Interaction of lattice dislocations with a grain boundary during nanoindentation simulation

Interaction of dislocations with a Σ = 5 (210) [001] grain boundary was investigated using molecular dynamics simulation with EAM potentials. The results showed that the dislocation transmitted across the grain boundary during nanoindentation and left a step in the boundary plane. Burgers vector analysis suggested that a partial dislocation in grain I merged into the grain boundary and it was dissociated into another partial dislocation in grain II and a grain boundary dislocation, introducing a step in the grain boundary. Simulation also indicated that, after the transmission, the leading partial dislocation in the grain across the boundary was not followed by the trailing partials, expanding the width of the stacking fault. The results suggested that the creation of the step that accompanied grain boundary motion and expansion of the stacking fault caused resistance to nanoindentation.     

Molecular dynamics simulations on nanoindentation mechanisms of multilayered films

Molecular dynamics (MD) simulations were carried out to study the effects of indention deformation, contact, and adhesion on Al, Ni, and Al/Ni multilayered films. The results show that when the indention depth of the sample increased, the maximum load, plastic energy, and adhesion increased. Jump-contact behavior was observed at the beginning of the loading process. Force relaxation and adhesion took place at the holding depth and during the unloading process, respectively. The glide bands of the interface were on the {1 1 1} 1 1 0 slip systems and the maximum width of the glide bands was about 1 nm. The mechanical responses of the indented films are also discussed.     

Evaluation of incipient plasticity from interfaces between ultra-thin gold films and compliant substrates

Nanoindentation experiments were conducted for 30 nm-thick Au films on two types of substrates, polyimide (compliant) and glass (stiff), to clarify the dominant mechanics of incipient plasticity from the interface. A high resolved shear stress τ_r could be effectively applied to the Au/polyimide interface due to the compliant substrate, and plastic deformation was initiated at the interface. The critical resolved shear stress τ_crss at the interface was determined to have a value of 0.4 ∼ 0.5 GPa. On the other hand, in Au/glass, τ_r peaked within the Au film, and the maximum values were 1.1 ∼ 2.2 GPa depending on the tip radius, whereas the values of τ_r at the Au/glass interface were almost identical at 0.5 ∼ 0.7 GPa. Therefore, plastic deformation might be initiated from the Au/glass interface. The values of τ_crss for heterogeneous nucleation at the interfaces were smaller than that for homogeneous nucleation in the Au films.     

Discrete dislocation simulation of nanoindentation

A methodology to describe nanoindentation by means of discrete dislocations is presented. A collocation method is used to calculate the arising contact stresses at each indentation step, which permits to realize an arbitrary shape of the indenter. Distributed dislocation sources are allowed to emit dislocations on predefined slip planes, when the critical value of the local shear stress for the emission is reached. After each indentation step, the newly emitted dislocations are brought to their equilibrium positions under the influence of the stresses induced by the contact stresses and the dislocations. As an application of our model, the plastic behavior of two materials with different densities of dislocation sources will be studied in detail.This work was financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung) Project P13908-N07.     

Multiscale analysis of the effects of nanocavity on nanoindentation

Based on the EAM (embedded atom method), multiscale simulations are performed to study the effects of a nanocavity on nanoindentation of copper film with a hard frictionless indenter by employing the quasicontinuum method (QCM). The crystallographic orientation of the film in this study is and five different shapes of nanocavities, i.e. circle, ellipse, triangle, rectangle and rhombus are thoroughly studied by gradually changing the geometrical parameters of each kind of nanocavity. In addition, we compared the load–displacements curves for different shapes of nanocavity with different geometrical properties and their relative positions from the top surface of thin film. The strong effects of the geometry of the nanocavity as a kind of defects in the film during the nanoindentation are observed. It is found that both the elastic part of the response and the dislocation nucleation largely depend on the shape of the cavity and its geometrical parameters and location.     

Atomistic simulation of nanoindentation behavior of amorphous/crystalline dual-phase high entropy alloys

High-entropy alloys(HEAs)are a new type of multi-principal metal materials that exhibit excellent me-chanical properties.However,the strength-ductility balance in the HEAs remains a challenge that needs to be addressed.The amorphous/crystalline(A/C)structure is a new design strategy to achieve high strength and excellent ductility of the HEAs.Here,the influences of amorphous layer spacing,indenter velocity,and indenter radius on the mechanical properties and microstructure evolution of the A/C dual-phase CoCrFeMnNi HEAs under nanoindentation were investigated by molecular dynamics(MD)simula-tion.The results indicate that the plastic deformation mechanism of the monocrystalline HEAs is mainly dominated by the nucleation and slip of dislocations,while the plastic deformation mechanism of the dual-phase HEAs is mainly dominated by the interaction between dislocations and amorphous phases.The results show that the average indentation force of the dual-phase HEAs increases with the increase of the amorphous layer spacing.The amorphous layer in the HEAs can hinder the expansion of disloca-tions,limiting them to the crystalline matrix between the two amorphous layers.The results also indicate that Young's modulus of the HEAs increases with the increase of the indentation velocity and indentation radius.However,the hardness of HEAs is positively correlated with the indenter velocity,and negatively correlated with the indenter radius.It should be noted that the critical indentation depth and critical in-dentation force for the plastic deformation of the dual-phase HEAs decrease with the increase of indenter velocity,which is opposite to that of the single-phase crystalline HEAs.     

Simulations of nanoindentation in a thin amorphous metal film

Nanoindentation was simulated in a two dimensional model metallic glass thin film using molecular dynamics. Strain localization was observed in simulations where the system was sufficiently structurally relaxed prior to deformation. Indentation simulations utilized an atomic indenter that adhered to the surface or a frictionless indenter. Boundary conditions were varied to constrain the film or allow the film to relax in-plane to examine the effect on shear band formation. The most constrained system, i.e. that with the atomic indenter and the constrained boundaries exhibited the highest hardness.     

Molecular dynamics simulation of silicon oxidization

We compare here the different oxidization protocols that can be used to generate an SiO₂/Si interface. All these protocols are based on molecular dynamics at high temperature but differ by the way the oxygen atoms are incorporated one-by-one. When they are inserted between two neighbouring Si atoms, forming one of the Si-Si pair closest to the surface, the silicon oxide grows layer-by-layer and it is structured as a random network of SiO₄ entities connected by vertices with only a small amount of SiO₃ and SiO₅ defects. On the contrary, when they are incorporated into the longest Si-Si bond instead of the highest one, a dendritic-like SiO₂ oxide spreads into the substrate in contradiction with experimental observations, which definitely rules out such protocols as realistic ones.     

Molecular dynamics simulations of motion of edge and screw dislocations in a metal

Motions of a straight edge dislocation and a kinked screw dislocation in BCC Mo, described by the Finnis–Sinclair potential, are studied in periodic simulation cells subjected to an applied shear stress. Procedures for setting up the initial atomic configurations in each case are described, and estimate is made of the local driving force due to the image interactions. Preliminary results show that at low temperature the edge dislocation moves primarily through kink nucleation, whereas the mobility of the screw dislocation is strongly facilitated by the presence of a kink.     

Molecular dynamics simulation of crack growth under cyclic loading

The mechanical behaviors around a crack tip for a system including both a crack and two tilt grain boundaries under cyclic loading are examined using a molecular dynamics simulation. Not only a phase transition but also the emission of edge dislocations is observed in order to relax stress concentration around a crack tip during the first loading. Then, a dislocation pile-up is formed near the grain boundary after the edge dislocations reach the grain boundary, because they cannot move beyond the grain boundary. During the first unloading, the edge dislocations emitted from the crack tip return to the crack tip and disappear in the system. We observe several vacancies generated around the crack tip and crack growth corresponding to an atomic scale during cyclic loading. Conclusively, we propose the fatigue crack growth mechanism for the initial phase of the fatigue fracture. That is, a fatigue crack propagates due to coalescence of the crack and the vacancies caused by the emission and absorption of dislocations.     

Molecular dynamics study of surface effects on atomic migration near aluminum grain boundary

In this paper, atomic migration near grain boundary of aluminum wiring line in micro-electronic device is analyzed by molecular dynamics (MD) simulation. Interatomic potential used is based on effective-medium theory (EMT). It is shown that junction point composed of grain boundary and surface is a region where active movement of atoms (atomic diffusion) appears. Under tensile loading, not only atomic diffusion but also slip between atomic layers (dislocation movement) is activated in the junction region. If there exists a certain constraint on the surface due to, for example, a passivation film attached on the aluminum line, atomic rearrangement near the junction changes remarkably.     

Molecular dynamics simulation of polarizable carbon nanotubes

This paper is aimed to develop a modified force field for molecular dynamics (MD) simulations of polarizable carbon nanotubes (CNTs). The effects of electrical polarization and the associated electronic degrees of freedom are represented by a network of negative charged shell particles which move relative to the surrounding positively charged carbon atoms in response to an applied electric field. In this setting, the negative and positive charges are exactly balanced so that the total system remains electrically neutral, and the motion of the shell particles relative to their equilibrium positions leads to polarization within the nanotube. Potential applications of the proposed model include simulations of controlled translocation of ions, water and polymers through solid-state CNT membranes.     

Uncertainty propagation in a multiscale model of nanocrystalline plasticity

We characterize how uncertainties propagate across spatial and temporal scales in a physics-based model of nanocrystalline plasticity of fcc metals. Our model combines molecular dynamics (MD) simulations to characterize atomic-level processes that govern dislocation-based-plastic deformation with a phase field approach to dislocation dynamics (PFDD) that describes how an ensemble of dislocations evolve and interact to determine the mechanical response of the material. We apply this approach to a nanocrystalline Ni specimen of interest in micro-electromechanical (MEMS) switches. Our approach enables us to quantify how internal stresses that result from the fabrication process affect the properties of dislocations (using MD) and how these properties, in turn, affect the yield stress of the metallic membrane (using the PFMM model). Our predictions show that, for a nanocrystalline sample with small grain size (4 nm), a variation in residual stress of 20 MPa (typical in today's microfabrication techniques) would result in a variation on the critical resolved shear yield stress of approximately 15 MPa, a very small fraction of the nominal value of approximately 9 GPa.     

Molecular dynamics simulation of loading rate and surface effects on the elastic bending behavior of metal nanorod

The bending behavior of copper nanorod is studied by three-dimensional molecular dynamics simulation. The embedded-atom-method (EAM) potential presented by Johnson was employed to represent the atomic interactions. Gear algorithm used to integrate Newton's equations of motion uses up to the fifth time derivative of the atom positions. The loading–deflection curves are obtained for different loading rates. It is found that the curves are not linear for impact loading rates because of time scale effect. For quasi-static loading, the atomistic simulation result of deflection is different from that predicted through continuum mechanics by using effective elastic modulus of copper nanorod. We owe this difference to the surface effect. Self-balanced stresses exist in the cross-section of the nanorod at the free relaxation state; inner is compression and near surface is extension. The ratio of surface-to-volume is remarkable for materials with nanoscale, and the materials cannot be considered as homogeneous. These nano features must be accounted into the continuum model to correctly predict the mechanical properties of structures and materials at nanoscale.     

Molecular dynamics study on the nano-void growth in face-centered cubic single crystal copper

Cylindrical nano-void growth in face-centered cubic single crystal copper is studied by mean of molecular dynamics with the Embedded Atom Method. The problem is modeled by a periodic unit cell containing a centered nano-sized cylindrical hole subject to uniaxial tension. The effects of the cell size, crystalline orientation, and initial void volume fraction on the macroscopic stress–strain curve, incipient yield strength, and macroscopic effective Young’s modulus are quantified. Defect evolution in terms of dislocation emission immediately after incipient yielding is also investigated. Obtained results show that, for a given void volume fraction, cell size has apparent effects on the incipient yield strength but negligible effects on the macroscopic effective Young’s modulus. Moreover, the macroscopic effective Young’s modulus and incipient yield strength of the [ 1 0]–[1 1 1]–[1 1 ] orientated system are found to be much more sensitive to the presence of void than those of the [1 0 0]–[0 1 0]–[0 0 1] system.     

Molecular dynamics study of the mechanical behavior of nickel nanowire: Strain rate effects

We present the analysis of uniaxial deformation of nickel nanowires using molecular dynamics simulations, and address the strain rate effects on mechanical responses and deformation behavior. The applied strain rate is ranging from 1 × 10⁸ s⁻¹ to 1.4 × 10¹¹ s⁻¹. The results show that two critical strain rates, i.e., 5 × 10⁹ s⁻¹ and 8 × 10¹⁰ s⁻¹, are observed to play a pivotal role in switching between plastic deformation modes. At strain rate below 5 × 10⁹ s⁻¹, Ni nanowire maintains its crystalline structure with neck occurring at the end of loading, and the plastic deformation is characterized by {1 1 1} slippages associated with Shockley partial dislocations and rearrangements of atoms close to necking region. At strain rate above 8 × 10¹⁰ s⁻¹, Ni nanowire transforms from a fcc crystal into a completely amorphous state once beyond the yield point, and hereafter it deforms uniformly without obvious necking until the end of simulation. For strain rate between 5 × 10⁹ s⁻¹ and 8 × 10¹⁰ s⁻¹, only part of the nanowire exhibits amorphous state after yielding while the other part remains crystalline state. Both the {1 1 1} slippages in ordered region and homogenous deformation in amorphous region contribute to the plastic deformation.     

Hot stage nanoindentation in multi-component Al–Ni–Si alloys: Experiment and simulation

The mechanical properties of individually pure and intermetallic phases of typical Al–Ni–Si piston alloys are investigated at different temperatures using hot stage nanoindentation. The hardness and the indentation modulus of a number of phases are determined at room temperature, 500 K and 650 K. Both, hardness and reduced modulus drop with increasing temperature in different ratios for the various phases. Increasing Ni content in the grains improves the mechanical stability of the material at elevated temperatures in general. The indentation patterns are studied using atomic force microscopy with particular reference to the indentation depths and pile-up effects. Site-specific samples from the material surrounding the nanoindents are prepared using a focussed ion beam field emission gun for examination in the transmission electron microscope. This allows direct observation of material changes as a result of the indentation process in the different phases within the alloy system.Corresponding linked atomistic finite element calculations have been carried out for Si and Ni–Al systems as a function of increasing Ni content at various temperatures. The results show only a small difference in the mechanical behaviour of Si between 300 K and 650 K as observed in the experiments. Large differences for Al at both temperatures studied result in an increase of plasticity with rising temperature and atomic motion that changes from slip in well-defined planes to a viscous fluid-like behaviour. The formation of dislocations and slip bands during indentation for the Ni–Al systems is studied.     

Contact and frictional behavior of rough surfaces using molecular dynamics combined with fractal theory

The microcontact behavior of a copper asperity on a diamond plate was carried out using a molecular dynamics (MD) simulation with the parallel algorithms atom decomposition method. The results show that the dynamic frictional force had an oscillated behavior when the flat diamond plane slipped through the copper asperity. The contact load, contact area, dynamic frictional force, and dynamic frictional coefficient increased as the contact interference increased at a constant loading velocity. The dynamic frictional force and dynamic frictional coefficient increased as the sliding velocity increased. Furthermore, the microcontact behavior can be evaluated between a rigid smooth flat plane and a rigid smooth hemisphere to a deformable rough flat plane by combining the deformed behavior of the asperity obtained from MD results and the fractal and statistic parameters.     

A molecular dynamics simulation on surface tension of liquid Ni and Cu

Molecular dynamics simulations of liquid transition metals Ni and Cu have been performed with the tight-binding potential model. The surface tensions of the liquid metals at different temperatures are evaluated using both methods of calculating the work of cohesion and of using the mechanical expression for the surface stress. The calculated surface tension data are compared with available experimental values. The simulated results for Ni are in good agreement with experiment, but those for Cu show about 10–20% underestimation. Comparing with the mechanical method, the data of surface tension calculated using the method of cohesive work show remarkable dependence on temperature, and the estimated temperature coefficients of liquid Ni and Cu are consistent with the experimental data.