• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.371-379
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• 2017

Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. In this paper, two crack growth criteria and the respective crack paths prediction in functionally graded materials (FGM) are compared. The maximum tangential stress criterion (${\sigma}_{\theta}-criterion$) and the minimum strain energy density criterion (S-criterion) are investigated using advanced finite element technique. Using Ansys Parametric Design Language (APDL), the variation continues in the material properties are incorporated into the model by specifying the material parameters at the centroid of each finite element. In this paper, the displacement extrapolation technique (DET) proposed for homogeneous materials is modified and investigated, to obtain the stress intensity factors (SIFs) at crack-tip in FGMs. Several examples are modeled to evaluate the accuracy and effectiveness of the combined procedure. The effect of the defects on the crack propagation in FGMs was highlighted.

• Journal of the Korean Society of Propulsion Engineers
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• v.5 no.1
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• pp.49-59
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• 2001

Functionally gradient materials(FGMs) generally consist of different material components, such as ceramics and metals. Continuous changes in their composition, microstructure, porositys, and so on result in gradients in the properties of FGMs. In this study AlN/Al-$Al_3$Ti FGM cubes were fabricated by the powder metallurgical process, and the characteristics of the FGMs were investigated. Powders of Mg and Ti mixed with Al in different ratios or the stack of the mixed powders having a stepwisely controlled compositional gradient from one plane to another were formed in a steel mold. The more the composition of Mg and sintering temperature are increased, the more the amount of AlN is formed. AlN and $Al_3$Ti distributed with continuously gradient composition were detected by XRD analysis and also revealed in optical microstructures, and microhardness tests.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.85-86
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• 2006

A theoretical model is applied to the analysis of thermomechanical properties of $Al-SiC_p$ FGMs in this study. Functionally graded $Al-SiC_p$ composites ($Al-SiC_p$ FGMs) consisted with 10 layers gradually changing volume fractions of Al and $SiC_p$ were fabricated using the pressureless infiltration technique. $Al-SiC_p$ FGMs plates of total thickness of 3mm, 5mm and 7mm with fairly uniform distribution and compositional gradient of $SiC_p$ reinforcement in the Al matrix throughout the thickness was successfully fabricated. The curvature of $Al-SiC_p$ FGM plates was measured to check the internal stress distribution predicted via a theoretical model for the analysis of thermo-mechanical deformation. The evolution of curvature and also internal stresses in response to temperature variations could be predicted for the different combinations of geometric thickness of FGM plates. Theoretical prediction of thermally induced stress distribution makes it possible to design FGM structures without any critical failure during the usage of them.

• Advances in nano research
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• v.7 no.6
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• pp.379-390
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• 2019

Putting emphasis on the effect of existence of porosity in the functionally graded materials (FGMs) on the dynamic responses of waves scattered in FG nanobeams resulted in implementation of a novel porosity-based homogenization method for FGMs and show its applicability in a wave propagation problem in the presence of axial pre-load for the first time. In the employed porosity-dependent method, the coupling between density and Young's moduli is included to consider for the effective moduli of the FG nanobeam by the means of a more reliable homogenization technique. The beam-type element will be modeled via the classical theory of beams, namely Euler-Bernoulli beam theory. Also, the dynamic form of the principle of virtual work will be extended for such nanobeams to derive the motion equations. Applying the nonlocal constitutive equations of Eringen on the obtained motion equations will be resulted in derivation of the nanobeam's governing equations. Depicted results reveal that the dispersion responses of FG nanobeams will be decreased as the porosity volume fraction is increased which must be noticed by the designers of advanced nanosize devices who are interested in employment of wave dispersion approach in continuous systems for specific goals.

• Journal of the Korean Ceramic Society
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• v.39 no.9
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• pp.890-895
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• 2002

Effect of the sintering time on the microwave dielectric properties of the layered Functionally Graded Materials(FGMs) of the Mg0.93Ca0.07TiO3(MCT) with (Ca0.3Li0.14Sm0.42)TiO3(CLST) ceramics was investigated. The dielectric constant of layered FGMs specimens showed a nearly constant value and did not change significantly with sintering time. The quality factor, however, was affected by the relative density and thermal stress developed in each dielectric layer. With an increase of the relative density and the decrease of the induced thermal stresses, quality factor of the layered FGMs specimens increased and the quality factor was incluenced sensitively by the change of compressive stress developed in MCT layers which had a lower thermal expansion coefficient than that of CLST. For the layered FGMs specimen sintered at 1300$^{\circ}C$ for 9h, the compressive stress developed in MCT layer showed the maximum value, which, in turn, the quality factor of the specimen was the minimum value.

• Proceedings of the Korean Ceranic Society Conference
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• 2003.10a
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• pp.19.1-19
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• 2003

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.06a
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• pp.7-11
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• 1997

SiC/C functionally gradient material (FGMs) were formed on graphite substrates by hot-wall chemical vapor deposition (CVD) technique using the SiCl$_4$-C$_3$H8-H$_2$ chemistry. Thermochemical equilibrium calculations were carried out to investigate the deposition process. The effect of process variables on the deposition yield and the SiC/C ratio in deposited layers was studied in detail. Calculated results showed a reasonable agreement with the experiment in a qualitative sense. SiC/C FGMs with excellent mechanical and thermal properties could be successfully formed on graphite substrates by carefully controlling the compositions in the deposited layers.

• Smart Structures and Systems
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• v.21 no.4
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• pp.469-477
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• 2018

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.16 no.4
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• pp.26-34
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• 2008

This article provides a comprehensive treatment of cracks in non-homogeneous structural materials such as functionally graded materials (FGMs). It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using laminated composite plate model to simulate the material non-homogeneity, we present an algorithm for solving the system based on Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. As a numerical illustration, transient thermal flow intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of non-homogeneous material with properties varying in the thickness direction.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.1067-1089
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• 2014

In this paper, three dimensional static and dynamic analyses of two dimensional functionally graded annular sector plates have been investigated. The material properties vary through both the radial and axial directions continuously. Graded finite element and Newmark direct integration methods have been used to solve the 3D-elasticity equations in time and space domains. The effects of power law exponents and different boundary conditions on the behavior of FGM annular sector plate have been investigated. Results show that using 2D-FGMs and graded elements have superiority over the homogenous elements and 1D-FGMs. The model has been compared with the result of a 1D-FGM annular sector plate and it shows good agreement.