Austin, Texas
EROSION, wear and tear, breakdown and decay-there is a universal pattern in this world. All that lives dies, and all that is put together eventually comes apart. Even the seemingly indestructible pyramids of Egypt, once smooth and geometrically perfect, have been broken down by wind and sand, the blows of looters and tourists, and the stresses of the unceasing cycle of hot days and cold nights.
Sometimes destruction comes quickly, as when a wayward stone shatters a window pane. For the pyramids and the surfaces of roads, or the rugged mountain peaks which turn through aeons to dull crumbling domes, it is a cruel, all but imperceptible process. But behind disintegration in all its forms lurks a single malevolent agent-the crack. Through the growth of fractures, fissures and rifts-sometimes large and sometimes microscopic-everything, quite literally, is cracking up.
It is satisfying to know the ultimate cause of decay, but as scientists we鈥檇 like to know more. What starts cracks off? How do they move? Why do they change direction, speed up or slow down? And what makes them spawn new cracks? Researchers like me are smashing things up in the laboratory, and breaking computer budgets down the hall, to try and tease out the answers to these questions. Understanding the strange ways of cracks may also help us to design materials that can defeat them.
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Since cracks lie behind the way things fall apart, they have received tremendous attention over the years. It was fairly easy to understand a single solitary crack moving on a straight and narrow path. But what of cracks that eschew straight lines or simple curves, following instead paths as bewilderingly crooked as lightning bolts? And what of the rough surfaces created when a crack rips through a brick, or the million fragments when a brick rips through a window pane? Snap a wafer of silicon in two and the newly formed surface, when magnified 300 times, seems rather smooth. But magnified 3000 times, it looks a little bumpy, and at 15 000 times, quite hilly. These pictures, taken by Ulrich Purbach, Alex Delozanne and Jens Hauch of the University of Texas at Austin, show that the closer you look, the rougher the surface becomes.
And the remarkable thing about these complex broken landscapes is that they always seem to turn out the same. In the past few years, scientists from Europe and the US have held veritable festivals of destruction in their labs, finding that all manner of materials break in what seems to be a universal way. Shatter a piece of plastic, snap a twig of Norwegian spruce, smash a chunk of ice, a brick or even a frozen potato, and you鈥檒l find that the resulting surfaces look much alike.
The resemblance is not just qualitative either. For any of these surfaces, as for silicon, the roughness becomes worse as it is looked at more closely, and in a precisely predictable way. For silicon, the bumpiness-a measure of how much the surface fluctuates up and down-goes up by around 1.6 for every twofold increase in magnification. Nearly identical numbers hold for the other materials, or for any other brittle stuff that you may care to destroy. There is, it seems, profound order within fractured disorder, and it is an ubiquitous feature of rough surfaces.
This is puzzling. Why don鈥檛 different materials break differently? And why, for that matter, aren鈥檛 newly broken surfaces smooth and mirrorlike, like the facets of cut gems? Smooth surfaces would seem especially likely when breaking perfect crystals. But it usually doesn鈥檛 work that way.
It鈥檚 all because of the curious behaviour of cracks-weightless little wedges of pure space-which hurtle through solids with minds of their own. Breaking things is easy, but it has taken a lot of observation, experimentation and hard thinking to work out their ways. Look at a piece of broken glass, for instance, and you鈥檒l see that near the crack鈥檚 origin, the surfaces on either side are smooth. But that simplicity doesn鈥檛 last. As the crack moves on a bit, the surface appears misty, and then a bit further, noticeably jagged.
In 1991, at the University of Texas at Austin, Jay Fineberg, Steve Gross, Harry Swinney and I set out to discover where this pattern came from. Hoping to learn about fracture in general, we set up a test rig capable of measuring the velocity of a crack tip with an accuracy of about 10 metres per second. We could make 50 000 or these measurements within the space of 2.5 milliseconds-a rate of 20 million measurements per second. In most of these experiments, the material we broke was Plexiglas, which in the light of what we learnt later wasn鈥檛 necessarily the best choice. But we were still able to discover that as cracks grow, they go through three phases of evolution.
If you take the Plexiglas-or any other brittle material-and pull its sides apart hard enough, a crack will suddenly form. We cut a notch in the side so that the crack would start where we wanted it to (see Diagram). In the first stage, the crack forms and jumps from rest to about 200 metres per second (720 kilometres per hour) in less than one-millionth of a second. For ordinary objects this would take an impossibly huge force: to make even a 20-gram bullet accelerate this fast you would somehow have to apply the entire thrust of a Saturn V booster. But for a crack there is no such problem because it has no mass: it鈥檚 just a hole.
In the second stage, the crack keeps accelerating, but at a much slower rate. In both of these first two stages of development, the crack leaves a smooth surface in its wake. But eventually, the crack gets moving so fast that it becomes unstable. Above a certain speed, it begins to move like an old jalopy going too fast down the freeway: it bucks and plunges, speeds up and slows down, and veers haphazardly to the left and right. As it does so, the crack leaves a very rough surface behind. So broken surfaces are rough, it seems, because cracks just can鈥檛 go fast and straight at the same time. After several years of further experiments, I now think that we have the makings of an explanation for this crazy behaviour.
Since fracture creates roughness all the way down to the atomic scale, the forces that make cracks grow must also be investigated all the way down at that scale. This is why Plexiglas makes things so difficult: it is a tangle of polymers, each a string of about a million molecules, which would put the Gordian knot to shame. To understand fracture instabilities it makes a lot more sense to look at brittle crystals, where simple atoms are spaced regularly, at precise locations that are easy to describe.
Breaking pieces of silicon is one way to go. Another is to think about crystals theoretically. In 1981, Leonid Slepyan, now at Tel-Aviv University in Israel, imagined a hypothetical brittle material. Its atoms exert forces on each other that happen not precisely to be realised by any of the genuine members of the periodic table, but these forces are not terribly distant from reality. The advantage of the model, as Slepyan showed, is that the motion of every atom can be determined in solutions written down with pencil and paper.
I recently turned to Slepyan鈥檚 model to study the way cracks move (see Diagram). First, it seems that cracks don鈥檛 like to run at just any speed. In the model, a crack simply cannot move any slower than a few hundred metres per second. Brittle cracks either run fast or they don鈥檛 run at all. Second, cracks can run through a crystal in an exceptionally efficient manner, consuming almost nothing but the minimum energy needed to sever the body. This produces a perfectly clean cut, with atomically flat surfaces and no roughness.FIG-mg20975101.GIF
Here we have a result that seems to contradict the observation that cracks usually leave rough surfaces, but the model can cope with this too. The highly efficient behaviour is a bit like crossing a tightrope: easiest to do at a walk and nearly impossible at a run. If the forces ripping the material apart-and causing the fracture-are just a little too strong, then the crack will begin to shudder as it labours to accommodate all the energy being forced into its tip. It鈥檚 like water being poured into a funnel. Pour a little and it flows through smoothly, but pour too much and it makes a mess by sloshing out the top. Similarly, all the energy to tear atoms apart has to flow through the crack tip, and if the flow becomes too great, the tip鈥檚 motion becomes irregular and the crack sprouts side branches. Small at first, these grow until some become independent cracks, which can cut the material to pieces.
It is possible to give a flavour for the instability, without mathematical apparatus, by looking at the patterns of stress that occur in a breaking material (see Diagram). As long ago as 1951, Elizabeth Yoffe of Cambridge University found-also by studying a theoretical model-that something peculiar happens to a crack as it approaches the speed at which sound waves move through a material. In general, atoms pull apart where the stresses in the material are greatest. For a slow crack, the stress pattern is nearly circular, though it is just a bit bigger toward the front. Since the largest stresses are ahead, the crack proceeds in a straight line. But for a faster-moving crack, the stress pattern becomes compressed and the greatest stresses appear to the sides. At some point, the change in stress pattern becomes so great that atoms to the side of the crack tip are ripped apart before those to the front, and the crack is drawn off path (see Diagram).FIG-mg20975104.GIF
Slepyan鈥檚 lovely solutions give a good qualitative picture of what happens, but only up to the point where the crack tip begins to shudder. Once the tip becomes unstable, describing it simply and precisely becomes difficult, and its behaviour is far from fully understood. But there are two interesting clues about what is going on-one from experiments, and the other from computer simulations.
The experimental observation comes from Fineberg and Eran Sharon at the Hebrew University of Jerusalem. When a crack in brittle plastic speeds past the point of instability, it begins to sprout side branches in increasingly large numbers. And the side branches themselves throw off further, secondary side branches. Fineberg and Sharon have taken careful pictures of these branches, and by looking at their shapes have discovered a similarity under magnification very much like that observed for rough surfaces.
Sideshow
When a side branch sprouts off from a crack, it does so much like the branch of a tree, and seems to form an angle of about 30 degrees with the main crack. But this simple picture is deceiving. For the closer you get to a side branch, the steeper it looks. That is, the angle between the branch and main crack increases under magnification. Curiously, the steepness of these side branches increases in just the same way as does the roughness of fractured surfaces. Magnify by a factor of 2, and the steepness increases by 1.6. It makes sense that side branches which are steeper at small scales would leave fractured surfaces that undulate more wildly and are therefore rougher at small scales. Because of this connection, it may be possible to make a theory for the origin of rough surfaces based on the way that big cracks emit little ones off to the side, although no such theory exists yet.
Other crack enthusiasts are looking into things through computer simulations. For example, Farid Abraham at IBM鈥檚 Almaden Research Center in California, Brad Holian, David Beazley, Peter Lomdahl and Shujia Zhou at Los Alamos National Laboratory in New Mexico, and Priya Vashishta and Rajiv Kalia at Louisiana State University in Baton Rouge, have all been simulating fracture by moving anything from a million to 100 million atoms around according to Isaac Newton鈥檚 laws of motion. From one point of view these are hardly large numbers. A million atoms couldn鈥檛 fill a box with a base one-hundredth the width of a human hair. But from another point of view they are immense. Printing in small type the locations and velocities of this many atoms would fill over 7000 issues of New 杏吧原创.
This wouldn鈥檛 make very informative reading, and a major challenge in conducting these simulations is to find alternative ways of representing the results that humans can comprehend. It is all too easy to burn a lot of computer power as you move atoms around, and learn absolutely nothing. But ideas from fractal geometry can help. The computer can easily examine rough and complicated arrangements of simulated atoms and see if they obey the same rules when viewed at different scales as their real-life counterparts. The Louisiana researchers have been doing just that. They have fractured computer silicon, computer silicon nitride and other brittle materials, and looked at the resulting surfaces at many magnifications, as we did earlier with silicon. The rough surfaces generated in these computer models obey the same rules as the real ones.
There is something a little baffling about scientists setting the world鈥檚 largest computers churning away for months at a time to reproduce something any child can do by dropping a plate on the floor. All the more so since investigations so far have served mainly to confirm rather obvious truths. In the future, though, they will be called upon to do more. The goal is to create new materials on the computer, and to predict their resistance to heat, abrasion and stress from virtual blows, rather than waiting for years of experiments to run their natural course.
And there is no better way to make confident predictions about the properties of new and unknown materials than to test our methods on familiar materials and see that known properties come out right. It is not enough to do these tests on smooth and simple cases. Materials have to be tested against the roughest handling they will ever endure. Knowing how cracks go unstable will not restore the surfaces of the pyramids. But it may help us to find materials that can outlast them.