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OCR for page 39
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
OCR for page 40
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
OCR for page 41
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
OCR for page 42
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.
OCR for page 43
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.
OCR for page 44
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
OCR for page 45
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.
OCR for page 46
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
OCR for page 47
~ 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.
OCR for page 48
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.
OCR for page 49
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.
OCR for page 62
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
OCR for page 63
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
~ :CERAM£S
'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.
OCR for page 64
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
OCR for page 65
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)
OCR for page 66
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
OCR for page 67
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
OCR for page 68
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.
OCR for page 69
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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Representative terms from entire chapter:
hierarchical structures
