101 Description

10.1.1 General

Functionally graded materials (FGMs) are materials that comprise a spatial gradation in structure and/or composition, tailored for a specific performance or function. FGMs are not technically a separate class of materials but rather represent an engineering approach to modify the structural and/or chemical arrangement of materials or elements. This approach is most beneficial when a component has diverse and seemingly contradictory property requirements, such as the necessity for high hardness and high toughness in wear-resistant coatings. Generally, it is very difficult to provide broad design guidelines for utilizing FGMs since the structures are complex and diverse. The purpose of this chapter is to give the reader an understanding of how specific gradations in structure and/or composition will affect specific material behavior. Because of the complexity of FGM systems, most of the information is qualitative and is meant to provide broad guidelines. Some of the descriptions are generic and apply to a large class of material and structural systems while others are quite specific, and only "work" for a small set of materials.

While the term functionally graded materials has only existed since the mid-1980s, the concept has been utilized in engineering for a relatively long time. For example, the concept behind surface hardening of steel by carburization has been understood for some 60 years and has been used for many hundreds of years. For a second example, as early as 1912 metal/glass sealing technologists developed graded structures for minimizing thermal residual stresses due to thermal expansion coefficients mismatch [1, 2]. A third example exists in graded band gap semiconductors for use in heterojunction bipolar transistors, introduced in 1957 [3, 4]. Finally, graded structures were introduced in structural composites in the 1970s [5]. Despite well-established guidelines for the latter applications, until recently no unified view of graded structures existed. By focusing research and development efforts on generic aspects of FGMs, further advancements may be made to understand which structures are desirable for specific applications. This chapter provides a current description and provides a framework for utilizing the FGM concept in engineering applications.

10.1.2 Classification

Perhaps FGMs are best classified according to processing, as illustrated in Fig. 10.1, which separates FGMs into those produced by constructive processes and those produced by transport-based processes [6]. In short, constructive processes rely on the placement of phases within a structure by the processing engineer. Transport-based processes rely on well-timed and designed in situ reactions or processes during material fabrication. Many protective coatings (e.g., thermal barrier coatings) fall into the former category. The carburization of steel

CHARACTERISTICS, BEHAVIOR, AND PERFORMANCE 467 Classification of FGMs According to Processing

CHARACTERISTICS, BEHAVIOR, AND PERFORMANCE 467 Classification of FGMs According to Processing

Conventional

Liquid Phase

Sintering

Infiltration

Reactive

Powder

- Plasma Spray

- Thermal Spray

- Laser Cladding

- Electroforming Vapor Deposition

- Diffusion from Surface: Steel Carburization and Nitridation

- Transport-Based Porous Preform Preparation

Conventional

Liquid Phase

Sintering

Infiltration

Reactive

Powder

Lamination

- Plasma Spray

- Thermal Spray

- Laser Cladding

- Electroforming Vapor Deposition

Deformation/ Martensitic Transformation

- Diffusion from Surface: Steel Carburization and Nitridation

- Other

Surface Mass Transport Grading Processes

Interdiffusion

Thermal Processes

- Transport-Based Porous Preform Preparation

- Macrosegregation and Segregative Darcian Flow Processes

- Infiltration Combined with Liquid Phase Sintering or Reactive Processing

Settling and Centrifugal Separation

FIGURE 10.1 Classification of functionally graded materials according to [5].

falls into the latter category. Naturally, a design approach in which a gradation is formed in situ, by a transport-based process, would be simpler and generally more desirable than a constructive approach.

10.2 CHARACTERISTICS, BEHAVIOR, AND PERFORMANCE

It is inappropriate to assign a unique property to a functionally graded material since the local properties vary throughout the material. Instead, the approach required is to super impose the various material properties within the FGM to predict a specific type of behavior. Thus, utilization of FGMs relies on controlling the spatial variation in material properties of a component so that the desired spatial variance of performance may be achieved. The challenge is to devise models that predict the characteristics, behavior, and performance of graded materials as a function of the constituent properties and the graded architecture. At the current time, only a few such specific models exist. The approach taken here is to provide a more qualitative framework to build models that predict material response. Various characteristics of graded materials are discussed next. The emphasis is on mechanical behavior.

10.2.1 Thermal Residual Stress Modification

Historically, one of the first purposes of constructively processed FGMs was to reduce thermal residual stresses in joints between dissimilar materials. The thermal residual stress results from cooling the joint from elevated temperature: Thermal expansion mismatch results in differential thermal strains that give rise to potentially deleterious stresses. While for bimaterial joints the thermal stresses are relatively simple to predict, for layered and graded systems, the situation is more complex. The schematic in Fig. 10.2 indicates an interlayer region between two materials that have different thermal expansion coefficients. Ideally, this interlayer region exhibits a spatially varying thermal expansion coefficient (TEC) whose value at any point is intermediate between the two materials. Specific optimum design of this interlayer region (e.g., whether its gradation is linear, parabolic, or stepwise) depends on many details, including the overall geometry (in the simplest case, whether the joint is a plate, a cylinder, or a coating—see Fig. 10.3), the specific material constituent properties, whether or not plasticity plays a role in relaxing stresses, and the particular design-related constraints. Some generic models have been developed to examine trends in stress distribution in FGMs, and these models provide the design engineer with guidance [6]. Figure 10.4 illustrates the kind of benefit attained by incorporating an FGM interlayer. The dashed curve indicates the (in-plane) stress distribution for a sharp Ni/Al2O3 interface, while the solid line indicates the stress distribution for the same interface that contains an FGM interlayer that exhibits linearly varying elastic modulus and thermal expansion coefficient. Note the reduction in maximum tensile stress from approximately 125 MPa in the sharp joint to about 25 MPa in the graded joint. These results indicate the kind of benefit FGMs can provide to dissimilar material joints. Even though a detailed understanding of stress distributions is complex and depends on many parameters, some qualitative generalizations may be made. The stress distributions depend on the component geometry (Fig. 10.3) and the graded architecture (Fig. 10.5). The differences are summarized qualitatively for a few general cases in Tables 10.1 and 10.2. More detailed, quantitative information may be found elsewhere [7-9]. It is highly

Continuous

Layered

Continuous

Layered

Material 1

Material 1

FIGURE 10.2 Schematic showing two graded joint geometries with material 1 (white) and material 2 (black). Architecture on left is layered or discrete while one on right is continuous.

material 1

material 2

graded layer

Cylinder

FIGURE 10.3 Examples of simple, axisymmetric geometries for which thermal residual stress distributions are very different. Table 10.1 gives qualitative information on effect of geometries in reference to stresses typically important in joints for structural applications (axial and shear stresses at edge and in-plane stresses in interior).

recommended that the engineer constructs a finite-element model for detailed stress distribution prediction.

Typically, the edges of a joint experience higher shear and normal thermal residual stresses than those predicted in the center of the joint. Because component edge regions frequently contain flaws from surface machining, these regions are particularly likely to experience high stress singularities that can result in premature crack propagation. Thus, special attention should be given to the development of stresses in edges and any singular regions. Work on mul-tilayered brittle symmetric composites in which a material with lower TEC is placed between two materials with higher TCE has shown that upon cooling, the inner layers, which normally experience compressive axial stresses in the bulk, may experience tensile axial stresses at the edge [10]. The magnitude of tensile stresses depends on the layer thickness but has been observed to drive channeling cracks at the edge in ceramic/ceramic systems [10]. Generally, gradation in material properties is an effective method to reduce edge stresses in nonsymmetric

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