scholarly journals A micropolar model for elastic properties in functionally graded materials

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401878952 ◽  
Author(s):  
Shengyao Fan ◽  
Zhanqi Cheng
Keyword(s):  
Particle Size ◽  
Elastic Properties ◽  
Functionally Graded Materials ◽  
Effective Properties ◽  
Matrix Material ◽  
Functionally Graded ◽  
Two Phase ◽  
Graded Materials ◽  
Micromechanics Model ◽  
Matrix Zone

By considering the description of phase volume fractions, a micromechanics model is presented for predicting the elastic mechanical properties of isotropic two-phase functionally graded materials. The particle size dependence of the overall elasticity of functionally graded materials is not generally considered by classical continuum micromechanics; however, being based on micropolar theory, the presented micromechanics model is able to study such size effects. As the effective material properties vary gradually along the gradation direction, a functionally graded material can be divided into two distinct zones: the particle–matrix zone and the transition zone. In the particle–matrix zone, the matrix material is idealized as a micropolar continuum and Mori–Tanaka’s method is extended to the micropolar medium to evaluate the effective elastic properties. The effective properties across the gradation forms are further derived and the effects of particle size on the effective properties of a functionally graded materials are also studied. The validity and effectiveness of the present model is demonstrated by comparing the model results with other model outputs and experimental data.

Effects of Particle Size on Fabrication of Al-TiO2 Functionally Graded Materials by Centrifugal Mixed-Powder Method

2016 ◽  
Vol 879 ◽  
pp. 1691-1697 ◽  
Author(s):  
Hisashi Sato ◽  
Junya Maeda ◽  
Motoko Yamada ◽  
Yoshimi Watanabe
Keyword(s):  
Particle Size ◽  
Wear Resistance ◽  
Functionally Graded Materials ◽  
Casting Process ◽  
Functionally Graded ◽  
The Other ◽  
Mixed Powder ◽  
Graded Materials ◽  
Powder Method ◽  
Al Matrix

As one of processing methods of functionally graded materials (FGMs), centrifugal mixed-powder method has been proposed. The centrifugal mixed-powder method is the casting process combined of centrifugal casting and powder metallurgy. This processing method has advantage that fine ceramics-particles, whose wettability with matrix melt is low, can be compounded into metallic material. However, effects of particle size on microstructure and mechanical properties of the FGMs fabricated by the centrifugal mixed-powder method are unclear. In this study, two kinds of Al-TiO2 FGMs rings are fabricated by the centrifugal mixed-powder method. One contains TiO2 particles having similar diameter with Al matrix particles (hereafter, small different-size (SD) TiO2 particles), and the other one compounds TiO2 particles with much smaller diameter than Al matrix particles (hereafter, large different-size (LD) TiO2 particles). In case of the Al-TiO2 FGMs ring containing SD-TiO2 particles, the TiO2 particles are homogeneously dispersed in Al matrix on outer surface of the ring. On the other hand, the TiO2 particles in the Al-TiO2 FGMs ring with LD-TiO2 particles are distributed along grain boundary of Al matrix. Moreover, Vickers-hardness and wear resistance around outer surface of the Al-TiO2 FGMs ring containing the SD-TiO2 particles is higher than that of the Al-TiO2 FGMs ring with LD-TiO2 particles. Since Al particles in the mixed-powder with LD-TiO2 particles are surrounded by the TiO2 particles, the Al particles can be hardly melted by heat of molten Al at casting process. As a result, the Al-TiO2 FGMs ring with LD-TiO2 particles has low hardness and wear resistance. Therefore, it is found that TiO2 particles having similar diameter with Al matrix particles are more suitable for fabrication of the Al-TiO2 FGMs rings.

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.

Investigation of Stress Behavior in the Vicinity of Singular Points of Elastic Bodies Made of Functionally Graded Materials

2018 ◽  
Vol 85 (6) ◽  
Author(s):  
Andrey Yu. Fedorov ◽  
Valerii P. Matveenko
Keyword(s):  
Elastic Properties ◽  
Functionally Graded Materials ◽  
Dissimilar Materials ◽  
Functionally Graded ◽  
Singular Points ◽  
Polar Coordinates ◽  
Graded Materials ◽  
Numerical Investigations ◽  
Elastic Bodies ◽  
Stress Behavior

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.

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