Publications

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A cohesive zone, finite element fracture analysis is based upon a traction-separation relation. Our recent work has used molecular dynamics simulations to derive general traction-separation relationships for interfacial fracture between two brittle materials under mix-mode loading conditions. Here we apply our method to explore the effects of elastic constants of the two materials on the traction-separation relationship. A comparison and discussion of our results will be provided.

This research utilizes a method for calculating an atomic-scale deformation gradient within the framework of continuum mechanics using atomistic simulations to examine bicrystal grain boundaries subjected to shear loading. We calculate the deformation gradient, its rotation tensor from polar decomposition, and estimates of lattice curvature and vorticity for thin equilibrium bicrystal geometries deformed at low temperature. These simulations reveal pronounced deformation fields that exist in small regions surrounding the grain boundary, and demonstrate the influence of interfacial structure on mechanical behavior for the thin models investigated. Our results also show that more profound insight is gained concerning inelastic grain boundary phenomena by analyzing the deformed structures with regard to these continuum mechanical metrics.

Understanding charge transport processes at a molecular level using computational techniques is currently hindered by a lack of appropriate models for incorporating anistropic electric fields in molecular dynamics (MD) simulations. An important technological example is ion transport through solid-electrolyte interphase (SEI) layers that form in many common types of batteries. These layers regulate the rate at which electro-chemical reactions occur, affecting power, safety, and reliability. In this work, we develop a model for incorporating electric fields in MD using an atomistic-to-continuum framework. This framework provides the mathematical and algorithmic infrastructure to couple finite element (FE) representations of continuous data with atomic data. In this application, the electric potential is represented on a FE mesh and is calculated from a Poisson equation with source terms determined by the distribution of the atomic charges. Boundary conditions can be imposed naturally using the FE description of the potential, which then propagates to each atom through modified forces. The method is verified using simulations where analytical or theoretical solutions are known. Calculations of salt water solutions in complex domains are performed to understand how ions are attracted to charged surfaces in the presence of electric fields and interfering media.

Non-destructive detection methods can reliably certify that gas transfer system (GTS) reservoirs do not have cracks larger than 5%-10% of the wall thickness. To determine the acceptability of a reservoir design, analysis must show that short cracks will not adversely affect the reservoir behavior. This is commonly done via calculation of the J-Integral, which represents the energetic driving force acting to propagate an existing crack in a continuous medium. J is then compared against a material's fracture toughness (J{sub c}) to determine whether crack propagation will occur. While the quantification of the J-Integral is well established for long cracks, its validity for short cracks is uncertain. This report presents the results from a Sandia National Laboratories project to evaluate a methodology for performing J-Integral evaluations in conjunction with its finite element analysis capabilities. Simulations were performed to verify the operation of a post-processing code (J3D) and to assess the accuracy of this code and our analysis tools against companion fracture experiments for 2- and 3-dimensional geometry specimens. Evaluation is done for specimens composed of 21-6-9 stainless steel, some of which were exposed to a hydrogen environment, for both long and short cracks.

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Materials with characteristic structures at nanoscale sizes exhibit significantly different mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscale materials phenomena and macroscale behavior, has eluded the research community.The goal of our project was to develop a consistent theory to model both the evolution ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J.Delph, Remi Dingreville, James W. Foulk III, Robert J. Hardy, Richard Lehoucq, Alejandro Mota,Gregory J. Wagner, Edmund B. Webb III and Xiaowang Zhou. Support for this project was pro-vided by the Enabling Predictive Simulation Investment Area of Sandia's Laboratory DirectedResearch and Development (LDRD) program.5

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To effectively integrate nanotechnology into functional devices, fundamental aspects of material behavior at the nanometer scale must be understood. Stresses generated during thin film growth strongly influence component lifetime and performance; stress has also been proposed as a mechanism for stabilizing supported nanoscale structures. Yet the intrinsic connections between the evolving morphology of supported nanostructures and stress generation are still a matter of debate. This report presents results from a combined experiment and modeling approach to study stress evolution during thin film growth. Fully atomistic simulations are presented predicting stress generation mechanisms and magnitudes during all growth stages, from island nucleation to coalescence and film thickening. Simulations are validated by electrodeposition growth experiments, which establish the dependence of microstructure and growth stresses on process conditions and deposition geometry. Sandia is one of the few facilities with the resources to combine experiments and modeling/theory in this close a fashion. Experiments predicted an ongoing coalescence process that generates signficant tensile stress. Data from deposition experiments also supports the existence of a kinetically limited compressive stress generation mechanism. Atomistic simulations explored island coalescence and deposition onto surfaces intersected by grain boundary structures to permit investigation of stress evolution during later growth stages, e.g. continual island coalescence and adatom incorporation into grain boundaries. The predictive capabilities of simulation permit direct determination of fundamental processes active in stress generation at the nanometer scale while connecting those processes, via new theory, to continuum models for much larger island and film structures. Our combined experiment and simulation results reveal the necessary materials science to tailor stress, and therefore performance, in nanostructures and, eventually, integrated nanocomponents.

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Ongoing research at Sandia National Laboratories has been in the area of developing models and simulation methods that can be used to uncover and illuminate the material defects created during He bubble growth in aging bulk metal tritides. Previous efforts have used molecular dynamics calculations to examine the physical mechanisms by which growing He bubbles in a Pd metal lattice create material defects. However, these efforts focused only on the growth of He bubbles in pure Pd and not on bubble growth in the material of interest, palladium tritide (PdT), or its non-radioactive isotope palladium hydride (PdH). The reason for this is that existing inter-atomic potentials do not adequately describe the thermodynamics of the Pd-H system, which includes a miscibility gap that leads to phase separation of the dilute (alpha) and concentrated (beta) alloys of H in Pd at room temperature. This document will report the results of research to either find or develop inter-atomic potentials for the Pd-H and Pd-T systems, including our efforts to use experimental data and density functional theory calculations to create an inter-atomic potential for this unique metal alloy system.

The performance and the reliability of many devices are controlled by interfaces between thin films. In this study we investigated the use of patterned, nanoscale interfacial roughness as a way to increase the apparent interfacial toughness of brittle, thin-film material systems. The experimental portion of the study measured the interfacial toughness of a number of interfaces with nanoscale roughness. This included a silicon interface with a rectangular-toothed pattern of 60-nm wide by 90-nm deep channels fabricated using nanoimprint lithography techniques. Detailed finite element simulations were used to investigate the nature of interfacial crack growth when the interface is patterned. These simulations examined how geometric and material parameter choices affect the apparent toughness. Atomistic simulations were also performed with the aim of identifying possible modifications to the interfacial separation models currently used in nanoscale, finite element fracture analyses. The fundamental nature of atomistic traction separation for mixed mode loadings was investigated.

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Lightweight and miniaturized weapon systems are driving the use of new materials in design such as microscale materials and ultra low-density metallic materials. Reliable design of future weapon components and systems demands a thorough understanding of the deformation modes in these materials that comprise the components and a robust methodology to predict their performance during service or storage. Traditional continuum models of material deformation and failure are not easily extended to these new materials unless microstructural characteristics are included in the formulation. For example, in LIGA Ni and Al-Si thin films, the physical size is on the order of microns, a scale approaching key microstructural features. For a new potential structural material, cast Mg offers a high stiffness-to-weight ratio, but the microstructural heterogeneity at various scales requires a structure-property continuum model. Processes occurring at the nanoscale and microscale develop certain structures that drive material behavior. The objective of the work presented in this report was to understand material characteristics in relation to mechanical properties at the nanoscale and microscale in these promising new material systems. Research was conducted primarily at the University of Colorado at Boulder to employ tightly coupled experimentation and simulation to study damage at various material size scales under monotonic and cyclic loading conditions. Experimental characterization of nano/micro damage will be accomplished by novel techniques such as in-situ environmental scanning electron microscopy (ESEM), 1 MeV transmission electron microscopy (TEM), and atomic force microscopy (AFM). New simulations to support experimental efforts will include modified embedded atom method (MEAM) atomistic simulations at the nanoscale and single crystal micromechanical finite element simulations. This report summarizes the major research and development accomplishments for the LDRD project titled 'Atomistic Modeling of Nanowires, Small-scale Fatigue Damage in Cast Magnesium, and Materials for MEMS'. This project supported a strategic partnership between Sandia National Laboratories and the University of Colorado at Boulder by providing funding for the lead author, Ken Gall, and his students, while he was a member of the University of Colorado faculty.

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Structural reorientations in metallic fcc nanowires are controlled by a combination of size, thermal energy, and the type of defects formed during inelastic deformation. By utilizing atomistic simulations, we show that certain fcc nanowires can exhibit both shape memory and pseudoelastic behavior. We also show that the formation of defect-free twins, a process related to the material stacking fault energy, nanometer size scale, and surface stresses is the mechanism that controls the ability of fcc nanowires of different materials to show a reversible transition between two crystal orientations during loading and thus shape memory and pseudoelasticity.

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We present a formulation for coupling atomistic and continuum simulation methods for application to both quasistatic and dynamic analyses. In our formulation, a coarse-scale continuum discretization is assumed to cover all parts of the computational domain with atomistic crystals introduced only in regions of interest. The geometry of the discretization and crystal are allowed to overlap arbitrarily. Our approach uses interpolation and projection operators to link the kinematics of each region, which are then used to formulate a system potential energy from which we derive coupled expressions for the forces acting in each region. A hyperelastic constitutive formulation is used to compute the stress response of the defect-free continuum with constitutive properties derived from the Cauchy-Born rule. A correction to the Cauchy-Born rule is introduced in the overlap region to minimize fictitious boundary effects. Features of our approach will be demonstrated with simulations in one, two and three dimensions.

This report is a collection of documents written by the group members of the Engineering Sciences Research Foundation (ESRF), Laboratory Directed Research and Development (LDRD) project titled 'A Robust, Coupled Approach to Atomistic-Continuum Simulation'. Presented in this document is the development of a formulation for performing quasistatic, coupled, atomistic-continuum simulation that includes cross terms in the equilibrium equations that arise due to kinematic coupling and corrections used for the calculation of system potential energy to account for continuum elements that overlap regions containing atomic bonds, evaluations of thermo-mechanical continuum quantities calculated within atomistic simulations including measures of stress, temperature and heat flux, calculation used to determine the appropriate spatial and time averaging necessary to enable these atomistically-defined expressions to have the same physical meaning as their continuum counterparts, and a formulation to quantify a continuum 'temperature field', the first step towards constructing a coupled atomistic-continuum approach capable of finite temperature and dynamic analyses.

We performed atomistic simulations to study the effect of free surfaces on the yielding of gold nanowires. Tensile surface stresses on the surfaces of the nanowires cause them to contract along the length with respect to the bulk face-centered cubic lattice and induce compressive stress in the interior. When the cross-sectional area of a (100) nanowire is less than 2.45 nm x 2.45 nm, the wire yields under its surface stresses. Under external forces and surface stresses, nanowires yield via the nucleation and propagation of the {l_brace}111{r_brace}<112> partial dislocations. The magnitudes of the tensile and compressive yield stress of (100) nanowires increase and decrease, respectively, with a decrease of the wire width. The magnitude of the tensile yield stress is much larger than that of the compressive yield stress for small (100) nanowires, while for small <111> nanowires, tensile and compressive yield stresses have similar magnitudes. The critical resolved shear stress (RSS) by external forces depends on wire width, orientation and loading condition (tension vs. compression). However, the critical RSS in the interior of the nanowires, which is exerted by both the external force and the surface-stress-induced compressive stress, does not change significantly with wire width for same orientation and same loading condition, and can thus serve as a 'local' criterion. This local criterion is invoked to explain the observed size dependence of yield behavior and tensile/compressive yield stress asymmetry, considering surface stress effects and different slip systems active in tensile and compressive yielding.

Accurate modeling of nucleation, growth and clustering of helium bubbles within metal tritide alloys is of high scientific and technological importance. Of interest is the ability to predict both the distribution of these bubbles and the manner in which these bubbles interact at a critical concentration of helium-to-metal atoms to produce an accelerated release of helium gas. One technique that has been used in the past to model these materials, and again revisited in this research, is percolation theory. Previous efforts have used classical percolation theory to qualitatively and quantitatively model the behavior of interstitial helium atoms in a metal tritide lattice; however, higher fidelity models are needed to predict the distribution of helium bubbles and include features that capture the underlying physical mechanisms present in these materials. In this work, we enhance classical percolation theory by developing the dynamic point-source percolation model. This model alters the traditionally binary character of site occupation probabilities by enabling them to vary depending on proximity to existing occupied sites, i.e. nucleated bubbles. This revised model produces characteristics for one and two dimensional systems that are extremely comparable with measurements from three dimensional physical samples. Future directions for continued development of the dynamic model are also outlined.