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A functionally-graded Al(subscript)2TiO(subscript)5/ZrO(subscript)2-Al(subscript)2O(subscript)3 (AT/zirconia-alumina) composite has been successfully synthesized by an infiltration process involving an alpha-Al(subscript)2O(subscript)3-ZrO(subscript)2 (90:10 by weight) green body and a solution containing titanium chloride. The mass gain after infiltration has been used to estimate the amount of new phase introduced into the system. The phase composition character of the functionally-graded material (FGM) has been determined by x-ray diffraction. The Rietveld "whole pattern" refinement method was applied to diffraction patterns of the sample which were collected from the surface and at several depths which were made by polishing away the material. Absolute weight fraction determination using the Rietveld external standard method showed that the concentration of AT reduces linearly from the surface to the core. In contrast, the alpha-alumina content increases with depth in a complementary manner. Low level amorphous phase was also observed. Other functionally-graded microstructural profiles examined were x-ray characteristic line intensity of Ti, Ti dot-mapping, and alpha-alumina grain size. The FGM also exhibits graded character in both thermal and mechanical properties, i.e. thermal expansion, microhardness, and Young's modulus. The thermal expansion coefficient (TEC) of the FGM increased with polishing-depth and approached that of the zirconia-alumina reference sample at a depth of 0.5 mm. / Relatively lower thermal expansion and softer surface layer in comparison to those of the core (TEC value of 5.9 x 10(subscript)-6 degrees celsius(subscript)-1 and microhardness of 6 GPa compared to 7.4 x 10(subscript)-6 degrees celsius(subscript)-1 and 12 GPa, respectively) render possibilities to implement the material to which thermal shock resistance surface but hard core, such as a metal melting crucible, are required. Load-dependent microhardness was obviously observed on the surface of the material but only slight dependence was observed in the core. This observation indicated that the material exhibit "quasi-ductile" surface but brittle core. In comparison to the reference specimen, the FGM displayed damage-tolerance and remarkable machinability.

Fracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate (ξησ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison.

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Yes / In recent times, the subject of effective cooling have become an interesting research topic for electronic and mechanical engineers due to the increased miniaturization trend in modern electronic systems. However, fins are useful for cooling various low and high power electronic systems. For improved thermal management of electronic systems, porous fins of functionally graded materials (FGM) have been identified as a viable candidate to enhance cooling. The present study presents an analysis of a convective–radiative porous fin of FGM. For theoretical investigations, the thermal property of the functionally graded material is assumed to follow linear and power-law functions. In this study, we investigated the effects of inhomogeneity index of FGM, convective and radiative variables on the thermal performance of the porous heatsink. The results of the present study show that an increase in the inhomogeneity index of FGM, convective and radiative parameter improves fin efficiency. Moreover, the rate of heat transfer in longitudinal FGM fin increases as b increases. The temperature prediction using the Adomian decomposition method is in excellent agreement with other analytical and method.

"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

Propagation of cracks in functionally graded materials (FGMs) under cyclic loading was investigated via experiments and finite element (FE) analysis. Alumina-epoxy composites with an interpenetrating-network structure and tailored spatial variation in composition were produced via a multi-step infiltration technique. Compressed polyurethane foam was infiltrated with alumina slip. After foam burn-out and sintering, epoxy was infiltrated into the porous alumina body. Non-graded specimens with a range of compositions were produced, and elastic properties and fatigue behaviour were characterised. An increase in crack propagation resistance under cyclic loading was quantified via a novel analytical approach. A simulation platform was developed with the commercial FE package ANSYS. Material gradient was applied via nodal temperature definitions. Stress intensity factors were calculated from nodal displacements near the crack-tip. Deflection criteria were compared and the local symmetry criterion provided the most accurate and efficient predictions. An automated mesh-redefinition algorithm enabled incremental simulation of crack propagation. Effects of gradient and crack-geometry parameters on crack-tip stresses were investigated, along with influences of crack-shape, crack-bridging, residual stresses and plasticity. The model provided predictions and data analysis for experimental specimens. Fatigue cracks in graded specimens deflected due to elastic property mismatch, concordant with FE predictions. In other FGMs, thermal or plastic properties may dominate deflection behaviour. Weaker step-interfaces influenced crack paths in some specimens; otherwise effects of toughness variation and gradient steps on crack path were negligible. Crack shape has an influence, but this is secondary to that of elastic gradient. Cracks in FGM specimens initially experienced increase in fatigue resistance with crack-extension followed by sudden decreases at step-interfaces. Bridging had a notable effect on crack propagation resistance but not on crack path. Similarly, crack paths did not differ between monotonic and cyclic loading, although crack-extension effects did. Recommendations for analysis and optimisation strategies for other FGM systems are given. Experimental characterization of FGMs is important, rather than relying on theoretical models. Opportunities for optimization of graded structures are limited by the properties of the constituent materials and resultant general crack deflection behaviour.

This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell⁰́₉s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells⁰́₉ interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.

In some applications the stress across the entire cross-section of a component is not uniform but varies with position. For example, maximum shear stress is highest at the inner surface of a thick-walled cylinder subjected to uniform internal pressure and it decreases continuously towards the outer surface. In such applications it would be more appropriate for the component, too, to have varying strength across the cross-section matching with the stress profile it is subjected to. The present work deals with obtaining such a functionally graded material (FGM), characterizing it and testing its mechanical properties in compression. Differential aging heat treatment was used to produce the functionally graded material in a precipitation hardenable Al-4.6%Cu alloy by changing the microstructure. Temperature gradient furnace was used to achieve the gradation in microstructure from one end of the sample to the other end by differential aging of the solution treated sample. Mechanical properties can be varied in any precipitation hardenable alloy by means of producing various precipitates, which will form during the aging sequence. In Al-4.6%Cu alloy one end of the solution treated sample was aged for 38 hours at 170°C and the other end at 70°C by means of a temperature gradient furnace in which the coil density varies along the axis of the furnace. Thus we achieved a difference in mechanical properties from 70°C side to 170°C side as the precipitation during differential aging varied from GP zones at one end to θ' precipitate at the other end. Characterization was done on isothermally aged samples and in FGM using XRD (X-ray diffraction) and TEM (Transmission Electron Microscopy). XRD result showed that the final equilibrium precipitate θ was not formed in any of the heat-treated samples. TEM result showed the various precipitation sequences from GP zones to θ' in the isothermally aged samples and the same was confirmed in the gradient sample by cutting the samples form 70°C side towards the 170°C side and doing TEM on each sample. The properties of FGM in compression were studied using a 9mmx9mmxl8mm-compression sample using DARTEC machine and it was compared with those of isothermally aged samples. For 70°C the 0.2% proof stress was 141MPa and for 170°C it was 226MPa. The corresponding ductility values at the point of inflection on the engineering stress-strain curve for 70°C sample was higher (33%) than the 170°C (22%) sample. For the gradient sample it gave a proof stress of 163MPa and a ductility value of 30%.

Today, nonhomogeneous materials are used in many technological applications. Nonhomogeneity can be introduced intentionally in order to improve the thermomechanical performance of material systems. The concept of functionally graded materials (FGMs) is an example of such an application. Nonhomogeneity can also be an intrinsic property of some of the natural materials such as natural soil. The main interest in this study is on the contact mechanics of nonhomogeneous surfaces. There is an extensive volume of literature on the contact mechanics of nonhomogeneous materials. In most of these studies, the elastic gradation is assumed to exist in depth direction. But, it is known that elastic gradation may also exist laterally. This may either occur naturally as in the case of natural soil or may be induced as a result of the applied processing technique as in the case of FGMs. The main objective in this study is therefore to examine the effect of the lateral nonhomogeneities on the contact stress distribution at the surface of an elastically graded material. In the model developed to examine this problem, a laterally graded surface is assumed to be in sliding contact with a rigid stamp of arbitrary profile. The problem is formulated using the theory of elasticity and reduced to a singular integral equation. The integral equation is solved numerically using a collocation approach. By carrying out parametric studies, the effects of the nonhomogeneity constants, coefficient of friction and stamp location on the contact stress distribution and on the required contact forces are studied.