Terry J. Delph

Conservation laws for multibody interatomic potentials

We consider here a formulation given by Hardy (1982 J. Chem. Phys. 76 622–8) that relates the interatomic potential to the conservation equations for linear momentum and energy. Hardys formulation was restricted to two-body interatomic potentials. We show that it can be extended to general multibody potentials. Of particular interest is a resulting general expression for the local Cauchy stress that results from the equation for conservation of linear momentum.

Prediction of instabilities at the atomic scale

Atomic-scale instabilities, in which atomic bonds are broken and reform as the body shifts into a lower-energy configuration, are responsible for a wide range of material behaviours of interest. Building upon previous work, we outline here the construction of a criterion for the prediction of such instabilities. The criterion is implemented within the context of the well-known embedded atom method family of interatomic potentials. We present two examples of the application of this criterion: oriented cavitation in an FCC crystal due to uniform triaxial stretching and dislocation nucleation due to nanoindentation of the (0?0?1) face of an FCC crystal.

A three-dimensional model for the probabilistic intergranular failure of polycrystalline arrays

A three-dimensional grain model, in which the grains are represented by regular truncated octahedra, has been developed to study probabilistic time-dependent intergranular failure in polycrystalline arrays. In this model, grain boundary facets are assumed to fail randomly in time, as a function of the facet normal stress. A simple approximate method for calculating the load shed by failed facets and a reasonable choice of failure criterion complete the model. This leads to a conceptually simple, but computationally complex, model capable of handling assemblages consisting of relatively large numbers (> 5000) of grains. The predicted scatter in the times-to-failure and the variation in number of failed facets with time are in quite reasonable agreement with available experimental data.

A harmonic transition state theory model for defect initiation in crystals

We outline here a model for the initiation of defects in crystals based upon harmonic transition state theory (hTST). This model combines a previously developed model for zero-temperature defect initiation with a multidimensional hTST model that is capable of accurately predicting the effects of temperature and loading rate upon defect initiation. The model has several features that set it apart from previous efforts along these lines, most notably a straightforward method of determining the energy barrier between adjacent equilibriumstatesthatdoesnotdependuponaprioriinformationconcerningthe natureofthedefect. Weapplythemodeltotwoexamples,triaxialstretchingofa perfectfcccrystalandnanoindentationofagoldsubstrate. Verygoodagreement is found between the predictions of the model and independent molecular dynamics (MD) simulations. Among other things, the model predicts a strong dependence of the defect initiation behavior upon the loading parameter. A very attractive feature of this model is that it is valid for arbitrarily slow loading rates, in particular loading rates achievable in the laboratory, and suffers from none of the limitations in this regard inherent in MD simulations. (Some figures may appear in colour only in the online journal)

Conservation laws for materials exhibiting power-law creep

Abstract Conservation laws are derived from materials whose constitutive behavior is characterized by power-law creep with elastic strains. This is accomplished by formulating an adjoint variational principle which has as its Euler-Lagrange equations the governing equations as well as a set of adjoint equations involving adjoint variables. Conservation laws are then derived by an application of Noether’s theorem to the variational principle. The results are analogous to those obtained in linear elasticity, in that conservation laws are shown to arise from translations of spatial and temporal coordinates, rigid-body rotations, and self-similar scalings. A path-independent integral formulation of one of the conservation laws, valid under special circumstances, is derived.

Transition saddle points and associated defects for a triaxially stretched FCC crystal

We demonstrate the use of a single-ended method for locating saddle points on the potential energy surface for a triaxially stretched FCC crystal governed by a Lennard-Jones potential. Single-ended methods require no prior knowledge of the defected state and are shown to have powerful advantages in this application, principally because the nature of the associated defects can be quite complicated and hence extremely difficult to predict ab initio. We find that while classical spherical cavitation occurs for high stretch values, for lower values the defect mode transitions to a non-spherical pattern without any apparent symmetries. This non-spherical mode plays the primary role in harmonic transition state theory predictions that are used to examine how instabilities vary with applied loading rate. Such a defect mode would be difficult to determine using double-ended methods for finding saddle points.

Atom-to-continuum methods for gaining a fundamental understanding of fracture.

This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the atomic J integral we developed is calculable and accurate at finite/room temperatures. In Chapter 6, we return in part to the fundamental efforts to connect material behavior at the atomic scale to that of the continuum. In this chapter, we devise theory that predicts the onset of instability characteristic of fracture/failure via atomic simulation. In Chapters 7 and 8, we describe the culmination of the project in connecting atomic information to continuum modeling. In these chapters we show that cohesive zone models are: (a) derivable from molecular dynamics in a robust and systematic way, and (b) when used in the more efficient continuum-level finite element technique provide results that are comparable and well-correlated with the behavior at the atomic-scale. Moreover, we show that use of these same cohesive zone elements is feasible at scales very much larger than that of the lattice. Finally, in Chapter 9 we describe our work in developing the efficient non-reflecting boundary conditions necessary to perform transient fracture and shock simulation with molecular dynamics.