CRACKS, COMPOSITES AND TEETH R.J.C.Wilding. BDS, Dip Pros. M.Dent. Ph.D

One of my children seems to leave a trail of wreckage. Ordinary every day items like door handles and toasters disintegrate in her hands. Her indignant defence is that it was already half broken anyway. This seems a poor excuse for the use of excessive force, but it may often be true. It does seem as though nothing breaks with just one catastrophic rupture.

A block of homogenous material under a uniform tension has an even distribution of stresses through the material. If a small crack appears, perhaps due to a local flaw, the stress in the block tends to extend the crack even further apart. This happens because the stresses which were shared out evenly before the crack developed, are now concentrated at the crack tip, making it more likely for bonds to break there than anywhere else. The crack may propagate very fast, or progress in spurts as the pattern of stress in the block shifts, due perhaps to other cracks developing. Whatever way it goes, and however fast it happens, when a structure breaks, it happens as a series of developing cracks, not a simultaneous rupture of all its internal bonds. So, when the garage door finally comes off its hinges, we have all contributed a few cracks. Its strange though, that it always seems to be the same member of the family, who is around when something finally breaks off.

Stresses will only concentrate at the crack tip, in a material which is very rigid and unyielding. Brittle materials like porcelain, glass and cement, have very low tensile strengths because they crack so easily. In a material which contains sites of more ductile material, the crack opens by deforming the softer material instead of breaking the bonds of the more brittle parts. The inclusion of less brittle components in a material, may therefore act as crack stoppers. There are special advantages to be gained if the resilient component is a fibre.

When fibres are dispersed in a matrix or binder the properties of the composite material may be a useful blend of both fibres and binder. Even if a few fibres break in the path of a crack, they do not completely lose their contribution to resisting tensile forces, which they would do if not bound in a matrix. Composite materials are both strong and light in comparison with single phase materials. The newer carbon fibre and aramid fibre composites are stronger than steel but only 20% of its weight.

One of the requirements for a successful composite is good adhesion between the fibres and the matrix. While glass fibres bond well to resins, they do not bond to builders cement. The adhesion of some fibres can be improved by coating the fibre with an agent which will adhere to the matrix. The ceramic particles in dental restorative composites are coated with a silane coupling agent to improve their adhesion to the resin matrix. Another requirement is that the fibres should be long. This is for two reasons. Firstly, if they are short they may pull out of the matrix without breaking. Secondly, the orientation of long fibres can be controlled more easily that short fibres. When the composite is being made the fibres can be placed in line with the expected tensions the structure will have to meet when it is in use. A woven fibre system, such as a fabric, resists tension best along the warp and the weft. Many composites are built like plywood, with several layers, each with its own specific contribution to overall strength.

The strategy of incorporating fibres into a brittle matrix can be traced back 500 million years. During the Devonian period, a new skeletal material appeared in the Osteichthyes which outclassed the other vertebrates who had skeletons of cartilage. These fresh water fish developed armour plates under the skin around the head; a successful form of protection for their brains, which to this day, we have retained. This crucial development required a new line of cells with a special capacity. They formed collagen fibres and a ground substance like cartilage, but in addition, they were able to concentrate calcium phosphate, until it would precipitate as crystals in between the collagen fibres. The resulting material, was bone. It had the advantages of the compressive strength and hardness of the bone salts (apatites), and solved the problem of their brittleness, by incorporating collagen fibres to act as crack stoppers. The fibres of the first formed embryonic or woven bone are a tangle, giving no particular strength in any direction. The demands made by weight bearing vertebrae and limbs would not be met without some refinements to such a disordered composite.

A natural composite which is obviously more structured than embryonic bone is wood. The fibres of wood are orientated along lines of tension, which makes it susceptible to splitting along the grain but very difficult to crack across the direction of the fibres. The fibre orientation works for trees, but when timber is used for building it is often laminated to prevent it splitting. It is the orientation of each layer in plywood which contributes to its strength. Lamination toughens materials even if there are no actual fibres. Samurai swords were made by repeated softening, rolling and folding of the steel blade, in the same way flaky pastry is made. The result was a sword resilient enough to withstand the clash of armour in battle, but so hard, that it could be honed razor sharp.

The legendry test of a good blade was that it should be able to slice through a silk handkerchief tossed into the air. It is fibre orientation and laminar structure which takes bone the crucial step from embryonic, woven bone to the order and strength of compact bone. The metabolic unit of compact bone is the osteon, a rod with concentric laminations, like the layers of a leek. The collagen fibres run in a concentric direction around each lamination and in a longitudinal direction down the length of the osteon. Down the middle runs a bundle of blood vessels which provides the transport and energy required for the regular replacement of bone in the osteon. The osteons are packed together into compact laminated bone and aligned along the length of a thick tube which makes up the shaft of long bones.

Synthetic composites follow the same rule of fibre orientation as bone does. The steel fibres of reinforced concrete can be seen sticking out of the ground on building sites, before the concrete is poured around them. A more sophisticated arrangements of fibres in a composite can be found in the drive shaft which links the tail rotor of a helicopter with the motor. The shaft must be long and thin but not whip or wobble. A system of circular fibres prevent collapse in the middle of the shaft; a helical pattern of fibres resists twisting of the shaft and longitudinal fibres prevent the shaft wobbling.

Teeth are composites of enamel and dentine and each of these material is itself a composite. Enamel consists almost entirely of hydroxyapatite crystals but there is a regular alignment of the crystals within each enamel prism. Within each tooth the enamel prisms radiate out, at right angles to the dentine core. So the crystal and the prisms of enamel comprise a sort of fibrous element rather like wood. And like wood, enamel is particularly vulnerable to splitting down its length. Every undergraduate dental student is taught to remove unsupported enamel from a cavity preparation, because if left, it will flake off later leaving a marginal defect. The earliest type of enamel, still found in sharks, has no prisms but is just a random arrangement of crystals which gives it great compressive strength. What selective advantage could mammals have derived from enamel prisms which were vulnerable to cracking off? In order to chew food, mammalian teeth have to work like any other cutting or grinding tool. The cutting edge must be sharp; close to it must be an escape-way for food particles, so as to avoid clogging the cutting edges. Mammalian teeth are not made ready to use; they only become sharp, after the rounded cusps have worn down, exposing a hard edge of enamel and a depression of dentine next to it. Some small mammals actually grind their teeth in utero so that when they are born their teeth are ready to go to work. Enamel prisms lie at a right angle to the surface of a tooth. As wear occurs, the edges of enamel do not round off and get blunt,

the way enameloid would do after small bits had flaked off; instead a whole prism comes away, the entire width of the enamel, leaving a flat blade with a sharp square edge. The carnassial teeth of a carnivore will have just one sharp edge, the molars of a herbivore will have a whole battery of them. So, far from being a backward step, the enamel prism was a selective advantage to mammals because it maintained a sharp cutting edge to chew on, something enameloid could never have done.

Dentine is also a composite, with the same bone salts as enamel, but in addition there is a significant component of collagen fibres. While a crack proceeds rapidly down the length of an enamel prism, it is halted when it reaches dentine. The forces at the tip of the crack are dissipated by deforming the more resilient material. The enamel crack also meets up with a fibre system which is running at right angles to the crack. For the crack to continue it would have to break through a web of collagen fibres. Thus while dentine would crack at a tangent to the pulp, it is less likely to crack following the path of an enamel fracture. The combination of enamel and dentine results in a tough tool for cutting and grinding food. Consider that the forces generated by the human jaws may be as high as 200 kg, and that these forces must be quite insignificant in comparison to the bone cracking power of carnivores like hyenas. The teeth are the tools which convey these forces, without showing any sign of breaking up under such stresses. Yet the destruction of teeth does occur, not due to cracks and fractures, but in the silence of an attack by acids.

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