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From:
Victor Birman and Larry W. Byrd, “Modeling and analysis of functionally graded materials and structures”, Applied Mechanics Reviews, Vol. 60, No. 5, pp 195-216, September 2007, doi:10.1115/1.2777164
ABSTRACT: 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.
Encyclopedia entry that defines “functionally Graded Materials (FGM):
A. Neubrand (Technische Universität Darmstadt, Germany), “Functionally Graded Materials” (FGM), Encyclopedia of Materials: Science and Technology, (no date nor publisher given; 2008?), pp. 3407-3413
doi:10.1016/B0-08-043152-6/00608-2
BEGINNING OF ARTICLE: A functionally graded material (FGM, or sometimes also ‘‘gradient material’’) is characterized by a gradual change of material properties with position. The property gradient in the material is caused by a position-dependent chemical composition, micro-structure, or atomic order. The spatial extension of the gradient may differ: in a bulk FGM the property variation extends over a large part of the material, whereas in a graded coating or joint it is restricted to the surface of the material or a small interfacial region.
Although FGMs attracted scientific interest only towards the end of the twentieth century, these materials are not new. In fact, spatial variations in the microstructure of materials have been exploited for millions of years by living organisms. In many structures found in plants, microstructural gradients are formed in order to produce optimum structural and functional performance with minimum material use. An example is the culm of bamboo, which consists of high-strength natural fibers embedded in a matrix of ordinary cells (Fig. 1(a)). The fiber content is not homogeneous over the entire cross-section of the culm but decreases from outside to inside (Fig. 1(b)). This gradation in fiber content is a natural adaptation of the plant to flexural loads—the fiber content is high only in those sections where the highest stresses occur.
There are also some examples of early synthetic materials taking advantage of property gradients such as case-hardened steels in which a hard surface is combined with a tough interior. Nevertheless, it was only in 1987 that Japanese scientists conceived graded materials as a new concept and defined an FGM as an ‘‘inhomogeneous composite, in which the material’s mechanical, physical, and chemical properties change continuously, and which have no discontinuities within the material’’ (Hirai et al. 1987). Meanwhile it has become common practice to use the term FGM not only for composites, but also for all materials with a macroscopic property gradient (see definition at the beginning of the article). Thus, materials containing only one phase such as graded glasses or graded single crystals are also FGMs. In such materials the spatial property variation is caused by a gradient in chemical composition. Nevertheless, the vast majority of FGMs are composite materials with a macroscopic micro-structural gradient. For example, the composite may contain a spatially varying volume fraction of one of the phases (Fig. 2(a)). In this case, the gradient material can be conveniently described by the use of a transition function f(x,y,z), where f is the volume fraction of one of the phases as a function of position. In many practical cases the compositional variation will be restricted to one coordinate, z, and the different gradients can then be described by a so-called transition function of the type: f(z) = (z/d)^p, where f denotes the volume fraction of one of the phases, d is the thickness of the graded region, and p is the so-called gradation exponent. However, a composition gradient is not inherent to all FGMs. Microstructural gradients may also be obtained in composites by changing the shape (Fig. 2(b)), orientation (Fig. 2(c)), or size (Fig. 2(d)) of the dispersed phase.
Properly designed property gradients in materials lead to a performance that cannot be achieved with a homogeneous material or by the joining of two different materials. The gradient can thus be regarded as an additional material design parameter which may be adapted and optimized to meet the requirements of a particular application. This leads to the unusual situation that the performance of the material is strongly influenced by geometric factors such as the shape of the material, and the extension and profile of the property gradient. Thus, a gradient material cannot be fully characterized by materials constants only, and already comprises certain aspects of the design of a component.
Most of the theoretical research on FGMs has been devoted to their macroscopic mechanical and thermal behavior and there has been considerable progress in understanding the effects of gradients on the stress distribution within such materials (reviewed by Suresh and Mortensen 1998). A gradation of the elastic modulus and\or of the thermal expansion coefficient…
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