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A study was carried out on the deformation of nanocrystalline cobalt. For cold-rolled nanocrystalline cobalt, the X-ray diffraction peaks narrowed instead of broadened on deformation. The results of transmission electron microscopy showed that grain size (17.8 nm on average) was not increased. The results can be explained in terms of the production and activity of vacancies and vacancy clusters.

Numerical simulations based on the RANS model are known to have drawbacks of low accuracy in predicting the turbulence quantities of the flow fields in stirred tanks. For this purpose, the detached eddy simulation (DES) model was employed to simulate the turbulent flow in an unbaffled dish-bottom stirred tank. The free-surface deformation was modelled by the volume of fluid (VOF) method. The numerical predictions were validated with LDV measurements reported by Haque et al. (Haque, J. N., Mahmud, T., Roberts, K. J., Liang, J. K., White, G., Wilkinson, D., Rhodes, D., Can. J. Chem. Eng. 89 (2011) 745)11. The results show that the predicted surface profiles using the combination of DES and VOF are generally better than their counterparts obtained by the k-ε model. The mean velocity components and turbulent kinetic energy are in good agreement with the experimental results. By comparison, the differences between the k-ε predictions and the LDV data are much greater. These findings indicate that DES works better than k-ε model in the prediction of the free-surface hydrodynamics in stirred tanks.

Decohesion is an important failure mode associated with layered composite materials. Here, the energy implications of material softening are explored in a thermodynamic framework with the result that the dissipated energy (fracture energy) is greater than the plastic work of the traction on the failure surface. It is also argued that if the traction and continuum constitutive equations are solved simultaneously, the resulting algorithm is as simple as that for conventional plasticity. For numerical simulations, the material point method displays the attributes of no mesh deformation so that remeshing is not necessary and the continuous tracking of material points avoids the need for remapping history variables such as decohesion. Compatibility is invoked in a weak sense with the result that no special algorithms are needed for mesh realignment along crack surfaces or for double nodes. Example solutions exhibit no sensitivity of delamination propagation with mesh orientation.

The surface stress distribution in an ordered quantum dot superlattice is investigated using classical molecular dynamics simulations. We find that the surface stress field induced by various numbers~ from 1t o 9! of Ge islands embedded in a Si~001! substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns. The short-ranged nature of this stress field implies that only the uppermost layers affect the surface growth and that their influence decreases rapidly with layer depth. @S0163-1829~99!52028-6#

The problem of dry friction between two metallic interfaces is discussed from the perspective of large scale molecular dynamics (MD) simulations. For flat interfaces between identical metals, two-dimensional MD simulations using embedded-atom-method potentials for copper have shown a variety of phenomena associated with a velocity weakening of the tangential force at high relative velocities (approaching significant fractions of the transverse sound speed). These include dislocation generation, dislocation motion both parallel and normal to the sliding interface, large plastic deformation, nucleation of microstructure, diffusive coarsening of microstructure, and material mixing. The early time behavior of a flat sliding interface is dominated by dislocation motion parallel to the interface. For this early stage, lower-dimensional models are useful in interpreting some of the simulation data. A two-chain forced Frenkel-Kontorova model reproduces some of the behavior of the larger scale simulations when the phenomenological damping is taken to be consistent with the MD simulations. This model exhibits four velocity regimes of steady state flow which will be discussed. Some of the implications for the nucleation of microstructure will be addressed.

A series of molecular-dynamics simulations has been performed in order to evaluate the effects of several physical factors on dynamic crack stability. These factors are the crystalline structure and the interatomic interaction modeled by various empirical potentials. For brittle crack propagation at low temperature we find that steady-state crack velocities are limited to a band of accessible values. Increasing the overload beyond ${\mathrm{K}}_{\mathrm{Ic}}$, the crack can propagate with a steady-state velocity, which quickly reaches the terminal velocity of about 0.4 of the Rayleigh wave speed. The magnitude of the terminal velocity can be related to the nonlinearity of the interatomic interaction. Further increasing the overload does not change the steady-state velocity dramatically, but significantly increases the amplitude of acoustic emission from the crack tip. Loading the crack even further leads to instabilities which take the form of cleavage steps, dislocation emission, or branching. The instability is closely related to the buildup of a localized coherent, phononlike field generated by the bond-breaking events. The form of the instability depends critically on crystal structure and on the crystallographic orientation of the crack system but can also be correlated with the relative ease of dislocation generation (and motion).

We performed embedded atom method calculations of surface energies and unstable stacking fault energies for a series of intermetallics for which interatomic potentials of the embedded atom type have recently been developed. These results were analyzed and applied to the prediction of relative ductility of these materials using the various current theories. Series of alloys with the B2 ordered structure were studied, and the results were compared to those in pure body-centered cubic (bcc) Fe. Ordered compounds with L12 and L10 structures based on the face-centered cubic (fcc) lattice were also studied. It was found that there is a correlation between the values of the antiphase boundary (APB) energies in B2 alloys and their unstable stacking fault energies. Materials with higher APB energies tend to have higher unstable stacking fault energies, leading to an increased tendency to brittle fracture.

We have discussed the prospects of applying massively parallel molecular dynamics simulation to investigate brittle versus ductile fracture behaviors and dislocation intersection. This idea is illustrated by simulating dislocation emission from a three-dimensional crack. Unprecedentedly, the dislocation loops emitted from the crack fronts have been observed. It is found that dislocation-emission modes, jogging or blunting, are very sensitive to boundary conditions and interatomic potentials. These 3D phenomena can be effectively visualized and analyzed by a new technique, namely, plotting only those atoms within the certain ranges of local potential energies.

From large-scale molecular-dynamics simulations of dynamic crack propagation, we find that cracks accelerate quickly to a relatively steady velocity. Energy released by bond breaking accumulates in a local phonon field that moves with the crack tip and promotes the emission of dislocations. Branching follows dislocation emission along a slip plane. The branching instability requires the crack to achieve a critical velocity, as well as in induction time for energy buildup at the crack tip. {copyright} {ital 1996 The American Physical Society.}

The effect of processing-induced fiber damage, or equivalently the effect of fiber length in discontinuously-reinforced composites, on the tensile stress-strain behavior of a fiber-reinforced ceramic or metal matrix is determined as a function of the extent of initial fiber damage and the pristine fiber strength distribution. The analysis combines a generalization of the analysis employed for the undamaged fiber problem [Curtin, W. A. (1991) Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Sec. 74, 2837-2845] and numerical simulations to predict the stress-strain curve, ultimate tensile strength and strain, fiber pullout, and work of pullout in terms of the underlying micromechanical material parameters. The results show that the characteristic scale of initial damage required to weaken the composite substantially is always of the order of one fiber break per length delta(c), where delta(c) is the critical fiber slip length in the undamaged composite (typically similar to 1 mm). Overall, the effect of damage on tensile strength, failure strain, and pullout is found to be fairly small, which is attributed to the load carrying capacity of broken fibers due to the sliding resistance of the fiber/matrix interface. However, the detailed stress-strain behavior of the composite is modified. The analysis is applied to a Nicalon/CAS composite in which ''premature'' fiber damage has been observed. The inclusion of initial fiber damage into the theory accurately accounts for the excess strain, lower tangent modulus, and lower ultimate strength (relative to the predictions in the absence of initial fiber damage) observed in this material.

Using the lattice Green function approach, we study the crack-dislocation effects in the fracture of crystalline materials. Firstly, we calculate the Green function for the defective lattice, with dislocation and crack, by solving the Dyson equation. After the lattice Green functions have been determined, the relaxation problem for the reconstituted bonds in the cohesive zone is solved. The external force F with tensile and shear components is applied, as a pair of forces, to the atoms at the center of the crack. In this calculation the dislocation emission is chosen to be on a cleavage plane as well as on a glide plane of the two-dimensional lattice (hexagonal and graphite lattices). We compare the cleavage and dislocation emission criteria of the atomistic simulation with those of linear elasticity theory.

A series of atomistic calculations is performed in order to evaluate the effects of several physical factors on dislocation emission in a model hexagonal lattice. The method of calculation is the lattice Green's-function method, together with several pair potentials with variable parameters. The physical factors of interest are the dislocation width (or, more precisely, maximum strain) and ``unstable stacking energy'' suggested by several continuum-based calculations, as well as the mode-I loading. We find that the continuum theories are surprisingly accurate, provided that some modifications are made. Typical discrepancies are of order 10% in the emission stress intensity. However, the atomistic calculations indicate that several of the assumptions underlying the continuum theories are inaccurate. In addition, we find strong mode-I--mode-II interactions, which are summarized in the form of a crack-stability diagram.

In this paper, we address some fundamental questions regarding the response of a crack to externally generated dislocations. We note that since dislocations that formed at external sources in the material must be in the form of loops or dipoles, the theory must be couched in terms of crack shielding in a plastically polarizable medium. There are strong analogies to dielectric theory. We prove two general theorems: (1) Dipoles formed in the emission geometry relative to a crack tip always antishield the crack and (2) when dipoles are induced during uniform motion of a crack through a uniformly plastically polarizable material, then the net shielding is always positive. We illustrate these general theorems with a number of special cases for fixed and polarizable sources. Finally, we simulate the self consistent time dependent response of a crack to a polarizable source as the crack moves past it. The results show that the crack is initially antishielded, but that positive shielding always dominates during later stages of configuration evolution. The crack may be arrested by the source, or it may break away from it, depending upon the various parameters (source strength and geometry, dislocation mobility, Griffith condition for the crack, etc.). The results indicate that the time dependence of crack shielding in the presence of a nonuniform density of sources will be very important in practical cases of brittle transitions in materials.

In this paper, we propose that, depending on their height, ledges on cracks can be efficient sources of dislocations at loadings well below the critical loading for homogeneous emission. Detailed 3-D elastic calculations are presented supporting this proposition. There are two configurations for emission: one which blunts the crack, and one we call a jogging configuration. By our calculations, the blunting configuration should be the more efficient source; however, jogging dislocations are more frequently observed, experimentally. We find that the ledge is only a finite source of dislocations, in the sense that the ledge height decreases as the dislocations are emitted. The atomic configuration at the ledge is composed of finite lengths of real dislocations, which is the reason why such dislocations can be emitted easier than homogeneously produced dislocations. The stresses at the ledge tip produce a cloud of bound dislocations near the ledge, pinned at the ledge ends, so that the ledge crack configuration becomes delocalized. Delocalization of the pileup dislocations in the jogging direction may explain why the jogging dislocations are more frequently seen. Implications for dislocation free zones and ductile transitions are discussed.

The behavior of jogged screw dislocations in γ-TiAl alloys have been investigated with largescale molecular dynamics (MD) simulations. We find a new mechanism for formation of pinning points in jogged screw dislocations. We also find that the critical height for the jogs in ±[110] directions on the (001) plane to move nonconservatively is between 3r0 and 4r0, where r0 is the nearest neighbor distance of aluminum atoms. Interstitials and vacancies are created during the nonconservative motions of the jogs. In addition, the formations of dislocation dipole and loops around the jogs are also observed.

A common failure mechanism in metallic thin-film interconnects is void propagation driven by electric fields and thermomechanical stresses. In this paper, a multiscale computational analysis is presented for predictive modeling of transgranular void dynamics. The modeling approach is hierarchical and involves atomistic simulations for property database development, molecular-dynamics simulations for understanding of void-tip mechanisms, and self-consistent mesoscopic simulations based on boundary-element methods and techniques for moving boundary propagation. An extremely rich void dynamical behavior is predicted, which includes faceting, facet selection, propagation of slits from the void surface, as well as formation of fine-scale crack-like features on the void surface, in agreement with recent experimental data.

We present the results of simulations for sliding copper interfaces for pressures in the kilobar range. The velocity dependence and density dependence are discussed and the evolution of plastic damage is described. Density dependent embedded atom model (EAM) potentials are used to describe the atomic interactions. Simulations were typically for N=65,000 atoms and were carried out using molecular dynamics on massively parallel CM200 and CM5 platforms. A transition to a low friction state at high velocities is discussed.

We have studied brittle and ductile behavior and their dependence on system size and interaction potentials, using molecular-dynamics (MD) simulations. By carefully embedding a single sharp crack in two- and three-dimensional crystals, and using a variant of the efficient sound-absorbing reservoir of Holian and Ravelo [Phys. Rev. B 51, 11275 (1995)], we have been able to probe both the static and dynamic crack regimes. Our treatment of boundary and initial conditions allows us to elucidate early crack propagation mechanisms under delicate overloading, all the way up to the more extreme dynamic crack-propagation regime, for much longer times than has been possible heretofore (before unwanted boundary effects predominate). For example, we have used graphical display of atomic velocities, forces, and potential energies to expose the presence of localized phonon-like modes near the moving crack tip, just prior to dislocation emission and crack-branching events. We find that our careful MD method is able to reproduce the ZCT brittle-ductile criterion for short-range pair potentials [static lattice Green's function calculations of Zhou, Carlsson, and Thomson, Phys. Rev. Letters 72, 852 (1994)].We report on progress we have made in large-scale 3D simulations in samples that are thick enough to display realistic behavior at the crack tip, including emission of dislocation loops. Such. calculations, using our careful treatment of boundary and initial conditions - especially important in 3D - have the promise of opening up new vistas in fracture research.

With a recently developed numerical technique, we have investigated failure processes in real fiber composites. This technique utilizes 3D lattice Green's functions to calculate load transfer from broken to unbroken fibers, and also includes the important effects of fiber/matrix sliding. It is found that the failure processes are more complex than previously thought: The fibers that break or slide are not necessarily located around the largest defect cluster. Rather, the breaking/sliding fibers accumulate, form several large clusters, coalesce and finally cause the fiber composite to fail. Only in some cases does one large defect dominate the damage evolution. Based on our observations of the irregular evolution of the damage, a simple model is developed to describe these different failure modes, and the failure criterion of the fiber composite is also discussed.

A series of atomistic calculations is performed in order to establish criteria for dislocation emission from cracks in a model hexagonal lattice. We find that except for special orientations, additional tensile broken-bond effects must be added to existing theories based on shear effects, in order to correctly estimate the critical stress intensity ${\mathit{K}}_{\mathit{e}}$ required for dislocation emission. From this, a new ductility criterion for materials is proposed which does not depend on the intrinsic surface energy, but contains only the unstable stacking fault parameter.

Using the lattice Green's function approach, we study the crack/dislocation effects in the fracture both of ductile and brittle (2D) materials. The lattice Green's function for the defective lattice, with dislocation and a crack, are obtained by solving the Dyson equation. The external force, F, with tensile and shear components is applied, as a pair of forces, to the atoms near the center of the crack. In this calculation, the dislocation emission is chosen to be cleavage plane as well as glide plane of the 2D lattice. We compare the cleavage and dislocation emission criteria of the atomistic simulation with those of the linear elasticity theory.

In this paper we compare a set of atomic calculations of interfacial crack structure and properties with the predictions of an augmented elastic theory. Our intent is to critique the elastic predictions, especially the mode conversion and displacement closure oscillation features of the elastic theory. A simple physical picture is developed based on a crack stability diagram, using two sets of stress intensity axes. The first set is the normal applied stress intensity K and the second is a local stress intensity factor k, defined to describe the physics of the core region. The Griffith condition and dislocation emission criterion are defined in terms of the local k, and its associated effective core size parameter. Unfortunately, the physical core size is not a unique parameter in the problem, but varies directly with the amount of shear in the core. Thus, the effective core size for the Griffith condition is different from that for dislocation emission. In each case, the effective core size is much smaller than the physical core size, which means that the mode shift at the crack tip is considerably larger than would be expected on the basis of linear elasticity. However, with appropriately defined effective core size parameters, the Griffith condition is well satisfied, and the emission criterion based on the Rice unstable-stacking-fault condition is also surprisingly well satisfied in the mode-II emission configuration. The crack is found never to exhibit displacement oscillations, in part, because of the necessary condition that the Griffith condition be satisfied at the crack tip, and in part because the amount of shear in the core is limited by dislocation emission.

The authors discuss the influence of external dislocations on the crack tip process mainly using the superdislocation pair model. They present a detailed comparison of dislocations emitted from external sources and dislocations emitted from the crack source. The results show that external dislocations play a very significant role in the crack tip process.