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3 SYNTHETIC HIERARCHICAL SYSTEMS INTRODUCTION It can be seen from the prior chapters that lessons can be learned from nature that may, if carefully deciphered, point the way to design of new classes of synthetic hierarchical materials. However, a number of caveats are in order. Vincent and Srinivasan (1992) point out "good scientists borrow ideas, but great scientists steal them. The greatness lies in realizing that an idea is worth stealing. Just as we need to know what ideas are available to be stolen from nature. . . we need to be sure that they are worth stealing...." This warning is appropriate for a number of reasons. The three examples that follow illustrate some of the dangers involved in copying from nature without thorough mechanistic understanding. First, natural materials are, more often than not, multifunctional. For example, the architecture and morphology of the cellular structures of woods provide strength in bending and compression, as well as resistance to fracture. However, channels in the structure are present that serve primarily a transport function (for nutrition, building, or repair). The nonstructural functional architectural elements of natural systems should not be routinely copied into a synthetic analog. Next, Vogel (1992) notes that nature has a very limited range of materials with which it works. In rigid composites, these tend to be calcium carbonates, calcium phosphates, and silica. In mollusk shells, thin layers that surround the stiff ceramic constituents, such as those 39

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40 Hierarchical Structures in Biology as a Guide for New Materials Technology in nacre, are proteinaceous. In addition, although natural composites exhibit outstanding combinations of properties, these material systems and their constituent components exhibit these properties over a temperature range too narrow for most engineering designs. It is useful to learn rules about adhesion, architecture, and composite elements in mechanical collaboration from nature and to apply them to other material components to make analogous synthetic structures. The natural constituents themselves have deficiencies in levels of properties. Finally, the influence of moisture upon the mechanical behavior of rigid composites has been noted by Vincent (1990~. Stiffness in natural rigid composite materials, such as horn and mollusk shells, diminishes with increasing moisture. However, the ductility and toughness increase dramatically as moisture content increases. With removal of the moisture, the mechanical effects appear reversible. In fiber-reinforced polymer-based composites that absorb significant amounts of moisture, stiffness decreases, and after an initial increase toughness eventually decreases. These effects are often not reversible upon removal of moisture. In order to focus on potentially important rigid hierarchical structures, it is useful to cite the case of nacre, which, as shown in Figure 3-1, exhibits better fracture toughness than most monolithic ceramics. It also has reasonable levels of specific strength. It should be noted that nacre is a highly filled polymer-based composite, with the filler being an ordered platelet ceramic (CaC03) phase in the form of flat hexagons. Other mollusk shells with different structural morphologies, such as prismatic and crossed lamellar (like plywood), are also highly filled polymer-based composites and also have interesting properties (Vincent, 1990), but they have not been studied to the extent that nacre has. Other rigid biological materials that have been studied include wood (Jeronimidis, 1980) and nut shells (Vincent, 1993~; the latter have been studied less extensively than the former. Modeling in these complex structures is still at a fairly early stage. Detailed studies of nacre show a wide range of micromechanisms of deformation and failure that have been observed in high

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ynthenc Hierarchical Systems 20 In 16 12 8 Al ~ 4 LL 41 . _ i/Co rufescens ~3-D'mensional ~ ~ ~ ~ ~(HP) ~ , 1 1 1 1 1 1 0 100 200 300 400 aminate Specific Flexural Strength [MPa/(g/cm3)] FIGURE 5-1 Fracture toughness versus specific flexural strength for abalone (Haliotis rufescene) shell nacre compared with monolithic ceramics and composites. Source: Sarikaya and Akesy, 1992. performance structural composites. A schematic example of the structure of nacre is shown in Figure 3-2. The toughening mechanisms revealed by fractographic analysis of fracture surfaces and indentation cracks include crack blunting and branching; microcrack formation; sliding and pullout of aragonite plates; polymeric ligament formation, akin to crazing, which bridges cracks; and possible strain hardening and shearing of the organic material. The challenge is to design synthetic discontinuous laminates that use as an example the architecture of nacre; that is, (1) lamination of the component phases should form a highly ordered microstructure; (2) the thick phase should have high hardness and be surrounded by the thin phase, which should be softer, tenacious, highly plastic, and capable of strain hardening; (3) interfaces should be strong but tailored so that delamination occurs before cracking across the stiff, brittle component; and, (4) no continuous path for easy fracture

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42 [hierarchical Snuctures in Biology as a Guide for New Materials Technology 4 microns ] 0.5 microns TSTRUCTURE OF ASSEMBLY _ _" ~ ~ ~ __ _ __ Aragonite Protein ~ COMPOSITION (BY VOLUME) Aragonite 95% Protein 5% FIGURE 3-2 Structure of nacre (echematic). should be presented (no interfaces should line up along directions of loading). When synthetic materials are manufactured with an emphasis on tailoring their properties through microstructural control, the extent of this control is generally at a specific length scale. For instance, the mechanical properties of most metallic materials are controlled through the manipulation of dislocations at the nanometer length scale, whereas the mechanical properties of ceramic materials are controlled through the propagation of cracks that are initiated from defects of micrometer length scales. For composites that are composed of two constituents, often of quite different character, the controls are much more complex even though mechanistic understanding in many instances is reasonably well in hand.

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Sy,Uhehc Hierarchical Systems 43 In contrast, many biologically produced materials, as discussed in the preceding section, are very complex in structural design at a spectrum of length scales that vary from atomic to macroscopic dimensions. These hierarchically structured materials display properties that are affected by processes that operate at all levels of the length scale spectrum. It is interesting to note that when attempts are made to engineer composites with performance-driven functions similar to those found in biological materials, the architectural design of the man-made materials also starts to display similar hierarchical features and multifunctionality. For instance, the architecture of fiber-reinforced automobile tires, which are designed to perform a multitude of functions, is very similar to the hierarchical design observed in intestinal tissue or elephant trunk. Several important classes of synthetic materials systems, defined by dimensionality, in which hierarchical architecture plays an important role are described in this chapter. The approach taken is to describe synthetic examples in one, two, and three dimensions. ONE-DIMENSIONAL HIERARCHY Polymeric Fibers All oriented polymers (net axial orientation function > ~0.7) possess a microfibrillar morphology. Synthetic fibers make up the largest group of oriented polymers, and all possess a hierarchical structure in the sense that they possess a repeat of fiber symmetry structure from the molecular to the macroscopic. The observation of hierarchical structure in synthetic fibers, as manifested in a series of district fibrillar substructures that have characteristic diameters in range from Angstroms to microns, is analogous to naturally occurring systems such as tendon, as described in Chapter 2 (Figure 2-2~. A summary of microfibrillar and hierarchical dimensions noted in synthetic fibers is shown in Table 3-1.

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44 Hierarchical Structures in Biology as a Guide for New Afatenals Technology The microstructure of synthetic fibers is made up of crystalline and noncrystalline elements. The choice of polymer and the details of the processing conditions control the ratio of crystalline to noncrystalline units, the net orientation associated with each phase (or subphase), and the connections between them. Synthetic fiber processing will be dealt with in more detail in Chapter 4. The microstructure of the typical 100-A-diameter microfibril can be described as an array of crystalline and noncrystalline elements in series, as shown diagrammatically in Figure 3-3. The crystalline portions of the fibril are characterized by size (normally hundreds of angstrom by about 100 A), net orientation, and nature of the crystal-non-crystal interface. While the equilibrium polymer crystal is composed of fully extended chains, kinetic conditions during practical crystallization almost inevitably cause the chains to fold, forming thin lamellar structures with the chains parallel to the thin dimension. While the regular nature of this folding and the concentration of tie molecules between lamellae are still debated in the literature, it is clear that tie molecule formation and less regular fold surfaces are aided by fast crystallization and chain orientation during or prior to the crystallization event. The thickness of lamellar crystals is a function of the temperature and time of crystallization, and lamellar crystals are subject to perfecting and thickening during annealing. The noncrystalline portion of the fibril is characterized by an orientation parameter and the concentration of chains that serve as interfibrillar tie molecules. For convenience and utility in property correlations, the noncrystalline portion of the fibril is often divided into two parts, an unoriented fraction (chains having end-to-end distance associated with the unoriented chain) and an oriented fraction that is characterized by an orientation parameter. The tie molecule concentration is difficult to measure explicitly and is usually deduced from thermomechanical measurements. In addition to these elements, microfibrils are linked together by intramolecular tie molecules. In highly oriented fiber structures, these chains are often fully extended and are referred to as the "extended chain" fraction in many models (see, for example, Ward, 1975~. When all of these elements are put into a model of fiber microstructure, what often emerges is a

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Synthetic Hierarchical Systems 45 TABLE 3-1 Microfibrillar and Hierarchical Dimensions in Angstrom Units in Synthetic Fibers (Tucker and George, 1972) Basic Fibrin Microfibril Fibril Macrofibul Cellulose and derivatives 3~75 Protein fibers 3~100 Polyacryloni~ile 50 Polyamides 30 Polyester Polyethylene 100 3SO, 35~500 800 4,000 100 250, 28~500 800-1,200 36,000 150 450 3,000 4,000 30,000 40,000 100 200, 40~500 2,000-5,000 30,000 40,000 100 200 400 1,200 5,000 30,000 40,000 100 200, 400 500 2,000-3,000 ~7 . ~it, \~1 W: \~11 ~ /1 MicrofibnIs I r Crystalline bridges Extended Chains FIGURE S-3 Microfibrillar structure with noncrystalline extended chain.

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46 Hierarchical Sn~uc~res in Biology as a Guide for New Afateno~ls Technology hierarchical structural array of interconnected fibrils in parallel, with each fibri! composed of crystalline and noncrystalline elements in series. Carbon Fibers Carbon fibers are produced through the orientation and subsequent thermal decomposition of hydrocarbon precursors (Edie and Stoner, 1993~. The dominant precursors for commercial carbon fibers are polyacrylonitrile (PAN) and pitch. Carbon fibers are composed of 99.9 percent pure carbon arranged into graphitic crystallites. As shown in Figure 3-4, the graphitic layer planes form imperfect crystals, referred to as turbostratic graphite, with slightly offset layer planes and increased interlayer spacing compared with pure graphite crystals. The fundamental properties of carbon fibers are a direct result of the carbon crystal structure and orientation. The layer plane orientation parallel to the fiber axis provides the high axial stiffness and strength because of the strong chemical bonds in the graphite layer planes. However, weak van der Waals bonds between layer planes lead to significantly inferior strength and stiffness normal to the fiber axis. PAN-based carbon fibers exhibit a fibrillar microstructure similar to that of the solution-precipitated PAN fiber precursor. The structure of a PAN-based carbon fiber has been modeled as an undulating ribbon structure of folded and interlinked layers, with the amplitude of undulation increasing from the fiber surface to the interior (Diefenclorf and Tokarsky, 1975; Johnson, 1987~. A schematic representation of the undulating ribbon model is shown in Figure 3-5. As a result of the structure of the precursor, PAN-based carbon fibers have a relatively low degree of axial orientation and low graphitization compared with pitch fibers. The microstructure of pitch-based carbon fibers is dictatecl by fiber spinning conditions and the resulting structure of the pitch mesophase precursor. Pitch fibers generally exhibit an extended graphitic-layer structure with high axial orientation and high

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~ If ~ direction ~7 ~ I... ~ a-direction , 1 3= ^ for Ma graph" & ~ _ =6^ ~ _ _ -~- ~ c-~irecllon FIGORE 3-4 Structure ~ Bite Id as approximate orientation in carbon fibers. Source: Edie and Stoner, logs. Figure 3-5 Schematic representation of undulating ribbon model of P~-b~ed capon fiber. Source: Johnson, lgB7.

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48 Hierarchical Structures in Biology as a Guide for New Materials Technology graphitization compared with PAN-based fibers. An example of the variation in pitch fiber microstructure can be seen when the flat-layer structure exhibited by Amoco's Thornel pitch fiber is compared with the folded-layer configuration observed in Kashima's Carbonic pitch fiber (Endo, l9RS). This is shown in Figure 3-6. Neither PAN- nor pitch-based fibers have optimized mechanical properties (Edie and Stoner, 1993~. PAN-based fibers, with their small crystallite size and imperfect orientation (caused by folded microstructure), have high strength and strain to failure but have relatively low stiffness compared with pitch fibers. In contrast, pitch- based fibers, with their high orientation and extended layer structure (large crystallites), have high modulus but lower strength and strain to failure than PAN fibers. Properties are compared in Table 3-2. Fibers from both PAN and pitch have poor compressive strength due to the low transverse strength, the deleterious effect of defects, and buckling instability. There are indications that irregularly shaped fibers could enhance compressive strength by increasing buckling stability and improve adhesion in composite applications (Edie and Stoner, 1993~. D7 Flat Layer Folded Layer , _ 1 (a) Thornel (b) Carbonic FIGURE 3-6 Microstructure for two types of pitch-based carbon fiber. Source Endo, 1988.

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Synthetic Hierarchical Systems 49 TABLE 3-2 Properties of Pitch-Based and PAN-Based Carbon Fibers Fiber Tensde Tenshe Padum In~r-layer Crys~dlim None Sponge Modulus Sawn q~s~g she den ~ (GPa) (GPa) (%) (nary) (nary) PITCH-BAS~D FIBER Thomel' P100 2.2 690 0.3 0.3392 24 P120 2.4 830 0.3 0.3378 28 Car bonicb H]450 2.8 490 0.6 0.3423 13 H~460 3.0 590 0.5 0.3416 15 H]480 3.5 790 0.4 0.3399 18 PAN-BASED FIBER TomycaC M46 2.4 450 0.5 0.3434 6.2 Amoco Performance Products, Inc. bKashima Oil Co. Moray Co. Source: Endo, 1988. TWO-DIMENSIONAL HIERARCHY Many examples exist of advances in the properties and performance of laminate materials (Wadsworth and Sherby, 1980~. Early classical work on steel laminates was the basis for Damascus steels, which were developed in the Middle East during the late iron age, more than 2000 years ago. The metallurgy that produced Damascus steel is based on a simple thermomechanical cycle that forms a composite microstructure of tough martensite containing ultrafine participates with hard strings of carbides decorating prior austenite grain boundaries. Many variations of these iron-based microstructures have since been developed by modifying thermomechanical treatments, most notably by "composite lamination," which incorporates both pure iron (soft and tough) and high and medium carbon steels (hard and strong). For example, the body of the samurai sword blade illustrated in Figure 3-7 is a hierarchical structure consisting of a soft inner core (ferrite) with a hard outer core (low-carbon martensite). The structure is formed through repeated folding and hammering of a laminated blank.

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62 Hierarchical Structures in Biology as a Guide for Mew Alatenals Technology monolithic material alone was able to supply. Early civilizations made use of rigid composite materials such as laminated bows employed for strength and straw and mud mixtures for building materials. They recognized that certain combinations of materials were synergistic for strength and toughness. In modern technology, the major attractions of synthetic structural composite materials are that they can be more resistant to high-temperature deformation, as well as lighter, stiffer, stronger, or tougher than their constituent single-component materials. Rigid synthetic composites are composed of two or more constituents in a wide variety of configurations. Some of these are shown by classification in Figure 3-15. Similarly, in natural biological materials, many diverse examples exist of rigid composites. Examples discussed in Chapter 2 include wood (Figure 2-4), bone, and the nacreous structure of a mollusk shell (Figure 2-5~. Composite Materials Fiber-reinforced Composites (fibrous composites) Single-layer Composites (including composites having single orientation and properties in each layer) Panicle-reinforced composites (particulate composites) Random Orientation Multilayered Composites Laminates Hybrids Continuous-fiber-reinforced Composites Unidirectional Bidirectional Reinforcement Reinforcement (woven reinforcements) Discontinuous-nber-reinforced Composites Random Orientation FIGURE 3-1S Classification methods for composites. Preferred Orientation Preferred Orientation

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Synthetic Hierarchical Systems Elastic Response of Rigid Composite Materials 63 In order to compare the behavior of some biological materials to synthetic materials, it is useful to look at functions of simple shapes. For example, if the goal is to minimize weight for a given stiffness for the buckling of a slender column or a tube, a plot such as that shown in Figure 3-16 can be useful. In this case, one can compare constant lines of VE/p, where "E" is Young's modulus and "p" is density, for wood products, synthetic polymers, composites, ceramics, and metallic alloys. 1000 C' - ~L 100 in J ~ 10 o An Ad o _ MODULUS- DENSITY , LON GITUOINAL WAY E VELOCITY _ ~ . ~_' 10'm/s ~ _ am. :':: . ~ ,''' ok' 3 x 103 m/s 1 01 1o3 Ql it,' ENGINEERING ~ :CERAMS 'a;) i- .., ~ENGINEER!N 'R'2'1 ~, ENGINEERING~ , ' COMPOSITE j POROUS \: .-1 CERAMICS a,' - '~ r ENGINEERING POLYMERS- | : :. :.:: 1 ..... ... . 1 ~ ~: j ~ x lO2m/s (ELASTOMERS 1.0 - .~ , ~ MFA/88 10 DENSITY, p (Mg/m3) FIGURE 3-16 The idea of a materials property chart: Young's modulus, E, is plotted against the density, p, for classes of materials. Log scales allow the elastic wave velocity ~ = (E/p)'h to be shown as parallel contours. Source: Reprinted from Act a Metallurgica, Volume 37, M. F. A'shby, On the Engineering Properties of Materials, Pp. 1273-1293, Copyright (1989) with kind permission from Eleevier Science, Ltd.

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64 Hierarchical Structures in Biology as a Guide for New Materials Technology For a better part of three decades, wide use has been made of the rule of mixtures for the analysis of simple composites undergoing elastic strain, for both particulate-reinforced ~ Broutman and Krock, 1967; Jones, 1975) and fiber-reinforced (Kelly and Davies, 1965) materials and for laminates (Lee et al., 1991~. This rule describes the elastic behavior of a continuous fiber- reinforced composite as: EC = VmEm + VFEF (age. 3-2) where: Ec is the Young's modulus of the composite Em is the Young's modulus of the matrix material Vm is the volume fraction of the matrix material EF is the Young's modulus of the fiber VF is the volume fraction of the fiber phase In the case of discontinuous reinforced composites, mixing rules are significantly more complex. Reinforcement size, shape, and distribution influence the behavior of the composite. For example, for a relatively simple case of a dispersion of cubic particles, the elastic modulus of the composite is (Iones, 1975~: Ec = Em + (Ep ~ Em) V2J3 Em Em + (Ep - E-)V213 (~-v1'3 where: Ec, Em and Vm are as above, and Ep is the Young's modulus of the particle Vp is the volume fraction of the particulate material

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Synthetic Hierarchical Systems 65 To account for directionality in laminates, two limiting cases that bound the elastic properties of two-phase composite systems are as shown in Figure 3-17. ,:3: a. Voigt Model (equal strain) / / FIGURE 3-17: Limiting cases for composites: stress (Reuse) model. / /,: ,,`~, - .~ ~ . ..! ,,, '.;'.,'%~',~',,',\~.4,-.,~...~ ~ ',.';'"'. me ,':: In' :~ b. Reuss Model (equal stress) (a) equal strain (Voigt) model; (b) equal The Voigt model (Eq. 3-4) is based on equal strain response in both constituents of the composite (Eq. 3-4 is essentially the same as Eq. 3-2~. The Reuss model (Eq. 3-5) is based upon an equalstress condition in both phases. EC ~ VFEF ~ (! VF) Em (Eq ) - E, (1-OF) c -F Em V P + ED (Eq. 3-5)

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66 Hierarchical Structures in Biology as a Guide for New Aiatenals Technology The foregoing basic relations have also been applied extensively in structural biomaterials (see, e.g., Vincent, 1990~. Ker ( 1977) modified the rule of mixtures relation for locust and beetle cuticles: EC ~ Em (~1-OF`) + EFVF (Z) (Eq. 3-6) where Z is a factor which is a function of stiffness, area, radius, spacing, length of fibers, and the change in shear in the matrix caused by the presence of the fiber. In a study of nacre (Jackson et al., 1988), a "shear lag" analysis by Padawer and Beecher (1970), which had been developed for platelet composites, provided a more complex relation for the modulus of the composite: Ec = Vp~ ED Let-1 (~ll~)/U] + (~~Vp) Em (Eg. 3~7) where: Ec is Young's modulus of the composite u = S{M Vp,/[Ep, (l-Vp,)~}'h S is the aspect ratio of the nacre platelet Vp~ is the volume fraction of the nacre platelet Ep, is the Young's modulus of the nacre platelet M is the shear modulus of the matrix This prediction and another shear lag model by Riley (1968) follow the trend of the actual mechanical behavior of nacre better than the predictions of the Voigt or Reuss models. However, additional refinement of the models is necessary. Analyses are much more advanced for synthetic materials, especially for polymer-based composites such as carbon-fiber- reinforced polymers or Kevlar-fiber-reinforced polymers. For those materials, a variety of plates and shell structures, including laminates, have been addressed, and simple structural load responses for configurations from idealized orthotropic to anisotropic to antisymmetric cross-ply and antisymmetric angle-ply composite

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Synthetic Hierarchical Systems 67 systems have been predicted with a measure of success (Hull, 1981; Ashton, et al., 1969~. The foregoing discussion centered on predictions of elastic moduli for synthetic and natural materials. However, precautions should be noted. As noted earlier, the moduli of many rigid biomaterials are very different in the wet condition than in the dry state. An example, given by Vincent (1990) is of horn keratin, which has a matrix phase Young's modulus of 0.9 GPa with 40 percent water and 6.1 GPa in the dry state. Similar effects, though perhaps not as dramatic, are observed in synthetic resin-matrix composites that take up moisture. Toughening Mechanisms for Rigid Composites Examination of the mechanical behavior of both synthetic and natural composites generally shows higher levels of toughness and resistance to cracking in carefully designed composites than in monolithic materials (Clegg et al., 1990~. Mechanisms for toughness improvements in ceramics and ceramic matrix composites have been described (Becher, 1991~. Among the examples cited are crack pinning, crack deflection, crack bridging and pull-out by dispersed particles and elastic reinforcing phases and grains, stress-induced microcracking, stress-induced martensitic transformation, and plasticity in metallic binder and dispersed phases. It has been demonstrated that providing weak interfaces in laminated ceramics can increase the work required to propagate a crack by a factor of over 100. A rationale for crack blunting in composite materials was provided by Cook and Gordon (1964~. The mechanism proposed is fairly widely accepted as being a major contributor to toughening of composites. The fracture path in nacre (mother-of-pearl) shows evidence of crack blunting and diversion (Figure 3-18~. The work of fracture is highly directional and is governed by crack stopping at interfaces, followed by crack diversion through delamination. The critical role of the thin matrix material between the ceramic (calcium carbonate) platelets making up simulated "brick wall" structure has been well established. The glue-like matrix, which is well bonded to the ceramic phase and is highly ductile, tough, and tenacious, is also complex in both hierarchy and function. Deformation and failure of the fibrillar structure of the matrix, the anchoring mechanism of the matrix to the ceramic platelets, the nature of the bonding between the

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68 Hierarchical Structures in Biology as a Guide for New Afatenals Technology complex constituents of the matrix (proteins, chitin), and the roles of different morphological types of superstructures (layer-laminated9 prismatic, cross-lamellar, etc.) all need to be studied more closely in order to arrive at directions for improvement of synthetic composites. ~:~:~:~:~:~:~:~: ..~ . . ~-- ~ -A If. FIGURE S-18 Fracture path through nacre. Source: Jackson et al., 1988. Tough laminate composites having high resistance to crack propagation have been mentioned earlier. The fracture of these metallic composites and the fracture of nacre that is illustrated above are similar in the blunting of cracks by delamination at the interfaces of the dissimilar layers during impact testing. If, however, interdiffusion occurs between layers in the metallic composite during processing, or if the bond strength is substantial, delamination may not occur, and the notch-impact properties will degrade. An example of a tough microstructure in a laminated composite of ultrahigh carbon steel and brass is shown in Figure 3-19.

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Synthetic Hierarchical Systems 69 FIGURE 3-19 Crack propagation in an ultrahigh carbon steel brass 40-layer composite. Courtesy D. R. Lesuer, Lawrence Li~rermore National Laboratory. In addition to crack blunting at interfaces, other energy-absorbing mechanisms can operate in both synthetic and natural composites. Shear yielding and microstructural defects that may create complex stress fields and cleflect propagating cracks can be effective energy dissipators. Strength Properties of Rigid Composites Strength properties of composites are not so straightforward as are elastic properties. Although mixing rules have been shown to be valid in specific cases, for example' tungsten wires in a copper matrix (Kelly and Davies, 1965), they generally do not work well for prediction of composite strength in inorganic crystalline materials because of factors such as the strong dependence of strength upon grain size, the presence of residual stresses, crystallographic orientation, etc. (Chawla, 1987~. Hull (1981) has described other

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70 [hierarchical Structures in Biology as a Guide for New Afatenals Technology possible complications that relate to a variety of failures that may occur within the composite locally before the ultimate strength is attained. For natural rigid composites that have a variety of reinforcements and matrices, and for adhesives, viscoelastic behavior adds other complications to strength predictions, as do factors such as nonlinear behavior of porous or cellular structures during deformation. The determination of the strength of composite structures and the prediction of mechanical responses to complex service environments have been studied in some detail (NRC, 1991~. The difficulty in the prediction and analysis of composite strength is compounded by the broad range of potential failure modes and operating environments. Composite failure modes tend to fit three broad categories: fiber- controlled failures, matrix- and interface- (or interphase-) controlled failures; or micro- and macro-instability failures. The dominant failure modes for composite structures include matrix cracking, delamination, tensile fiber failure, microbuckling, and global instability. Also to be considered is the effect that service environmental factors such as moisture, temperature, chemical or electrochemical interactions, and radiation have in altering the mechanical properties and hence the mechanical response of the composite system. Four factors have been identified that have hampered progress in the structural analysis of rigid synthetic composites and in the ability to predict failure events (NRC, 1991~: 2. 3. 4. implementation of design and analysis paradigms that neglect the effects of microstructural detail on the macroscopic response of composite materials; perception of the need to characterize fully the bewildering number of systems available; lack of consensus concerning failure modes and failure criteria; and persistent use of design and analysis paradigms that are based on metal technology. The same general inhibitions apply in the case of natural composites. While complex composite analyses have been undertaken, for example, on insect cuticle (Gunderson and Whitney, 1991, 1992),

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S5nthcac Hierarchical Systems 71 they have resulted in limited success. A better understanding of the micromechanisms of deformation and failure in complex systems and of the application of analysis methods on multiple size scales is needed before additional progress is made in analytical mechanics and in the development of suitable analogues of such natural materials in synthetic composites.

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