Peter Gumbsch

Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model

Abstract A new method for combined finite-element and atomistic analysis of crystal defects has been developed. The coupling between the atomistic core and the surrounding continuum is described in terms of non-local elasticity theory. Static and dynamic tests demonstrate the satisfactory performance of this method. The model is applied to crack propagation on cleavage and non-cleavage planes in b.c.c. crystals, using potentials for iron and tungsten as examples. On the cleavage planes, pronounced directions of ‘easy’ crack propagation, besides less favourable directions, are found. On the preferred cleavage plane {100}, easy propagation is possible in any macroscopic direction by microscopic facetting of the crack front into easy directions, while on the secondary cleavage plane {110}, there is only one macroscopic direction in which cracks will propagate easily. On all other planes studied here, plastic processes at the crack tip (twinning and/or dislocation emission) intervene before brittle crack prop...

Anisotropic mechanical amorphization drives wear in diamond

Diamond is the hardest material on Earth. Nevertheless, polishing diamond is possible with a process that has remained unaltered for centuries and is still used for jewellery and coatings: the diamond is pressed against a rotating disc with embedded diamond grit. When polishing polycrystalline diamond, surface topographies become non-uniform because wear rates depend on crystal orientations. This anisotropy is not fully understood and impedes diamonds widespread use in applications that require planar polycrystalline films, ranging from cutting tools to confinement fusion. Here, we use molecular dynamics to show that polished diamond undergoes an sp(3)-sp(2) order-disorder transition resulting in an amorphous adlayer with a growth rate that strongly depends on surface orientation and sliding direction, in excellent correlation with experimental wear rates. This anisotropy originates in mechanically steered dissociation of individual crystal bonds. Similarly to other planarization processes, the diamond surface is chemically activated by mechanical means. Final removal of the amorphous interlayer proceeds either mechanically or through etching by ambient oxygen.

Low-speed fracture instabilities in a brittle crystal

When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack. 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, 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. 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, and significant advances have been made recently in understanding their origin. 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.

Anticrack Nucleation as Triggering Mechanism for Snow Slab Avalanches

Snow slab avalanches are believed to begin by the gravity-driven shear failure of weak layers in stratified snow. The critical crack length for shear crack propagation along such layers should increase without bound as the slope decreases. However, recent experiments show that the critical length of artificially introduced cracks remains constant or, if anything, slightly decreases with decreasing slope. This surprising observation can be understood in terms of volumetric collapse of the weak layer during failure, resulting in the formation and propagation of mixed-mode anticracks, which are driven simultaneously by slope-parallel and slope-normal components of gravity. Such fractures may propagate even if crack-face friction impedes downhill sliding of the snowpack, indicating a scenario in which two separate conditions have to be met for slab avalanche release.

A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation

We propose a dislocation density measure which is able to account for the evolution of systems of three-dimensional curved dislocations. The definition and evolution equation of this measure arise as direct generalizations of the definition and kinematic evolution equation of the classical dislocation density tensor. The evolution of this measure allows us to determine the plastic distortion rate in a natural fashion and therefore yields a kinematically closed dislocation-based theory of plasticity. A self-consistent theory is built upon the measure which accounts for both the long-range interactions of dislocations and their short-range self-interaction which is incorporated via a line-tension approximation. A two-dimensional kinematic example illustrates the definitions and their relations to the classical theory.

An ab initio study of the cleavage anisotropy in silicon

Abstract Total-energy pseudopotential calculations are used to study the cleavage fracture processes in silicon. It is shown that bonds break continuously and cracks propagate easily on {111} and {110} planes provided crack propagation proceeds in the 〈 1 10〉 direction. In contrast, if the crack is driven in a 〈001〉 direction on a {110} plane the bond breaking process is discontinuous and associated with pronounced relaxations of the surrounding atoms. The discontinuous process is partly a result of some load sharing between the crack tip bond and the neighbouring bond, which results in a large lattice trapping. The different lattice trapping for different crack propagation directions can explain the experimentally observed cleavage anisotropy in silicon single crystals.

An atomistic study of brittle fracture: Toward explicit failure criteria from atomistic modeling

Atomistic techniques are used to study brittle fracture under opening mode and mixed mode loading conditions. The influence of the discreteness of the lattice and of the lattice-trapping effect on crack propagation is studied using an embedded atom potential for nickel to describe the crack tip. The recently developed FEAt (Finite Element-Atomistic) coupling scheme provides the atomistic core region with realistic boundary conditions. Several crystallographically distinct crack-tip configurations are studied and commonly reveal that brittle cracks under general mixed mode loading situations follow an energy criterion (G-criterion) rather than an opening-stress criterion (Kl-criterion). However, if there are two competing failure modes, they seem to unload each other, which leads to an increase in lattice trapping. Blunted crack tips are studied in the last part of the paper and are compared to the atomically sharp cracks. Depending on the shape of the blunted crack tip, the observed failure modes differ significantly and can drastically disagree with what one would anticipate from a continuum mechanical analysis.

Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation

A discrete dislocation simulation has been developed to investigate thin-film plasticity on a mesoscopic scale. Dislocation interactions and dislocation self-stresses are calculated within the isotropic linear elasticity theory. The simulation is used to investigate the formation of dislocation pile-ups in a single columnar grain, where the boundaries are introduced as impenetrable obstacles. In analogy to the Hall-Petch model global plastic deformation is assumed to occur when the stress on the grain boundary exerted by the pile-up exceeds a certain critical value. The production of dislocations by a Frank-Read source and the dislocation evolution in the glide plane are simulated. For sources which are small compared to the grain size and for small numbers of dislocations the flow stress is well described by an analytical model of Friedman and Chrzan (1998 Phil. Mag. A 77 1185) if an appropriate Hall-Petch constant is used. If the source size scales with grain size, the flow stress depends on the inverse grain size instead of the square root of the inverse grain size below a critical size.

The evolving quality of frictional contact with graphene

Graphite and other lamellar materials are used as dry lubricants for macroscale metallic sliding components and high-pressure contacts. It has been shown experimentally that monolayer graphene exhibits higher friction than multilayer graphene and graphite, and that this friction increases with continued sliding, but the mechanism behind this remains subject to debate. It has long been conjectured that the true contact area between two rough bodies controls interfacial friction. The true contact area, defined for example by the number of atoms within the range of interatomic forces, is difficult to visualize directly but characterizes the quantity of contact. However, there is emerging evidence that, for a given pair of materials, the quality of the contact can change, and that this can also strongly affect interfacial friction. Recently, it has been found that the frictional behaviour of two-dimensional materials exhibits traits unlike those of conventional bulk materials. This includes the abovementioned finding that for few-layer two-dimensional materials the static friction force gradually strengthens for a few initial atomic periods before reaching a constant value. Such transient behaviour, and the associated enhancement of steady-state friction, diminishes as the number of two-dimensional layers increases, and was observed only when the two-dimensional material was loosely adhering to a substrate. This layer-dependent transient phenomenon has not been captured by any simulations. Here, using atomistic simulations, we reproduce the experimental observations of layer-dependent friction and transient frictional strengthening on graphene. Atomic force analysis reveals that the evolution of static friction is a manifestation of the natural tendency for thinner and less-constrained graphene to re-adjust its configuration as a direct consequence of its greater flexibility. That is, the tip atoms become more strongly pinned, and show greater synchrony in their stick–slip behaviour. While the quantity of atomic-scale contacts (true contact area) evolves, the quality (in this case, the local pinning state of individual atoms and the overall commensurability) also evolves in frictional sliding on graphene. Moreover, the effects can be tuned by pre-wrinkling. The evolving contact quality is critical for explaining the time-dependent friction of configurationally flexible interfaces.

On the continuum versus atomistic descriptions of dislocation nucleation and cleavage in nickel

A hybrid atomistic-finite-element model is compared with the continuum-based Peierls-Nabarro model for several crack orientations in a nickel crystal. Both methods incorporate the same embedded-atom potential for Ni, in order to make the comparison as valid as possible. The agreement (expressed in terms of a stability diagram showing envelopes in loading space where fracture or dislocation nucleation are likely to occur) is excellent in the case of a crack lying on a (111) plane, with a crack front running along a (211)-type direction, subject to mixed-mode I-II loadings. That orientation involves dislocation nucleation on the prolongation of the crack plane, and hence no ledge is formed upon dislocation nucleation. In other geometries considered (involving a crack on a (100)-type plane), the agreement seems to get poorer with increasing size of the ledge the is created when a dislocation nucleates. In all geometries, the atomistic model shows that incipient dislocation-like features are present before dislocation nucleation takes place, which serves as additional validation of the continuum Peierls-Nabarro model.