Erik Saether

Transverse mechanical properties of single-walled carbon nanotube crystals. Part I: determination of elastic moduli

Abstract Carbon nanotubes naturally tend to form crystals in the form of hexagonally packed bundles. An accurate determination of the effective mechanical properties of nanotube bundles is important in order to assess potential structural applications such as reinforcement in future composite material systems. Although the intratube axial stiffness is on the order of 1 TPa due to a strong network of carbon–carbon bonds, the intertube interactions are controlled by weaker, nonbonding van der Waals forces which are orders of magnitude less. A direct method for calculating effective material constants is implemented in the present study. The Lennard–Jones potential is used to model the nonbonding cohesive forces. A complete set of transverse moduli is obtained and shown to exhibit a transversely isotropic constitutive behavior. The predicted elastic constants obtained using the direct method are compared with available published results obtained from other methods.

Self-Consistent Properties of Carbon Nanotubes and Hexagonal Arrays as Composite Reinforcements

A self-consistent set of relationships is developed for the physical properties of single walled carbon nanotubes (SWCN) and their hexagonal arrays as a function of the chiral vector integer pair, (n,m). Properties include effective radius, density, principal Youngs modulus, and specific Youngs modulus. Relationships between weight fraction and volume fraction of SWCN and their arrays are developed for the full range of polymeric mixtures. Examples are presented for various values of polymer density and for multiple SWCN diameters.

Dynamics of nanoscale grain-boundary decohesion in aluminum by molecular-dynamics simulation

The dynamics and energetics of intergranular crack growth along a flat grain boundary in aluminum is studied by a molecular-dynamics simulation model for crack propagation under steady-state conditions. Using the ability of the molecular-dynamics simulation to identify atoms involved in different atomistic mechanisms, it was possible to identify the energy contribution of different processes taking place during crack growth. The energy contributions were divided as: elastic energy—defined as the potential energy of the atoms in fcc crystallographic state; and plastically stored energy—the energy of stacking faults and twin boundaries; grain-boundary and surface energy. In addition, monitoring the amount of heat exchange with the molecular-dynamics thermostat gives the energy dissipated as heat in the system. The energetic analysis indicates that the majority of energy in a fast growing crack is dissipated as heat. This dissipation increases linearly at low speed, and faster than linear at speeds approaching 1/3 the Rayleigh wave speed when the crack tip becomes dynamically unstable producing periodic dislocation bursts until the crack is blunted.

A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.

Transverse mechanical properties of carbon nanotube crystals. Part II: sensitivity to lattice distortions

Abstract Perfect crystals of carbon nanotubes tend to form aligned bundles that assume a hexagonal packing configuration in a minimum energy state. The theoretical constitutive relation for these defect-free crystals is highly anisotropic with a large axial stiffness due to a network of strong delocalized carbon–carbon bonds and transverse properties that are orders of magnitude lower due to a sole dependence on non-bonding van der Waals forces. The assemblage of a large number of collimated nanotubes may be expected to exhibit a distribution of lattice sites containing imperfections caused by packing faults or inclusions that will function as ‘weak-links’ and adversely affect local stiffness and strength. The present study is therefore directed towards quantifying the effects of distorted bundle configurations on mechanical properties. To illustrate distortion sensitivity, the transverse shear and bulk moduli are calculated by considering various magnitudes of random perturbations in nanotube packing. Monte Carlo simulations are performed to obtain a statistical distribution of predicted moduli. The present analysis demonstrates that even small perturbations to the lattice geometry give rise to large variations in transverse moduli, and suggests that chemical functionalization to improve nanotube bundle cohesion may be required for successful structural applications.

Multiscale Modeling of Grain-Boundary Fracture: Cohesive Zone Models Parameterized from Atomistic Simulations

A multiscale modeling strategy is developed to study grain boundary fracture in polycrystalline aluminum. Atomistic simulation is used to model fundamental nanoscale deformation and fracture mechanisms and to develop a constitutive relationship for separation along a grain boundary interface. The nanoscale constitutive relationship is then parameterized within a cohesive zone model to represent variations in grain boundary properties. These variations arise from the presence of vacancies, interstitials, and other defects in addition to deviations in grain boundary angle from the baseline configuration considered in the molecular-dynamics simulation. The parameterized cohesive zone models are then used to model grain boundaries within finite element analyses of aluminum polycrystals.

A Continuum-Atomistic Analysis of Transgranular Crack Propagation in Aluminum

A concurrent multiscale modeling methodology that embeds a molecular dynamics (MD) region within a finite element (FEM) domain is used to study plastic processes at a crack tip in a single crystal of aluminum. The case of mode I loading is studied. A transition from deformation twinning to full dislocation emission from the crack tip is found when the crack plane is rotated around the [ 111 ] crystallographic axis. When the crack plane normal coincides with the [112] twinning direction, the crack propagates through a twinning mechanism. When the crack plane normal coincides with the [011] slip direction, the crack propagates through the emission of full dislocations. In intermediate orientations, a transition from full dislocation emission to twinning is found to occur with an increase in the stress intensity at the crack tip. This finding confirms the suggestion that the very high strain rates, inherently present in MD simulations, which produce higher stress intensities at the crack tip, over-predict the tendency for deformation twinning compared to experiments. The present study, therefore, aims to develop a more realistic and accurate predictive modeling of fracture processes.

Multiscale Modeling for the Analysis for Grain-Scale Fracture Within Aluminum Microstructures

Multiscale modeling methods for the analysis of metallic microstructures are discussed. Both molecular dynamics and the finite element method are used to analyze crack propagation and stress distribution in a nanoscale aluminum bicrystal model subjected to hydrostatic loading. Quantitative similarity is observed between the results from the two very different analysis methods. A bilinear traction-displacement relationship that may be embedded into cohesive zone finite elements is extracted from the nanoscale molecular dynamics results.

Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models

A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.

Modeling Near-Crack-Tip Plasticity From Nano- to Micro-Scales

Several efforts that are aimed at understanding the plastic deformation mechanisms related to crack propagation at the nano-, meso- and micro-length scales including atomistic simulation, discrete dislocation plasticity, strain gradient plasticity and crystal plasticity are discussed. The paper focuses on discussion of newly developed methodologies and their application to understanding damage processes in aluminum and its alloys. Examination of plastic mechanisms as a function of increasing length scale illustrates increasingly complex phenomena governing plasticity.