composites by zhangyun


									                        Natural composites

Bone: Hydroxyapatite (calcium phosphate) mineral ribbons
reinforcing collagen fibers

Horn and hoof: Keratin fibers stuck together with resin

Wood: Cellulose fibers stuck together by lignin and hemicelluloses

Insect Cuticle: Chitin fibers stuck together with resin. Mineralized
in crustaceans

The composition of bone is collagen 1/3 of dry weight, 50% of volume. The reinforcing mineral
is hydroxyapatite Ca10(PO4)6(OH)2, in plates 2nm x 20-50nm (aspect ratio 10-20). This (density
about 2 g/cc) is 65 wt%, 50vol% of the bone. Bone also contains water which keeps it tougher.

Bone is a short fiber composite. The crystals are ribbons with an l/t ratio here is of about 25. For
maximum strength we need an interfacial strength about 1/50-1/10 of crystal strength (=s c.t/2l),
but we don't know what is in bone.

The obvious advantages of the bone structure are the high volume fraction of mineral and its
parallel orientation. This is hard to achieve in moldable synthetic composites where the maximum
packing density is low.
Antler (totally different from horn, which is keratin) is selected for toughness, while
enamel has chemical resistance and hardness.

The mineral (HAP) modulus is 130GPa, the strength about 100MPa in an unnatural
sintered form.

Collagen has a modulus of 1 GPa, and strength of 50 MPa.

At 50% parallel fibers the modulus would be 65.5GPa according to the parallel model, the
serial model (for spherical filler or transverse fibers) gives 2 GPa. Hence bone is much
better than a simple filled composite.

The strength is better than any model as we can't get good HAP for comparison, it is not
even clear that a "reference" can exist except as a very long, 4nm thick, HAP ribbon.
Hydroxyapatite naturally contains a high level of carbonate. Fluoride can
be picked up to replace the OH, but fluorapatite is much less soluble. The
thin ribbon-like morphology is not formed synthetically, there is some kind
of control by the system.

Sharks have calcified cartilage, not bone. There is acellular bone in some

Shark teeth are fluorapatite, with F replacing the OH.

Bone remodels, grows on compressive, not tensile faces to strengthen
heavily loaded regions. The rules are not clear but may be driven by a
tendency to eliminate surface stress gradients.

Bone is piezoelectric and there has been discussion of whether control is
due to the piezoelectric response of HAP or collagen. It isn’t.
 Compact Bone
                  Parietal bone of the
Cancellous bone   skull: cross-section
                  Compare to metal: same
                      right through
Bone does not act as a simple solid material but is arranged in a
complex hierarchy.

a) Woven bone: Random collagen fibrils plus mineral

b) Lamellar bone: planes few microns thick, with a preferred direction
of collagen.

These two are arranged as Woven (W), Lamellar (L), Haversian
cylinders round a blood vessel (L) or Laminar (mix of planes of
W&L). These in turn are arranged at the higher length scale into
Compact or Cancellous. For cancellous bone the modulus is about
1/60 of compact and the strength 1/30. It provides a light support
structure to the interior of the bones.
Bone shows a 10% extension to break, 10x any equivalent synthetic
material. This occurs through microcracking, small holes forming,
probably between the lamellae. The tearing of collagen across these
cracks may be the source of the energy absorption and so toughness.
Exactly how this works is not yet known. John Currey is the expert in
this field and has written many reviews.
In compact bone the osteons run in various directions but with an
overall orientation. Hence the structure is not highly aligned and
modulus does not fall rapidly with change of angle. This agrees with the
intermediate modulus between the parallel and series estimates.
Joints between osteons may be a source of creep and splintering.
Fracture starts from osteocytes and blood vessels. These are the price to
be paid for adaptability. High rate gives smoother surfaces.
There is also calcified tendon, which works differently. In our tendons,
local calcification smooths the stress transfer to bone. Long turkey leg
tendons are all calcified.
Synthetic hydroxyapatite-polymer composites are much inferior to bone
How do bones grow? Around the outside and from the middle
Bone is a composite

Bone is Anisotropic

Bone is hierarchical

Bone repairs itself

Bone remodels

Growth factors control the deposition of bone and conversion of
mesenchymal cells to chondrocytes, osteoblasts, osteoclasts
                                Keratin Properties

Feather keratin: beta-sheet with an 8 GPa modulus. It is a block copolymer with
crystalline and non-crystalline regions, like silk. The choice for feathers is
probably based on stiffness/weight ratio.

Skin strength at low humidity is about 2 MPa, relatively low. The main function of
keratin in skin is to be a flexible barrier layer, so it must fail by intercellular
separation. It cracks when dry and softens when wet but is maintained moist but
not wet by a continuous flux of water vapor from the body. Amphibian skin is a
beta-sheet keratin because of the need to tolerate continuous water immersion.

Hair styling is a combination of stretching to beta sheet and recoiling in steam and
breaking and remaking the crosslinked amorphous material by mercaptans (-SH) :
R1-S-S-R2 + R3-SH <--> R1-S-S-H + R3-S-S-R2

Wool and hair are not uniform in cross-section but have a skin layer and a core.
Why is not clear.

Keratin seems like a real plastic: available as moldings, films and fiber with
properties tuned to the application.
The modulus of wool is 1.2 GPa and that of hoof and hair 4GPa. Yields at 150 MPa,
modulus drops to 0.4 GPa after yield as the chains unravel to beta-sheets.

Keratin is very tough (excellent for hooves), and has a high hysteresis, due to the alpha-
beta transition.

This insoluble polysaccharide is expressed and embedded in a swollen

Mechanism of formation unknown?

Oxidative cross-linking hardens the protein to form hard cuticle.

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