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.

Multiresolution molecular dynamics approach on parallel computers has been used to investigate fracture in ceramic materials. In microporous silica, critical behavior at fracture is analyzed in terms of pore percolation and kinetic roughening of fracture surfaces. Crack propagation in amorphous silicon nitride films is investigated, and a correlation between the speed of crack propagation and the morphology of fracture surfaces is observed. In crystalline silicon nitride films, temperature-assisted void formation in front of a crack tip slows down crack propagation.

Several activation configurations of dislocation embryos emanating from cleavage crack tips at the verge of propagating have been analyzed in detail by the variational boundary integral method, as central elements of the rate controlling process of nucleation governed fracture transitions from brittle cleavage to tough forms, as in the case for BCC transition metals. The configurations include those on inclined planes, oblique planes and crack tip cleavage ledges. Surface ledge production resistance is found to have a very strong embrittling effect. Only nucleation on oblique planes near a free surface and at crack tip cleavage ledges are found to be energetically feasible to explain brittle-to-ductile transition temperatures in the experimentally observed ranges.

A focused ion beam (FIB) system has been applied to prepare a thin foil specimen of Si, MgO and alumina which contained cracks in the plane of foil. It was possible to observe a much larger area at and near a crack tip than has been hitherto possible. FIB was also applied to observation of microstructure near a crack tip evolved during severe rolling contact fatigue in a steel.

The characteristic features of the brittle-to-ductile transition are explained using a model of cooperative dislocation generation. In two dimensions, the onset of the ductile behavior corresponds to a thermally-driven, stress-assisted dissociation of many atomic-size dislocation dipoles in the vicinity of the crack tip above a critical temperature Tc. The instability is caused by thermally induced screening of dislocation interactions as in the Kosterlitz-Thouless phase transition. However, the critical temperature is well below the melting temperature in the presence of a stress. The nature of dislocation dynamics in the vicinity of the crack tip is also described and its role in the onset of the cooperative instability is examined. The origin of the correlation between the strain-rate dependence of the transition temperature and the temperature dependence of dislocation mobility is explained.

Direct interactions of externally generated dislocations with a moving, non-emitting crack tip, have been investigated. Dislocations of the appropriate Burgers vector, initially residing in a strip ahead of the incoming crack tip, are funneled toward the tip, with their motion restricted to the slip plane. Once drawn into the vicinity of the tip, these dislocations inevitably cause local, atomic scale blunting of the tip. The resulting crack trapping process is modelled, resulting in the temperature, crack velocity, and dislocation density dependent, tip toughness.

The stress-assisted Kosterlitz- Thouless (K-T) transition was proposed by Khantha, Pope and Vitek [1] as a possible mechanism for the abrupt transition from brittle to ductile behavior of single crystals as a function of temperature. We argue that in a two-dimensional crystal under elevated temperature and applied shear stress, the microscopic mechanism of the stressassisted K- T transition is the nucleation of dislocation dipole pairs with a preferred Burgers vector orientation. This defect population gives rise to an anisotropic hexatic phase with quasi-long range order along one axis and short-range order along the orthogonal axis. The laboratory signature of such a phase is scattering peaks that are “streaked,” i.e. strongly broadened along a single direction. We discuss experimental data for an analogous twodimensional system which displays order of this type. Potential implications for the brittleductile transition in three dimensions are outlined.

The behavior of mode I cracks in α-Fe is investigated using molecular statics methods with EAM potentials. A double ended crack of finite size embedded in a cylindrical simulation cell and fixed boundary conditions are prescribed along the periphery of the cell, whereas periodic boundary conditions are imposed parallel to the crack front. The displacement field of the finite crack is represented by that of an equivalent pileup of opening dislocations distributed in a manner consistent with the anisotropy of the crystal and traction free conditions of the crack faces. The crack lies on the {110} plane and the crack front is located either along á100ñ, á110ñ or á111ñ directions. The crack tip response is rationalized in terms of the surface energy (γs) of the cleavage plane and the unstable stacking energies (γus) of the slip planes emanating from the crack front.

Using large-scale molecular dynamics simulation on a massively parallel computer, we have studied the initiation of cracking in a Monel-like alloy of Cu-Ni. In a low temperature 2D sample, fracture from a notch starts at a little beyond 2.5% critical strain when the propagation direction is perpendicular to a cleavage plane. We discuss a method of characterizing crack tip position using a measure of area around the crack tip.

The effects of surface stress on fracture are reviewed. Calculations by Thomson et al. seem to suggest that surface stresses do not affect cleavage fracture when the crack propagates in a self similar manner even though the surface stress can lead to large stresses near the crack tip. However, surface stresses may have an important effect on dislocation emission near the crack tip. A simple analysis is offered to show how these effects may be incorporated into a modified Rice ductile-brittle fracture criterion by adding a term to the unstable stacking energy that takes into account the energy to form an incipient ledge.

Theories of toughness of materials depend on an understanding of the characteristic instabilities of the crack tip, and their possible interactions. In this paper we examine the effect of dislocation emission on subsequent cleavage of a crack and on further dislocation emission. The work is an extension of the previously published Lattice Greens Function methodology[1, 2, 3]. We have developed a Cavity Greens Function describing a blunt crack and used it to study the effect of crack blunting under a range of different force laws. As the crack is blunted, we find a small but noticeable increase in the crack loading needed to propagate the crack. This effect may be of importance in materials where a dislocation source near the crack tip in a brittle material causes the crack to absorb anti-shielding dislocations, and thus cause a blunting of the crack. It is obviously also relevant to cracks in more ductile materials where the crack itself may emit dislocations.

We present results obtained by molecular dynamics simulations on the propagation of fast cracks in triangular 2D lattices. Our aim is to simulate Mode I fracture of brittle isotropic materials. We propose a force law that respects the isotropy of the material. The code yields the correct imposed sound c║, shear c┴ and surface VR wave speeds. Different notch lengths are systematically studied. We observe that initially the cracks are linear and always branch at a particular critical velocity c* ≈0.8VR and that this occurs when the crack tip reaches the position of a front emitted from the initial crack tip and propagating at a speed c = 0.6 8VR.

We use atomistic Monte-Carlo simulations to investigate the dynamics of cracks which sizes are smaller than the Griffith length. We demonstrate that such cracks can irreversibly grow proviso their size is larger than a certain critical length which is smaller than the Griffith length, as recently suggested [ L. Golubović and A. Peredera, Phys. Rev. E51, 2799 (1995)]. We show here that this thermally assisted creep crack growth is dominated by irreversible changes in the region of the crack tip, primarily in the form of dislocation emissions and nucleation of microcavities and voids. These processes act together during the crack growth: the crack tip region acts as a source for emissions of dislocations which subsequently serve as seeds for creation of vacancy clusters in a region away but still close to the crack tip. Eventually, passages between these vacancy clusters and the mother crack are formed and the crack thus increases in size. As this process repeats, the crack grows.

We present a simulation procedure for fracture that self-consistently accounts for dislocation emission, dislocation migration and crack growth. We find that the dislocation microstructure in front of the crack tip is highly organized and shows a complex temporal-spatial evolution. The final dislocation microstructure and the number of emitted dislocations immediately proceeding fracture varies rapidly with the loading rate. For high loading rates, fracture occurs at smaller loads with increasing loading rate. However, the load at fracture shows a maximum with respect to loading rates.

A simulation of structure and motion of edge dislocations in ordered Ni3Al was performed by atomic stiffness matrix method. In this method the equilibrium positions of the atoms were obtained by solving a set of linear equations formed by a stiffness matrix, whose terms consisted of derivatives of the interaction potential of EAM (embedded atom method) type. The superpartial dislocations, separated by an antiphase boundary (APB) on (111), dissociated into Shockley partials with complex stacking faults (CSF) on (111) plane. The core structure, represented by the Burgers vector density distribution and iso-strain contours, changed under applied stresses as well as upon addition of boron. The separation between the superpartials changed with the addition of B and antisite Ni. As one Shockley partial moved out to the surface, a Shockley partial in the interior moved a large distance to join the lone one near the surface, leaving behind a long CSF strip. The decrease in the width of the APB upon addition of B and antisite Ni has been explained by a reduction of the strength of directional bonding between Ni and Al as well as by the dragging of B atmosphere by the superpartials.

Though atomistic simulation of 3D dislocation configurations is an important objective for the analysis of problems ranging from point defect condensation to the operation of Frank-Read sources such calculations pose new challenges. In particular, use of finite sized simulation cells produce additional stresses due to the presence of fixed boundaries in the far field which can contaminate the interpretation of these simulations. This paper discusses an approximate scheme for accounting for such boundary stresses, and is illustrated via consideration of the lattice resistance encountered by straight dislocations and simulations of 3D bow out of pinned dislocation segments. These results allow for a reevaluation of the concepts of the Peierls stress and the line tension from the atomistic perspective.

The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in a-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

This paper presents a synopsis of already published work for cracks on interfaces and new results on the effect of changing the chemistry of the atoms at the interface. Once the appropriate cut-off for the oscillatory singularity in the interface analysis is determined, the physics of the crack is determined in terms of an appropriate driving force for a particular event of interest, and a lattice resistance to the event. Analytic approximations are available for the driving forces, and the lattice resistance is determined on the basis of a block construction for the lattice. We show that for the case where the chemical bonding at the interface is different from that in the matrix, the same ideas are applicable, provided the different chemistry is incorporated correctly in the lattice resistance construction.

The fracture of a thin metal foil constrained between alumina or sapphire blocks has been studied by a number of investigators. The systems that have been investigated include Al [1,2], Au [3], Nb [4], and Cu [5]. Except for Al/ Al2O3 interfaces, these systems exhibit a common fracture mechanism: pores form at the metal/ceramic interface several foil thicknesses ahead of the crack which, under increasing load, grow and link with the initial crack. This mechanism leaves metal on one side of the fracture surface and clean ceramic on the other. This has not been the observation in Al/ A12O3 bonds where at appropriate thicknesses of Al, the fracture appears to proceed as a ductile rupture through the metal.

The failure of sandwich geometry samples has been considered in several published models, e.g., [6,71. The predictions of these models depend on the micromechanic mechanism of crack extension. For example, Varias et al. proposed four possible fracture mechanisms: (i) near-tip void growth at second phase particles or interfacial pores and coalescence with the main crack, (ii) high-triaxiality cavitation, i.e., nucleation and rapid void growth at highly stressed sites at distances of several layer thicknesses from the crack tip, (iii) interfacial debonding at the site of highest normal interfacial traction, and (iv) cleavage fracture of the ceramic. Competition among the operative mechanisms determines which path will be favored.

This paper addresses the question of why the fracture of the A1/A12O3 system appears to be different from other systems by probing the fracture mechanism using X-ray tomographic microscopy (XTM). We have experimentally duplicated the simplified geometry of the micromechanics models and subjected the specimens to a well defined stress state in bending. The bend tests were interrupted and XTM was performed to reveal the mechanism of crack extension.