Low-speed fracture instabilities in a brittle crystal

Abstract

When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack(1). 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(2). The way the crack propagates, however, is entirely determined by atomic- scale phenomena, because 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(1,3). The physical interplay of multiple length scales makes brittle fracture a complex 'multi-scale' phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known(1), and significant advances have been made recently in understanding their origin(4,5). Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack- tip reconstruction that makes low-speed crack propagation unstable on the ( 111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto ( 111) planes, as previously observed experimentally(6,7)

Crack tip blunting and cleavage under dynamic conditions

“…It is well-known that continuum fracture mechanics is unable to explain many important fracture phenomena, including lattice trapping [7][8][9], crack tip instabilities [10][11][12][13], and crack velocities in steady-state [14], all of which depend intimately on the details of bonding between atoms [15]. Atomistic simulations have therefore become increasingly popular for studying crack tip deformation mechanisms and their implications for ductility [16], both in quasi-static [17][18][19][20] and dynamic [21][22][23][24] conditions. In the latter case, model interatomic potentials have found great utility in molecular dynamics simulations [12,13,[25][26][27][28][29].…”

Capturing material toughness by molecular simulation: accounting for large yielding effects and limits

“…For instance, in their early work, Thomson et al (1971) have shown that the discrete nature of matter at the atomic scale leads to a lattice trapping of the crack, an effect unknown in continuum fracture mechanics. Likewise, a great deal of research efforts was devoted to various atomic scale peculiarities of fracture mechanics: competition between crack propagation and dislocation emissions (Rice and Thomson 1974;Celis et al 1983;Cheung and Yip 1994), role of inter-atomic potentials (Sinclair 1975;Holian and Ravelo 1995;Marder 2004;Buehler and Gao 2006), role of phonons (Holian and Ravelo 1995;Zhou et al 1996;Gumbsch et al 1997), crack velocity (Marder and Gross 1995;Buehler and Gao 2006), dynamic instability (Marder and Gross 1995;Abraham and Broughton 1998;Buehler and Gao 2006;Kermode et al 2008), effects of crystal orientation and grain boundaries (Miller et al 1998;Abraham and Broughton 1998;Pérez and Gumbsch 2000), effect of chemical environment and impurities (Lawn 1983;Kermode et al 2013). A long standing issue in atomic scale studies is the size effect that may arise at such small scales.…”

Laser-based Determination of Decohesion and Fracture Strength of Interfaces and Solids by Nonlinear Stress Pulses

“…In the well studied case of cracking along the Si{111} cleavage plane, for example, it is possible to discriminate between clean continuous propagation of a crack along {111} by breaking sixmember rings and discontinuous fracture by the formation of five-and seven-member rings in a recontruction process, as illustrated in Fig. 10. In the bulk, plastic deformation along the dislocation glide is prohibited if the Peierls stress for the movement of nucleated dislocations is too high, as assumed for low temperatures (Kermode et al, 2008). Recent simulations of the fracture mechanism in silicon nanowires by the modified embedded atom method (MEAM) potential indicate that cleavage is initiated by nucleation of a surface microcrack, while shear failure is initiated by the nucleation of a dislocation at the surface (Kang & Cai, 2010).…”