Double kink mechanisms for discrete dislocations in BCC crystals

We present an application of the discrete dislocation theory to the characterization of the energetics of kinks in Mo, Ta and W body-centered cubic (BCC) crystals. The discrete dislocation calculations supply detailed predictions of formation and interaction energies for various double-kink formation and spreading mechanisms as a function of the geometry of the double kinks, including: the dependence of the formation energy of a double kink on its width; the energy of formation of a double kink on a screw dislocation containing a pre-existing double kink; and energy of formation of a double kink on a screw dislocation containing a pre-existing single kink. The computed interaction energies are expected to facilitates the nucleation of double kinks in close proximity to each other and to pre-existing kinks, thus promoting clustering of double kinks on screw segments and of ‘daughter’ double kinks ahead of ‘mother’ kinks. The predictions of the discrete dislocation theory are found to be in good agreement with the full atomistic calculations based on empirical interatomic potentials available in the literature.     

Stacking fault energies and slip in nanocrystalline metals

The search for deformation mechanisms in nanocrystalline metals has profited from the use of molecular dynamics calculations. These simulations have revealed two possible mechanisms; grain boundary accommodation, and intragranular slip involving dislocation emission and absorption at grain boundaries. But the precise nature of the slip mechanism is the subject of considerable debate, and the limitations of the simulation technique need to be taken into consideration. Here we show, using molecular dynamics simulations, that the nature of slip in nanocrystalline metals cannot be described in terms of the absolute value of the stacking fault energy-a correct interpretation requires the generalized stacking fault energy curve, involving both stable and unstable stacking fault energies. The molecular dynamics technique does not at present allow for the determination of rate-limiting processes, so the use of our calculations in the interpretation of experiments has to be undertaken with care.     

Two-phonon Raman scattering of light in rare gas crystals

In this paper we calculate the two-phonon efficiency for light scattering from rare gas crystals at all temperatures. We use a Lennard-Jones potential and the Lorentz-Lorenz model following previous theoretical work and use the first-order self-consistent phonon theory, supplemented by a simple model giving the phonon anharmonic widths and shifts. Our results, though larger than the experimental results, agree well with earlier calculations at 0 K and related molecular dynamics work. The calculated spectra show a rich structure that varies with temperature. We suggest that further experiments could lead to significant new insights into the nature of excitations in rare gas solids as a function of temperature.Work submitted in partial fulfillment of the requirements of the Ph.D. degree at Rutgers University.     

A review of slip transfer: applications of mesoscale techniques

In this review article, we present and discuss recent mesoscale modeling studies of slip transmission of dislocations through biphase interfaces. Specific focus is given to fcc/fcc material systems. We first briefly review experimental, atomistic, and continuum-scale work that has helped to shape our understanding of these systems. Then several mesoscale methods are discussed, including Peierls–Nabarro models, discrete dislocation dynamics models, and phase field-based techniques. Recent extensions to the mesoscale mechanics technique called phase field dislocation dynamics are reviewed in detail. Results are compiled and discussed in terms of the proposed guidelines that relate composite properties to the critical stress required for a slip transmission event.     

Dislocations in crystals and in continua: A confrontation

We consider Bravais crystals under volume-conserving plastic deformation. The crystal is the prominent prototype of a metric solid. In fact, it allows the measurement of lengths by counting atomic steps and applying Pythagoras' law. This remains true even when , in a thought experiment, the lattice spacing is made smaller and smaller. If in this process care is taken for the conservation of the local dislocation content, then the distance between the scaled down dislocations, when measured in (scaled down) atomic distances goes to infinity so that the dislocations remain discrete objects in the now-called continuized crystal. In particular Frank's definition of the dislocation remains valid. Since numbers and types of discrete dislocations can be determined, at least in thought experiments, the dislocation density can be introduced as an explicit state quantity in the continuized crystal. By explicit state quantities we understand those which enter the energy expression explicitly as independent variables.

On the other hand, in ordinary structureless continua dislocations, as defined by Burgers, are not state quantities. As a result, these dislocations do not appear as dynamical variables in the pertaining field theory, whereas dislocations in crystals do. Hence the mechanical theory of (ordinary structureless) continua, proven most valuable in many applications, is not appropriate in situations where the internal mechanical state (here the dislocation state) suffers significant changes.     

The study of grain boundary density effect on multi-grain thin film under tension

The grain-size effect on the yield strength and strain hardening of thin film at sub-micron and nanometer scale closely relates to the interactions between grain boundary and dislocation. Based on higher-order gradient plasticity theory, we have systematically investigated the size effect of multi-grain thin film arising from the grain boundary density under tensile stress. The developed formulations employing dislocation density and slip resistance have been implemented into the finite element program, in which grain boundary is treated as impenetrable interface for dislocations. The numerical simulation results reasonably show that plastic hardening rate and yield strength are linear to the grain boundary density of multi-grain thin film. The aspect ratio of grain size and orientation of slip system have distinct influence on the grain plastic properties. The research of slip system including homogeneous and nonhomogeneous distribution patterns reveals that the hardening effect of low-angle slip system is greater than that of high-angle slip system. The results agree well with the experimentally measured data and the solutions by discrete dislocation dynamics simulation.     

Molecular Dynamics Study on Interfacial Energy and Atomic Structure of Ag/Ni and Cu/Ni Heterophase System

The results of molecular dynamics calculations on the interfacial energies and atomic structures of Ag/Ni and Cu/Ni interfaces are presented. Calculation on Ag/Ni interfaces with low-index planes shows that those containing the (111) plane have the lowest energies, which is in agreement with the experiments. Comparing surface energy with interfacial energy, it is found the order of the interfacial energies of Ag/Ni and Cu/Ni containing the planes fall in the same order as solid-vapor surface energies of Ag, Cu and Ni. In this MD simulation, the relaxed atomic structure and dislocation network of (110)Ag||(110)Ni interface are coincident to HREM observations.     

Simulation of dislocations and strength in thin films: A review

Crystalline thin films have mechanical properties that cannot be predicted based on bulk scaling laws. Owing to their importance in technology, a great deal of effort has gone into modeling and simulation of the behaviors of dislocations in thin films. In this review, the successes and failures of modeling dislocations in thin films via analytical techniques, 2D dislocation dynamics simulations, and 3D discrete dislocation dynamics (DDD) simulations are discussed. Brief discussions of phase field models and level set methods are also included. The unique importance of 3D DDD simulations is highlighted, as these simulations allow study of realistic dislocation behavior that is otherwise difficult or impossible to observe. The utility of 3D DDD in discovering the mechanisms that control deformation in films is demonstrated, and first steps towards construction of a strain hardening model based on those mechanisms are described.     

Fatigue crack nucleation: Mechanistic modelling across the length scales

This paper presents an assessment of recent literature on the mechanistic understanding of fatigue crack nucleation and the associated modelling techniques employed. In particular, the important roles of (a) slip localisation and persistent slip band formation, (b) grain boundaries, slip transfer and interfaces, (c) microtexture and twins, and (d) nucleation criteria and microcracks are addressed in the context of the three key modelling techniques of crystal plasticity (CP), discrete dislocation (DD) plasticity and molecular dynamics (MD) where appropriate. In addition, the need for computational fatigue crack nucleation methodologies which incorporate mechanistic understanding is addressed.Key challenges identified include (i) the overall need for multiscale models for fatigue crack nucleation which are continuum-based but mechanistically informed; (ii) full (3D) crystal slip models to capture slip localisation at a DD level; (iii) MD modelling methodologies for slip transfer to inform DD models; and (iv) rigorously validated dislocation structure models at the DD and CP levels.     

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an, China.     

Stability analysis of autonomously controlled production networks

In this paper we present a stability analysis of autonomously controlled production networks from mathematical and engineering points of view. Roughly speaking stability of a system means that the defined state of the system remains bounded over time. The dynamics of a production network are modelled by differential equations (macroscopic approach) and discrete event simulation (microscopic approach), respectively. Both approaches are used to perform a stability analysis. As a result of the stability analysis of the macroscopic approach we calculate parameters, which guarantee stability of the network for arbitrary inputs. These results are refined for a certain (varying) input using the microscopic approach, where we derive the smallest maximal production rates of the plants for which stability of the overall system can be guaranteed. Furthermore, the microscopic approach includes two different autonomous control methods: the queue length estimator (QLE) and the pheromone based (PHE) method. These methods allow additional autonomous decision making on the shop floor level. The approach presented in this paper is to calculate stability conditions by mathematical systems theory to guarantee stability for production networks, to identify a stability region and to refine this region by simulations.     

Discrete dislocation dynamics simulations of surface induced size effects in plasticity

Experiments have shown that the presence of free surfaces may induce harder as well as softer deformation behaviors in a crystalline solid. In order to shed some light on these apparently contradictory findings, two-dimensional discrete dislocation dynamics simulations are performed to investigate the surface induced size effects. The simulations indicate that, depending on the surface density of dislocation sources, a free surface may act either as a dislocation sink or as a net dislocation source, and can accordingly exert opposite effects on dislocation density over a boundary layer thickness of up to 500 nm into the bulk. This finding provides a possible explanation for the apparent contradictions in experimental observations.     

Optimization of 3C–SiC/Si heterointerfaces in epitaxial growth

In this article, we present the basic formalism of the S-correlated theory of misfit induced interface superstructures (MIIS) and nucleation centers for misfit dislocation network (NCMDN). Two main properties play an important role in the theory. The first one is the S factor, which is the ratio of effective elastic constants over the material atomic density: this factor can be identified from the standard equations of the elasticity theory which, in our approach, represents the basic background. This implies a realistic lattice dynamics model which enables to interpret the velocity of longitudinal, transverse and shear vibrational waves in solids. The second property, n_S is a geometric parameter related to the extension of MIIS and to the lattice spacing of misfit dislocation network (MDN). We then apply this theory to several heterosystems and we demonstrate that it can be used to optimize heterointerfaces between host materials characterized by large lattice mismatch.     

Dynamics of fast dislocations

Plastic deformation of crystalline solids at ultra-high strain rates may involve dislocations moving at supersonic speeds, the feasibility of which has been demonstrated via molecular dynamics simulation. The motion of these dislocations in a crystal depends on the defects they encounter, which may slow, or even pin, them down. Recently, we have conducted a series of investigations on the dynamics of transonic dislocations during their interactions with other dislocations, small voids and small interstitial loops, using the molecular dynamics method. The results indicate that a transonic dislocation will be slowed down to subsonic speed by a subsonic dislocation in front of it, and that approaching dislocations at sufficiently high velocities may not form a stable dipole. Small defects, like voids and interstitial clusters, on the other hand, will only temporarily slow down a segment of the transonic dislocation, which absorbs the interstitial loop by forming jogs, and sweeps the void into a few smaller defects of vacancy type. Upon release from the clusters, this segment of dislocation regains speed and becomes transonic again. In view of the possible important role played by high-speed dislocations during high-speed deformation, and from the point of scientific interest, we summarize this series of investigations, and discuss their implications in the present paper.     

Coupling in situ experiments and modeling – Opportunities for data fusion,machine learning,and discovery of emergent behavior

This paper reviews recent studies, that not only includes both experiments and modeling components, but celebrates a close coupling between these techniques, in order to provide insights into the plasticity and failure of polycrystalline metals. Examples are provided of studies across multiple-scales, including, but not limited to, density functional theory combined with atom probe tomography, molecular dynamics combined with in situ transmission electron miscopy, discrete dislocation dynamics combined with nanopillars experiments, crystal plasticity combined with digital image correlation, and crystal plasticity combined with in situ high energy X-ray diffraction. The close synergy between in situ experiments and modeling provides new opportunities for model calibration, verification, and validation, by providing direct means of comparison, thus removing aspects of epistemic uncertainty in the approach. Further, data fusion between in situ experimental and model-based data, along with data driven approaches, provides a paradigm shift for determining the emergent behavior of deformation and failure, which is the foundation that underpins the mechanical behavior of polycrystalline materials.     

The feedback loop between theory,simulation and experiment for plasticity and property modeling

Recent advances in theory, simulation and experiment are leading to new capabilities for understanding and characterizing the relation between dislocation substructure evolution and materials properties and performance. With the emergence of large-scale computational capabilities, techniques such as three-dimensional discrete dislocation dynamics simulations are providing new insights to a range of materials deformation phenomena. Such simulations provide direct measures of dislocation motion and substructure development at small and continuously increasing length scales and time scales. Concurrently, the advent of new experimental techniques promises to revolutionize our ability to directly characterize dislocation substructures and their relationship to the microstructure of a range of material systems. Taken by themselves, the simulations and experiments will greatly advance our understanding of materials behavior. We argue, however, that close linkage of the two will provide critically needed validation and enable progress in solving some of the most challenging problems of plasticity, thereby profoundly impacting our ability to predict properties and performance of materials in engineered systems.     

Shear circular dislocation loops investigated with elasticity theory and atomistic simulations

The elastic fields of displacements, strains, and stresses for a shear circular loop are obtained with the Burgers formula. In addition, interactions between two shear circular loops are obtained based on elasticity theory. A series of molecular dynamics (MD) simulations on a shear circular partial dislocation loop in copper have been performed to examine the elastic solutions. It is found that the results of the MD simulations are in good agreement with those of elasticity theory for a loop with radius 7.5 nm.