Functionally Graded Material System Research Articles

Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field

This paper deals with the determination of displacement function and thermal stresses of a finite length isotropic functionally graded hollow cylinder subjected to uniform temperature field. The solution of the governing thermoelastic equation is obtained, as suggested by Spencer et al. for anisotropic laminates. Numerical calculations are also carried out for FGM (Functionally graded material) system consisting of ceramic Alumina (Al2O3), along with Nickel (Ni) as the metallic component varying with distance in one direction and illustrated graphically.

Finite Element Modelling for Static and Free Vibration Response of Functionally Graded Beam

A 1D Finite Element model for static response and free vibration analysis of functionally graded material (FGM) beam is presented in this work. The FE model is based on efficient zig-zag theory (ZIGT) with two noded beam element having four degrees of freedom at each node. Linear interpolation is used for the axial displacement and cubic hermite interpolation is used for the deflection. Out of a large variety of FGM systems available, Al/SiC and Ni/Al2O3 metal/ceramic FGM system has been chosen. Modified rule of mixture (MROM) is used to calculate the young's modulus and rule of mixture (ROM) is used to calculate density and poisson's ratio of FGM beam at any point. The MATLAB code based on 1D FE zigzag theory for FGM elastic beams is developed. A 2D FE model for the same elastic FGM beam has been developed using ABAQUS software. An 8-node biquadratic plane stress quadrilateral type element is used for modeling in ABAQUS. Three different end conditions namely simply-supported, cantilever and clamped- clamped are considered. The deflection, normal stress and shear stress has been reported for various models used. Eigen Value problem using subspace iteration method is solved to obtain un-damped natural frequencies and the corresponding mode shapes. The results predicted by the 1D FE model have been compared with the 2D FE results and the results present in open literature. This proves the correctness of the model. Finally, mode shapes have also been plotted for various FGM systems.

Property estimation in FGM plates subject to low-velocity impact loading

A property estimation sequence is presented for determining local elastic properties of a two-phased, twoconstituent functionally graded material (FGM) plate subject to impact loading. The property estimation sequence combines the use of experimentally determined strain histories, finite element simulations of the experimental impact events, and an analytical model of the impact tests. The experimental, computational, and analytical models are incorporated into a parameter estimation framework, based on optimization theory, to solve for material properties of individual graded layers in the FGM plate specimens. The property estimation sequence was demonstrated using impact tests performed on a titanium-titanium boride (Ti-TiB) FGM plate system. The estimated material properties of the Ti-TiB FGM from the sequence were shown to correlate well with published material properties for the titaniumtitanium boride FGM system. The estimated properties were further input into a finite element model of the impact events and were shown to approximate the experimental strain histories well. This property estimation framework is formulated to apply to virtually any two-phase FGM system and is thus an invaluable tool for research engineers studying the response of FGMs under load.

Crack-Free Joint in a Ni-Al<SUB>2</SUB>O<SUB>3</SUB> FGM System Using Three-Dimensional Modeling

With the recent emphasis on the importance of successfully joining materials, researchers have tried to join metals and ceramics with different coefficients of thermal expansion (CTEs) by using the functionally graded material (FGM) method. This involves inserting interlayers with composition gradients that range from one material to the other, thereby minimizing the stress caused by differences in CTE values. In this study, the FGM that included 10 layers of Ni-Al 2 O 3 with eight inter-layers was studied. Previous studies have focused on controlling the composition of inter-layers and optimizing the dispersion process to prevent cracks. Thermal stress was reduced by varying the weights of the inter-layers and increasing the green-body density by using several powder sizes. The powders were well-dispersed during fabrication by using simultaneous dispersion and dry processes followed by a cold isostatic press (CIP) and pressure-less sintering in an inert atmosphere. As a result, a crack-free Ni-Al 2 O 3 FGM joint was obtained. The residual stress in each layer was calculated to predict cracks using ANSYS simulation and maximum principal stress criterion; experimental values matched simulation results. In addition, an oriented Vickers indentation test was used to assess the quality of the joint. Crack-paths were not deflected across the interface, indicating good bond strength between interfaces. Sample density was measured using the Archimedes method; the sintered joint was less dense than its theoretical density but was denser than the results obtained by using previous methods.

Functionally-graded fiber-reinforced cement composite: Processing, microstructure, and properties

A functionally-graded material system has been developed with a spatially tailored fiber distribution to produce a four-layered, functionally-graded fiber-reinforced cement composite (FGFRCC). Fiber volume fractions were increased linearly from 0% in the compression zone to 2% in the tensile zone so that more fibers were available to carry tensile stress in a bending beam experiment. Extrusion was used to produce single homogeneous layers of constant fiber volume fraction and highly oriented fibers. The FRCC layers with different fiber volume fractions were stacked according to the desired configuration and then pressed to produce an integrated FGFRCC. Polished cross-sections of the FGFRCC were examined using a scanning electron microscope (SEM) to measure the fiber distribution. Flexural tests were carried out to characterize the mechanical behavior and to evaluate the effectiveness of the designed fiber distribution. No delamination between layers was observed in the fractured specimens. Compared to homogeneous FRCC with the same overall fiber volume fraction, the FGFRCC exhibited about 50% higher strength and comparable work of fracture.

Boundary element analysis of crack problems in functionally graded materials

The present study examines the crack problems in a functionally graded material (FGM) whose upper and bottom surfaces are fully bonded with dissimilar homogeneous materials. A so-called generalized Kelvin solution based boundary element method is used in the numerical examination. The multi-region method and the eight-node traction-singular boundary elements are used for the crack evaluation. The layer discretization technique is utilized to approximate the depth material non-homogeneity of the FGM layer. The proposed method can deal with any depth variations in both the shear modulus and the Poisson ratio of the FGMs. Results of the present analysis are compared very well with the exact analytical solutions available in the literature, which demonstrates that the proposed method can accurately evaluate the stress intensity factors (SIFs) for cracks in FGMs. The paper further evaluates the effect of the functionally graded variations in the Poisson ratio on the stress intensity factors. The paper also assesses the elliptical cracks in the FGM system. The paper presents the influence of both the non-homogeneity and the thickness of the FGM layer on the three SIFs associated with the elliptical cracks.

Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients

In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.

Fabrication and characterization of Ti-TiB2 functionally graded material system

In this work, a five-layer metal-ceramics Ti-TiB2 functionally graded material (FGM) system was fabricated using a powder metallurgy route. The fabricated FGM system was found to possess 50 pct more fracture toughness than the conventional monolithic TiB2 ceramics. The composition and microstructure of the FGM fabricated were analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDX), and the results are presented and discussed in this article. Vickers hardness and fracture energy of each compositional layer in the FGM were also measured. The significant fracture toughness improvement observed in the FGM system is attributed to the operation of a crack deflection mechanism. The present experimental results were compared with the theoretical predictions reported in the literature on operating crack deflection criteria of layered systems.

Geometry effects of substrate and coating layers on the thermal stress response of FGM structure

Due to transient temperature change, the plane strain elastic-plastic problem for a functionally graded material (FGM) bonded to a homogeneous coating layer and a metal substrate is considered by the use of the finite element method (FEM). The substrate and the coating are assumed to be aluminum and partially stabilized zirconia, respectively. The FGM layer is a particulate composite of aluminum and partially stabilized zirconia with volume fractions continuously varying through the thickness. Generally in high temperature applications, the FGM system is sandwiched between a substrate layer and a coating layer. The coating layer increases the protection from heat but decreases the thermal shock resistance while the substrate layer increases the rigidity of the structure and decreases strength-related properties at high temperature. In order to compromise the thickness of both the coating and substrate layers, different values of the substrate and coating thickness are studied in order to evaluate their effects on the thermal stress response of the FGM structure. Since the main objective of the FGMs is using them in different applications with severe thermal loading conditions, the thermal stresses may be so high that some reinforcements may be fractured and/or debonded from the matrix giving a weakening effect instead of a reinforcing one. Hence, the behaviors of the reinforcements and the matrix are essential to be studied. In this regard, microscopic constitutive equations along with the temperature-dependent properties of the constituent materials are considered to enable us obtaining more realistic results of thermal stresses. Since the FGM structures are fabricated at high temperatures, thermal residual stresses are produced. In order to find out the importance of the consideration of the residual stresses arising from the fabrication process, the FGM structure with stress-free conditions is heated to the operating temperature, and its thermal stress response is compared with that one where the residual stresses are taken into account. Also, several functional forms of gradation of the constituents in the FGM layer are examined to reach the optimum profile giving the minimum stress level for the FGM structure under thermo-elasto-plastic behavior.

Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature‐Independent Material Properties

We have presented a numerical technique for analyzing one‐dimensional transient temperature distributions in a circular hollow cylinder that was composed of functionally graded ceramic–metal‐based materials, without considering the temperature‐dependent material properties. The functionally graded material (FGM) cylinder was assumed to be initially in a steady state of gradient temperature; the ceramic inner surface was exposed to high temperature, and the metallic outer surface, which was associated with its in‐service performance, was exposed to low temperature. Then, the FGM cylinder was cooled rapidly on the ceramic surface of the cylinder, using a cold medium. The transient temperature and related thermal stresses in the FGM cylinder were analyzed numerically for a model of the mullite–molybdenum FGM system. The technique for analyzing the temperature distribution is quite simple and widely applicable for various boundary conditions of FGMs, in comparison with methods that have been proposed recently by other researchers.

Thermal residual stresses in a functionally graded material system

A one-dimensional calculation of thermal residual stresses, arising from the fabrication of a Functionally Graded Material (FGM) system, is presented. As a first step, calculations have been limited to the linear elastic case. The FGM system consists of ceramic (Al 2O 3) and metal (Ni) phases varying with distance in one direction. Several functional forms of gradation of constituents were examined to arrive at the optimum profile giving the minimum residual stress level. A linear variation in composition from fully ceramic to fully metal showed the least residual stress. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The character (tension or compression) of stresses is dependent on the functional form of gradation. A low residual stresses state close to that of the continuously graded structure can be achieved also in a multilayer FGM system having several layers (typically > 11) of constant composition. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.

Residual stress characteristics of a FGM joint: T. Itoh et al, (Toshiba Corp, Yokohama, Japan), J Japan Soc Powder and Powder Metallurgy, Vol 39, No 4, 1992, 287–290. (In Japanese)

A one-dimensional calculation of thermal residual stresses, arising from the fabrication of a Functionally Graded Material (FGM) system, is presented. As a first step, calculations have been limited to the linear elastic case. The FGM system consists of ceramic (Al2O3) and metal (Ni) phases varying with distance in one direction. Several functional forms of gradation of constituents were examined to arrive at the optimum profile giving the minimum residual stress level. A linear variation in composition from fully ceramic to fully metal showed the least residual stress. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The character (tension or compression) of stresses is dependent on the functional form of gradation. A low residual stresses state close to that of the continuously graded structure can be achieved also in a multilayer FGM system having several layers (typically > 11) of constant composition. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.