Carnegie Mellon University
January 08, 2014

Even Materials Get Stressed: Amit Acharya’s Work on Line Defects

Even Materials Get Stressed: Amit Acharya’s Work on Line Defects

The visualization is of the collective stress field of dislocation line defects that move on a slip plane when an external load is applied. Here the dislocations cause a ‘pile up’ on encountering an obstacle at the left end. Often the material constitution is such that there are other stronger particles, inclusions etc. that intersect these planes. When this occurs the dislocations cannot go through, and get jammed up against them. A pile up is such a ‘traffic jam’ as pictured above.The visualization is of the collective stress field of dislocation line defects that move on a slip plane when an external load is applied. Here the dislocations cause a ‘pile up’ on encountering an obstacle at the left end. Often the material constitution is such that there are other stronger particles, inclusions etc. that intersect these planes. When this occurs the dislocations cannot go through, and get jammed up against them. A pile up is such a ‘traffic jam’ as pictured above.

CEE Professor Amit Acharya is interested in the causes of stress, but not in the usual sense. Acharya, a professor in CEE’s Mechanics, Materials, and Computing (MMC) research group, studies how structural imperfections, or defects, in crystalline materials interact and evolve. 

“A defect is essentially when the lattice of a crystalline material gets a little messed up,” Acharya explains. “And when the lattice gets messed up, certain parts of the material become stressed. As soon as there is stress in the material, that stress interacts with other defects and forms loops and curves of defects within the lattice called line defects. The most common one is called a dislocation.” Acharya is studying how these defects in a material move and spread and making mathematical models that reflect how crystalline materials behave under stress.

“The Holy Grail in manufacturing is to develop material that is high-strength and high-ductility, which means the material can tolerate high levels of stress and won’t crack when its stress limits are reached,” Acharya says. “For example, people in the auto industry want to make alloys from steel that are as strong as steel but as ductile as aluminum. But even today, there is not a completely predictive theory that can tell you how a simple crystalline material will behave under specified stresses.” Understanding the behavior of defects in materials is critical in the predictive design and manufacture of turbines used in power generation and aircraft engines, which operate in high-temperature, high-pressure environments. 

As dislocations form and grow within a material, many of them are also moving. This movement leads to large-scale flow or deformation. Sometimes, Acharya explains, engineers can take advantage of this flow. “When you take a sheet of metal and you stamp it in a shape that will be part of the body of a car, you use that flow to make the metal deform a huge amount. But you also want to do it in a controlled way; if the auto part has deformations that are concentrated in a particular section, it will split,” he says. “And to really understand this macroscopic behavior, you have to understand the underlying theory first.” 

Acharya and PhD student Xiaohan Zhang are particularly interested in the process of yielding, which is the threshold applied load required to observe plastic flow. At the scale of an individual dislocation, this translates to the load required to move a single dislocation, the phenomenon called pinning. For almost seventy-five years, scientists have believed that any mathematical model that does not account for the discreteness of the atomic lattice cannot predict such a threshold. Through their theory and careful simulations, Acharya and Zhang show a different mechanism for such a threshold arising from the details of equations describing nonlinear wave propagation. While it is too early to say whether such a physical mechanism is indeed at play for crystal dislocations, nevertheless Acharya and Zhang take satisfaction in having developed a new class of pattern-forming equations, motivated by and closely related to the mechanics and physics of dislocation behavior, that show pinning. 

Ultimately, Acharya envisions the group’s research being used to aid in the prediction of earthquakes. Acharya and Paul Christiano University Professor Jacobo Bielak are collaborating to study this topic, known as rupture dynamics. “In an earthquake, a small region in the fault plane slips,” Acharya explains. “The boundary of that slip region is again a dislocation, and the mathematical description is exactly the same as that of a defect nucleating and propagating in a small volume of material. This is the power of general mathematics; you’re talking about earthquakes and about defects at the nanoscale, but at some level, they’re the same thing!” Modeling the formation, movement, and interaction of defects in crystalline materials can be a useful tool in understanding and anticipating earthquakes.

Acharya is also looking at the behavior of defects in amorphous materials, such as metallic glasses. Unlike a crystalline material, an amorphous material’s structure does not follow a pattern, making it particularly prone to defects. “In a crystalline material, you can identify a basic unit cell which can be replicated to fill space without stress,” he says. “But amorphous materials don’t have that structure or basic units that can fill space without deformation, and therefore the material becomes ‘geometrically frustrated’; it becomes stressed and develops lots of defects even without loads. And if we can phrase these kinds of things mathematically, we can then analyze them and develop a better understanding of their macroscopic properties.

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(Pictured above: Professor Amit Acharya with PhD student Xiaohan Zhang)