Cracking the Story of Fracture
A crack slicing through a brittle material may be a more complicated process than researchers previously thought. A team reporting in the 29 January Physical Review Letters wedged apart a piece of Plexiglas and saw three different fracture processes, depending on the speed of the moving crack. Their results help to further the basic physical understanding of material fracture and, ultimately, material failure.
To learn how solids break, material scientists want to understand the relationship between “how hard you pull [the crack open] and how fast the crack moves,” says Michael Marder of the University of Texas at Austin. The harder you pry the crack apart, the faster the crack tip moves forward. But the relationship between the prying force and the speed depends on a third quantity, the so-called fracture energy–the energy required for the moving crack to break the solid and expose a unit area of cracked surface. If this required energy goes up with increasing stress, then the crack slows down, relatively speaking, as it expends more energy breaking through. So understanding fracture energy is essential to learning how cracks propagate.
At crack speeds above about 330 meters per second in Plexiglas, researchers have seen fracture energy increase with speed, explained by small, secondary cracks branching out in multiple directions and requiring extra energy. But below this speed, based on limited data, the fracture energy appeared to be relatively constant, except that there was an unexplained jump from its value at zero speed to the previously obtained data points between 200 and 300 meters per second. “Explaining this discrepancy was the main purpose of our work,” says Daniel Bonamy of France’s Atomic Energy Commission (CEA) in Saclay.
Bonamy and his colleagues drilled a small hole in a chunk of Plexiglas and drove a crack into it with a tiny wedge, like splitting wood with a finely-tuned chisel. This technique allowed them to investigate much slower crack speeds than previous experimenters. They laid a fine grid of conductive metal on the surface of the Plexiglas. By detecting when these metal lines were broken, they could measure the velocity of the crack, and they calculated the applied stress based on the position of the “chisel.” They also examined the inner surfaces of the crack with a microscope.
The team found that the fracture energy at 100 meters per second matched the zero-speed value and then increased rapidly, tripling itself between 100 and 165 meters per second, where the curve suddenly flattened out again. At this speed they also saw fish-scale-shaped marks on the fracture surfaces, signifying micron-scale flaws inside the material. These shattered, disk-shaped regions had been seen before, but no one had observed their sudden appearance at a specific crack speed.
To explain their data, Bonamy and his colleagues propose that there are three distinct types of fracture, depending on the crack speed. Starting from about 100 meters per second, as speed and stress increase, the material no longer stretches like a perfect spring. This inelastic flexing dissipates more energy the faster the crack moves. At about 165 meters per second, the stresses that build up in front of the crack tip are strong enough to trigger weak regions of the material to shatter and form the disk-shaped flaws. It then costs less energy to make the main crack move, as it can travel more easily through these damaged regions than through unbroken material. So the fracture energy increases more gradually with crack speed in this range. Above 330 meters per second, fracture energy increases more steeply because of “microbranching,” as reported in previous work.
Whether the results apply to a wide range of brittle materials, like glass, will depend on confirming experiments on other materials, says Marder. If those experiments agree, “this would be an important part of our understanding of cracks,” he says. Direct applications to industrial processes are in the future, as the field of fracture dynamics is still establishing fundamental principles. “Right now we’re just doing basic work,” says Marder.
–Stephanie Chasteen
Stephanie Chasteen is a freelance writer and physics graduate student at the University of California at Santa Cruz.