and researchers in materials science, both academic and in industry.

Fused filament fabrication (FFF) is a key extrusion-based additive manufacturing (AM) process for fabricating components from polymers and their composites. Functionally gradient materials (FGMs) exhibit spatially varying properties by modulating chemical compositions, microstructures, and design attributes, offering enhanced performance over homogeneous materials and conventional composites. These materials are pivotal in aerospace, automotive, and medical applications, where the optimization of weight, cost, and functional properties is critical. Conventional FGM manufacturing techniques are hindered by complexity, high costs, and limited precision. AM, particularly FFF, presents a promising alternative for FGM production, though its application is predominantly confined to research settings. This paper conducts an in-depth review of current FFF techniques for FGMs, evaluates the limitations of traditional methods, and discusses the challenges, opportunities, and future research trajectories in this emerging field.

Directed energy deposition (DED) is an important approach to fabricate metallic functionally gradient materials (FGMs). During DED process, two kinds of metallic powder are blown into molten pool with gradually changing powder feed rates to achieve material gradients in FGM. DED process always causes poor surface roughness and limited dimensional accuracy, which have to be overcome by machining. Different mechanical properties of two powder materials generate heterogeneous mechanical properties in FGM, which seriously influence cutting mechanism, such as cutting temperature, surface roughness, and tool wear, especially if one material is a hard-to-cut material. However, so far, there has not been any research particularly focused on this problem. This work investigated hybrid manufacturing FGMs involving DED and machining. SS316L and IN718 were fabricated into FGM specimen with DED process. Then, a tungsten carbide (WC) milling cutter machined the FGM specimen under dry peripheral milling condition. A series of material tests were performed to characterize the material properties of FGM specimen. Additionally, surface roughness, machining temperature observations, and tool wear were studied to investigate machining mechanism. Based on the experimental results, it is found that the cutting temperature close to IN718 region was higher than the cutting temperature close to the SS316L region. After machining, the surface colors of IN718 and SS316L regions were bright blue and bright silver, respectively. The surface roughness of SS316L region was greater than that in the IN718 region. In FGM (from 100% SS316L to 100% IN718) after machining, the machined surface colors were shown as yellow, bright yellow, and purple, with the surface roughness found decreasing gradually. Since IN718 is a typical hard-to-cut material, milling cutter is also observed to have obvious wear close to IN718 side. This work firstly studied the fabrication of FGM part with hybrid manufacturing (DED and machining) and provided valuable experimental data of machining the SS316/In718 FGM.

As functionally gradient materials (FGMs) reveal innovative mechanical properties, they have aroused huge interest in multiple industry areas. In this study, a hybrid manufacturing (HM) technique that combines a directed energy deposition (DED)-type additive manufacturing (AM) fabrication process with milling-type machining is investigated. In the DED process examined, Inconel 718 (IN718) and stainless steel 316L (SS316L) metal powders were blown into the molten pool at different and varying respective flow rates to achieve specific composition ratios for different printed layers so that a smooth gradient transition from SS316L to IN718 was achieved. Due to the attendant generation of rough surfaces common to such FGMs, partition milling was employed after fabrication, and the cutting temperatures and forces were simultaneously recorded considering the significant anisotropy in mechanical properties. The surface roughness of each FGM gradient section and tool wear mechanism were also measured after machining. Through analysis of the experimental results, the machining mechanism was revealed, which provides new insights into the machinability of SS316L/IN718 FGMs.

Stelite-6/Inconel 718 functionally gradient materials (FGM) is a heat-resisting functional gradient material with excellent strength performance under ultra-high temperatures (650–1100 °C) and, thus, has potential application in aeronautic and aerospace engineering such as engine turbine blade. To investigate the effect of initial temperature on the microstructure and properties of laser metal deposition (LMD) functional gradient material (FGM), this paper uses the LMD technique to form Stelite-6/Inconel 718 FGM at two different initial temperatures: room temperature and preheating (300 °C). Analysis of the internal residual stress distribution, elemental distribution, microstructure, tensile properties, and microhardness of 100% Stelite-6 to 100% Inconel 718 FGM formed at different initial temperatures in a 10% gradient. The experimental results prove that the high initial temperature effectively improves the uneven distribution of internal residual stresses. Preheating slows down the solidification time of the melt pool and facilitates the escape of gases and the homogeneous diffusion of elements in the melt pool. In addition, preheating reduces the bonding area between the gradient layers, enhancing the metallurgical bonding properties between the layers and improving the tensile properties. Compared with Stellite-6/Inconel 718 FGM formed at room temperature, the mean yield strength, mean tensile strength, and mean elongation of Stellite-6/Inconel 718 FGM formed at 300 °C are increased by 65.1 Mpa, 97 MPa, and 5.2%. However, the high initial temperature will affect the hardness of the material. The average hardness of Stellite-6/Inconel 718 FGM formed at 300 °C is 26.9 HV (Vickers hardness) lower than that of Stellite-6/Inconel 718 FGM formed at 20 °C.

Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed.

Functionally gradient material (FGM) in service often experience temperature variations that can affect the propagation characteristics of guided waves. This investigation aims to study the propagation of thermoelastic guided waves in the FGM plate. A computational method for the state vector and Legendre polynomials hybrid approach, which is proposed based on the Green–Nagdhi theory of thermoelasticity. The heat conduction equation is introduced into the governing equations, and optimized using univariate nonlinear regression for arbitrary gradient distributions of the material components. To study their dispersion characteristics, a non-hierarchical calculation for the dispersion curves of FGM plates versus temperature is realized. In addition, a frequency domain simulation model is developed and compared with theoretical data to evaluate the accuracy and feasibility of the proposed theory. Then, the influence of Legendre orthogonal polynomial cut-off order on dispersion curve convergence is investigated. Subsequently, the shift of the gradient index and temperature variation on the fundamental mode in dispersion curve is analyzed. The results indicate that changes in both gradient index and temperature lead to a systematic shift in the phase velocity of fundamental modes in the low frequency range. Meanwhile, anti-symmetric modes exhibit higher sensitivity. On this basis, the study can provide theoretical support for the acoustic non-destructive characterization of FGM plates versus temperature.

Given the shortcomings of existing methods of preparing functionally gradient materials based on PDMS, such as insufficient raw material mixing, a single preparation method, and high preparation cost, a device that incorporates the production and preparation of functionally gradient products is proposed. Simulations using the COMSOL software were employed to determine an optimization model for the mixing conditions during the preparation of functionally gradient material mixtures. Furthermore, the mixing capabilities of the device were compared when using constant-size and variable-size stirrers. The simulation research results indicate that the preparation device, in combination with the variable-size stirrer, can effectively stir the mixing. The mixing efficiency of the device when using the variable-size stirrer increased by approximately 36 % from that when using the constant-size stirrer. Actual samples were prepared and observed using a Hitachi electron microscope at a 200x magnification. The observation results show that the SiC particles in the sample prepared with a variable-size stirrer were distributed more uniformly than those in the sample prepared with a constant-size stirrer. The product prepared using the proposed device met the conditions for manufacturing functionally gradient products.

In order to solve the problem of non-uniform powder concentration in electrical discharge machining (EDM) working fluid, a mathematical model of powder particle movement in stirred tank was established, and the flow field and solid-liquid suspension uniformity were simulated in this paper. The factors of slot shape, depth-diameter ratio, blade angle, blade installation height, and solid particle volume fraction which affected flow field distribution, solid suspension particle uniformity, and power consumption were researched, and the stirred tank structure was optimized. When the ratio of spherical stirred tank depth to diameter is 0.8, the blade design angle is 45°, and the installation height of impeller blade is 120 mm, the suspension uniformity of solid particles is the best and the power consumption is the smallest. Under the conditions of Al powder concentration 4 g/L, pulse width 175 μs, and pulse interval 75 μs, the powder-mixed EDM experiment of SiC/Al functionally gradient material was carried out with this optimized stirring device. The results show that the material removal rate of powder-mixed EDM increased by 24.82% and the surface roughness decreased by 27.28% than that of the conventional EDM.

Isogeometric analysis (IGA) has gained prominence in the investigation of FGMs applied to structural problems, owing to its ability to precisely represent complex geometries and significantly improve solution accuracy. This research employs NURBS-based isogeometric analysis to systematically investigate the stability response of FGM plates under combined thermomechanical loading. The proposed framework integrates FSDT with von Kármán’s nonlinear strain assumptions, enabling accurate characterization of large deflection behavior in FGM structures. Through numerical discussion, we verify the accuracy of the model for FGM plate prediction, providing an effective tool for analyzing its behavior in the thermo-mechanical coupling field.