Scientists would like to design high-strength structural materials, but much about this work depends on laborious trial and error due to the complexity of plastic deformation — that is, how materials can deform irreversibly. Now researchers propose a unified theory for plastic deformation of face-centered cubic metals, which includes copper, nickel, aluminum, silver, gold, platinum and lead, among others. The findings are detailed in the Proceedings of the National Academy of Sciences.
The elastic deformation of metals — that is, how materials can reversibly deform — is fully described by Hooke’s law, discovered in 1660. However, a similar law describing the plastic deformation of metals has eluded scientists for centuries.
Physicist Se Kyun Kwon at the Pohang University of Science and Technology in Korea and his colleagues focused on face-centered cubic metals. These materials organize their atoms at the corner of lattices shaped like cubes, with atoms also present in the middle of the face of each cube. They include alloys such as the austenitic stainless steels, the most common grades of stainless steel used around the world.
Face-centered cubic metals can undergo plastic deformation in three distinct ways. Twinning happens when defects possessing a mirror symmetry arise within a crystal’s lattice. Full slip takes place when layers of atoms slide a substantial interatomic distance away from their original positions while maintaining their face-centered cubic structure. Stacking faults occur when layers of atoms rearrange themselves from a face-centered cubic structure to a different crystal structure, a hexagonal close-packed lattice — essentially, a lattice of atoms resembling a solid whose bottom and top faces are hexagons and whose side faces are rectangles.
Different face-centered cubic metals deform in different ways. For example, copper and aluminum prefer to deform via twinning and full slip, while manganese predominantly deforms via stacking faults.
Scientists knew the microscopic structure of materials influenced plastic deformation — for instance, key factors included the size and orientation of the small crystals or “grains” that make up materials. Kwon and his colleagues use computer simulations of molecular dynamics to analyze the effect the orientations of grains had on how face-centered cubic metals deformed. Each simulation involved about 140,000 atoms.
The researchers discovered they could predict how a metal would deform by looking at two factors — the intrinsic level of energy needed for each metal to slip, known as the intrinsic slip barrier, and the energy needed for a stacking fault to form, known as the stacking fault energy.
If the stacking fault energy divided by the intrinsic slip barrier was less than -1/2, as is the case with titanium or zirconium, only stacking faults would occur regardless of the way grains were oriented; if between -1/2 and zero, as is the case with chromium, iron and manganese, both stacking faults and full slips occur, depending on the direction in which shear forces are applied; if between zero and two, twinning can be seen along with full slip; if greater than two, full slip dominates.
“Our theory of plasticity is simple enough, like Hooke’s law,” Kwon says.
Kwon notes this research could help develop advanced high-strength steels. “The steel industry and metallurgists are desperately working on them to realize stronger but lighter materials aiming, for instance, to automotive applications with high performance and energy efficiency,” Kwon says. “The main physical factor that governs their superior mechanical properties is plastic deformation. Our theory will lead to a significant contribution to the current efforts of optimizing mechanical properties of advanced high-strength steels.”
The scientists are currently analyzing other crystal structures, such as hexagonal close-packed and body-centered cubic lattices. “Developing the theory in the case of other crystal lattices will certainly meet further obstacles,” says study co-author Levente Vitos at Sweden’s Royal Institute of Technology in Stockholm. “But with our deep commitment and interest, we are quite confident that with these skillful young people around us and with the support from our senior mentors, we will cope with such difficulties as well.”