Session L26: Focus Session: Friction, Fracture and Deformation Across Length Scales - Dislocations and Fracture

How dislocations and grain boundaries control wear at the nanoscale

Ceramics show outstanding mechanical properties such as high strength and high hardness over a wide range of temperatures and are stable in harsh environments. However, the low fracture toughness of ceramics limits their practical utility for instance as wear-resistance coatings. There have been several reports of improving wear resistance of ceramics by reducing the grain sizes and/or the dimension of the cutting tools to the nanometer regime. Using SiC as a model covalent ceramic, we performed molecular dynamics (MD) simulations of wear for both single crystal and nanocrystalline material. We determined the role of dislocations and grain boundary sliding in improving wear resistance of SiC and we have quantified contributions from these mechanisms to friction and wear. We have discovered instabilities that control sliding of the amorphous-like highly disordered grain boundaries in SiC, in analogy to instabilities and deformation mechanisms that occur in bulk amorphous materials. In this talk we will also present our newly developed analytical model for plowing friction in nanoscale contacts, which model has been validated for both ceramics and metals. In order to isolate the contribution from grain boundary sliding to deformation of nanocrystalline materials, we have performed MD simulations of nanoindentation and uniaxial testing on ultrananocrystalline diamond (UNCD). We have shown that in the absence of dislocation plasticity, hardness and yield strength of nanocrystalline materials scale linearly with the grain boundary shear strength, where the latter property can be controlled by grain boundary doping. Our findings explain the experimental observations that hardness and elastic properties of UNCD decrease with an increasing H content.   

Plastic flow and failure in metallic glass/nanocrystal composites

The exploitation of metallic glasses' high strength in structural applications is limited by their lack of any hardening subsequent to yield. This lack of hardening leads to plastic localization as evidenced by the spontaneous formation of shear bands. One proposed method of forestalling such instabilities is to introduce nanocrystal inclusions to disrupt shear band nucleation and propagation. We have undertaken a series of molecular dynamics simulations of glasses with different morphologies of nanocrystallites. We report the resulting plastic response, and we use various simulations of these types to test the applicability of the shear transformation zone (STZ) constitutive relation for modeling such complex nano-composite materials.   

Atomic Origins of Friction Reduction in Metal Alloys

Gold is a desirable material for use in high performance electrical contacts because it offers low contact resistance, does not corrode or oxidize, and can be easily made into thin sheets. However, gold contacts generally suffer from high adhesion and friction. The tribological issues are mitigated in nanocrystalline gold alloys (with, for example, Ni or Co), which can exhibit both low friction and low contact resistance. The atomic scale mechanisms responsible for the change in frictional response are poorly understood. We will present the results of large scale molecular dynamics simulations which study the tribological response of nanocrystalline films of pure gold and alloys under a variety of sliding conditions. Our results indicate that in pure metals, cold welding and microstructural reorientation lead to the formation of a commensurate sliding interface and high friction resulting from dislocation controlled plasticity. In alloys, however, differing lattice constants suppress the reorientation of grains at the contact point, which leads to grain boundary sliding and lower friction.   

Deformation Initiation by Non-planar \{10-12\} Twinning Nucleation in Magnesium Crystal

The nucleation mechanism of experimentally most commonly observed twinning in Mg crystal initiating deformation process are studied using molecular dynamic simulation. We observed nucleation of radially growing \{10-12\} twinning under tensile loading in Mg rectangular wire system without artificial creation of an twinning. The twinning nucleation mechanism is very different from the conventional twinning mechanism in that the twin nucleates from a point source rather than the fault plane following the partial dislocation line in FCC crystal. The wire axis is normal to basal plane of Mg crystal. The tensile deformation in c-axis nucleates \{10-12\} twinning starting at the corner of square of cross section of the wire. The twin boundary is spherical at the beginning and become linear boundaries in \{10-12\} planes as time goes by.   

Softening of nanocrystalline materials at small grain size

We examine the dependence of the mechanical properties of nanocrystalline materials on grain size. Our extensive atomistic simulations for several nanocrystalline solids show a universal softening at grain sizes of less than a few nanometers. The elastic constants decrease as the average grain size becomes smaller, in analogy with the reverse Hall-Petch effect for nanocrystalline metals. This behavior is explained by the increase of the fraction of grain boundary atoms as grain size decreases. We derive simple scaling laws for various mechanical properties as a function of the grain size by decomposing the energy into contributions from atoms in the bulk of grains and from atoms at the interfaces. Our theoretical predictions fit very well our results from atomistic simulations of different nanocrystalline materials, from nanocrystalline metals to ultrananocrystalline diamond. It is therefore argued, and quantitatively explained, that softening at small grain size is a general nanoscale effect.   

Large scale NEMD simulations of polycrystalline Al sliding interfaces

We present the results of NonEquilibrium Molecular Dynamics (NEMD) simulations for the frictional force between polycrystalline Al samples. Polycrystalline Al samples of order 26M atoms with grain sizes from 10 - 20 nm at compressions of 15 GPa are condsidered as a function of sliding velocity . Typical sample dimensions are 58nm in the sliding and transverse directions and 116nm in the direction normal to the sliding interface. A constant temperature (300K) and constant tangential velocity boundary condition is imposed at the boundaries in the direction normal to the sliding plane. We discuss the modes of plastic deformation and polycrystalline deformation which determine the steady state frictional force and compare these results with results for defect free Al single crystals and highly defective Al single crystal samples.   

Fracture In Disordered Media: Nucleated, Critical or Percolative?

Fracture is often considered to be an abrupt transition and is modeled by nucleation theory. However, the precursor events leading to macroscopic failure display scaling behavior and are understood in terms of critical phenomena. Further, the universal roughness properties of fracture surfaces have been explained by modeling fracture as a percolative process. We attempt to unify these disparate descriptions of fracture in one comprehensive theory. We study the random fuse network as a typical model of disordered brittle media. We show that in this model fracture can be nucleated, critical or percolative depending on the behavior of the tail of the distribution of fuse strengths. We explore the phase diagram by using numerical simulations as well as theoretical arguments.   

Homogeneous Dislocation Nucleation

We perform atomistic computer simulations to study the mechanism of homogeneous dislocation nucleation (HDN) in a 2D hexagonal crystalline film under circular indentation. The nucleation process is governed by vanishing of energy associated with a single normal mode. For fixed film thickness, $L$, the spatial extent, $\xi$, of the critical mode grows with indenter radius, $R$. For fixed $R/L$, $\xi$ scales roughly as $\xi\sim L^{0.4}$. We perform a \emph{mesoscale} analysis to determine the lowest energy normal mode for regions of varying radius, $r_{\rm meso}$, centered on the critical mode's core. The energy of the lowest normal mode $\lambda_{\rm meso} \to 0$ rapidly as $r_{\rm meso}\to \xi$. The lowest mode shows a spatial extent, $\xi_{\rm meso}$, which increases sublinearly for $r_{\rm meso}\leq \xi$ and saturates at $r_{\rm meso} \approx 1.5\; \xi$. We demonstrate that the $\xi_{\rm meso}/ \xi$ versus $r_{\rm meso}/ \xi$ curve is \emph{universal} (independent of $L$ or $R$). Hence small regions, $r_{\rm meso}\leq \xi$, \emph{can} reveal the presence of incipient instability but give excellent estimates for the critical mode's energy and spatial extent \emph{only} for $r_{\rm meso} \geq 1.5\; \xi$. Thus HDN is a \emph{quasi-local} phenomenon.   

Fracture Energy Issues of Brittle, Microcrack Brittle, and Dislocation Ductile Materials

Somigliana elasticity models(1915) for dislocation-microcrack defect discontinuities in a material form an analog basis to relate dislocation density evolution to microcrack density evolution near an existing idealized crack-tip. Thus, a recent idealized field solution derived for stochastic dislocation density evolution near a crack-tip in a ductile material is also an analog applicable field solution for stochastic microcrack density evolution in a brittle material near a crack-tip. A non-equilibrium thermodynamic functional is derived and integrated to evaluate rates of dislocation and microcrack internal energy evolution due to the singularity terms of these crack-tip solutions in an arbitrary spatial crack-tip neighborhood and during an arbitrary fracture toughness load-up time interval of [0, t*]. At some time greater than t*, the available inter-atomic lattice(analog recoverable elastic) internal energy at a crack-tip becomes probabilistically sufficient, in an energy transfer-stability sense of Gibbs[1906], Griffith[1920], and Eshelby[Phil Trans Roy Soc, 1951], to be configurationally transported from locally recoverable internal energy at a crack-tip to non-recoverable crack-tip surface energy as a crack-tip propagates.   

Role of interactions and damage in a cohesive fracture model

We study the influences of local and long range interactions in a numerical model of tensile fracture. Our model simulates fracture events on a 2D square lattice plane with a Metropolis algorithm. We chose a Hamiltonian that is written as a function of the crack separation (offset field) and includes contributions from an external field, interactions, as well as a cohesive energy across the crack surfaces. Included in our study is both a ferromagnetic-type (attractive) and antiferromagnetic-type (repulsive) interactions. We test both of these interactions individually as well as a hybrid interaction in which over a short range the interaction is antiferromagnetic and in the long range the interaction becomes ferromagnetic. This dual interaction approximates a Lennard-Jones potential. We also propose a characterization of damage and investigate the increase of damage in time for fractures occurring by a static-load as well as a time-dependent load. Damaged sites do not interact with neighboring sites and cannot hold any load. We compare our damage model to previous studies of fiber-bundle models.   

Indentation of Graphene Membranes: Non-Linear Response, Nano-Fracture, and Crack Propagation

Recent indentation experiments on graphene have revealed its exceptional strength, making it an excellent candidate for the design of nano- and micro- electromechanical systems. Therefore, it is critical to understand the mechanical properties of graphene, and its response to a wide range of loading pressures beyond the elastic regime. In this work molecular dynamics (MD) simulations of indentation of circular graphene membranes were performed with a newly developed interatomic potential, specifically designed to study graphene under extreme tensile stress. The indentation curves confirmed the experimental observation of a non-linear response at large loads, as well as the brittle failure of the membranes via the generation of nano-cracks. Our MD simulations showed that the fracture process consists of two consecutive stages: an initial bond-breaking event followed by the formation and propagation of cracks. The kinetic theory of bond breaking was applied to determine the breaking strength of graphene and its dependence on the indenter radius, as well as the waiting time for failure. MD simulations were used to provide an atomic-scale description of fracture dynamics.   

Investigation of Nonlinear Elastic Behavior of Two-Dimensional Molybdenum Disulfide

The present study investigates the nonlinear elastic properties of a single-layer molybdenum disulfide crystal through experiment, finite element modeling, and density functional theory. Suspended single-layer molybdenum disulfide crystals are suspended over circular holes that were etched on a silicon oxide surface. Crystals are loaded at the center with an atomic force microscope until fracture occurs. The load-displacement curve is used to determine the pretension and linear-elastic response of the crystal. The force at which fracture occurs gives insight into the intrinsic strength and higher order elastic constants of the crystal. These experiments provide a platform to validate first-principles derivation of fifth-order elastic constants for in-plane stiffness using density functional theory. The derived higher order elastic constants are used in a finite element model to predict the breaking strength of two-dimensional molybdenum disulfide. The study bridges the gap between density functional theory and finite element analysis with experimental evidence.