Low speed fracture instabilities in brittle crystals

Journal reference: external link: Nature 455, 1224-1227 (30 October 2008)

crack Materials failure is of central importance to many technologies, from electronic devices to armour and from solar cells to coatings. When a brittle material (such as a ceramic, an oxide or a semiconductor) is loaded to the limit of its strength, it fails by nucleation and propagation of a crack. The conditions for crack propagation, which determine when the material will fail, 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.

Using computer simulations, we began by studying the motion of atoms that takes place when cracks occur in brittle materials. The instabilities that occur when the crack propagates at high speeds are well-known, and scientists have already made significant advances in understanding the origin of these. However, instabilities and the related roughness had not been observed and studied in cracks that propagate at low speeds.

ridgesUntil recently, scientists studied cracks primarily by continuum mechanics techniques, but now advances in computer power have made it possible to simulate materials by describing the motion of each atom, rather than making the approximation that matter is continuous. While most simulations of cracks ignore the quantum-mechanical nature of the bonds between the atoms, we were able to overcome this limitation using our recently developed technique called “Learn-on-the-fly” (LOTF). This method allowed us to use a quantum-mechanical description of bonding near the tip of the crack, where it is essential, coupled almost seamlessly to a large (on the atomic scale) region described with an interatomic potential, which is a faster but non-quantum-mechanical method. The combined description was essential for correctly predicting the motion of the crack tip. The simulations surprised us when they showed that even in a brittle material like silicon, rearrangements of atoms right at the crack tip, usually associated with ductile materials like metals, can occur, but, unlike in the case of metals these plastic deformations remain trapped at the crack tip. Therefore, rather than shielding the tip from high stress and resulting in ductility, they result in an instability of the crack path. The rearrangements, which we call crack tip reconstructions, are asymmetric with respect to the orientation of the crack and this opens up the possibility of observing them in macroscopic experiments. We developed a meso-scale model, which links the newly discovered atomic scale phenomena to macroscopic length scales, and showed how the crack tip reconstructions could lead to ridges on the crack surface with a well-defined shape. A key concept turned out to be dynamic steering of the atomic motions: when the crack propagates faster than a critical velocity, the sequentially breaking bonds follow one another in such a short time that the system is steered away from the reconstructed state. This is why the surface left behind a fast crack should be smooth.

Our research team also carried out single-crystal fracture experiments in which this instability was observed for the first time at a range of low speeds. We conducted experimental studies of the cracks at low speeds using a novel technique for applying very small but steady and well-controlled tensile loads by exploiting the difference in thermal expansion between the sample and the sample holder. The surfaces left behind by the crack showed the ridge-shaped features, very similar to those seen in the computer models. Such corrugations are unexpected on the (111) surface of silicon, because that surface was considered to be the "best" one for cleavage.


On the other hand, crack path instabilities on a different crystallographic surface, the (110), have been observed before, but their origin was a mystery. Our simulations showed that a very different mechanism takes place there. In this orientation, there are two kinds of bonds to be broken, the distinction is made by their orientation with respect to the crack opening. Very slow cracks break the bonds sequentially in an orderly fashion, but as the crack picks up speed, it sometimes "stumbles", and breaks two bonds of the same type, rather than alternately. This leads to a deflection of the crack path onto the (111) plane, on which fast cracks propagate more easily.

The simulation results and experimental observations indicate that more is happening at crack tips in brittle materials than previously suspected. Preliminary simulations indicate that similar phenomena occur at the tips of cracks in silicon carbide and diamond.