Microstructural design of connective base cells for functionally graded materials

9 - Metal-ceramic functionally graded materials (FGMs)

Functionally Graded Material (FGM) is a material with engineered gradients of composition, structure and/or specific properties aiming to become superior over homogeneous material composed of same or similar constituents. In the recent years, research has been undertaken on manufacturing of functionally graded materials (FGM) using numerous techniques like powder metallurgy, melt processes, centrifugal casting, electrophoretic deposition, spark plasma sintering, physical vapor deposition, chemical vapor deposition etc. Most of these techniques may be well suited for a specific application yet they suffer from one or more limitations like lower graded thickness, low deposition rate, complexity in process requirement, or high processing cost. To circumvent these limitations innovative technique called laser assisted manufacturing technique is applied for manufacturing functionally graded materials. Three methods that employ Laser for synthesis of FGM is elaborated in this work (i) 3-D Laser Cladding, (ii) LENS and (iii) Selective laser sintering. Laser Cladding is used for obtaining coatings of FGM by direct powder injection into the laser beam. 3-D Laser-engineered net shaping (LENS) is used to fabricate FGM directly from CAD solid models and thus further reduce the lead times for metal art fabrication. Selective laser sintering (SLS) is a layered manufacturing based freeform fabrication approach for constructing three dimensional structures in functionally graded composites. All these methods are used to manufacture FGMs in a short interval of time and the process can be controlled digitally, thus all these methods come in the heading of rapid manufacturing (RM). These methods have a huge industrial potential and can be commercialized for manufacturing bulk FGM.

Functionally Graded Materials (FGMs) can outperform their homogeneous counterparts. Advances in digitalization technologies, mainly additive manufacturing, have enabled the synthesis of materials with tailored properties and functionalities. Joining dissimilar metals to attain compositional grading is a relatively unexplored research area and holds great promise for engineering applications. Metallurgical challenges may arise; thus, a theoretical critical analysis is presented in this paper. A multidisciplinary methodology is proposed here to unify optimal design, multi-feed Wire-Arc Additive Manufacturing (WAAM), and image-based characterization methods to create structure-specific oriented FGM parts. Topology optimization is used to design FGMs. A beam under pure bending is used to explore the layer-wise FGM concept, which is also analytically validated. The challenges, limitations, and role of WAAM in creating FGM parts are discussed, along with the importance of numerical validation using full-field deformation data. As a result, a conceptual FGM engineering workflow is proposed at this stage, enabling digital data conversion regarding geometry and compositional grading. This is a step forward in processing in silico data, with a view to experimentally producing parts in future. An optimized FGM beam, revealing an optimal layout and a property gradient from iron to copper along the build direction (bottom-up) that significantly reduces the normal pure bending stresses (by 26%), is used as a case study to validate the proposed digital workflow.

An edge crack in a strip of a functionally graded material (FGM) is studied under transient thermal loading conditions. The FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip. Thus the material is elastically homogeneous but thermally nonhomogeneous. This kind of FGMs include some ceramic/ceramic FGMs such as TiC/SiC, MoSi2/Al2O3 and MoSi2/SiC, and also some ceramic/metal FGMs such as zirconia/nickel and zirconia/steel. A multi-layered material model is used to solve the temperature field. By using the Laplace transform and an asymptotic analysis, an analytical first order temperature solution for short times is obtained. Thermal stress intensity factors (TSIFs) are calculated for a TiC/SiC FGM with various volume fraction profiles of the constituent materials. It is found that the TSIF could be reduced if the thermally shocked cracked edge of the FGM strip is pure TiC, whereas the TSIF is increased if the thermally shocked edge is pure SiC.

The spatial organisation of mechanical cues is increasingly recognised as a key regulator of tissue development and disease, yet in vitro systems capable of replicating such environments remain limited. Fibroblast migration and the fibroblast-to-myofibroblast transition, which affect scar formation, are examples of mechanisms affected by mechanical cues. We report a photolithographic platform that enables precise, spatial patterning of the Young's modulus of gelatin methacryloyl (GelMA) hydrogels, using a ruthenium/sodium persulfate (SPS) photoinitiation system. By altering light intensity, we achieved Young's modulus tunability between 4 kPa and 46 kPa in non-patterned gels. By displaying a binary light intensity pattern over the gel, the Young's modulus could be switched from 10 kPa to 45 kPa, representing healthy and fibrotic Young's moduli, over a distance of ∼20 μm (2.3MPa·mm⁻¹). This system could also generate relatively linear Young's modulus gradients that are more physiologically relevant, ∼10 kPa⋅mm-1. Non-patterned and binary-patterned gels confirmed that increasing the Young's modulus drives the fibroblast-to-myofibroblast transition, observed by significantly greater cell volumes and α-smooth muscle actin (α-SMA) stress fibre formation, from encapsulated cardiac fibroblasts after 7 days. In gradient-patterned gels, fibroblasts exhibited a progressive, modulus-dependent increase in both cell volume and α-SMA stress fibre formation, alongside expressing a durotactic response, moving from healthy to fibrotic environments, and also aligning themselves between ±45 degrees to the Young's modulus gradient. Beyond cardiac fibrosis, this versatile platform enables rapid generation of biologically relevant mechanical landscapes for diverse mechanobiological applications, bridging the gap between simplified, mechanically uniform models and the heterogeneous microenvironments of native tissues. STATEMENT OF SIGNIFICANCE: This study developed a platform for spatially controlling the Young's modulus of GelMA using a digital light projection system. Using this system, a change in Young's modulus from 10 kPa to 45 kPa was achieved with a resolution of 20 µm. Natural Young's modulus gradients observed in tissues (∼10 kPa·mm⁻¹) can also be achieved. The fibroblast-to-myofibroblast transition was controlled spatially in the patterned gels, evidenced by changes in cell volume and α-SMA fibrillation. Fibroblasts demonstrated alignment and migration to the Young's modulus gradient. Our photopatterning system demonstrates ease of pattern/gradient definition with adaptability to a diverse range of systems, highlighting the impact of mechanical properties on cardiac scar formation, offering avenues for studying these effects.

Tailored Functionally Graded Materials design and concurrent topology optimization with implicit fields

A thin circular rotating disk having a concentric hole and a functionally graded material (FGM) coating at the outer surface is considered with a view to analyzing the thermoelastic characteristics due to a thermal load and rotation of the disk. The FGM coating is assumed to have exponentially varying Young's modulus, coefficient of thermal expansion (CTE), and density in the radial direction of the disk. The Poisson's ratio is assumed to be constant throughout the disk. The incompatible eigenstrain developed in the disk owing to the nonuniform CTE and variation of temperature is taken into consideration. Using the two-dimensional thermoelastic theories, the two-dimensional plane stress axisymmetric problem is formulated as a second order differential equation. A finite element model is developed using the variational approach and Ritz method to obtain the numerical solution of the differential equation. The validity of the finite element model is justified for a rotating circular disk of homogeneous material by comparing the finite element results with analytical solution obtained by Timoshenko. Then the finite element model is applied to the problem of an Al disk with an Al2O3/Al FGM coating at its outer surface. The numerical results of the thermoelastic field demonstrate that the temperature distribution profile, angular speed of the disk, and FGM coating thickness are the crucial factors to be considered in controlling the thermoelastic characteristics of a rotating disk with an FGM coating.

Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a logarithmic function, and a sine function are selected to simulate spatial thermal conductivity profile in FGMs respectively. The steady-state temperature fields of 2-D thermal transfer problem are analyzed by the MOLs. Numerical results show that different material thermal conductivity function has obvious different effect on the temperature field.

Analytical formulations and solutions for natural frequency analysis of functionally graded material (FGM) plates based on two higher-order refined shear deformation theories with 9 and 12 degrees-of-freedom are presented. The displacement model with 12 degrees-of-freedom considers the effect of both transverse shear and normal strain/stress while the other considers only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also presented for the evaluation purpose. For mathematical modeling purposes, the Poissons ratio of the material is considered as constant whereas Youngs modulus is assumed to vary through the thickness according to the power law function. The equations of motion are derived using Hamiltons principle. Solutions are obtained in closed-form using Naviers technique and solving the eigenvalue equation. The accuracy of the theoretical formulations and the solution method using the present two higher-order refined models is first established by comparing the results generated in the present investigation with the 3D elasticity solutions already reported in the literature. After establishing the accuracy of predictions, benchmark results for the natural frequencies using all the four models are presented for single layer FGM plate and multi layered FGM sandwich plate with varying edge ratios and side-to-thickness ratios.

Large Deflections of Heated Functionally Graded Clamped Rectangular Plates with Varying Rigidity in Thickness Direction

: Crack tip deformations and fracture parameters in functionally graded glass-filled epoxy beams are experimentally evaluated under static and dynamic loading conditions. Beams with unidirectional, monotonic elastic gradients and cracks along the gradient are examined. SEN samples with increasing or decreasing Young's modulus ahead of the crack tip are studied in symmetric four-point bending and one-point impact loading configurations. Optical method of Coherent Gradient Sensing (CGS) is used to measure crack tip deformations prior to crack initiation. For impact loading experiments, CGS is used in conjunction with high-speed photography for recording instantaneous deformation fields. Stress intensity factors (SIF) or SIF-histories in functionally graded materials (FGM) based on locally homogeneous material descriptions in the immediate crack tip vicinity are evaluated and compared with companion finite element simulations. The influence of elastic gradients in FGM samples with cracks on the compliant and stiff sides of the beam are quantified relative to their homogeneous counterparts and with each other. Under static loading conditions, the crack tip located on the compliant side of the beam is elastically shielded when compared to the situation when the crack is on the stiffer side of the same FGM beam. Under dynamic conditions, however, elastic gradients affect crack initiation differently. Crack initiation in an FGM with a crack on the stiff side of the beam and impact occurring on the compliant edge is delayed when compared to the opposite configuration. Independent finite element simulations of FGMs with idealized elastic gradients with identical crack tip elastic properties suggest that lower crack tip loading rate in the former is responsible for the differences.

Analysis of crack problems in functionally graded materials under thermomechanical loading using graded finite elements

Functionally graded materials (FGMs) are a class of composite materials that exhibit inhomogeneous distributions of different components on the scale of the entire material. Because of its properties, FGM can be used for engineering applications where mono-component materials or homogeneous composites fail. Processing techniques used to produce FGM include solidification processing, chemical vapor deposition, powder metallurgy, and co-sedimentation. Among these techniques, the most promising one for the fabrication of large products with continuous and smooth variations in composition and in microstructure is co-sedimentation. The process involves the selection of raw material powders with appropriate sizes and ratios, followed by the segregation of particles and liquid in a gravitational field to create a desired gradient in suspension, and finally the solidification of the spatially graded structure. Various FGMs, such as metal-ceramics and metal-alloy-ceramics, have been successfully synthesized by this method [1—13]. However, the technology remains in its experimental stage, mainly due to a lack of theoretical study on this method. The objective of the present work is to set up a model that reveals the relations between the compositional distribution of deposited body and the powder characteristics of raw materials as well as the settling parameters. In the present study, the “powder characteristics” refers to the density and the particle size distribution of raw material powder. Theoretical study on co-sedimentation is separated into two parts, prediction and design. Prediction refers to the calculation of the compositional distribution in FGM based on the powder characteristics and settling parameters, whereas design refers to the computation of the powder characteristics and settling parameters based on the compositional distribution in FGM. Here we confine our discussions to the prediction element.

Capability of multiwalled carbon nanotubes (CNTs) to create in-depth gradients in properties and functionalities of conventional materials has been investigated for the first time. Functionally graded material (FGM) concept has also been employed for the first time to bridge conventional materials to their advanced nanocomposites containing a high concentration of CNTs, which is promising for unexplored yet novel structural, electronic and biomaterial applications. In this study, α-alumina ceramics considered as the most challenging case has been used as the matrix. Bulk, layered, nanostructure-controlled, CNT-based, functionally graded α-alumina ceramics have been fabricated employing a recently established powder processing technology. In-depth gradients in microstructure, grain size and hardness have been successfully achieved in alumina ceramic without cracking, delamination or warping, after homogeneous and gradual incorporation of the CNTs within the alumina ceramic matrix. The FGM approach showed promise to successfully bridge conventional ceramics to their nanocomposites containing a high concentration of CNTs.

We attempted to reproduce foamed or porous materials with inhomogeneity similar to that of functionally graded materials (FGMs) using a 3D printer, and to evaluate their mechanical properties. Using a lattice model, we evaluated the compressive properties by changing the thickness. As a result, it was found that the lattice model can sufficiently express the mechanical properties of foamed materials. Young’s modulus of the “Square model”, in which the cells are square, decreased sharply as the thickness increased, reaching about half the value of 1 layer. On the other hand, Young's modulus of the Wide model material, in which the cells are horizontally elongated, did not decrease. Furthermore, a model was created to express the internal irregularity of the holes (lattice) such as FGM, and a comparison was attempted using the same mechanical test. It was found that the Young's modulus depended on the thickness of the “Square model” layer. Furthermore, when compared to an alternating laminate model sample with an increased number of interfaces to evaluate the effect of the uneven interface of the bubbles, it was found that although the Young's modulus increased as the thickness of “Square model” layer decreased, the slope decreased slightly in the region of increased density where there was a rapid increase in stress because of the interface. This was found to be due to the presence of large voids in the uneven lattice distribution at the interface.