Cracks

with bits about dragonflies, fields, frogs, glaciers, pottery, railways, roads and trees

14th April 2001    Back to Bridges    back to Home Page

Here is a cantilever bridge of a type which is found in several places in Gloucestershire and Wiltshire.  This one crosses the Barnwood bypass, east of Gloucester.  There is another one about a kilometre to the east.  The narrow roads leading up to these bridges exhibit cracks which are typical of slumping on embankments.  The local ground is largely clay.  Pictures at right show some of these cracks.  The last picture shows soil nearby, cracking during drying out and shrinking.  Why do you think that the cracks follow the line of the footpath through the crop?

Shortly after the pictures were taken, some of the cracks were "repaired" by covering them with tar and gravel.  Shortly after that, the holes began to appear again.  Some weeks later, an entire new layer of tarmac was placed.

Here a crack that has been marked for "repair" has been populated by small plants.  Larger plants would follow, with the build-up of soil.  In winter, the freezing of moist soil would exert pressure on the sides of the crack.  Over the years, a neglected structure is gradually taken over by vegetation.

The picture shows the join between one cantilever and the suspended span of the bridge mentioned above.  Moss is beginning to grow in the space.  Eventually soil will build up, enabling small plants to grow.

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 next picture shows a modelling that allows for dislocations in the cracks.

We have to be very careful when simulating physical phenomena.  Firstly, we need to be sure that the pseudo-random numbers are "random" enough, that is, there are no correlations which could affect the results.  Secondly, we need to adopt the correct procedures.  The next diagram shows three different ways of applying random numbers to lines which propagate from left to right.

In the top curve the procedure was as before – to create a point, add a random displacement to the vertical position of the previous point.  In the second curve, the randomness was applied to the slope instead of the position.  This has the effect of reducing the higher frequency components: indeed there is a definite drift in one direction, corresponding to a very low frequency.  This operation is a crude integrator.  In the third curve, an effort was made to control the drift by applying a correction term which was proportional to the displacement.  An oscillation built up almost from the start.  

You can’t be too careful when simulating.  And this is only for a very simple system.  If you wish to simulate animal populations, global temperatures, and other complex systems, you need very carefully constructed computer programs in order to avoid artefacts.  The discovery of chaos theory sprang from calculations that were intended to be determinate, with none of the randomness used here.  The large long term effects of small changes in the initial conditions was a complete surprise.  It turned out that these effects were not artefacts: they were real, and so the existence of chaos began to be recognised.

Here, the pressure of the soil, and the waterlogged ground have caused a large retaining wall to move.

A crack has opened from top to bottom.  Apart from that, the integrity of the wall has not been compromised, but it will need watching from now on.

Once cracks have opened, they can let in water, which in frost conditions can cause more damage by expansion.  In spite of their name, the Saxifrages cannot actually break up rocks: they only grow in existing cracks, like the plant shown here (not a saxifrage).  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.  The soil holds water which can further damage the rock.  Fungi, too, can generate enormous pressure.  

The cracks shown in the first four pictures below, developed in a flat footpath on flat ground, within a year of construction.  The fourth picture shows red seeds that fell into the crack in the first autumn.  These seeds will probably not develop, because of lack of soil, but smaller species certainly will, allowing the eventual formation of soil.

The fifth and other pictures show 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 last pictures show plants that have taken root in the crack between kerb-stones and pavement, and moss, spreading from cracks in the pavement on a bridge.  Without maintenance, many structures will slowly degenerate into wildness.  That doesn’t mean that we cannot allow pockets of wildlife habitats here and there.

These plants take advantage of cracks in rocks 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, thus making cracks wider.  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 growing on a structure indicate neglect or age.  If you look above the ground floor of the buildings in a town, you may sometimes see shrubs, often buddleia, growing out of cracks or gaps.

Crack Generation and Propagation

Banging nails into wood introduces tensile stresses.  Eventually the wood may crack.  The last picture shows the final result on the right.

A problem with stress concentrations occurs in designing the fuselage of a pressurised aircraft, or the deck of a ship, when material has to be removed from the ideal tube. The fuselage of an aircraft has to be pierced by various holes for doors, windows, wheels, antennas, and so on. The openings have to be designed carefully, to prevent stress concentrations. The Comet 1 airliner suffered explosive decompression when fatigue, starting at a hole, resulted in catastrophic spreading of cracks. This phenomenon is now much better understood, and all designs would now include measures to reduce the probability of cracks being generated, and also measures to prevent their propagation over long distances in the structure.

Pressurised Aircraft

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 very 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 about 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.

If a square hole can generate stress concentration, what about adding a negative square hole, that is, doubling the thickness of a square area by welding to gluing a square patch to the surface?

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 just there, and he removed a large section, resulting in an elegant design that evolved further during his lifetime and has been influential ever since.  See 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.

Here are pictures of cracks in a piece of glass.  Glass is a rigid material, but it is not useful for large structures, because it cannot absorb much energy before breaking.  In other words, although it does not bend as much as some other materials, it breaks under a smaller deflection.  Glass is not normally a crystalline solid: in fact it behaves in some ways like an extremely viscous liquid.  When heated, glass does not melt at a certain temperature, like a metal, it slowly softens.  In some very old buildings, glass windows can be found that are thicker at the bottom, where they have slowly crept over the centuries.

Stress Concentration

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 indeed.

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 left.

In the picture at right, a piece of paper has been provided with a semicircular notch and a V shaped notch, and pulled.  It failed at the point of the V, where the stress was greatest.  Note the similarity to the cracks at the top of this page, and to a flash of lightning, though the details differ.  All these examples are a combination of randomness with a preferred direction of propagation.

If a narrower crack propagates more easily than a wider one, what about a substance with no cracks?  It could be thought of as having an infinitely narrow crack, which ought to propagate very fast indeed.  Look at the wording of the question – it is wrongly stated.  In what way?  Nevertheless, if we can pull hard enough to separate one plane of atoms from another, we have made a very sharp radius at the tip of the crack.

The diagram below shows a simulation of stress lines around a hole in a large slab, only a part of which is shown.

Compare this diagram with the photographs at left.  The same diagram can represent an electric or magnetic dipole in a uniform field, and the laminar flow of a liquid past a circular obstacle.  Pictures and films of Jupiter show similar effects around the great red spot, albeit with subsidiary loops.

The smaller the radius of a hole, or the tip of a crack, 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.  The example shows a piece of paper in which cracks have been persuaded to go towards the holes.

Here are pictures of pieces of plastic fencing.  This type of fence usually has rounded holes.  Sharp corners would make the sheets much easier to rip.

So – we have seen that cracks can start at a hole and finish at a hole, rather like the case of the man in the fable, who blew hot and cold with the same breath.  There was of course, good physics behind his actions – cooling his soup, he was blowing away some energetic molecules that had escaped from the soup, creating disequilibrium, and enabling more to escape, and he was using the expansion of his breath from a narrow orifice to cool his breath.  Warming his hands, he had his mouth wide open, and was blowing air on his hands that was warmer than the ambient air.

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.

Recently, after a derailment in England, a section of rail about 30 metres long was found to have broken into about 300 pieces.  That’s about one break per ten centimetres.  When you look at a rail, a long piece of tough steel, this beggars belief.  But think about it.  The carriages, and more especially the locomotive, are very heavy, and they rest on hard steel wheels.  Mathematically, a circular wheel meets a straight rail at a point, giving infinite pressure.  But of course what actually happens is that wheel and rail deform, elastically we hope, until the each is able to deliver the required pressure.  Nevertheless, the contact area is very small.

As the wheel rotates, the stressed area moves around the wheel, every part of the wheel experiencing an oscillatory stress, and an oscillatory strain.  The rail undergoes a similar torture.  This is a recipe for fatigue.  In older times, up to the mid-twentieth century or so, you could stand in a station and watch a man walking along a train, tapping all the wheels with a tool.  A cracked wheel, like a cracked bell, does not ring.  The defect damps the sound, and a short sound makes a wide bandwidth, producing a dull sound instead of a clear ring.  

This is a fundamental theorem in physics, and you can even find it in those unbelievably small objects, "elementary" particles.  Lives as short as 10^-23 seconds can be measured using not a stop-watch, but a weighing machine, because the weight is related to energy, and energy is related to frequency, and, as we saw with the bell, frequency bandwidth is related to decay time.  Many species of particles live so short a time that they cannot be detected, except by collecting the debris from their disintegrations and calculating the mass.  We’re way off the subject here, but that is what this web-site is really about:  everything is related to everything else.  You can go out and find your own examples – a better occupation than reading this.

The rubber tyres of a road vehicle or an aircraft also undergo cyclic stresses: you can see many a shredded tyre on or by the road, any day of the year.

If you stand in a station and watch a train slowly moving past, you can see what happens as the wheels cross the gaps in the rails, unless the track is a continuously welded one.  You see the track deform, producing a little step at the junction.  If the fish-plate is loose, the step can be quite big.  It’s not often that you can see the deflection of a structure, because it is usually too rigid.  Sometimes you can see the wings of aircraft bending, as they pass through air moving with different velocities.  The wings of a high performance glider may almost touch the ground when staionary, but as it gathers speed they start to straighten out and bend upwards.  During a launch by winch they bend even more than they do during normal flight: there is a launching speed limit for each type of glider.  You can see the same effect in a B52 at an air show.  The B47 was even more flexible.

Going back to the railway tracks, perhaps we can see why they are not just bolted down on to a "rigid" concrete road.  Usually the rails are bolted or clipped on to beams called sleepers, which rest on stone ballast.  Why do you think they are built like this?  Effectively each rail is a beam bridge on many supports, and the longest bridges in any country that has railways are the railways themselves.

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 left, 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.

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.

Useful Cracks?

In ancient times, one way to split blocks of stone out of a quarry was to insert dry wood into cracks or rows of holes.  Soaking the wood made it expand, causing the rock to break away.  Cleaving slate into thin plates makes a very good roofing material.  Another laminar mineral, mica, has been used for the windows of lamps, for the support of the heater in an electric iron, and for the insulator in a capacitor.

Imagine that you have created 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, the "Large Glass", by Marcel Duchamp, he did not seem to be annoyed.  Other versions of the work do not have 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, near a crack, the tension must be almost parallel to the crack, causing new cracks to be at right angles.  For the same reason, a crack will usually reach the edge of an object at about 90 degrees.

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 again, in the paint on a wall, we see the newer cracks touching older cracks at about right angles.  We also see some graffiti to add to the distress of the surface.

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 on a wheel, rather than moulded.

This piece of wood has a couple of places where cracks have curved to meet others at right angles, as in the pottery.

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.

Nobody would want to make something that broke on purpose, would they?  But an electrical fuse is a deliberate weak link in a system, designed to break when fault conditions threaten other components.  Fuses come in many kinds, slow-blow, quick-blow, semiconductor, and they all melt when too much current flows.  Once fused, they cease to conduct.  Other protection devices become almost a short circuit with over-voltage, clamping down the voltage to protect the system.

Mechanical weak links can be useful as well.  A glider launched by a wire from a truck or winch on the ground experiences a downward force in addition to its weight.  This imposes extra bending moment at the wing-roots.  To prevent over-stress, a weak link is placed in the cable, near the glider.  It protects both cable and glider from damage.  By making weak links from a standard material in a standard size, they can be made to perform reliably.  In the long run, of course, a weak link may fail from fatigue induced by the cyclic stress.  Normally it would be replaced before this happened.  Because gliders vary in size and weight, a gliding club may use two or more sizes of weak links, in conjunction with rules about launching speeds.  The diagram below shows a typical weak link.

In the Charpy and Izod impact tests, a V-notch is made in a specimen, which is then struck in a controlled way by a heavy pendulum.  These tests evaluate the energy needed to fracture teh specimen.

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 usually meet at about 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, leading to the expression "wrong side of the tracks", this, in Britain, usually being on the east side, because of the prevailing wind.

The first picture above shows the roads leading west from Cointrin Airport, Geneva, and the second shows Brighton.  The A23 to London reaches the left side of the frame, while the A27 runs almost vertically up near the left side.  The sandy beach is visible, also the pier, and beyond it the white cliffs leading to Rottingdean and Saltdean.  The lines of the railways can also be seen.

The fourth picture above shows Rottingdean, Saltdean and Peacehaven in Sussex, and the white chalk cliffs that separate them from the sea.

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 Charles de Gaulle, with its twelve radiating streets, is visible in this picture.  This deliberately geometrical construction is a complete contrast with the organic and apparently haphazard development of old towns.  The route péripherique also makes its mark, but the dominating feature is, of course, the river Seine, its meanders fossilised by concrete walls.  The many arrondissements and smaller areas join with dislocations like those between domains in a crystal.  

New York city, on the other hand, represents the extreme domination of the rectangle (apart from Broadway and some other streets).  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 north-south and east-west, in a propitious location 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.  Animals, too, can have quite sharply bounded territories.  We might not expect plants to have territories, but among the entries for the Wildlife Photographer of the Year for the year 2000, there is a photograph showing the phenomenon of "crown shyness", which prevents the tops of trees from touching each other, even when they are crowded.  Narrow strips of sky are seen between the trees, making a tessellation of brightly outlined polygons overhead.  Why do you think this happens?

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.  The angle seems to depend on the difference in size, or more accurately, in hierarchical level, between the veins that meet.

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 wing.  It shows very well the strong leading edge, especially from the root to the nodus, and the more flexible trailing edge, which work together with the thorax 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.  Evolution is affected by every stage of life.

The cracks in the coating on this road sign do not seem to follow the patterns described above.  What do you think has happened here?

Here is a large leaf.  We can see some of the same effects here as in the dragonfly wing and the pottery.  The topology of the veins is especially interesting in the regions where the leaf is about to divide into lobes.

But we must distinguish carefully between the veins in the wings of leaves, and the veins in the wings of insects.  Both provide stiffness, but the veins in leaves also provide for the flow of fluids, throughout the life of the leaf, and the angles take this into account.  But the flow in the veins of an insect occurs only once, when the wings are expanded, and the emphasis is on the pressure, rather than the flow.  And so, in general, if we look at a lot of leaves and a lot of wings, we shall see differences as well as similarities.

In a sense, the stiffening veins in wings and insects are like negative cracks, providing strength where needed.  See also Leaves.

If you see in a structure two members that meet at an acute angle, what does that tell you?

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.  The third example again has a comparison with an electric field.  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.

Here we can see the top and side views of some cracks in a fence post.  Many of the posts in the fence had similar cracks, even though the fence is quite new.

Here is another type of crack in wood, and below are some other shapes.  Do some of these pictures remind you of laminar flow of a fluid around an obstacle, or a magnetic field around a superconductor, or even the great red spot on Jupiter?

The diagram below shows a simulation of stress lines around a hole in a large slab, only a part of which is shown.  This field of lines also describes laminar flow of a fluid.  Evidently the growth of wood around an emerging branch is very similar.

Cracks are often formed when an object expands differentially, for example, a glass object plunged into hot water.  The bark of trees often shows this effect, like the crusts of bread and cakes, which of course are subject to tension on a much shorter time-scale.  Bark

Breaks

When things are cracked, they are liable to break if force is applied.  When an object is stressed, a crack may zip through it at lightning speed, so that the break looks instantaneous.

The picture at left shows a snapped blade of a rusty old pair of scissors.  The material is not ductile.  The blade was being used as a lever, which was a bad idea.

If we look at the shape and texture of surfaces made by different stresses, we see distinct differences.  Examples are bending, compression, tension, torsion, and fatigue.

Sometimes an object is made to break deliberately by cutting it partly through and letting it snap off.  Here are some tree stumps that were created in this way.  The fracture shows where the wood was cut, and also shows the fibrous nature of the wood.  Other pictures show natural breaks caused by storms.

       GREAT_RIFTVALLEY

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_RiftValley 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 Glen is the result of the same type of action as the San Andreas Fault – two pieces of ground sliding past each other.  The Great Rift Valley resulted from land pulling apart, allowing a gigantic area to move downwards.

The great tectonic plates are moving at rates up to centimetres per year, in some places sliding past one another, in 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.  In other places, plates are moving towards each other, producing great mountain ranges such as the Andes and the Himalayas.  

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 pictures of cracks on the moons of the giant outer planets.

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These cracks were generated in layers of gold leaf on the surface of a vase made of black glass and a cup made of white glass.  The effect is rather like the result of the break-up of the seasonal Arctic and Antarctic ice-sheets.  The final picture shows the eye of a common frog, Rana temporaria.  In this example the gold flecks are more like the Japanese makie technique of depositing gold dust on lacquer.  This type of eye pattern is found in frogs of many countries; in some species the pattern looks more obviously like the result of expansion.

Extending this behaviour into the third dimension we see phenomena like the Giants’ Causeway and frost polygons.

Quantum Cracks

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, which has enabled people to understand atoms and molecules.  In these, energy is quantised into levels, between which there are states in which the object cannot exist.  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.

Another type of split appears in the many-worlds interpretation of quantum mechanics, in which both choices of a dichotomy occur, but only on is visible to any one observer.  Given the vast number of choices, this idea would apparently lead to an unimaginable number of parallel worlds.

The ultimate boundary is the event horizon between a black hole and the outside world.  Everything mentioned in this page can vibrate: can the event horizon vibrate?