Cracks

The diagram below shows how slumping can occur on a hillside or an embankment. The ground often breaks along a roughly cylindrical surface.

These lines were made using pseudo- random numbers to simulate random deviations from a line. There is some resemblance to the cracks, which roughly follow the stress lines, but are deviated by random variations in the ground.

The cracks shown below developed in a flat footpath on flat ground. Once cracks have opened, they can let in water, which in frost conditions can cause more damage. Another agent is the arrival of seeds and the growth of plants. In spite of their name, the Saxifrages cannot actually break up rocks: they only grow in existing cracks. But once a rock has cracked, the development of plants, especially trees, can accelerate the process of breaking up, as the roots spread and more soil is generated. Fungi, too, can generate enormous pressure. The fourth picture shows a piece of tree bark. The picture has been stretched lengthways by about 30 %. The pattern seems to be somewhat similar to the patterns of the cracks in the path.

The sixth picture shows plants that have taken root in the crack between kerb-stones and pavement. Without maintenance, many structures will slowly degenerate into wildness. That doesn't mean that we cannot allow pockets of wildlife habitats here and there.

This plant takes advantage of a crack in a rock in the Alps. No plant can break a rock, not even, in spite of its name, a saxifrage. What they can do is to help the process of colonization by living things. This helps the process of increasing the amount of soil. Moisture in the soil can freeze, exerting forces on the rock as it expands. Over a long period, rocks and walls can slowly disintegrate. During this period they can be a home for many different kinds of animals, from woodlice to snakes.

Plants such as buddleia, growing on a building, are a sign of neglect.

Let's calculate the total force due to atmospheric pressure on the fuselage of a large airliner, such as a Boeing 747. Let's use a cabin length 57 metres and a cabin diameter 6 metres.

The area of the cylindrical surface is roughly 3.14 X 6 X 57 m², which is about 1100 m². If the cabin is pressurised to the equivalent of 2500 m, and the aircraft flies at 10000 m, the pressure difference across the skin is about 0.075 - 0.025 MPa = 0.05 MPa. Multiplying this by the area gives the total force, about 50 MN, equivalent to 5000 tonnes.

To find the energy stored, we can multiply by half the radius to get a rough value, giving 75 MJ. That's a lot of energy. If an explosive decompression occurs, the result is quite unpredictable. A Boeing 737 survived the loss of a huge piece from its fuselage, forward of the wing, and was landed successfully. But in other cases, quite small holes, caused by explosions or structural faults, have had catastrophic consequences. The famous early example is the loss, in 1954 of Comet 1s G-ALYP and G-ALYY, caused by explosive decompression.

Metal Fatigue

A test at RAE Farnborough using Comet 1 G-ALYU duplicated the cracking of the fuselage after many cycles of compression and decompression. By using water instead of air the energy released was held to a low value, because of the minute change in volume of water when subjected to a change in pressure. A decompressing airliner has to get rid of two-thirds of the air in the cabin to equalize the pressure.

Since that time, examples of airliners are subjected to load simulations on the ground at a rate that keeps "aging" much faster than the ones that are actually flying.

The Comets are now a part of history. But history isn't bunk, and all designers now know about "metal fatigue". When a piece of metal is stressed to a level below its elastic limit, and then let go, it will return exactly to its original size and shape. But in some cases, the appearance is deceptive. The structure of the material has changed, extremely slightly, but changed nevertheless. After another application of stress it has changed again. The effects accumulate. The material contains its own history. The Comets that crashed were not the Comets that left the factory. In effect, at certain highly stressed places, such as at the corners of holes, they were made of weaker material than those that left the factory.

Newspapers occasionally report the finding of cracks in aircraft. In many cases these can be tolerated because the structure is designed to prevent the cracks passing certain boundaries. Nevertheless these cracks are watched during periodic inspections.

See "Black Box" by Nicholas Faith (Boxtree) ISBN 0 7522 1084 X, and "Air Disasters" by Stanley Stewart (Ian Allen and Promotional Reprint Company) ISBN 1 85648 182 4.

Cracks in Concrete

Cracks in reinforced concrete bridges can sometimes be tolerated unless they allow the entry of so much moisture that the steel rods are endangered by corrosion. They are caused by tensile stress, which stretches the reinforcing bars.

When cracks appeared in a concrete bridge designed by Robert Maillart, he didn't respond by strengthening the design for subsequent bridges. He realised that the concrete wasn't actually doing much, and removed a large section, resulting in an elegant design that evolved further during his lifetime and has been influential ever since. Robert Maillart The discovery of a new phenomenon in engineering or nature has often resulted from an observation which could easily have produced a different response.

Microscopic Cracks

A small glass fibre used for optical communication can suffer from the creation of cracks if it is bent too sharply. Each crack can scatter some light out of the fibre, or at least in the wrong direction. The loss in dB per km will increase.

But very thin fibres of glass and other substances can be relatively very strong compared with larger samples, simply because the probability of a crack existing is small.

Why do holes have such a dramatic effect on cracks? Look at the diagram below, showing a piece of metal with two small notches in it.

If we apply a tension to the object, we might expect that in the two planes including the notches, the stress would be slightly increased because of the slightly reduced cross-sections, with a stress flow somewhat as in the diagram below. We would be wrong - very wrong.

Remembering that the stress is greater where the lines are closer, we see that a large part of the bar has greater energy than it would have without the notch. What actually happens is that any stressed object tends to the configuration of minimum energy. In this example such a configuration of stresses is much like the one without a notch, but with a perturbation around the notch. The area of higher energy is quite small. It is called a stress concentration.

Around a sharp notch the effect is rather like the diagram below.

The smaller the radius of the tip, the higher the stress. So we can stop a crack from propagating by cleanly drilling a relatively large hole at its tip. That's not a very good solution for a boat or an aeroplane, but it's better than having a crack go right round. This contrasts with the use of holes to enable postage stamps to be pulled cleanly from a sheet. Once the crack starts to lengthen, the remaining material is narrowed, and the stress increases. Eventually the rate of movement becomes catastrophic.

Railway lines can crack. If the crack becomes a break, a train can be derailed. If the crack is detected while it is short, the surface of the rail can be ground off. The rail may be "weaker" by a couple of mm, but in a sense it is stronger, because the crack has gone. Grinding off not quite enough is no good, because it leaves the deadly tip of the crack, ready to propagate again. The combination of a crack and the intermittent loads from the wheels is a recipe for fatigue.

What do you think were the causes of the cracks illustrated below left? And what governed the direction of propagation? Why didn't they propagate vertically by zig-zagging among the bricks? What about the one shown below right, where a wall butts on to a building? In contrast to some of the other cases, this crack has gone right through several bricks.

Although holes can be used to stop the propagation of cracks, they are commonly used to help the separation of postage stamps, kitchen tissues, and many kinds of forms which have a return slip.

Notches may also be used to induce breaking in controlled circumstances, making a mechanical equivalent of an electrical fuse. The launching cable of a glider has a weak link which is typically a strip of metal with a round cut-out on each side. This link is designed to break at a force below the maximum allowed tension for the glider.

Thermal Expansion

Thermal expansion of long objects requires measures to counteract the possibility of damage. Many railways have gaps between the rails to allow for expansion. Many bridges have gaps between sections, with rollers to allow for changes in length. Long pipelines have bends or meanders to allow for changes in length without cracking. Large, fast aircraft such as Concorde expand significantly at cruising speed. Since they employ so many different materials, great care must be taken in the design, especially of the longer parts.

You create a work of art based on two big sheets of glass. It is shipped to an art gallery. When the crate is opened the glass is found to be cracked all over. What do you say? When this happened to a famous work by Marcel Duchamp, he did not seem to be annoyed. Other versions exist without the cracks.

Can cracks ever be useful? These are cracks in the glaze of a small Japanese cup. They are induced quite deliberately by using a glaze that shrinks much more than the ceramic on cooling. Some ceramics even have two layers with different average sizes of the cells, creating an interesting effect. Good examples of crackle may be found in Song Guan ware and Longquan ware from China. Excellent examples may be seen in the Baur Collection in Geneva, the Percival David and British Museum collections in London, and the Ashmolean Museum in Oxford.

The initial cracks may follow the stresses induced when the pot was thrown. Note how the cracks generally meet at angles that are close to 90 degrees. Suppose that one crack has already been created. As the glaze shrinks, there will be tensile stress in all directions. But tension cannot cross a crack, and so, close to a crack, the tension must be almost parallel to the crack, causing new cracks to be at right angles.

This type of effect can sometimes be seen in old paint on a bridge, and also in the reflecting film that is sometimes glued to windows. On a gigantic scale it can be seen in Arctic and Antarctic pack-ice when it begins to break up.

A large-scale map of field boundaries can show similar effects. Some of the field boundaries in this picture are curved to avoid very acute angles. The distribution of angles is clearly biassed away from zero and towards ninety degrees. Why do you think this was done?

Here is another picture showing field boundaries. In many areas of Britain, stone walls and hedges mark boundaries that may be centuries old.

Here are more examples of multiple cracks

If a crack propagates towards another crack at a shallow angle, it will turn towards the earlier crack as it approaches it, as if attracted, because it forms at right angles to the tension. In a sense the cracks reveal a history of the stresses in the glaze. The big frog is one of the series "Raku Creatures" by John Hine. Raku ware was created by Chorjiro Raku, a Korean potter, and his assistants, who emigrated to Japan. The last picture illustrates the history idea, very well, because the helical trend of the cracks around the side of the bowl shows how the bowl was turned, rather than moulded.

Unwelcome patterns of cracks are sometimes seen in old layers of paint and other coatings.

The development of cracks like those in glazing can be rather like the development of streets in an old village. Perhaps three or four roads meet, and a ribbon of houses appears along each. Then a road or two may be built between some of these main roads. Over the years a network of roads builds up. In some cases the roads imitate cracks by bending to meet a main road at right angles, to aid visibility for drivers. Older junctions may have quite acute angles. This might happen as in the imaginary example below.

Here is a small town in which these processes of growth have been happening over a long period. Sometimes the growth is not organic, as when an area is stripped out and replaced in a modernizing program. Then an entire suburb is often planned at one time. Nevertheless, the roads often still meet at right angles despite the curves that the designers put in.

When a town or city becomes large enough, it may be furnished with very large roads and ring-roads. These act as huge cracks which cut through between neighbourhoods, making movement between them difficult, except by subways, or footbridges with long ramps, difficult for people with prams or baggage, old people, and people with disability. Railways have been separating parts of towns for much longer.

The patterns of the fields form a record of history, if only we could read it. When we look at the patterns of the fields in the pictures above, we cannot now discover the alliances, marriages, quarrels or feuds that may have led to the creation of these patterns. We certainly become aware of history when we are on a country road which has too many corners, and seems to go round three sides of a square all too often, and all because some people would not let it through their land.

This view of Paris reminds us that human constructions are sometimes extremely geometrical without using right-angles. La Place de l'Etoile, with its twelve radiating streets, is visible in this picture.

New York city, on the other hand, represents the extreme domination of the rectangle. This type of construction is found all over the world. It is, of course, not new. Grid layouts, with due care about alignment with the compass and with geographical features, are found in ancient Chinese and Japanese cities. Kyoto's grid is aligned N - S and E - W, and is situated in a propitious site with hills to the north, east, and west.

Large numbers of fields or streets are collected together in large units, such as parishes, rural districts, and urban districts. These in turn are grouped into counties. In a large country like the USA, a large number of counties comprises a state. At all levels, from field to nation state, boundaries are sometimes natural, for example rivers or mountain ridges, or artificial, often being straight lines.

During periods of stress or conflict, the effects of boundaries between people can be as divisive and complete as those of cracks in metal.

This part of a dragonfly wing shows clearly how the main wing veins turn towards the trailing edge, for the same reason as new cracks turning to join old ones. Even the subsidiary veins tend to touch the trailing edge and the main veins at about 90 degrees, whereas in the tiny cells the angles are often around 60 degrees, minimising the material used, as in a honey-comb.

No detail is too small for nature to optimise, as long as the overall effect, however tiny, on reproductive probability, is positive. Nature has had plenty of time to get it right. In fact, this design has changed little in 200 million years. The picture below shows an even older design, a damselfly. It shows very well the strong leading edge, especially from the root to the nodus, and the more flexible trailing edge, which helps to provide the required changes in angle of incidence as the wing flaps. The arrangement of the veins has to satisfy the requirements of expansion of the crumpled soft wings after emergence, and also those of flight.

The cracks in this piece of wood are governed by the stresses. They resemble the lines of force in the space around two unequal electric or magnetic poles of the same polarity, as in the diagram below. When electric lines of force reach a conductor, they do so at right angles, just like cracks reaching an edge. At the top left of this picture you can see the cracks curving towards the edge like the dragonfly's veins. This piece of wood probably comes from a place near a fork in the trunk.

In a more typical piece of wood the cracks have radial symmetry, apart from the usual small irregularities. In the second example there are a few tangential cracks and some cracks along the direction of cutting. Cracks in dried out ground often form at angles nearer to 60 degrees than 90 degrees, because they can result from simultaneous stresses rather than sequential ones.

Here we see some cracks from the side. Presumably they are radial within the wood, like the ones in the previous pictures.

The deviation of the crack near the knot reveals something about the stresses in the wood in that region.

Great cracks can open in the earth as a result of faulting and earthquakes. Even quite narrow cracks on hillsides can open up into great valleys as a result of subsequent erosion by water and weather. Cracks can result from sliding (shear) or from pulling apart (tension).

The Great Rift Valley in Africa and the San Andreas Fault are two famous examples of fault action. The Great Glen in Scotland can easily be seen on a map, slicing Scotland in two.

The great tectonic plates are moving at rates up to centimetres per year, some sliding past one another, others pulling apart as hot material wells up from below. The Mid-Atlantic Ridge is a classic example. It even emerges from the ocean, in Iceland, where frequent volcanic eruptions reveal clearly that the earth's activity has not died down. Presumably this activity is fed partly by long lived radioactivity deep below the surface.

These movements produce the longest cracks on earth. Some are direct discontinuities between plates, where material is upwelling from inside the earth: others are transcurrent faults and transform faults where the location of a spreading ridge undergoes a sideways dislocation. Yet other discontinuities occur where one plate is subducted under another.

Such is the progress of technology that space craft can transmit photographs of cracks on the moons of the giant outer planets.

Here are some landscapes resulting largely from glacier action following orogenesis.

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And here are some actual glaciers and snowfields.

< Big JPEGs >

Near the top of a glacier there is often a crevasse called a bergschrund, where the moving ice and snow have pulled away from the material which remains attached to the rock. Crevasses aren't dangerous unless you fall in. If there is a snow bridge the crevasse can be undetectable, even if you are looking for the signs.

But the really dangerous cracks in snow are those that precede an avalanche. Merely walking or skiing across a large slab of snow that overlies a poorly attached layer can start a crack. After that, everything moves with great speed. Escape is unlikely.

Although a large piece of ice can be shattered by a hammer blow, ice can flow slowly under pressure. In a glacier that is hundreds, or even thousands, of metres deep, the pressures are enormous, and the ice flows inexorably downwards, deepening its own valley using rocks embedded in its base.

But where the ice passes a change of direction or slope, the ice cannot respond quickly enough, and huge crevasses open up. These cracks show clearly where the tensile stresses are too much for the ice on the operative time-scale. As a glacier flows over a cliff, pieces of ice as big as a house may break off and fall to the next level. These are bad places for mountaineers. Huge cracks in ice are seen during the annual break-up of the Arctic and Antarctic ice sheets.

In the physics department of the University of Glasgow there is a model of a glacier, consisting of a block of pitch in a wooden box which is divided into two levels. The box has a slot at one side. Since the model was made in the 19th century, some of the pitch has flowed down from the upper level, like a glacier, with a wrinkled surface that looks very like an ice-fall.

These behaviours remind us that the distinction between solids, liquids and gases is not always as clear cut as we sometimes think. At sufficiently high temperatures, the interface between a liquid and its vapour vanishes, and cannot be recreated by any amount of pressure. That temperature is called the critical temperature

Substances like glass will slowly flow if given enough time and stress. They are like supercooled liquids, without the crystalline order than is typical of so many solids. But glass will crack and shatter if stress is too large or too sudden. Lead, too, can creep down a slope. These effects can sometimes be seen in old buildings.

Liquids and gases are not associated with cracking, but even they can exhibit discontinuities. We even speak of the crack of a whip. If the position of the sun is right, you can sometimes see the position of an incipient shockwave over the wing of a Boeing 747, as the sharp change in density refracts the light. Water can undergo cavitation behind propeller blades, causing serious erosion as the water collapses back on to the surface.

We see that discontinuities in a material can be caused by static forces which are too strong, or by more dynamic effects on a time-scale which is too fast.

What are the smallest possible cracks? The smallest objects known to take part in collective motion are quarks and gluons, in a quark-gluon plasma. As this is not solid, this medium cannot crack. On the next scale up, nuclear matter is a candidate. There is not enough material in a nucleus to form a solid substance, but in a neutron star it is conceivable that there are solid regions, in which dislocations would be possible. As the neutron star loses energy, there could be internal rearrangements, causing fault lines and star-quakes.

In aerodynamics, narrow gaps can be deliberately introduced in order to increase lift. Many large aircraft have leading edge slats which are moved forward to provide extra lift for take-off and landing. Although leading edge slats (Kruger slats) can be formed by simply hinging parts of the leading edge, providing slots under the slats has a dramatic effect on the air-flow. Some tailplanes have permanent slats. Similar slots are provided between trailing-edge flaps. The wing-tips of large soaring birds have several slots between the feathers.

Other deliberate slots in aircraft are used to make efficient radio aerials without protrusions into the airflow.

Your train starts to move. Slowly but surely, so very smoothly, it accelerates. You finally get past the train that was next to you in the station, and then your brain does a double-take. It was the other train that was moving, not yours.

We are so used to smooth changes in energy that we take it for granted. Yet this could be an illusion. At the microscopic level, things are very different. Electrons can behave like waves. Waves in a crystal exhibit behaviour that seems strange to us. Certain ranges of wavelength in a periodic cannot be sustained. Because wavelength is related to momentum, and therefore to energy, a crack opens up in the allowed distribution of electron energies in the material.

This gap is not a gap in physical space, but in an abstract space, and it is not a crack in the sense that it can propagate. But it is as real as a crack in a piece of metal. The effects are profound. The distinction between conductors and insulators results directly from it, and the properties of semiconductors depend on it. Most of modern electronics depends on these behaviours. And the understanding of the chemistry and physics of materials has developed largely as a result of quantum theory. What was once a specialist theory now affects every aspect of our lives.

An extreme example of this type of gap was invented by Paul Dirac, who suggested that electrons could have any energy, except for values between m_ec² and - m_ec². The ones corresponding to negative energy were later found to be anti-electrons.