Solidification Processing of Functionally Graded Materials by Sedimentation

1999 ◽  
Author(s):  
J. W. Gao ◽  
S. J. White ◽  
C. Y. Wang
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Computer Code ◽  
Functionally Graded ◽  
Particle Volume ◽  
Particle Sedimentation ◽  
Graded Materials ◽  
Free Zone ◽  
Free Region

Abstract A combined experimental and numerical investigation of the solidification process during gravity casting of functionally graded materials (FGMs) is conducted. Focus is placed on the interplay between the freezing front propagation and particle sedimentation. Experiments were performed in a rectangular ingot using pure substances as the matrix and glass beads as the particle phase. The time evolutions of local particle volume fractions were measured by bifurcated fiber optical probes working in the reflection mode. The effects of various processing parameters were explored. It is found that there exists a particle-free zone in the top portion of the solidified ingot, followed by a graded particle distribution region towards the bottom. Higher superheat results in slower solidification and hence a thicker particle-free zone and a higher particle concentration near the bottom. The higher initial particle volume fraction leads to a thinner particle-free region. Lower cooling temperatures suppress particle settling. A one-dimensional solidification model was also developed, and the model equations were solved numerically using a fixed-grid, finite-volume method. The model was then validated against the experimental results, and the validated computer code was used as a tool for efficient computational prototyping of an Al/SiC FGM.

Transport Phenomena During Solidification Processing of Functionally Graded Composites by Sedimentation

2000 ◽  
Vol 123 (2) ◽  
pp. 368-375 ◽  
Author(s):  
J. W. Gao ◽  
C. Y. Wang
Keyword(s):  
Volume Fraction ◽  
Pure Water ◽  
Particle Volume Fraction ◽  
Solidification Process ◽  
Processing Parameters ◽  
Functionally Graded ◽  
Particle Volume ◽  
Solidification Model ◽  
Free Zone ◽  
Free Region

A combined experimental and numerical investigation of the solidification process during gravity casting of functionally graded materials (FGMs) is conducted. Focus is placed on understanding the interplay between the freezing front dynamics and particle transport during solidification. Transparent model experiments were performed in a rectangular ingot using pure water and succinonitrile (SCN) as the matrix and glass beads as the particle phase. The time evolutions of local particle volume fractions were measured in situ by bifurcated fiber optical probes working in the reflection mode. The effects of important processing parameters were explored. It is found that there exists a particle-free zone in the top portion of the solidified ingot, followed by a graded particle distribution region towards the bottom. Higher superheat results in slower solidification and hence a thicker particle-free zone and a higher particle concentration near the bottom. The higher initial particle volume fraction leads to a thinner particle-free region. Lower cooling temperatures suppress particle settling. A one-dimensional multiphase solidification model was also developed, and the model equations were solved numerically using a fixed-grid, finite-volume method. The model was then validated against the experimental results and subsequently used as a tool for efficient computational prototyping of an Al/SiC FGM.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

On the mechanical properties of functionally graded materials reinforced by carbon nanotubes

2017 ◽  
Vol 232 (9) ◽  
pp. 1632-1646 ◽  
Author(s):  
Saeed Rouhi ◽  
Seyed H Alavi
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Elastic Modulus ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Single Walled Carbon Nanotubes ◽  
Functionally Graded ◽  
Graded Materials ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In this paper, the elastic properties of functionally graded materials reinforced by single-walled carbon nanotubes are studied. Three different matrices, including steel-silicon, iron-alumina and alumina-zirconia are considered. Besides, the effects of nanotube length, radius and volume fraction on the Young’s modulus of functionally graded matrices reinforced by single-walled carbon nanotubes are investigated. It is observed that short nanotubes not only cannot increase the longitudinal elastic modulus of the matrices, but sometimes decrease their elastic modulus. Of the three selected matrices, steel-silicon matrix would have the most enhancement. Investigation of the effect of nanotube volume fraction on the mechanical properties of nanocomposites shows that increasing the volume fraction of long single-walled carbon nanotube results in increasing the elastic modulus of the nanocomposites.

Flexural Sensitivity of a V-Shaped AFM Cantilever Made of Functionally Graded Materials

2010 ◽  
Author(s):  
M. Rahaeifard ◽  
M. H. Kahrobaiyan ◽  
S. A. Moeini ◽  
M. T. Ahmadian ◽  
M. Hoviattalab
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Contact Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Graded Materials ◽  
Resonant Frequencies ◽  
Mass Distributions ◽  
Lateral Contact

In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of volume fraction of materials and geometric parameters on resonant frequencies and sensitivities is studied. Results show that natural frequencies and sensitivities are significantly affected by volume fraction of material constituents and geometric parameters. Using these results, optimum geometric parameters and mass distributions of material constituents can be chosen so that high resolution images could be obtained.

Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

2020 ◽  
Vol 234 (18) ◽  
pp. 3650-3666 ◽  
Author(s):  
Souhir Zghal ◽  
Fakhreddine Dammak
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Mixed Formulation ◽  
Shear Stresses ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Vibrational Behavior

This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model based on a refined mixed formulation and its ability to predict the vibrational behavior of functionally graded beams with good accuracy.

Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory

2017 ◽  
Vol 29 (5) ◽  
pp. 741-763 ◽  
Author(s):  
Ali Kiani ◽  
Moslem Sheikhkhoshkar ◽  
Ali Jamalpoor ◽  
Mostafa Khanzadi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Simply Supported

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

Indentation of a transversely loaded functionally graded rectangular plate by a rigid spherical indentor

2012 ◽  
Vol 227 (4) ◽  
pp. 663-682 ◽  
Author(s):  
Ali Nikbakht ◽  
Mojtaba Sadighi ◽  
Alireza Fallahi Arezoodar
Keyword(s):  
Stress Distribution ◽  
Numerical Method ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Graded Materials ◽  
Stress Strain Relation ◽  
Finite Element Package ◽  
Spherical Indentor

Functionally graded materials are multiphase composites mainly composed of a ceramic and a metal; thus, they merge the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. Many of the present and possible applications of functionally graded materials involve contact loading. Here, the contact problem of a functionally graded simply supported plate with finite dimensions by a rigid spherical punch is studied by an analytical–numerical method. The contact rule will be derived by solving the equations of equilibrium analytically in terms of the displacement field components and by taking advantage of a numerical method in finding the contact parameters. The stress–strain relation is assumed to be linear and is represented by a refined volume fraction based model originally proposed by Tamura–Tomota–Ozawa model. The results of the analytical–numerical approach are validated by using ABAQUS finite element package. The analytical–numerical results are used to investigate the effect of parameters such as material distribution, punch radius, plate span and thickness on the contact rule and stress distribution in the plate. The obtained results show that the influence of the material non-homogeneity on the contact rule and stress distribution is quite significant. In addition, the acquired results illustrate that increasing the indentor diameter and the thickness of the plate increase the contact force for equal amount of indentation.

Effect of Functionally Graded Materials on Resonances of Bending Shafts Under Time-Dependent Axial Loading

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Arnaldo J. Mazzei ◽  
Richard A. Scott
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Functionally Graded Materials ◽  
Parametric Resonance ◽  
Axial Load ◽  
Volume Fraction ◽  
Axial Loading ◽  
Functionally Graded ◽  
Time Dependent ◽  
Graded Materials

The effect of functionally graded materials (FGMs) on resonances of bending shafts under time-dependent axial loading is investigated. The axial load is taken to be a sinusoidal function of time and the shaft is modeled via an Euler–Bernoulli beam approach (pin-pin boundary conditions). The axial load enters the formulation via a “buckling load type” approach. For generality, two distinct particulate models for the FGM are considered, namely, one involving power law variations and another based on a volume fraction approach, for both Young’s modulus and material density. The spatial dependence in the partial differential equation of motion is suppressed by utilizing Galerkin’s method with homogeneous beam mode shapes. To check the accuracy of this approximation, numerical solutions for the boundary value problem represented by the original partial differential equation are obtained using MAPLE®’s PDE solver. Good agreement (within 5%) was found between the PDE results and the one-mode approximation. The approximation leads to ordinary differential equations that have time-dependent coefficients and are prone to parametric and forced motions instabilities. Hill’s infinite determinant approach is used to study stability. The main focus is on the primary parametric resonance. It was found that in most cases the FGM shafts increase the parametric resonance frequencies substantially, while decreasing the zone thicknesses, both desirable trends. For instance, for an axial load about one-third of the buckling value, an aluminum/silicon carbide shaft, when compared to a pure aluminum shaft, increases the primary parametric resonance by 21% and decreases instabilities by 23%. For one model of FGM, the sensitivity of the results to volume fraction variations is examined and it was found that increasing the volume fraction is not uniformly beneficial. Results for other parametric zones are also presented. Forced resonances are also briefly treated.

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