Effects of atoms on brittle fracture

Abstract

Abstract. This article aims to answer two related sets of questions. First: in principle, how large an effect can structure at the atomic scale have upon the fracture of two macroscopically identical samples? The answer to this question is that the effects can be very large. Perfectly sharp cracks can be pinned and stationary under loading conditions that put them far beyond the Griffith point. Crack paths need not obey the rule K I I = 0. Crack speeds can vary from zero to the Rayleigh wave speed under identical loading conditions but depending upon microscopic rules. These conclusions are obtained from simple solvable models, and from techniques that make it possible to extrapolate reliably from small numerical calculations to the macroscopic limit. These techniques are described in some detail. Second: in practice, should any of these effects be visible in real laboratory samples? The answer to this second question is less clear. The qualitative phenomena exhibited by simple models are observed routinely in the fracture of brittle crystals. However, the correspondence between computations in perfect two-dimensional numerical samples at zero temperature and imperfect three-dimensional laboratory specimens at nonzero temperature is not simple. This paper reports on computations involving nonzero temperature, and irregular crack motion that indicate both strengths and weaknesses of two-dimensional microscopic modeling.

Theory of dynamic crack branching in brittle materials

“…The Griffith criterion and the principle of local symmetry predict adequately the path and the stability of slowly propagating cracks (Adda-Bedia and Pomeau, 1995;Adda-Bedia and Ben Amar, 1996;Bouchbinder et al, 2003;Marder, 2004). Controlled experiments on quasi-static cracks confirm the theoretical results (Yuse and Sano, 1993;Ronsin et al, 1995).…”

Crack tip blunting and cleavage under dynamic conditions

“…As has been widely discussed [14,15], continuum-level analyses of crack tip deformation mechanisms such as cleavage and dislocation emission are not wrong, but simply incomplete. The first reason is that atoms play an important role in crack tip phenomena, such as lattice trapping (in quasi-static fracture) and forbidden steady-state velocities (in dynamic fracture).…”

“…Although the 3D simulations are more computationally costly, they might also be more realistic: crack front variation in 3D might enable cracks to propagate when they would instead arrest in 2D. In other words, 2D materials might be artificially resistant to cleavage [15].…”

“…However, it is also possible that atomic-scale effects are important. 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.…”

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.…”