Brittle Fracture at the Atomic Scale
- James Kermode (University of Warwick, United Kingdom)
- Alessandro De Vita (King's College London and University of Trieste, United Kingdom)
- Peter Gumbsch (Fraunhofer Institute for Mechanics of Materials IWM, Freiburg and Karlsruhe Institute of Technology, Germany)
- Gianpietro Moras (Fraunhofer Institute for Mechanics of Materials IWM, Germany)
This workshop will gather a group of world-leading experts to analyse the status of theoretical modelling and experiment on fracture in brittle materials. It will focus on the nanoscale processes underlying fracture, and how to advance our current understanding of them. These processes are crucial for brittle fracture: when brittle materials break under mechanical load, the fracture development is determined by, and extremely sensitive to, the precise space- and time-pattern of bond-breaking events induced by stress concentration .
The fundamental scientific importance and huge practical interest of understanding fracture and the remarkably difficulties this poses provide a main stimulus for this proposal. In particular, modelling brittle fracture at the atomic level has proven to be distinctively difficult. Indeed, many attempts have gradually made clear that fracture in pure phases such as glasses, crystalline semiconductors and minerals, as well as in complex systems such as advanced ceramic fuel cells, thermal barriers or biomimetic coating films, poses far more challenging problems to theory than it does in metallic phases , where a simple description is often sufficient to capture the ductile behaviour response. This is mainly because high accuracy and large system sizes are both necessary ingredients for modelling failure in brittle materials. On one hand, the ionic or covalent bond-breaking and formation associated with brittle fracture advancement (accompanied e.g., by surface reconstruction, chemical attack by inflow of corrosive species, or reactions with pre-existing impurities) require interatomic potentials truly capable of quantum chemical accuracy. On the other hand, the need to capture faithfully the stress concentration phenomena requires large scale (~10^6 atom) model systems. All the above has made brittle fracture an extremely hard problem to tackle at the atomic level.
Recently, however a novel opportunity has arisen due to (i) the availability of new and highly accurate (multiscale and classical MD) schemes efficiently implemented on massively parallel computing platforms and (ii) the development of high precision experiments involving e.g. ultralow loading rates and AFM techniques, whose findings can be accurately matched with the theoretical ones . This has made it possible to develop and validate quantitatively accurate atomistic fracture models, and to address problems like e.g. propagation instabilities at high  and low  speeds, and stress corrosion under subcritical loading .
Until relatively recently, most modelling of failure in brittle materials has been at the continuum level [1-2,7]. This kind of analysis has been sometimes sufficient to describe brittle fracture in carefully prepared single crystal samples . However, in more complication situations, atomistic details become highly relevant. The current state of the art in the simulation of brittle fracture using molecular dynamics based on empirical potentials typically uses massively parallel codes to perform fully three-dimensional fracture simulations on the world’s largest supercomputers . MD simulations of this kind can be profitably combined with AFM experiments. For example, in amorphous silica cracks have been observed to progress through the growth and coalescence of nanoscale cavities [10, 11]. The Digital Image Correlation (DIC) technique allows the full displacement field to be extracted from images of the fracture surface, for a range of length scales spanned by different techniques from AFM to optical microscopy, facilitating a direct connection between theory and experiment [12,13].
Analytically solvable lattice models  have been also used to show that the discreteness of an atomic lattice can impose constraints on accessible steady-state crack velocities at low temperatures, leading to the “velocity gap” concept . This is related to the phenomenon of “lattice trapping” whereby cracks are inhibited until the load is increased above that predicted by the Griffith energy-balance approach [16,17]. Lattice models have been combined with classical atomistic simulation to help to explain crack limiting velocities and supersonic cracks [18-21].
The classical molecular dynamics approaches described above work well in systems where accurate force-fields are available (e.g. FCC metals), but it’s difficult to accurately include the effects of chemical complexity. This is particularly important in oxide materials where cracks can propagate very slowly under subcritical load in a corrosive environment . For instance, the mechanism underlying stress-corrosion cracking is currently the subject of intense debate: it may be that the local chemical action of aggressive species at the crack tip leads to slow crack advance, or that there is widespread water penetration and consequent porosity-induced softening in the material ahead of the tip . AFM imaging has ruled out cavities larger than 10 nanometers  indicating that atomistic simulation has a key role to play.
Chemically complex scenarios can be addressed by Hybrid QM/MM simulations, in which a quantum mechanical description of crack-tip bond breaking processes is embedded within a much larger empirical description of the elastic response of the surrounding material, have been used to describe brittle fracture in single-crystal silicon, with the extent of lattice trapping approximately in agreement with experiment [8, 25], and to explain both high- and low- speed fracture instabilities [4-5]. These simulations have been limited to two dimensions until now, and to simulation times of the order of tens of picoseconds, and although in principle a DFT-level description of crack tip processes allows arbitrary chemical complexity to be accurately included , this has not yet been fully exploited to describe stress-corrosion reactions in oxides.
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