Papers by Keyword: Functionally Graded Material (FGM)

Abstract: In the present study, the problem of geometrically nonlinear free vibrations of functionally graded rectangular plates (FGRP) is studied. A homogenization technique has been developed to reduce the FGRP problem under consideration to that of isotropic homogeneous rectangular plate. The material properties of the functionally graded composites examined herein are assumed to be graded in the thickness direction of the plate and estimated through the rule of mixture. The proposed theoretical model is based on the classical plate theory and the Von Karman relationships, and the amplitude equation is derived in the form of a set of non-linear algebraic equation using Hamilton’s principle and a multimode approach. The fundamental nonlinear frequency parameters and the bending stress are then calculated using the iterative and explicit methods of solution to show the effect of the vibration amplitudes and the material distributions. The results obtained in this study are found to be in a good agreement with the published ones dealing with the problem of large vibration of functionally graded plates.

Abstract: This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented for various values of the volume fraction index n showing hardening type non-linearity. The distribution of the radial bending stress associated to the non-linear mode shape is also given for various vibration amplitudes, and is compared with those predicted by the linear theory.

Abstract: The geometrically non-linear axisymmetric free vibration of functionally graded annular plate (FGAP) having both edges clamped is analyzed in this paper. The material properties of the constituents are assumed to be temperature-independent and the effective properties of FGAP are graded in thickness direction according to a simple power law function in terms of the volume fractions. Based on the classical Plate theory and von Karman type non-linear strain-displacement relationships, the nonlinear governing equations of motion are derived using Hamilton’s principle. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to twice the plate thickness. The numerical results are given for the first two axisymmetric non-linear mode shapes, for a wide range of vibration amplitudes and they are presented either in a tabular or in a graphical form, to show the significant effects that the large vibration amplitudes and the variation in material properties have on the non-linear frequencies and the associated bending stresses of the FGAP.

Abstract: In this paper, the W-Cu functionally graded material (FGM) was prepared by using the non-aqueous tape-casting technique combined with vacuum hot-pressing sintering. The graded composite material with high density, uniform transition and graded component was designed by 7 layers with the copper content range from 40 to 100 wt. %. Then the structures and properties of the composite were characterized. The scanning acoustic microscope (SAM) results for the W-Cu graded material showed that the interface between different layers was of high smoothness and parallel. The SEM-EDS results of cross section show that the W and Cu content changed gradually along the laminating direction after sintering. The equivalent electrical conductivity and the equivalent thermal conductivity of the W-Cu graded material were 0.3976×10⁸ S/m and 323.5 W/(m·K), respectively, which were much higher than that of the W-40 wt. % Cu homogeneous composite. The Vickers hardness of the high tungsten content surface and the high copper surface were 163 HV and 80 HV, respectively, which were same with that of the homogeneous material.

Abstract: Geometrically nonlinear model and numerical solutions of large deformation of imperfect functionally graded materials conical shell subjected to both mechanical load and transversely non-uniform temperature rise are given. The material properties of functionally graded shell are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. On the basis of geometrically nonlinear theory of shell, governing equations of the axi-symmetrical deformation are derived. Numerical solutions are obtained by using a shooting method.

Abstract: This paper presents an investigation on the free vibration of rectangular nanocomposite plates reinforced by aligned single-walled carbon nanotubes (SWCNTs). The CNT reinforcement may be uniformly distributed (UD) or functionally graded (FG) over the thickness direction of a plate. The material properties of the CNT composite are determined through a micromechanical model. The eigenvalue equation governing the plate vibration problem is derived by the p-Ritz method through minimizing the virtual strain and kinetic energies of a CNT composite plate. The influences of CNT distribution and reinforcing angle, plate thickness ratio, aspect ratio and support conditions on the vibration behaviour of the plates are discussed.

Abstract: The paper serves as an introduction to investigation of mechanical properties of functionally graded materials and deals with elastic nanoindentation numerical models. The models were based on the finite element method. Young's moduli were estimated by Oliver-Pharr method. The indenter geometry for which numerical solutions were accomplished was a rounded cone indenter. The effect of tip sharpness was examined by applying an increasing spherical tip radius. The results show that the apparent Young's modulus and the hardness increase linearly with increasing radius of the tip. The effect of approaching interface between two elastic materials on the apparent hardness and indentation modulus was identified in 3D model. The specimen consisted of two materials. First, the interface was linear and parallel to the direction of indentation, so that the Young's modulus changed suddenly. Second, the Young's modulus was continuously changing. The dependence on various boundary conditions of the specimen was also considered.

Abstract: The effect of grit-blasting on the development of residual stress field during the surface treatment of the cold rolled mild steel was characterized by means of neutron diffraction, nanohardness measurement and electron back-scatter diffraction. The neutron diffraction revealed strong residual compressive stress with the maximum value (about-100 MPa) situated just under the sample surface of the grit-blasted sample. The deformation profiles obtained by the nanoindentation and electron back-scatter diffraction (band slope signal) revealed the strain hardening after grit blasting up to depth of approximately 100 μm.

Abstract: In this article, circumferential SH wave propagation in functionally graded material (FGM) hollow cylinders is investigated. Based on the Kelvin-Voigt viscoelastic theory, the controlling differential equations in terms of displacements are deduced. By the Legendre polynomial method, the asymptotic solutions are obtained. Through the numerical results, the influences of gradient profile and the influences of the radius to thickness ratio on dispersion and attenuation are illustrated. The work is crucial for guided ultrasonic nondestructive evaluation for graded hollow cylinders.

Abstract: A numerical procedure of assessment of Thermal Stress Intensity Factors (TSIFs) of an edge crack in a strip made of Functionally Graded Material (FGM) subjected to thermal cooling process was elaborated. In order to perform it own subroutines in ABAQUS code were created. The analyzed ZrO₂+Ti₆AlV material in the form of the FGM is applied as cylinder liners (Thermal Barrier Coatings TBC) of aircrafts engines and is subjected to extremely quick temperature changes during the engine work. Therefore estimation of the TSIF to determine fracture process in the ZrO₂+Ti₆AlV material is important for designing of the structural element thermal protection and further safety of aircrafts passengers.