Figure 1. Visualization of an atomistic simulation of the evolution of a grain surrounded by two other grains.  The inner grain does not rotate, in contrast to the grain surrounded by a single crystal matrix, because of frustration.
Figure 1. Visualization of an atomistic simulation of the evolution of a grain surrounded by two other grains. The inner grain does not rotate, in contrast to the grain surrounded by a single crystal matrix, because of frustration.

We apply computational methods including first principles, tight binding, interatomic potentials, and coupling of length scales approaches to the simulation of mechanical properties. Applications range from static calculations of quantities such as ideal strength and ductility criteria, to dynamic simulations of finite-temperature ideal strength and dynamic fracture.

Mechanical properties are determined by the interactions of atoms in the material, whether in a homogeneous deformation (i.e. uniform strain) or a localized one (e.g. bond breaking at a crack tip). Different computational methods can be used to simulate the atoms, from classical interatomic potentials to quantum mechanical descriptions of bonding such as tight-binding and density functional theory. The structure of the material is also important, since the lattice determines the nature of defects, such as dislocations and grain boundaries, and the defects can control the response of the material.

Grain boundaries are an example of an important defect, because they can block, create, or destroy dislocations that mediate plasticity in metals. The Hall-Petch effect, where the strength of a ductile material increases as grain size decreases, is the manifestation of this interaction. Recent theoretical and simulation studies indicate that grain boundary motion is coupled to the translation and rotation of the adjacent grains. However, the geometry of the system can strongly modify this coupling. We have simulated the evolution of grains in two geometries that are similar to experimental systems that have been studied. The first, a small circular grain embedded in a matrix consisting of two other grains, shows that rotation can be suppressed by geometric frustration, but the coupling slows the grain boundary motion. The second, a bicrystal cut into a wedge shape, shows that free boundaries can act as sinks for grain boundary dislocations thereby stopping or even reversing the rotation caused by grain boundary motion. These observations suggest that an experimentally relevant theory of grain boundary motion needs to consider the effects of microstructure and sample geometry.

Figure 2. Top: visualization of crack-tip reconstruction from coupled simulation of fracture in Si.  Center: result of mesoscopic model showing how this reconstruction could manifest itself macroscopically.  Bottom: AFM scan of Si fracture surface showing similar feature.
Figure 2. Top: visualization of crack-tip reconstruction from coupled simulation of fracture in Si. Center: result of mesoscopic model showing how this reconstruction could manifest itself macroscopically. Bottom: AFM scan of Si fracture surface showing similar feature.

The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen. The way the crack propagates, however, is entirely determined by atomic–scale phenomena, since brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front. The physical interplay of multiple length scales makes brittle fracture a complex “multi–scale” phenomenon. The occurrence of various instabilities in crack propagation at very high speeds is well known and significant advances have been made recently in understanding their origin. We have recently investigated low speed propagation instabilities in silicon using quantum–mechanical hybrid multi–scale modelling and single–crystal fracture experiments. The multiscale approach couples a density functional theory description of bonding at the crack tip with a large sample described with ineratomic potentials. Our simulations predict a crack tip reconstruction that makes low–speed crack propagation unstable on the (111) cleavage plane, conventionally thought of as the most stable cleavage plane. We have confirmed these results buy comparing with experiments in which this instability is observed at a range of low speeds.

We are continuing our studies of fracture in silicon and extending them to other conditions, for example, finite temperatures and other materials such as silicon carbide. We are also developing new multiscale coupling methods that combine continuum elasticity, interatomic potentials and quantum-mechanics while maintaining energy conservation.
Principal Investigator: Noam Bernstein