Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model

Multiscale modeling of nanoindentation and nanoscratching by generalized particle method

Most concurrent multiscale methods that expand atomistic region by continuum domain suffer from inconsistent material constitutive properties, which affect the integrity of model in the interface of atomistic and continuum domains. In this paper, the Generalized Particle (GP) method is employed to simulate nanoindentation and nanoscratching of a single-crystal aluminum sample. The main advantage of the GP method lies in its ability to extend the simulation model while maintaining consistent atomic properties across all scales. Coarsening of the atomic domain has been conducted through two-scale and three-scale GP model. The results showed a strong consistency between the results of full atomic simulations and those achieved through the GP method for both nanoindentation and nanoscratch simulations. Also, wave reflections were not seen at the interfaces. The study revealed that an increase in the number of distinct particle domains led to a reduction in the accuracy of multiscale simulations.

Three-dimensional multiscale modeling of nanoindentation

Concurrent multiscale methods have been developed to reduce the degrees of freedom and reduce the effects of boundary conditions on the results of atomic simulations. In this paper, two simplified concurrent multiscale methods, one with handshake region and another without handshake region are used to investigate the nanoindentation process on a single crystal of Al at room temperature. The multiscale models are validated by observing reasonably well similarities in the load-depth curves obtained from multiscale and full MD simulations. Refining the element size down to atomic spacing resulted in high computational efforts while the analysis results do not improve significantly. Also, it is shown that by defining the thermostat in the atomistic part, wave reflections are eliminated at the interface of atomic and continuum domains. It is shown that by selecting appropriate dimensions of the atomic domain, there is no need to use nonlinear elasticity in the continuum region. Also, hardness is more affected by sample size than the elastic modulus.

Cleavages along {110} in bcc iron emit dislocations from the curved crack fronts

Body-centered-cubic (bcc) transition metals, such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}α-Fe and W, cleave along the {100} plane, even though the surface energy is the lowest along the {110} plane. To unravel the mechanism of this odd response, large-scale atomistic simulations of curved cleavage cracks of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}α-Fe were conducted in association with stress intensity factor analyses of straight crack fronts using an interatomic potential created by an artificial neural network technique. The study provides novel findings: Dislocations are emitted from the crack fronts along the {110} cleavage plane, and this phenomenon explains why the {100} plane can be the cleavage plane. However, the simple straight crack-front analyses did not yield the same conclusion. It is suggested that atomistic modeling, at sufficiently large scales to capture the inherent complexities of materials using highly accurate potentials, is necessary to correctly predict the mechanical strength. The method adopted in this study is generally applicable to the cleavage problem of bcc transition metals and alloys.

Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers

The objective of investigating macroscopic polymer properties with a low computing cost and a high resolution has led to the development of efficient hybrid simulation tools. Systems generated from such simulation tools can fail in service if the effect of uncertainty of model inputs on its outputs is not accounted for. This work focuses on quantifying the effect of parametric uncertainty in our coarse-grained molecular dynamics-finite element coupling approach using uncertainty quantification. We consider uniaxial deformation simulations of a polystyrene sample at T = 100 K in our study. Parametric uncertainty is assumed to originate from parameters in the molecular dynamics model with a nonperiodic boundary (the force constant between polymer beads and anchor points, the number of anchor points, and the size of the surrounding dissipative particle dynamics domain) and a parameter to blend the energies of particles and continuum (weighting factor). Key issues that arise in uncertainty quantification are discussed on the basis of the quantities of interest including mass density, end-to-end distance, and radial distribution function. This work reveals the influence of key input parameters on the properties of polymer structure and facilitates the determination of those parameters in the application of this hybrid molecular dynamics-finite element approach.

Mesoscopic and multiscale modelling in materials

The concept of multiscale modelling has emerged over the last few decades to describe procedures that seek to simulate continuum-scale behaviour using information gleaned from computational models of finer scales in the system, rather than resorting to empirical constitutive models. A large number of such methods have been developed, taking a range of approaches to bridging across multiple length and time scales. Here we introduce some of the key concepts of multiscale modelling and present a sampling of methods from across several categories of models, including techniques developed in recent years that integrate new fields such as machine learning and material design.

Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review

The bridge between classical continuum plasticity and crystal plasticity is becoming narrower with continuously improved computational power and with engineers’ desire to obtain more information and better accuracy from their simulations, incorporating at the same time more effects about the microstructure of the material. This paper presents a short overview of the main current techniques employed in crystal plasticity formulations for finite element analysis, as to serve as a point of departure for researchers willing to incorporate microstructure effects in elastoplastic simulations. We include both classical and novel crystal plasticity formulations, as well as the different approaches to model dislocations in crystals.

Multiscale Assessment of Nanoscale Manufacturing Process on the Freeform Copper Surface

The nanocutting has been paid great attention in ultra-precision machining and high sealing mechanical devices due to its nanometer level machining accuracy and surface quality. However, the conventional methods applicable to reproduce the cutting process numerically such as finite element (FE) and molecular dynamics (MD) are challenging to unveil the cutting machining mechanism of the nanocutting due to the limitation of the simulation scale and computational cost. Here a modified quasi-continuous method (QC) is employed to analyze the dynamic nanocutting behavior (below 10 nm) of the copper sample. After preliminary validation of the effectiveness via the wave propagation on the copper ribbon, we have assessed the effects of cutting tool parameters and back-engagement on the cutting force, stress distribution and surface metamorphic layer depth during the nanocutting process of the copper sample. The cutting force and depth of the surface metamorphic layer is susceptible to the back-engagement, and well tolerant to the cutting tool parameters such as the tool rank angle and tool rounded edge diameter. The results obtained by the QC method are comparable to those from the MD method, which indicate the effectiveness and applicability of the modified QC method in the nanocutting process. Overall, our work provides an applicable and efficient strategy to investigate the nanocutting machining mechanism of the large-scale workpiece and shed light on its applications in the super-precision and high surface quality devices.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Multiscale simulation of thin-film lubrication: free-energy-corrected coarse graining

The quasicontinuum method was previously extended to the nonzero temperature conditions by implementing a free-energy correction on non-nodal atoms in coarse-grained solid systems to avoid the dynamical constraint, [Diestler, Wu, and Zeng, J. Chem. Phys. 121, 9279 (2004)]. In this paper, we combine the extended quasicontinuum method and an atomistic simulation to treat the monolayer film lubrication with elastic (nonrigid) substrates. It is shown that the multiscale method with the coarse-graining local elements in the merging regions between the atomistic and continuous descriptions of the substrates can reasonably predict the shear stress profile, the mean separation curve, and the transverse stress profile in the fully atomistic simulation for the tribological system. Moreover, when the nonlocal elements are placed in the merging regions, the inhomogeneous solid atoms in the near regions covered by the cut-off circles of the nonlocal elements replace the homogeneous ones at the equilibrium configuration for the free-energy correction on the non-nodal atoms. The treatment can cause an unphysical sliding between the near and far regions of the upper substrate. It is shown that if the free-energy correction on the non-nodal atoms in the coarse-grained merging regions is removed, the multiscale method can still well reproduce the shear stress profile, the mean separation curve, and the transverse stress profile obtained from the fully atomistic simulation for the system.

Concurrent Multiscale Modeling of Embedded Nanomechanics

We discuss concurrent multiscale simulations of dynamic and temperature-dependent processes found in nanomechanical systems coupled to larger scale surroundings. We focus on the behavior of sub-micron Micro-Electro-Mechanical Systems (MEMS), especially micro-resonators. The coupling of length scales methodology we have developed for MEMS employs an atomistic description of small but key regions of the system, consisting of millions of atoms, coupled concurrently to a finite element model of the periphery. The result is a model that accurately describes the behavior of the mechanical components of MEMS down to the atomic scale. This paper reviews some of the general issues involved in concurrent multiscale simulation, extends the methodology to metallic systems and describes how it has been used to identify atomistic effects in sub-micron resonators.

Multiscale Simulations of Brittle Fracture and the Quantum-Mechanical Nature of Bonding in Silicon

We simulate the microscopic details of brittle fracture in silicon by dynamically coupling empirical-potential molecular dynamics of a strained sample to a quantum-mechanical description of interatomic bonding at the crack tip. Our simulations show brittle fracture at loads comparable to experiment, in contrast with empirical potential simulations that show only ductile crack propagation at much higher loading. While the ductility of the empirical potentials can be attributed to their short range, it is unclear whether the increased range of the tight-binding description is sufficient to explain its brittle behavior. Using the multiscale method we show that at a temperature of 1100 K, but not at 900 K, a dislocation is sometimes nucleated when the crack tip impinges on a vacancy. While this result is too limited in length and time scales to directly correspond to experimental observations, it is suggestive of the experimentally observed brittle to ductile transition.

Pressure Waves in Microscopic Simulations of Laser Ablation Leonid

Laser ablation of organic solids is a complex collective phenomenon that includes processes occurring at different length and time scales. A mesoscopic breathing sphere model developed recently for molecular dynamics simulation of laser ablation and damage of organic solids has significantly expanded the length-scale (up to hundreds of nanometers) and the time-scale (up to nanoseconds) of the simulations. The laser induced buildup of a high pressure within the absorbing volume and generation of the pressure waves propagating from the absorption region poses an additional challenge for molecular-level simulation. A new dynamic boundary condition is developed to minimize the effects of the reflection of the wave from the boundary of the computational cell. The boundary condition accounts for the laser induced pressure wave propagation as well as the direct laser energy deposition in the boundary region.

Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method

A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples.

A methodology for coupling an atomic model with a continuum model using an extended Lagrange function

We propose a hybrid method combining an atomic model and a continuum model, in which the displacement field of the continuum is introduced as a new degree of freedom by extending Andersen's Lagrange function for constant-pressure molecular dynamics. We applied our method to a one-dimensional hybrid model which is composed of an atomic chain and springs. Large-scale fluctuation of the atomic system is found in the hybrid model. The density of states of the phonon is derived, and the large-scale fluctuation induces the generation of a variety of states of phonons. It is shown that the hybrid model proposed by our methodology enables us to perform large-scale simulations without intensive computations.

Multiscale modeling of two-dimensional contacts

A hybrid simulation method is introduced and used to study two-dimensional single-asperity and multi-asperity contacts both quasistatically and dynamically. The method combines an atomistic treatment of the interfacial region with a finite-element method description of subsurface deformations. The dynamics in the two regions are coupled through displacement boundary conditions applied at the outer edges of an overlap region. The two solutions are followed concurrently but with different time resolution. The method is benchmarked against full atomistic simulations. Accurate results are obtained for contact areas, pressures, and static and dynamic friction forces. The time saving depends on the fraction of the system treated atomistically and is already more than a factor of 20 for the relatively small systems considered here.

Hybrid atomistic-coarse-grained treatment of multiscale processes in heterogeneous materials: A self-consistent-field approach

A treatment of multiscale quasistatic processes that combines an atomistic description of microscopic heterogeneous ("near") regions of a material with a coarse-grained (quasicontinuum) description of macroscopic homogeneous ("far") regions is presented. The hybrid description yields a reduced system consisting of the original atoms of the near regions plus pseudoatoms (nodes of the coarse-graining mesh) of the far regions, which interact through an effective many-body potential energy V(eff) that depends on the thermodynamic state. The approximate nature of V(eff) gives rise to "ghost forces," which are reflected in spurious heterogeneities close to interfaces between near and far regions. The impact of ghost forces, which afflict all previous hybrid schemes, is greatly diminished by a self-consistent-field hybrid atomistic-coarse-grained (SCF-HACG) methodology. Tests of the SCF-HACG technique on a fully three-dimensional prototypal model [Lennard-Jones (12,6) crystal] yield thermomechanical properties (e.g., local stress) in good agreement with "exact" properties computed in the fully atomistic limit. The SCF-HACG method is also successfully used to characterize the grain boundary in a Lennard-Jones bicrystal.

Coarse-grained free-energy-functional treatment of quasistatic multiscale processes in heterogeneous materials

A new treatment of quasistatic (reversible) multiscale processes in heterogeneous materials at nonzero temperature is presented. The system is coarse grained by means of a finite-element mesh. The coarse-grained free-energy functional (of the positions of the nodes of the mesh) appropriate to the thermodynamic-state variables controlled in the relevant process is minimized. Tests of the new procedure on a Lennard-Jonesium crystal yield thermomechanical properties in good agreement with the "exact" atomistic results.

Thermomechanical continuum representation of atomistic deformation at arbitrary size scales

A thermomechanical equivalent continuum (TMEC) theory is developed for the deformation of atomistic particle systems at arbitrary size scales and under fully dynamic conditions. This theory allows continuum interpretation of molecular dynamics (MD) model results and derivation of thermomechanical continuum constitutive properties from MD results under conditions of general macroscopically transient thermomechanical deformations, which are not analysed by statistical mechanics. When specialized to the more specific conditions of non-deforming systems in macroscopic equilibrium, this theory yields certain results that are identical to, or consistent with, the results of statistical mechanics. Coupled thermomechanical continuum equations and constitutive behaviour are derived using MD concepts in a time-resolved manner. This theory is a further advancement from the purely mechanical equivalent continuum (EC) theory developed recently. Within the meaning of classical mechanics, the TMEC theory establishes the ultimate atomic origin of coupled thermomechanical deformation phenomena at the continuum level. The analysis is based on the decomposition of atomic particle velocity into a structural deformation part and a thermal oscillation part. On one hand, balance of momentum at the structural level yields fields of stress, body force, traction, mass density and deformation as they appear to a macroscopic observer. On the other hand, balance of momentum for the thermal motions relative to the macroscopically measured structure yields the fields of heat flux and temperature. These quantities are cast in a manner as to conform to the continuum phenomenological equation for heat conduction and generation, yielding scale-sensitive characterizations of specific heat, thermal conductivity and thermal relaxation time. The structural deformation and the thermal conduction processes are coupled because the equations for structural deformation and for heat conduction are two different forms of the same balance of momentum equation at the fully time-resolved atomic level. This coupling occurs through an inertial force term in each equation induced by the other process. For the structural deformation equation, the inertial force term induced by thermal oscillations of atoms gives rise to the phenomenological dependence of deformation on temperature. For the heat equation, the inertial force term induced by structural deformation takes the phenomenological form of a heat source.

An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature

Covering the solid lattice with a finite-element mesh produces a coarse-grained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the two-dimensional Lennard-Jones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress) in excellent agreement with "exact" fully atomistic results.

"Learn on the fly": a hybrid classical and quantum-mechanical molecular dynamics simulation

We describe and test a novel molecular dynamics method which combines quantum-mechanical embedding and classical force model optimization into a unified scheme free of the boundary region, and the transferability problems which these techniques, taken separately, involve. The scheme is based on the idea of augmenting a unique, simple parametrized force model by incorporating in it, at run time, the quantum-mechanical information necessary to ensure accurate trajectories. The scheme is tested on a number of silicon systems composed of up to approximately 200 000 atoms.

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. II

A new hybrid atomistic-coarse-grained (HACG) treatment of reversible processes in multiple-scale systems involving fluid-solid interfaces was tested through isothermal-isobaric Monte Carlo simulations of the quasistatic shearing of a model two-dimensional lubricated contact comprising two planar Lennard-Jones solid substrates that sandwich a softer Lennard-Jones film. Shear-stress profiles (plots of shear stress T(yx) versus lateral displacement of the substrates) obtained by the HACG technique, which combines an atomistic description of the interfacial region with a continuum description of regions well removed from the interface, are compared with "exact" profiles (obtained by treating the whole system at the atomic scale) for a selection of thermodynamic states that correspond to systematic variations of temperature, load (normal stress), film-substrate coupling strength, and film thickness. The HACG profiles are in excellent agreement overall with the exact ones. The HACG scheme provides a reliable description of quasistatic shearing under a wide range of conditions. It is demonstrated that the elastic response of the remote regions of the substrates can have a significant impact on the static friction profile (plot of maximum magnitude of T(yx) versus load).

Coupled atomistic and discrete dislocation plasticity

A computational method for multiscale modeling of plasticity is presented wherein each dislocation is treated as either an atomistic or continuum entity within a single computational framework. The method divides space into atomistic and continuum regions that communicate across a coherent boundary, detects dislocations as they approach the boundary, and seamlessly converts them from one description to another. The method permits the study of problems that are too large for fully atomistic simulation while preserving accurate atomistic details where necessary, but is currently limited to a 2D implementation. A validation test is performed by comparing the method against full atomistic simulations for a 2D nanoindentation problem.

Coupling length scales for multiscale atomistics-continuum simulations: atomistically induced stress distributions in Si/Si3N4 nanopixels

A hybrid molecular-dynamics (MD) and finite-element simulation approach is used to study stress distributions in silicon/silicon-nitride nanopixels. The hybrid approach provides atomistic description near the interface and continuum description deep into the substrate, increasing the accessible length scales and greatly reducing the computational cost. The results of the hybrid simulation are in good agreement with full multimillion-atom MD simulations: atomic structures at the lattice-mismatched interface between amorphous silicon nitride and silicon induce inhomogeneous stress patterns in the substrate that cannot be reproduced by a continuum approach alone.

Controlling crystal surface termination by cleavage direction

We have investigated the cleaving behavior of potassium bichromate (K(2)Cr(2)O(7)) crystals using atomic force microscopy. This crystal has a double layered AB structure along [001]. We find that, upon cleavage along the [001] plane in the <100> directions, one side is completely A terminated, while the other is B terminated. Moreover, the cleavage plane (between an A and a B layer, or between B and A) depends on the imposed direction of cleavage, i.e., [100] or [*100]. This means that the molecular layer that terminates the crystal surface can be controlled by choosing the macroscopic direction of the cleavage force. One of the two terminations is metastable and partly reconstructs to the stable termination.

Directional anisotropy in the cleavage fracture of silicon

Total-energy pseudopotential calculations are used to study the cleavage anisotropy in silicon. It is shown that cracks propagate easily on 111 and 110 planes provided crack propagation proceeds in the <1;10> direction. In contrast, if the crack is driven in a <001> direction on a 110 plane the bond breaking process is discontinuous and associated with pronounced relaxations of the surrounding atoms, which results in a large lattice trapping. The different lattice trapping for different crack propagation directions can explain the experimentally observed cleavage anisotropy in silicon single crystals.

Computer simulations of the mechanical properties of metals

Atomic-scale computer simulations can be used to gain a better understanding of the mechanical properties of materials. In this paper we demonstrate how this can be done in the case of nanocrystalline copper, and give a brief overview of how simulations may be extended to larger length scales. Nanocrystline metals are metals with grain sizes in the nanometre range, they have a number of technologically interesting properties such as much increased hardness and yield strength. Our simulations show that the deformation mechanisms are different in these materials than in coarse-grained materials. The main deformation is occurring in the grain boundaries, and only little dislocation activity is seen inside the grains. This leads to a hardening of the material as the grain size is increased, and the volume fraction of grain boundaries is decreased.

Controlling factors for the brittle-to-ductile transition in tungsten single crystals

Materials performance in structural applications is often restricted by a transition from ductile response to brittle fracture with decreasing temperature. This transition is currently viewed as being controlled either by dislocation mobility or by the nucleation of dislocations. Fracture experiments on tungsten single crystals reported here provide evidence for the importance of dislocation nucleation for the fracture toughness in the semibrittle regime. However, it is shown that the transition itself, in general, is controlled by dislocation mobility rather than by nucleation.