Engineered Ceramics: Current Status and Future Prospects

Part 1

Materials Design and Characterization

1

An Introduction to Materials by Design Including a Dynamic Stress Environment

James W. McCauley

Army Research Laboratory and Johns Hopkins University

Abstract

Materials by Design, conceptually, describes a process of designing materials from the atomic to the macroscopic scale for a particular suite of mechanisms and properties that are required for defined performance/applications. Very simply, it is not about how to design components (systems) with existing materials, but about how to select and design materials for defined applications. Initially, the importance and definition of materials characterization are presented. including a materials unique signature at the atomic, microstructure, and macrostructure scales. A brief history of the emergence of Materials by Design is summarized, followed by progressively more complex examples, including atomic structure and microstructure design in ceramic matrix composites. Historically, the Materials by Design approach has been primarily used for systems in quasi-static mechanical environments; utilization in extreme dynamic environments presents significant challenges. A simplified example of the approach for solid-on-solid impact on a structural ceramic is described. Finally, the influence of this approach in a strategic materials basic research program and the new transformational Materials in Extreme Dynamic Environments program at the Army Research Laboratory is briefly summarized.

Keywords: Materials by Design; characterization; materials selection; unique signature; ceramic matrix composites; extreme dynamic environments

1.1 Introduction

Materials are ubiquitous in all Army materiel. The performance and function of every Army system are determined by the underlying properties of the materials and the structural/electrical design of the engineering system. In turn, the properties of the materials themselves are products of the hierarchy of structures found within. From atoms, to unit cells, to crystals, to grains, to assembly of grains, and to multiphase materials, the final performance of any system is a sum of the parts, sometimes synergistic, of the underlying physics down to the smallest (nano/atomic) scale, or simplified as follows.

1.2 Crystal Structure ↔ Microstructure ↔ Macrostructure ↔ Property Relationships

In real estate, the three most important factors are location–-location–-location. In materials, it is structure—structure—structure.

The potential to gain extraordinary system or component improvements through the effective design and control of the constituent materials remains untapped. Enabling the design of these hierarchical material structures in concert with the overall design and function of the system will allow for transformational gains in the performance of engineering systems. This vision is consistent with the National Materials Genome Initiative to Discover, develop, manufacture, and deploy advanced materials in a more expeditious and economical way… [1].

1.3 Scope of Manuscript

First, the appropriate context will be established by introducing the importance of the definition of materials characterization, especially in materials science and engineering research and development. This will lead to the development of the material unique signature concept at multiple scales. A brief history of the emergence of a formalized materials selection process and the Materials by Design (MbD) approach in the 1990s is then introduced. This is followed by progressively more complex examples of MbD:

RADOME materials: materials selection, combining mechanical and electrical properties;

Multilayer ceramic capacitors (MLCCs) combining electrical, geometry, and MbD at the single crystal/grain level;

Particulate dispersion ceramic matrix composites demonstrating atomic and microstructural control of mechanical and thermal properties; and

MbD in a dynamic mechanical environment.

Finally, a case is made that the use of the MbD approach in the Materials R&D environment significantly improves the probability of success in the utilization of new materials. This is followed by a brief description of the new Army Research Laboratory program, Materials in Extreme Dynamic Environments (MEDE), which utilizes the multiscale MbD approach in a robust modeling and simulation and advanced experimental framework.

1.4 Characterization of Materials and Unique Signatures at Multiple Scales

Professor Rustum Roy, the founder and Director of the Materials Research Laboratory at Penn State for many years, published a catalytic paper in 1965, emphasizing the importance of material characterization in materials science and engineering [2]. It is believed that this paper led to an important National Academy Materials Advisory Board study in 1967, focusing on the characterization of materials [3]. The most important conclusion from the committee, besides underscoring the importance of materials characterization, was a universally agreed-upon definition of Materials Characterization as follows:

CHARACTERIZATION DESCRIBES THOSE FEATURES OF THE COMPOSITION AND STRUCTURE (INCLUDING DEFECTS) OF A MATERIAL THAT ARE SIGNIFICANT FOR A PARTICULAR PREPARATION, STUDY OF PROPERTIES, OR USE, AND SUFFICE FOR REPRODUCTION OF THE MATERIAL

Building on these recommendations, the Army Materials and Mechanics Research Center, in cooperation with Syracuse University, convened the twentieth Sagamore Army Materials Research Conference on Characterization of Materials in Research—Ceramics and Polymers at the Sagamore Conference Center, Raquette Lake, New York, during September 11–14, 1973. At this conference, McCauley [4] presented a paper titled Structural and Chemical Characterization of Processed Crystalline Ceramic Materials. The following is a quotation from this paper: Research on new materials demands systematic characterization, not only to optimize fabrication parameters and to insure future quality control, but also to enable optimum engineering properties to be achieved. Any processed ceramic material should be uniquely defined by a necessary and sufficient set of parameters including composition, grain size, shape orientation, and packing. Quantitative relationships derived among these parameters, engineering properties and utilization functions can be used to control and optimize their properties and use. A simple material defining equation was suggested to uniquely define a material:

These concepts were later reworked [5] into a unique signature of a material to represent the critical importance of processing defects:

The unique signatures for boron carbide (nominally B4C) at five scales are illustrated in Figure 1.1.

Figure 1.1 Unique signatures at multiple scales for polycrystalline boron carbide (B4C).

In addition, utilization functions were introduced [4], which were defined as a mathematical combination of critical properties which can quantitatively predict how well a material will perform in a certain use or environment. These two simple ideas form the basis of what is now called Materials by Design and material Figures of Merit. Finally, a flow chart for materials research and development (Figure 1.2) was presented to emphasize the importance of characterization in several stages of an overall materials development program. Using these concepts can help define materials science and materials engineering:

Materials Science = the creation of new materials and the understanding of the relation of material characteristics [unique signature = chemistry (c), microstructure (M), defects (PD)] to properties.

Materials Engineering = the fabrication (processing) of materials with controlled properties for certain performance. Materials Figures of Merit (FoM) are a critical link here as they define a quantitative relationship between combinations of properties to desired performance.

Figure 1.2 Flow chart for materials research and development.

1.5 Historical Emergence of Materials by Design

In the 1990s, the stage was being set by a few key publications and activities. Mike Ashby from Cambridge University published a classic work on Materials Selection in Mechanical Design in 1992 [6]. Ashby introduced the concept of a Material Index, which is a combination of material properties that characterizes the performance of a material in a given application. A simple example is the material index (M) for a light, stiff structural beam:

where E is Young's modulus (stiffness) and ρ is the density. The objective is to maximize M. This index can also be referred to as a Figure of Merit (FoM).

In 1997, Professor Greg Olson [7], from Northwestern University, building on the work by Cyril Stanley Smith [8], published a seminal paper in Science titled Computational Design of Hierarchically Structured Materials, In this paper, he presented a very simple model (Figure 1.3) that he called the central paradigm of materials science and engineering. The important aspect of multiple material scales to the atomic level was also introduced.

Figure 1.3 Three-link chain model of the central paradigm of materials science and engineering (permission obtained from Science).

In this same year, Dr. Anita K. Jones, then Director of Defense Research and Engineering for the US Department of Defense (DoD), recognizing the importance of this emerging materials science approach, challenged the DoD scientists and engineers with a grand vision to use advanced materials design and evolving computational capabilities to optimize armor materials—she projected that this atoms to armor goal might be possible in the early part of the twenty-first century. At the time this was a revolutionary concept since armor material development was primarily by an Edisonian/empirical approach. This historical paradigm could be significantly impacted in materials research and development by carrying out more strategic basic research that is coupled by a design-based process to identified applications. Then in 1998, a special workshop on New Directions in Materials Design Science and Engineering (MDS&E) was organized by Georgia Tech and Morehouse College [9]. A key output of this workshop was captured as follows: Materials Design Science and Engineering (MDS&E) is the invocation of science and engineering principles to tailor material structures to achieve a high degree of predictable, controllable functionality in applications. By necessity, MDS&E is a multi-disciplinary enterprise, with interactions of material science and engineering, engineering science and systems design, materials chemistry, physics and biology, the computing and information sciences, and applied mathematics. This new paradigm strongly implies significant cultural changes in US universities, industries, and the overall materials research and development enterprise and it is so different from the historical approach that implementation is extremely difficult.

An understanding of Materials by Design began to gain traction in the community. Very simply, it is not about how to design components (systems) with existing materials, but about how to select and design materials for defined applications.

At the heart of this concept is a materials science and engineering approach described in Materials Science and Engineering for the 1990's, [10] in the following quotes: … that the properties and phenomena associated with a material are intimately related to its composition and structure at all levels (scales), including what atoms are present and how the atoms are arranged in the material, and that this structure is the result of synthesis and processing. It is these elements—properties, structure and composition, synthesis and processing, and performance and their strong interrelationship among them—that define the field of materials science and engineering.

A systematic approach to strategic materials science and engineering research is conceptualized in Figure 1.4: performance requirements are translated into the required properties (material selection), which then can be translated (MbD) into the required material characteristics at the various scales. Path 1 is for a known, more conventional design, whereas path 2 is a clean paper/new design that will require an optimum performance with a much-reduced weight, for example.

Figure 1.4 Conceptual approach to using Materials by Design.

1.6 Selected Examples of MbD in Quasi-Static Mechanical Environments

Example 1.1 RADOME Materials—Materials Selection

A typical Ashby Diagram for selecting appropriate materials for an RADOME is illustrated in Figure 1.5. In the diagram, the Material Index or Figure of Merit is C:

where σf is the failure strength, ϵ is the dielectric constant, and tan δ is the loss tangent. This is a more complicated material index combining a mechanical property with electrical properties. The obvious result is that a material with a high failure strength and very low dielectric loss (ϵ tan δ) is the material of choice. In this particular example, all of these properties can be adjusted/designed by controlling the microstructure, processing defects, and phases/chemistry of the dielectric material and in some cases down to the atomic structure scale. This simple example does ignore thermal and high strain rate effects that can be very important in the actual application.

Figure 1.5 Materials selection diagram plotting strength versus dielectric loss (from Ashby 1993, personal communication).

Example 1.2 Multilayer Ceramic Capacitors

Another, more complicated example, is for MLCCs that have almost ubiquitous use in a huge number of electronic devices. One goal is to reduce the size of the MLCC while maintaining the appropriate capacitance; this will allow for a reduction in the size and weight of a cell phone, for example. The capacitance (C) of single layer (disc) capacitor can be determined as follows [11]:

where K = dielectric constant of the dielectric (BaTiO3), A = area of the electrodes, and t = thickness of the dielectric layer. There are, therefore, three ways to increase the volumetric efficiency:

Increase in K—a material property

Increase in A (geometry)

Reduction in t (geometry)

The capacitance of an MLCC with many active layers is as follows:

where T = the thickness of the active layers in the MLCC. Decreasing the active thickness (t) allows MLCCs to be made smaller, while maintaining the same capacitance. In this case, there are geometric constraints as well as material properties. For a polycrystalline BaTiO3 dielectric material, the dielectric constant is adjusted by adjusting the grain size, the individual grain core/shell structure (Figure 1.6), and chemistry of the grain and the grain boundary characteristics, and these can be designed atom by atom for optimized properties; decreasing the particle size, while maintaining the original capacitance, also allows for thinner layers [12].

Example 1.3 Designed Particulate Dispersion Composites: Demonstrating Atomic Level and Microstructural Control

In many single-phase, high-performance brittle oxide ceramics, it can be difficult to modify and enhance their mechanical and thermal properties solely by grain size, grain boundary engineering and continuous fiber composites, or other approaches. There are many potential applications for structural oxide ceramics in extreme structural and temperature environments that require improved toughness and thermal shock resistance. The use of particulate dispersion composites, much like the control of fillers in polymer composites, can open up new windows of opportunity. Work by Lange [13] and Cook and Gordon [14] strongly suggested that the incorporation of a second phase, and especially one with a plane of weakness, increasing or maintaining the flexure strength and reducing the elastic modulus, could potentially enhance the mechanical properties. In addition, combining these ideas with thermal shock and damage resistance figures of merit determined by Hasselman [15] led McCauley [16–21] to develop Ba-mica/Al2O3 composites exhibiting much-improved toughness, impact strength and thermal shock properties, as well as being able to control thermal conductivity. Natural micas, like hydroxyphlogopite (KMg3Si3Al O10(OH)2), have graphite-like structures, with an easy plane of weakness and very low thermal conductivity; however, their thermal stability is fairly low because of the presence of the hydroxyl anion. Atomic substitution of Ba for K and F for OH results in a Ba-mica (BaMg3Al2Si2O10F2) with a lower E than Al2O3 and a high enough thermal stability to enable coprocessing with Al2O3 [16–18]. The toughness and impact FoM can be approximated by σf²/E, the failure strength divided by the elastic modulus; increasing σf² and decreasing E should increase the toughness and impact strength. The thermal shock resistance FoM (ignoring thermal expansion) is ≈ σf/E and the thermal shock damage resistance is ≈ E/σf². In order to test these FoMs, two sets of Ba-mica/Al2O3 composites using 5–50 v% 30- and 90-μm Ba-mica in Al2O3 matrices were fabricated by hot pressing and subsequently evaluated. Figure 1.7 illustrates examples of their microstructures and the influence of a plane of weakness on crack propagation and branching.

Figure 1.8 illustrates the various mechanical properties determined for these composites. It is clear that by decreasing the elastic modulus and increasing the flexure strength, the impact strength and toughness can be significantly enhanced. The thermal shock properties of these materials were also improved as shown in Table 1.1. Samples were equilibrated at successively higher temperatures and then dropped into water at 25°C. Both the critical thermal shock temperature and the strength after thermal shock were significantly increased. Figure 1.9 illustrates both the thermal conductivity [19] and diffusivity [20] of the 30-μm Ba-mica/Al2O3 composites determined perpendicular to the mica flakes. It is very clear that substantial control of these properties can be achieved.

Figure 1.6 Core-shell microstructure of a BaTiO3 grain.

Figure 1.7 Microstructures of designable Ba-mica/Al2O3 composite.

Table 1.1 Thermal shock properties of Ba-mica/Al2O3 composites

ΔTc = change in equilibrated thermal shock temperature from quenching water temperature.

St = strength before thermal shock.

Sa = strength after thermal shock.

Figure 1.8 Four-point flexure strengths, elastic moduli, fracture energy, and impact strengths of Ba-mica/Al2O3 composites.

Figure 1.9 (a) Thermal conductivity and (b) thermal diffusivity of 30-μm Ba-mica/Al2O3 determined perpendicular to the mica flakes.

Example 1.4 Structural Materials by Design in a Dynamic (High Strain Rate)/High Stress Environment–-Solid-on-Solid Impact Event on a Structural Ceramic

Utilization of the MbD approach in a dynamic (high strain rate)/high stress environment is a significant challenge with the addition of high strain rates to the mix. The Ashby and Olson paradigms, for the most part, mostly assume quasi-static structural environments where conventional engineering mechanical properties are very relevant. Linear extrapolation of the quasi-static properties to the high strain rates in question cannot be justified in most cases, especially if there are dramatic changes in the mechanisms or properties with increasing strain rates. In extreme dynamic environment events (blast/impact), a very large amount of energy is deposited over a very short period of time over large volumes of the material. The result is that the energy deposited and the stress varies in space and time in the material. The objective in protection materials is to control energy consumption/dissipation to delay or completely prevent catastrophic failure in the event. Energy can be consumed in elastic and inelastic deformation, and failure (fracturing) mechanisms as well as phase transformations, chemical reactions, and other mechanisms. Clearly, a major objective is to maximize energy mitigation in the nonfailure mechanisms or to significantly increase the stress or energy required for failure mechanisms, and it is these mechanisms (and not just properties) that dominate in extreme dynamic events. These mechanisms will, of course, depend on the material and the nature of the event. So determining the underlying, physics-based mechanisms, and the quantification of the event characteristics is critical to using the MbD approach to design and produce materials that have the required mechanisms at the various scales.

Table 1.2 [22] summarizes some simplified examples of key differences between conventional quasi-static mechanical testing and a dynamic impact event on a rectangular plate sample. The strain rate for quasi-static mechanical testing is on the order of 10−3 s−1, whereas dynamic events can be in the range of 10² to 10⁶ s−1. Basically, the stressed volume in most impact events can be much larger than conventional quasi-static testing, resulting in the activation of a much larger distribution of defects, microstructural inhomogeneities, and other stress concentration entities. Sequences of shock waves are generated in an impact event consisting of a surface wave (Rayleigh wave), compression/longitudinal wave (dilatational, push, or p wave), and a shear (transverse, shake, or s wave) wave. Assuming a harmonic normal load in the impact event, the total energy in the shock waves is roughly partitioned as follows: 67% in the Rayleigh (R) wave, 26% in the shear (s) wave, and 7% in the compression (C) wave, so the influence of the Rayleigh and shear waves is predominant [23].

Table 1.2 Some examples of simplified differences between quasi-static and dynamic stress impact environments

Mechanisms and resulting properties at scales from the crystallographic unit cell (nanometers, crystal structure) to the component (meters) all can contribute to the final performance. However, the varying magnitude of the mechanism contribution at the various scales will vary from material to material and event to event. High strain rate testing becomes critical as well as diagnostics that can reveal the change in mechanisms during a test. And since atomic scale mechanisms may be important, diagnostics at this scale may also be critical. In addition, modeling at the various scales must be integrated into the MbD approach here to test the various mechanisms determined so that new materials can be designed and fabricated and performance evaluated. Examples of various mechanisms and properties at the various scales are schematically illustrated in Figure 1.10 along with their relationship to the more large-scale, continuum computer codes.

Figure 1.10 Relationship of multiscale mechanisms and properties to final performance models and computer continuum simulations.

As previously discussed, at the heart of an MbD approach is the Figure of Merit. This presents a real challenge since in an extreme high stress/high strain rate environment, rather than properties per se, the underlying, foundational scientific grand challenges are determining the energy dissipative mechanisms at the atomic, microstructure, and macrostructure material scales that together contribute to the deformation, damage, and failure in extreme dynamic environments simplistically formulated as follows.

1.7 Total Energy Dissipation = f (Atomic Mechanisms + Micro-Material Mechanisms + Macro-Material Mechanisms)

In the late 1960s when ceramics were just beginning to emerge as viable personnel protection materials, a common metric that was used is as follows: (unknown author)

So the general conclusion at that time was that hard, stiff, and low-density ceramics would work the best. However, this very simple formula does not capture the important mechanisms that have been determined since that time. Other Figures of Merit have emerged, some of which were reviewed in 2006 by McCauley [24–31]. It is clear from Table 1.2 and Figure 1.10 that a dynamic impact event can be a complex interaction of many stages, properties, and mechanisms. A simplified, schematic representation of the various events or stages in an impact event is pictured in Figure 1.11. The projectile velocity is plotted on the x-axis, while the velocity of the projectile in the material is plotted on the y-axis. For lower velocities the projectile will not penetrate substantially into the material—it will dwell. At some higher velocity, the projectile will begin to penetrate with increasing velocity because of a variety of Hertzian-type mechanisms of radial and cone cracking and the formation of a comminuted or Mescal zone. It is in this latter zone that a ceramic type of plasticity (quasi plasticity) can play an important role. Basically, in the impact event, the total energy consumption/dissipation is a competition between the nonfailure elastic and inelastic mechanisms (quasi-plasticity) and the failure (macro-cracking) mechanisms. Very rough, nominal approximations of the contributions of the various stages to total failure in the impact event are listed in Table 1.3 for thin and thicker plates.

Table 1.3 Impact stages—rough percent contribution to total failure

Figure 1.11 Stages/separable parts in projectile impact and penetration—simplified.

Converting these contributions into a Figure of Merit for thin and thick plates is as follows and results in fairly complex formulas:

Thin plates: FoMthin = f [0.1(Shock) + 0.4 (Dwell) + 0.25 (Hertzian) + 0.05 (Frag Pen) + 0.2 (Rigidity)]

Thick plates: FoMthick = f [0.1(Shock) + 0.3 (Dwell) + 0.35 (Hertzian) + 0.2 (Frag. Pen) + 0.05 (Rigidity)]

In terms of the armor ceramic alone, ignoring the shock, fragment penetration, and rigidity stages, the armor ceramic response is dominated by the dwell and Hertzian stages. So, a figure of merit for this stage may be very important to the response of the ceramic and will contribute substantially to the impact response.

In general, it has long been known that the hardness of ceramics correlates well with gross impact performance, however, not to a degree useful for materials development [32]. Wilkins et al. [33] were the first to point out the apparent importance of ceramic plasticity or inelastic deformation mechanisms in BeO and AlN in impact performance. Later, Heard and Cline, in 1980, carried out their classic work quantifying the effect of confinement on the plasticity of BeO, AlN, and Al2O3 [34]. Lankford reaffirmed the important role of plasticity in the compressive failure of high-strength ceramics [35, 36]. A quote from the latter paper reaffirmed the importance of plasticity: Clearly, the ceramic would never fail if it could be constrained to flow indefinitely. More recently, Lundberg et al. have made compelling arguments that the compressive yield strength (related to hardness) augmented by the amount of plasticity in ceramics correlates well to transitional velocities (dwell), that is, the velocity (or impact pressure) where penetration begins [37]. A direct measure of plasticity has not been determined, unlike ductility in metals, although Pickup and Barker have suggested that specially designed test specimens in a Split Hopkinson Pressure Bar (Kolsky Bar) may be able to, at least qualitatively, determine the extent of dynamic plasticity [38]. Rhee et al. have carried out an elegant analytical analysis of spherical quasi-static Hertzian indentation deriving critical contact loads for cone crack formation and first yield—initiation of quasi-plasticity; it is stressed that the quasi plasticity and the size of the quasi-plastic zone are a volume property, which is difficult to measure [39]. In their paper, they also have developed a Brittleness Index that is related to the amount of stress for first yield to brittle cone crack formation. In a more recent paper, Asenov and colleagues conclude that brittleness is a decisive property for the behavior of ceramics [29]. Quinn and Quinn have also determined a Brittleness Index, using an elegant analysis of load/hardness curves [40]. However, there is another complexity involving the interaction between defects and quasi plasticity. The presence of defects can, as Lankford has pointed out, cause failure before the activation of quasi-plasticity mechanisms in the ceramic. Quasi-plasticity can be defined as all of the inelastic (nonlinear) deformations prior to catastrophic failure (macro-cracking) from a variety of nano-/micro-mechanisms, including, for example, twinning, stacking faults, slip, dislocations, amorphization, micro-cracking, micro-cleavage, phase transitions, localized melting, etc., which is quite different from metallic ductility mechanisms, although in AlN dislocations can play a significant role in the plasticity [41–45]. It was shown quite definitively using systematic confined high strain rate Kolsky bar experiments on AlON that the presence of defects can prevent the activation of these quasi-plasticity mechanisms and that the material will fail prior to the formation of a significant amount of quasi plasticity [46]. The defects can be any of the following stress concentration entities: inclusions, large anomalous grains, porosity, macro-residual stress, micro-residual stress and micro-cracking at grain boundaries due to thermal expansion mismatch and anisotropic elasticity mismatch,