Mechanical Properties of Ceramics and Composites

technology considered. Such diversity makes generating a clear and self-consis- tent set of definitions to cover all bodies complex and uncertain. The first of two points resolving this issue for this book is that the great majority of microstructures considered can be reasonably described by classical or ideal microstructures or limited modifications of these. Second, while increased sophistication in defining and measuring microstructures is important, the more immediate need is to better document key microstructural dependences of mechanical properties considered in order better to define or refine the mechanisms involved. These tasks are the focus of this book, which is limited to existing microstructural characterization. However, some of the complexities of real microstructures and limitations or challenges in meeting measurement needs for even typical microstructures are discussed along with some information on improved definitions and measurements.

Consider now the definition of grain and particle, since they are fundamental to this book and to understanding the behavior of most ceramics and ceramic composites. The terms are related, partially overlapping and basic to describing most, but not all, solid bodies, though they are not always adequate, at least by themselves, for some amorphous or complex bodies. Grain refers to the primary microstructural unit in polycrystalline bodies or in other polycrystalline entities, e.g. fibers or some powder particles, as well as the basic crystalline units in partially crystalline bodies. Grains are typically single-phase single crystals, whose identity is delineated by the difference in crystal orientation or structure from abutting grains or amorphous material, and the resultant grain boundaries formed between them to accommodate these differences. Thus an ideal polycrystalline body consists of one phase whose grain structure describes its microstructure.

Particle is a broader term, referring in general to a discrete solid entity of either glassy, i.e. noncrystalline, structure, or of single-crystal or polycrystalline character, or some combination of these, i.e. a particle may consist of differing compositions of one or more compositionally or structurally different phases as well as some possible porosity. The term particle is commonly used in two somewhat more restricted senses in the literature and in this book. The first is as the solid entities of a powder, i.e. as used to make many single phase or composite bodies, where the particle size, compositional, structural, and morphological character are selected or controlled to give the desired body consistent with the fabrication and related processing parameters. The second, more restricted, use of the term particle is to identify a discrete, typically minority, microstructural unit in a body containing two or more phases differing in composition, structure, or both. While such particles may be of one or more impurities, they more commonly are an intentionally added phase in a body, i.e. in a matrix of different composition than of the particles. The matrix is typically the larger volume fraction constituent, as well as the continuous phase (though

again more complex bodies can occur). The matrix and the dispersed particles can both be crystalline, or one can be amorphous, but usually not both (unless they are immiscible, which again leads to microstructures not totally described by the above concepts of grains and particles). In the case of a crystalline matrix its grain parameters are still often important in the behavior of the composite along with the particle parameters discussed below. An amorphous matrix derived by sintering may retain some of the original particle character of its powder origin, most commonly when the particles are delineated by substantial residual porosity. Thus the ideal or classical composite consists of a continuous amorphous single-crystal, or polycrystalline matrix with a disperion of solid particles of a distinct second phase, usually mainly or exclusively of singlecrystal or polycrystalline character.

The above ideal microstructures can be broadened to encompass many other bodies of interest via two modifications. The first is to include some porosity of either intergranular or intragranular locations, and often varying combinations of both, e.g. depending on grain size. (Porosity can be considered a [nonsolid] second phase. Modeling its effects by using composite models in which properties of the “pore phase” are set to zero is commonly used, but this approach, while often used, can also be very misleading [1].) Note that while real microstructures often have some porosity, which typically plays a role, often an important one in physical properties, their effects are treated extensively elsewhere [1]. In this book the focus is on microstructural effects with no or limited porosity, the latter commonly corrected for the effects of the porosity [1]. The second and broader modification is the introduction of a solid phase in addition to, or with no, pore phase in one or more of the following fashions: (1) along part, much, or all of the matrix grain, particle–matrix, or both boundaries or (2) within the grains, particles, or both, e.g. from some phase separation process such as precipitation.

Finally, a note on ceramic composites, which were originally the result of empirically derived bodies based on processing natural raw materials, with compositions based on the raw materials and processing available and the resultant behavior. Porcelains and whitewares, which are important examples of composites of silicate glasses and oxide crystalline phases still in broad use today, are treated to some extent in this book. Another related, more recent and often complex family of ceramic composites are those derived by controlled crystallization of glasses of compositions selected for their processing-property opportunities. These are also treated to some extent in this book. In more recent years, many composites of designed character, primarily of a crystalline matrix with significant dispersions of primarily single crystal particles, have become of interest. These composites of either or both oxide or nonoxide phases are more extensively covered in this book following evaluation of the grain dependence of properties of nominally single-phase, i.e. monolithic, ceramics.

B.Grain and Particle Parameters

The most fundamental parameter of grains and particles is their composition, hence generally of the body (i.e. in the absence of significant reaction or impurity phases). For composites, both the compositions (and associated crystal or amorphous structures) and the volume fractions of each phase are needed to define the composition. Beyond body composition, the key microstructural parameters of grains or particles are their amounts, sizes, shapes, orientations, and the numerical and spatial distributions of these. These parameters, while having some relation to composition, especially in composites, are extensively dependent on fabrication/processing parameters. This combined composition-fabrica- tion/processing dependence of microstructural parameters, which determines resultant body properties, is addressed in this book via its focus on microstructural effects.

Size naturally refers to the physical dimensions of grains and particles. While this can be complicated in definition, measurement, or both, e.g. due to effects of shape and orientation, it is most easily and commonly defined when the shape is approximately spherical or regular polyhedral. In this simple, common, useful, but not universal, case, the grain or particle size is typically simply and logically defined by an average grain or particle diameter (G or D respectively). However, even in such simple cases there are important questions of which average is most pertinent to the properties or phenomena of interest, as discussed in Section IV. Further, the statistical variation in size, e.g. the width of the size distribution, is also of importance, as may be also the spatial distribution of grains of different sizes, especially the clustering of larger grains.

While grain and particle size are commonly the most important microstructural parameters beyond the body composition (and the amount and character of porosity, if present), grain and particle shape and orientation are also often important individually, as well as through frequent interrelations among them and other parameters. Shape clearly refers to the three-dimensional shape of grains and particles, which becomes important primarily when it deviates considerably from an equiaxed shape, i.e. a spherical or regular polyhedral shape (typically with > six sides). While shape is a basic factor for all grains and particles, it is particularly important as it also relates to their crystal structure for single crystal grains or particles. Thus while larger grains or particles resulting from substantial growth are often equiaxed, they can also frequently be tabular or acicular in shape, i.e. respectively either more like platelets or rods/needles. Composites of ceramic platelets or whiskers in ceramic matrices, which have been the focus of substantial research, a few being in commercial production, are important examples of more extreme shaped particles. Grain and particle shapes impact both the designation and the measurement of the size of such grains or particles and are themselves difficult to measure in situ since conversion of the

typical two-dimensional measurement to a three-dimensional shape requires assumptions about the grain or particle shape.

Grain or particle shapes may also significantly affect their orientation, both locally and globally in the bodies in which they occur; both again in turn affect size measurements and body properties. Property effects occur most extensively when grain or particle shapes reflect aspects of the crystallographic character, which is common. In such cases, global orientation of such shaped grains or particles imparts a corresponding degree of anisotropy of properties in proportion to the crystalline anisotropy and the degree and volume fraction of orientated grains or particles. This encompasses all properties of noncubic materials, as well as various properties of cubic materials such as elastic moduli, fracture (i.e. cleavage, fracture energy, and toughness), and strengths, since cubic materials, while being isotropic in some properties such as dielectric constant and thermal expansion, are generally anisotropic in other properties such as those noted. Local grain or particle orientation effects can impact properties via effects on local crack generation (i.e. microcracking), propagation, or both. It can also result in grain clusters, i.e. colonies, that act collectively as a larger grain or particle, as discussed below and later.

Composites where the particles are single crystals, i.e. like grains in a polycrystalline matrix, are most common and most extensively treated in this book, including those where the dispersed particles are of more extreme morphological shapes, i.e. platelets or whiskers. When such latter composites are discussed, they will typically be specifically identified as platelet or whisker composites, and composites with more equiaxed particles will be referred to as particulate composites. However, the term particle or particulate composite will sometimes be used in the genetic sense irrespective of particle shape/morphology. Grain or particle orientation refers to the spatial orientation of either their physical shape or especially of their crystal structure, which are commonly related.

Measurement adequately to reflect size, shape, and orientation and their interrelation and spatial distributions is a large, imperfectly met challenge that is often inadequately considered. Thus the location, shape, and orientation, and sometimes the size, of pores are often related to grain, and especially particle, shape and orientation. For example, pores in platelet composites commonly remain at the platelet–matrix interface [2], and such pores often are larger and typically somewhat platelet in shape. Similar effects have been indicated in fiber composites (Chap. 8, Sec. III.E, Ref. 1) and are likely in whisker composites. Particle, and especially grain, growth can be significantly enhanced by impurities, with resultant larger grains or particles being equiaxed or often tabular or acicular in shape. Some of these effects are illustrated in the next section, and later in the book. Resulting effects are further frequently complicated by the need to define and address their correlation with other microstructural factors

such as other phases or pores, e.g. grain boundary or interfacial ones. Issues of such measurements and effects are discussed further in this chapter and elsewhere in this book.

The grain and particle parameter addressed most extensively is their size, which is generally of greatest importance and is widely addressed in the literature. However, the shape and orientation parameters, as well as the statistical and spatial distributions of these parameters and of sizes of grains and particles, are also treated to the extent feasible, since these parameters can also be important. Though interaction and distributions of these parameters are often neglected, causing considerable variation in the literature, they often play a role in determining many important physical properties of ceramic composites and monolithic ceramics.

II.RELATIVE EFFECTS AND INTERACTIONS OF MICROSTRUCTURAL PARAMETERS ON PROPERTIES

In focusing on grain and particle parameters it is important first to recognize the relative roles and interactions of microstructural features on ceramic properties, especially porosity, which is a dominant factor, as recently comprehensively reviewed [1]. In making ceramic (and other) bodies, processes used can result in either substantial or limited porosity, depending on both the fabrication process and the parameters selected. While a variety of factors impact the choice of fabrication method, e.g. the size, shape, and cost of components to be made, the amount and character of the porosity sought or tolerated in the component is also an important factor. Often, one is dealing with either of two, extreme, cases. In one case a desired, ideally a designed, pore structure is sought for favorable attributes needed from the amount and character of the porosity balanced against limitations of other pertinent properties such as stiffness, strength, conductivity, etc. imposed by the porosity. In the other case one seeks to minimize porosity to approach, or achieve, high levels of properties limited by porosity as a function of cost and performance. In polycrystalline materials grain parameters, and for composites particle parameters, play important, often similar, roles in many properties, depending on porosity content.

Typically the most significant role of grain and particle parameters on properties occurs where low porosity is sought for high levels of properties. This arises because some key ceramic properties, such as strength and fracture, hardness, wear, and erosion behavior, are significantly impacted by grain and particle parameters, of which size is often most important. Thus in order to achieve high levels of important properties in a selected material, porosity must first be minimized, since this commonly reduces properties substantially, e.g. by 1 to 2 orders of magnitude at intermediate and higher porosities. However, beyond increases from reduced porosity, some important properties can

be further increased, e.g. by 50 to a few hundred percent, by obtaining desired grain or particle sizes, often as small as feasible. Achieving this entails tradeoffs in terms of amounts and character of residual porosity, since at lower levels of porosity, further heating to reduce porosity commonly leads to grain growth and attendant sweeping of grain boundaries past previously intergranular pores. Resultant intragranular pores are often less detrimental to properties, and may even possibly counter some reductions of properties due to grain growth. While this approach of accepting some residual, especially intragranular, porosity is ultimately limiting in properties, it is often a factor in production of bulk ceramics. At the other extreme of product size, i.e. production of ceramic fibers, achieving very fine grains (typically << 1 m) with 0% porosity is essential to achieving strengths up to an order of magnitude higher than in bulk bodies. Achieving such benefits of fine grain sizes with 0% porosity in bulk bodies has also been sought. However, this can entail serious problems of residual impurities in some materials, particularly in attempting to achieve nano-scale grain or particle sizes for effects expected from extapolations of conventional grain or particle size dependences, or for possible novel behavior at such fine grain or particle sizes. Such problems, which have not been addressed in the nanomaterial literature, are addressed in this book.

In cases where porosity is needed for functions, grain and particle parameters often still play a role in determining properties, but such effects are usually secondary to those of the pore structure and are typically at fine grain and particle sizes. Obtaining such fine sizes often entails retaining substantial porosity due to low processing temperatures used to limit grain or particle growth, and in the common case of sintering, starting with fine particles. However, since some growth of grains, particles, or both occurs, often inversely to the level of porosity, grain size effects must also be considered, especially as porosity decreases, as is extensively addressed elsewhere [1].

A qualitative overview of the relative impacts of pores, grains, and particles on various properties, mainly at moderate temperatures (the primary focus of this book), is summarized in Table 1.1, by indicating whether these features have a primary (P) or a secondary (S) effect on that property. Primary effects are intrinsic to the presence of the pore, grain, or particle structure in the body, but vary with compositions and their amounts, sizes, shapes, and orientations. Secondary effects, which can occur alone or in addition to primary effects arise from combinations of composition, size, shape, and orientation via local and especially global grain (or particle) orientation and hence anisotropy or microcracking, the latter occurring only above a critical grain or particle size for a given body composition. While many primary effects are very substantial, e.g. most porosity effects, and many secondary effects are of lesser impact, this is not always so. Thus while particles in a composite have intrinsic effects on all properties shown, these are often modest, since particle property impacts typically

a–d P = a primary, i.e. an inherent, dependence on the presence of pores, grains, or particles and their parameters. S = a secondary dependence, which occurs only for some body compositions and some aspects and ranges of microstructural parameters. Secondary effects arise in addition to or instead of primary effects, but arise only for some compositions and often only some ranges of grain and particle parameters and associated microcracking, and gram boundary impurities or phases, or pores (primary or common ones noted for different properties). Particles dispersed in a matrix, i.e. for a composite, have primary effects on all properties, commonly proportional to the property difference of the particle and matrix phases, i.e. varying across a substantial range, but often less than from pore or grain parameters. Significant secondary effects often occur and can be ≥ than primary effects.

e Thermal expansion only depends on porosity via its effects on other factors, primarily microcracking.

scale with the difference in that property for the particles and the matrix and with the volume fraction of particles.

The summary of Table 1.1 can be put in better perspective by recalling basic aspects of the isotropic versus anisotropic behavior of crystalline materials. Thus noncubic materials often have substantial variation of properties with crystal direction, i.e. are anisotropic. On the other hand cubic materials are intrinsically isotropic for several important properties such as thermal expansion, electrical and thermal conductivities, dielectric constant, and refractive index. However, cubic materials are intrinsically anisotropic in some properties, particularly elastic moduli, fracture energy and toughness, tensile and compressive strength, and electrical breakdown.

Grain parameters, especially size, play a primary role in most mechanical

properties as well as a number of secondary effects that occur due to other factors. Most of this dependence is similar in both cubic and noncubic materials, but there can be some differences in noncubic materials due to secondary effects, especially microcracking, which can play an important role in fracture toughness. Key exceptions to this grain size dependence of mechanical properties are elastic properties, which have no intrinsic dependence on grain size, only a secondary dependence to the extent that it impacts microcracking (i.e. typically above a certain, material dependent, grain size). Elastic properties also have a secondary to substantial dependence on overall, i.e. global, preferred grain orientation in all noncubic materials, and essentially all cubic ones due to their anisotropy as noted above. Grain size has no primary effect on thermal expansion of cubic or noncubic materials. It has limited or no effect on thermal conductivity in noncubic materials at, and especially above, room temperature, but it can have increasing, generally modest, effects at lower temperatures in noncubic materials. Electrical conductivity generally follows similar trends but can have greater grain size dependence in noncubic materials, since it covers a much broader range of values as a function of material composition and crystal phase character than thermal conductivity. Optical scattering also has a primary, but generally limited, dependence on grain size, as well as some significant secondary dependence in noncubic materials. However, these intrinsic effects are commonly much smaller than the effects of microcracking (in noncubic or composite materials), or pores or boundary impurities in either cubic or noncubic materials. Dielectric constant has some crystalline anisitropy in noncubic materials, hence some dependence on global, i.e. preferred, grain orientation, but no intrinsic grain size dependence. Electrical breakdown, which is intrinsicaly dependent on crystal orientation in both cubic, and especially noncubic, materials, is quite sensitive to secondary effects correlating with grain size, i.e. microcracking, intergranular pores, and phases.

Composite properties have a primary, as well as a secondary, dependence on the particle character. However, these dependences, especially the primary ones, are generally dependent, in decreasing order of importance, first on the differences between the matrix and particle properties (hence their compositions), second on the volume fraction of the particulate phase, and third on the particle size, shape, and orientation. Particle size is mainly a factor in the primary dependence of mechanical, other than elastic, properties, where such effects generally parallel those of grain size in nominally single-phase materials. Particle size effects on nonmechanical properties occur mainly in conjunction with the often substantial effects of particle volume fraction and shape and orientation via their effects on contiguity of the particulate phase. These effects are generally greater for thermal and particularly electrical conductivity, as well as electrical breakdown, especially where the second phase has substantially higher conductivity or lower electrical breakdown than the matrix. Particle size