This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation

On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam

We present a generalized shear deformation theory in combination with isogeometric (IGA) approach for nonlinear transient analysis of smart piezoelectric functionally graded material (FGM) plates. The nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Karman strains, which includes thermo-piezoelectric effects, and solved by Newmark time integration scheme. The electric potential through the thickness of each piezoelectric layer is assumed to be linear. The material properties vary through the thickness of FGM according to the rule of mixture and the Mori–Tanaka schemes. Various numerical examples are presented to demonstrate the effectiveness of the proposed method.

Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads

3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

Porous ceramics of lead zirconate titanate (PZT) were prepared by sintering powder compacts consisting of PZT and stearic acid powders in an air atmosphere; stearic acid was added as a pore-forming agent (PFA). The dielectric, elastic and piezoelectric properties of uniformly porous PZT ceramics were investigated as a function of the porosity volume fraction. Furthermore, a beam-shaped PZT actuator sample with a graded porosity content across its thickness was fabricated by sintering PFA-graded powder compacts. The electric-field-induced bending displacement characteristics of the actuator samples were measured by using strain gauges and were found to be in good agreement with the theoretical predication based on a classical lamination theory.

Fabrication and Evaluation of Porous Piezoelectric Ceramics and Porosity-Graded Piezoelectric Actuators

The PZT/Pt composites with various compositions were fabricated by using powder processing, and their mechanical, dielectric, piezoelectric and elastic properties were evaluated with the purpose to develop piezoelectric actuators with functionally graded microstructure (FGM). The piezoelectric and dielectric constants of the PZT/Pt composites decreased monotonously with increasing Pt content, whereas the addition of the Pt particles greatly improved the mechanical properties, particularly the fracture toughness in the composites. Miniature bimorph-type FGM actuators that consist of a composite internal-electrode (70 vol.%PZT/30 vol.%Pt) and three piezoelectric layers (100 vol.%PZT to 80 vol.%PZT/20 vol.%Pt) were fabricated by powder stacking and normal sintering techniques. The electrically-induced deflection characteristics of such an FGM actuator were measured with electric strain gages mounted on the top and bottom surfaces of the actuators, and the measured data were consistent with the analytical results given by the modified classical lamination theory model (CLT).

Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators

https://iopscience.iop.org/article/10.1016/S1468-6996(02)00017-7/pdf

Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator

The objective of this study was to develop bending-type piezoelectric ceramic actuators having functionally graded microstructures (FGM). Porosity-graded lead zirconate titanate (PZT) ceramics were selected as a model material. Miniature porosity-graded actuator samples with three layers of different porosities (0, 10, 20%) were fabricated by sintering layer-stacked powder compacts that consist of PZT and pore-forming agent (PFA) powders in air atmosphere, whereby stearic acid was added as a pore-forming agent. In order to fabricate PZT/Metal or PZT/Polymer FGM actuators using porosity-graded PZT ceramics as a preform, another pore-forming agent, polymethylmethacrylate (PMMA) powder was also used to increase open porosity. The electric-field-induced deflection characteristic of the beam-shaped actuator samples was measured with electric strain gages, and compared with the values calculated from the modified classical laminate theory using the elastic and piezoelectric constants of the non-FGM porous PZT ceramics. It was found that the experimentally measured deflection values of the obtained actuator samples well agreed with the calculated data. An optimum porosity profile that gives the largest deflection was also determined by the modified classical lamination theory. Introduction In recent years a great deal of development has been made on intelligent materials utilizing piezoelectric functions. A well-known application is a smart structure for controlling vibration and noise in aircraft wings and precision manufacturing facilities, which are based on the principle of flexural actuators [1-3]. Unimorph and monomorph actuators are two typical types of flexural piezoelectric device, which produce large displacement by the electric-field-induced strain. Conventional unimorph actuators consist of piezoelectric plates and metal shims that are bonded together with an organic glue. Therefore, a discontinuity of strain, which induces stress concentration, appears at the interfaces when the actuator works. Such a problem may result in the deterioration in bonding integrity with decrease in the bonding strength after a long period of use. The concept of functionally graded materials (FGM) is expected to be effective in enhancing the mechanical reliability of piezoelectric ceramic actuators [4]. Numerical analyses [5] and experimental evaluations [6] show that FGM piezoelectric actuators relax the stress concentration. Zhu and Meng [7] have developed an FGM actuator with a compositional gradient from high piezoelectric and low dielectric material to low piezoelectric and high dielectric Materials Science Forum Online: 2003-05-15 ISSN: 1662-9752, Vols. 423-425, pp 405-410 doi:10.4028/www.scientific.net/MSF.423-425.405 © 2003 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-10/03/20,17:33:11) material. The authors have previously designed and fabricated a functionally graded PZT/Pt bimorph actuator that has low stress concentration but high deflection characteristics [8]. Another possibility has been proposed by Kawasaki and Watanabe [9] to obtain flexural deflection by introducing a porosity gradient. This will give us a new type of piezoelectric actuators that have no distinct hetero interface, which will cause stresses to result in the actuator degradation. The present work was focused on the fabrication of this new type of FGM piezoelectric actuator having a porosity gradient across the thickness by P/M method. The porosity gradient was formed in-situ by sintering layer-stacked PZT powder compacts with stepwisely varied contents of stearic acid or PMMA (poly-methyle-methacrylate) as pyrolyzable pore-forming agent (PFA), which is burned out during sintering. The electric-field-induced deflection characteristics of the resultant porosity-graded piezoelectric plates were evaluated and compared with the values calculated from the modified classical lamination theory using the measured elastic and piezoelectric constants of monolithic PZT ceramics with various porosities. Model for the Graded Monomorph Actuator Figure 1 shows the layer configuration of the miniature functionally graded monomorph actuator in the present study. The porosity distribution is expressed by the Eq(1): m l l d x C C C C       = ∆ + ∆ +

Ryuzo Watanabe

Papers

Fabrication and Evaluation of Porous Piezoelectric Ceramics and Porosity-Graded Piezoelectric Actuators

Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators

Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator

Development of Piezoelectric Ceramic Actuators with Graded Porosity

Piezoelectric Ceramic/Metal Bending Actuators with Functionally Graded Microstructures