Suppose there was a fourth little pig. This one was a physicist. Unlike his brother the engineer, who built a house out of tried-and-true bricks, the physicist pig chose a building material by doing calculations based on fundamental principles. He settled on a substance made from silicon and oxygen, an abundant material with high bond strength and the aesthetic bonus of transparency. It was safe from huffing and puffing. But then the wolf learned to throw stones.
Physicists have had a tough time explaining why it’s a bad idea to build glass houses. While engineers from the Bronze Age to the Space Age have relied on trial and error to decide which materials work best, physicists seek deeper, scientific explanations.
“Can you predict from first principles what kinds of material will be very strong, and what will be brittle?” says Jay Fineberg, a physicist at the Hebrew University in Jerusalem. “It’s kind of strange, but we don’t know.”
Trying to find out has occupied the materials scientists who investigate how what begins as a rift between a few atoms spreads far enough to take down buildings and bridges. The goal is to engineer failure-free materials by understanding why materials fail in the first place.
“You can learn an enormous amount about materials by pushing them to their limits,” says materials scientist Markus Buehler of MIT.
In the process, scientists are exposing the cracks in existing theories. By shattering breakable Jell-O to model glass fracture in slo-mo, Fineberg and his colleagues have found that established equations of crack movement don’t apply near the tip of a fissure. In supercomputer simulations of billions of atoms stretching, Buehler and his colleagues discovered that the shuffling of a few atoms just ahead of the tip holds the reins on a crack’s speed.
And after centuries of making materials that can break too easily, scientists are deconstructing nature to uncover new ways of building stronger, more efficient materials. Efforts at biomimicry have already led to designs inspired by sponges made of glass and to tough ceramics based on mollusk shells. Together, these studies could usher in a golden age of atoms-up design.
Cracking theory up
A quick tour through the history of engineering underscores why finding failure-free materials is so important. A molasses tank in Boston burst in 1919, flooding the streets with sweet goo and killing 21 people. The S.S. Schenectady cracked almost in half in 1943 while sitting calmly in a harbor outside Portland, Ore. In 1988, the roof of Aloha Airlines Flight 243 tore off during flight, killing a flight attendant and injuring several passengers. A Missouri Air National Guard F-15C broke in two during flight in 2007, and the entire U.S. Air Force fleet of F-15s was grounded for weeks.
These disasters share an important feature: They all probably started with an imperceptible crack. So studying how a small crack propagates might help prevent such disasters in the future.
Way back in the late 1910s, English engineer Alan Griffith noticed that the stress theoretically required to break atomic bonds is 1,000 times larger than the stress actually needed to break those same bonds in a material.
“I could take a millimeter-thick strand of glass, and I could lift a grand piano with it,” Fineberg says. “A strand of glass can reach these strengths; it’s not science fiction. But the minute you have a flaw, it shatters.”
Griffith realized that existing ideas about how materials fracture were too simple. He reasoned that there must be some critical point (now known as the Griffith point) at which a crack gets so long that the strain pulling the material apart overwhelms the threshold energy required to form a new surface. His insight led to the current fundamental theory of fracture, which suggests that, because of the physical limits of energy transport through a material, a crack can’t travel faster than the speed of sound on the material’s surface.
But recent work reveals that even this theory, called linear elastic fracture mechanics, is too simple. Some cracks can travel faster than sound’s surface speed. In 1999, geophysicists observed an earthquake in Kocaeli, Turkey, that split rock at speeds exceeding several kilometers per second, faster than the speed of sound on the rock’s surface. The same phenomenon was observed in earthquake simulations three years later. And in 2004, physicists Michael Marder of the University of Texas at Austin, Robert Deegan, now of the University of Michigan in Ann Arbor, and colleagues found that rubber balloons also show unexpectedly fast fissures when popped with a pin.
“You can do this experiment in the comfort of your own home — preferably aided by children,” Marder says.
Knowing that something is still wrong with existing theory, scientists are at it again —ripping down old ideas to make room for new ones.
Breaking the mold
Crack movement is difficult to study in the lab because of the extreme speeds involved. But Fineberg’s team has a new way to slow things down.
“Instead of breaking glass or steel or brittle ceramics,” he says, “what we break is Jell-O.”
In this case, the gelatin is actually squares of polyacrylamide gel, a watery polymer used in DNA studies. “These are slippery little buggers,” he says. “They slipped and fell and looked like they shattered like plates of glass.”
In a series of studies published in 2005, Fineberg and two students showed that the way cracks move through the gel is identical to the way cracks move through glass, with one important difference: Cracks that would run through glass at 3,000 meters per second crawl through gels at just 5 m/s.
“You have a lot more time to see what’s going on,” Fineberg says.
Armed with a fast camera, Fineberg and colleagues have found a major flaw in linear elastic fracture mechanics. The theory assumes that the stress placed on a material is proportional to the strain it feels. But in a paper still in preparation, Fineberg and theorist Eran Bouchbinder, also of Hebrew University, show that this is true only far away from the crack’s tip. As measurements of cracks slogging through gelatin get closer to the point where the material splits completely, more and more terms need to be added to the equation of motion to describe how energy fuels the crack — and therefore how the crack propagates.
Fineberg says the gelatin method could also help explain how and why a crack changes direction, the way rippled edges form in popped balloons, for example. Aside from tip activity, cracks moving in straight lines seem to agree with the predictions of linear elastic fracture mechanics. But if those cracks deviate, the equations governing their motions are unknown. And fast, crooked cracks can emit small daughter cracks, or split completely into multiple fractures.
“The fundamental question is why cracks become unstable,” he says. “I believe that with these gels we can start to unravel this, just because we can slow things down.”
Assemblies of atoms
Though the camera that captures Jell-O cracks has speed on its side, for a truly fundamental theory of fracture, scientists would like a camera that also zooms to the atomic scale.
Buehler uses the next best thing: a supercomputer that models billions of atoms. His lab at MIT investigates fracture in materials ranging from nickel and silicon to bone and protein. “We can simulate atoms and get an equation of state or density or melting point of a material,” he says. “It’s really exciting.”
The simulations calculate each atom’s trajectory based on Newton’s laws of motion and the quantum mechanical interactions between that atom and those around it. To introduce a crack, Buehler simply removes a few atoms. To make the crack spread, he adds some stretch.
“The beauty of this approach and why I get really excited about this, it really is very simple,” he says. “Atomistic simulation doesn’t need much input. All it is, is chemistry.”
Buehler’s work offers an explanation for why cracks, under some conditions, move in a punctuated rather than a gradual way. In modeling a few-nanometers–long crack in silicon, Buehler noticed that some of the silicon atoms, which usually link up to form hexagons, had rearranged themselves. At the very tip of the crack, two six-atom rings had transformed into a five-atom ring and a seven-atom ring sitting side by side. The crack didn’t push forward until another bond, this one shared between the seven-atom ring and a six-atom ring ahead of it, broke — at which point the crack split through the subsequent six-atom rings like a zipper.
The transformation from six-atom rings to five- and seven-atom rings is the material’s response to extreme pressure, Buehler explains. In the same way that solids melt when heated, silicon shifts its atoms around under stress. This shift could help keep the crack from spreading, up to a point, by dissipating the constant energy applied to the material. Simulations in more substances may reveal how such changes in the atomic structure of materials could contribute to a new fundamental theory of fissure.
But atomistic simulations are slow and intensive — a recent model of a small piece of a protein network in a cell took weeks to render, Buehler says. And even the best supercomputers are years away from being able to handle the numbers of atoms that make up life-size objects.
Buehler sidesteps this problem by breaking materials into chunks. He’ll simulate a large ensemble of atoms, and draw a black box around it. The next level of simulations zooms out to the scale where the black box is a particle, and so on.
“We start at the fundamental scale and build up,” he says.
Conveniently, scientists have found, biological materials are actually organized in this hierarchical structure. Buehler’s fondest dream is to use multi-scale modeling to help build new substances inspired by life.
Nature builds it up
Some materials scientists are already creating new materials based on how natural substances fail, or fail to fail. Robert Ritchie and Tony Tomsia of Lawrence Berkeley National Laboratory in Berkeley, Calif., and colleagues, for example, made a material based on seashells in late 2008.
“Ceramics are wonderful: They’re lightweight, they’re very strong,” Ritchie says. “They’re ideal, bar one thing — they’re brittle as hell.”
Seashells, on the other hand, can take an impressive beating. Research has shown that it takes 3,000 times more energy to break nacre, the material that gives mollusk shells their mother-of-pearl sheen, than nacre’s chief component, aragonite, a brittle calcium carbonate mineral. In a seashell, the aragonite is sandwiched between microscopic layers of soft organics that provide cushioning.
“Its final properties in terms of resistance to fracture are so much better than either of the constituents,” Ritchie says. “That’s what we’re trying to emulate.”
Ritchie, Tomsia and their colleagues mixed alumina, a simple ceramic, with water, and then froze the mixture to create a lattice of ice. When the ice melted and left behind a ceramic scaffold, the scientists filled the spaces between the alumina layers with a common polymer, polymethyl methacrylate.
The team tested the resulting ceramic’s fracture resistance by introducing a small crack and forcing it to spread. The material was 300 times tougher than its constituents, the researchers reported in Science in 2008. The toughness comes from the polymer, which acts as a lubricant, allowing layers of ceramic to slide over each other rather than sever.
“This little thin layer of polymer allows the material to give a little bit, and reduces the stresses,” Ritchie says. “Nature does the exact same thing. This is not our idea, it’s nature’s.”
Ritchie and colleagues have made only a few cubic inches of the substance so far, but considering that most other biomimetic materials have been made on the nanoscale, that’s a lot. “As far as we know, no one has ever made a bulk material like this,” Ritchie says.
Bringing down the house
By studying another life-form, scientists have found that nature succeeds where the fourth little pig failed: It can make a glass house that’s immune to stones.
The amount of effort it took to break a deep-sea sponge surprised Joanna Aizenberg of Harvard University when she first tried to crush it. The species, Euplectella aspergillum, is made entirely of glass. She found one in a curiosity shop in San Francisco and brought it back to her lab.
“I jumped on it,” she admits. Though it’s made from the same stuff as windows, its primary structure held up under Aizenberg’s feet.
“You could hear the shattered glass,” she says. “You break some of the fibers and some of the connections, but the integrity is preserved.”
Aizenberg deconstructed the sponge’s structure using visible light and scanning electron microscopy, reporting the details in a paper in Science in 2005. She found that, as with the mollusk shells, levels of complexity contribute to the sponge’s strength (SN: 3/25/06, p. 184).
Each glass fiber consists of concentric layers of silica and protein, which help stop cracks from spreading — even if one layer succumbs to stress, its neighbors can back it up. But the way the fibers are arranged also contributes to the sponge’s resilience. The glass fibers form a cylindrical lattice of square windows crossed by diagonal bars, a common feature in architecture that keeps windows from tilting sideways. And the whole structure has spiral ridges running from top to bottom to prevent it from collapsing like an empty soda can when squeezed.
“It’s pretty much the most stable and mechanically strong glass structure that exists,” Aizenberg says.
Since describing the sponge in Science, Aizenberg has started designing models of the sponge architecture that lack certain structural features — the spiral ridges, say, or the diagonal bars — and building them out of polymers with a 3-D printer. She has been subjecting the models to a battery of tests, bending, stretching and squeezing to see what they can take. “This is where fracture appears,” she says.
Materials scientists like Aizenberg, Fineberg and Buehler hope such efforts will lead scientists away from traditional materials and toward ones that perform better. A more fundamental, and accurate, theory of material failure may be built up from clues gleaned as scientists break things down.
“Understanding failure,” says Buehler, “is the key to success.”