Are the cohesive laws of interfaces sufficient for modelling fracture in polycrystals using the cohesive zone model? We examine this question by comparing a fully atomistic simulation of a silicon polycrystal to a finite element simulation with a similar overall geometry. The cohesive laws used in the finite element simulation are measured atomistically. We describe in detail how to convert the output of atomistic grain boundary fracture simulations into the piecewise linear form needed by a cohesive zone model. We discuss the effects of grain boundary microparameters (the choice of section of the interface, the translations of the grains relative to one another, and the cutting plane of each lattice orientation) on the cohesive laws and polycrystal fracture. We find that the atomistic simulations fracture at lower levels of external stress, indicating that the initiation of fracture in the atomistic simulations is likely dominated by irregular atomic structures at external faces, internal edges, corners, and junctions of grains. Thus, cohesive properties of interfaces alone are likely not sufficient for modelling the fracture of polycrystals using continuum methods.
The mechanical properties of the stoichiometric B2 $β$-phase of NiAl are well established, however the effect of off-stoichiometric composition on the fracture toughness has not yet been systematically studied over the entire composition range of 40-50% Al. Here we use microbending tests on notched cantilever beams FIB-milled from NiAl single crystals with an aluminized as well as an oxidation-induced composition gradient to determine the influence of the Al concentration on the mechanical properties. The fracture toughness is maximal for the stoichiometric composition. It decreases with incre…
The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip deformation mechanisms under mode-I loading based on classical interatomic potentials yield contradicting predictions. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a ma…
Molecular dynamics simulations of crack propagation are performed for two extreme cases of complex metallic alloys (CMAs): In a model quasicrystal the structure is determined by clusters of atoms, whereas the model C15 Laves phase is a simple periodic stacking of a unit cell. The simulations reveal that the basic building units of the structures also govern their fracture behaviour. Atoms in the Laves phase play a comparable role to the clusters in the quasicrystal. Although the latter are not rigid units, they have to be regarded as significant physical entities.
We use classical molecular dynamics (MD) simulations to investigate the mechanical properties of pre-cracked, nano-porous single layer MoS2 (SLMoS2) and the effect of interactions between cracks and pores. We found that the failure of pre-cracked and nano-porous SLMoS2 is dominated by brittle type fracture. Bonds in armchair direction show a stronger resistance to crack propagation compared to the zigzag direction. We compared the brittle failure of Griffith prediction with the MD fracture strength and toughness and found substantial differences that limit the applicability of Griffith criteri…
This paper describes atomistic simulations of deformation and fracture of Al reinforced with carbon nanotubes (CNTs). We use density functional theory (DFT) to understand the energetics of Al-graphene interfaces and gain reference data for the parameterization of Al-C empirical potentials. We then investigate the load transfer between CNTs and Al and its effect on composite strengthening. To this end, we perform uniaxial tensile simulations of an Al crystal reinforced with CNTs of various volume fractions. We also study the interaction of the embedded CNTs with a crack. We show that the intera…
We have investigated through fully atomistic reactive molecular dynamics and DFT simulations, the mechanical properties and fracture dynamics of novamene, a new 3D carbon allotrope structure recently proposed. Our results showed that novamene is an anisotropic structure with relation to tensile deformation. Although novamente shares some mechanical features with other carbon allotropes, it also exhibits distinct ones, such as, extensive structural reconstructions (self-healing effect). Novamene presents ultimate strength (~ 100 GPa) values lower than other carbon allotropes, but it has the hig…
Silicene, a 2D analogue of graphene, has spurred a tremendous research interest in the scientific community for its unique properties essential for next generation electronic devices. In this work, for the first time, we present a molecular dynamics (MD) investigation to determine the fracture strength and toughness of nanocrystalline silicene (nc silicene) sheet of varied grain size and pre existing crack length at room temperature. Our results suggest that the transition from an inverse pseudo Hall Petch to a pseudo Hall Petch behavior in nc silicene occurs at a critical grain size of 17.32 …
We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard-Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy-Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic potential. We then study how uncertainties in the parameters propagate to the quantities of interest relevant to crack propagation, namely, the critical stress intensity factor and the lattice trapping range. For our numerical investigation, we rely on an…
In this paper the problem of a plane strain hydraulic fracture propagating in an elasto-plastic material is analyzed. A new stress redistribution model for the proximity of the fracture tip is formulated and a resulting plasticity-dependent crack propagation condition is introduced. A modified variant of the KGD problem that accounts for the plastic deformations in the near-tip zone only is proposed. It is demonstrated that this model can be a credible substitute for the full elasto-plastic hydraulic fracture problem in the case of moderate plastic deformation. The crack-tip shielding effect i…
The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity
Atomistic understanding of hydrogen bubble-induced embrittlement in tungsten enabled by machine learning molecular dynamics
University of Science and Technology Beijing（北京科技大学）；Fuzhou University（福州大学）；Beijing Advanced Innovation Center for Materials Genome Engineering, University of Science and Technology Beijing（北京科技大学材料基因组工程高等创新中心）；Aalto University（阿尔托大学）；Tel Aviv University（特拉维夫大学）
We examine the atomistic scale dependence of material's resistance-to-failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a way incompatible with Griffith's relationship between fracture and free surface energy. Its value finds its origin in the matching between the continuum displacement field at the engineering scale, and the discrete nature of solids at the atomic scale. The generic asymptotic form taken by this field near the crack tip provides a solution for this matching, an…
The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is deter…
Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress-strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated b…
We formulated a technique which combines the first-principles, micromagnetic and microstructural calculations and allows us to study the nature of hysteretic phenomena in hard magnets. Two distinct sources of coercivity in polytwinned CoPt type magnets, domain wall pinning at antiphase boundaries and splitting at twin boundaries, are illustrated for a realistic microstructure. Methodology of multiscale modelling of hysteretic phenomena in nanoscale magnets is discussed.
We study propagating mode-I fracture in two dimensional amorphous materials using atomistic simulations. We used the continuous random network (CRN) model of an amorphous material, creating samples using a two dimensional analogue of the WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which had not yet been achieved by other atomistic models for a…
This paper reviews the status of molecular dynamics as a method in describing solid-solid phase transitions, and its relationship to continuum approaches. Simulation work done in NiTi and Zr using first principles and semi-empirical potentials is presented. This shows failures of extending equilibrium thermodynamics to the nanoscale, and the crucial importance of system-specific details to the dynamics of martensite formation. The inconsistency between experimental and theoretical crystal structures in NiTi is described, together with its possible resolution in terms of nanoscale effects.
Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the $Γ$-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. In special cases, the cell formula can be significantly simplified. Our approach applies e.g. to …
We present simulations of metallization morphologies under ionized sputter deposition conditions, obtained by a new theoretical approach. By means of molecular dynamics simulations using a carefully designed interaction potential, we analyze the surface adsorption, reflection, and etching reactions taking place during Al physical vapor deposition, and calculate their relative probability. These probabilities are then employed in a feature-scale cellular-automaton simulator, which produces calculated film morphologies in excellent agreement with scanning-electron-microscopy data on ionized sput…
A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is ap…
In this work, a multiscale approach based on phase field was developed to simulate the microstructure's evolution under irradiation in binary systems, from atomic to microstructural scale. For that purpose, an efficient numerical scheme was developed. In the case of AgCu alloy under Krypton ions irradiation, phenomenological parameters were computed using atomistic methods, as a function of the temperature and the irradiation flux. As a result, we predicted the influence of the irradiation flux and the temperature on the formation of patterned microstructures. In the case of AgCu, our model wa…
We provide a fundamental insight into the microscopic mechanisms of the ageing processes. Using large scale molecular dynamics simulations of the prototypical ferroelectric material PbTiO3, we demonstrate that the experimentally observed ageing phenomena can be reproduced from intrinsic interactions of defect-dipoles related to dopant-vacancy associates, even in the absence of extrinsic effects. We show that variation of the dopant concentration modifies the material's hysteretic response. We identify a universal method to reduce loss and tune the electromechanical properties of inexpensive ce…
We present a novel micromechanics-based phase field approach to model crack initiation and propagation in carbon nanotube (CNT) based composites. The constitutive mechanical and fracture properties of the nanocomposites are first estimated by a mean-field homogenisation approach. Inhomogeneous dispersion of CNTs is accounted for by means of equivalent inclusions representing agglomerated CNTs. Detailed parametric analyses are presented to assess the effect of the main micromechanical properties upon the fracture behaviour of CNT-based composites. The second step of the proposed approach incorp…
We present a framework dedicated to modelling the resistive switching operation of Valence Change Memory (VCM) cells. The method combines an atomistic description of the device structure, a Kinetic Monte Carlo (KMC) model for the creation and diffusion of oxygen vacancies in the central oxide under an external field, and an ab-initio quantum transport method to calculate electrical current and conductance. As such, it reproduces a realistically stochastic device operation and its impact on the resulting conductance. We demonstrate this framework by simulating a switching cycle for a TiN/HfO$_2…
In this work, a combined modelling approach for crack propagation in defective graphene is presented. Molecular dynamics (MD) simulations are used to obtain material parameters (Young's modulus and Poisson ratio) and to determine the energy contributions during the crack evolution. The elastic properties are then applied in phase-field continuum simulations which are based on the Griffith energy criterion for fracture. In particular, the influence of point defects on elastic properties and the fracture toughness are investigated. For the latter, we obtain values consistent with recent experime…
The width of fracture process zones in geomaterials is commonly assumed to depend on the type of heterogeneity of the material. Still, very few techniques exist, which link the type of heterogeneity to the width of the fracture process zone. Here, fracture processes in geomaterials are numerically investigated with structural network approaches, whereby the heterogeneity in the form of large aggregates and low volume fibres is modelled geometrically as poly-dispersed ellipsoids and mono-dispersed line segments, respectively. The influence of aggregates, fibres and combinations of both on fract…
The novel carbon allotrope with particular and unique 2D arrangement of carbon atoms similar to a Cairo pentagonal tiling, with interplay of $sp^{3}$ and $sp^{2}$ hybridized carbon atoms is called of Penta-graphene (PG). Previous theoretical investigations have shown that PG monolayer is mechanically and thermodynamically stable, possessing also a large band gap of $3.25eV$. This new carbon allotrope with unique carbon atom arrangement in a network (non-coplanar pentagons) is the focus of the theoretical investigations in this work. Using the non-equilibrium molecular dynamics simulations with…
Quantum-accurate computer simulations play a central role in understanding phase-change materials (PCMs) for advanced memory technologies. However, direct quantum-mechanical simulations are necessarily limited to simplified models, containing no more than a few hundred or a thousand atoms. Machine learning (ML) based potential models that are "trained" on quantum-mechanical data are an emerging alternative approach, currently evolving from highly specialised to more widely applied simulation tools. Here we show that a universal, compositionally flexible ML model can describe a wide range of fl…
Neutron irradiation progressively changes the properties of zirconium alloys: they harden and their average c/a lattice parameter ratio decreases with fluence. The bombardment by neutrons produces point defects, which evolve into dislocation loops that contribute to a non-uniform growth phenomenon called irradiation-induced growth (IIG). To gain insights into these dislocation loops in Zr we studied them using atomistic simulation. We constructed and relaxed dislocation loops of various types. We find that the energies of <a>-loops on different habit planes are similar, but our results indicat…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away from defects and interfaces. We propose a new class of matching conditions between the atomistic and continuum regions. These conditions ensure the accurate passage of large scale information between the atomistic and continuum regions and at the same time minimize the reflection of phonons at the atomistic-continuum interface. They can be made adaptive if w…
We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the…
A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh…
Molecular dynamics simulations have been performed to understand the influence of temperature on the tensile deformation and fracture behavior of $<$111$>$ BCC Fe nanowires. The simulations have been carried out at different temperatures in the range 10-1000 K employing a constant strain rate of $1\times$ $10^8$ $s^{-1}$. The results indicate that at low temperatures (10-375 K), the nanowires yield through the nucleation of a sharp crack and fails in brittle manner. On the other hand, nucleation of multiple 1/2$<$111$>$ dislocations at yielding followed by significant plastic deformation leadi…
While CNTs are found to have ultra high stiffness and strength, an enormous scatter is also observed in available laboratory results. This paper studies the effects of randomly distributed Stone Wales (SW or 5 7 7 5) defects on the mechanical properties of single walled nanotubes (SWNTs) using the technique of atomistic simulation (AS). A Matern hard core random field applied on a finite cylindrical surface is used to describe the spatial distribution of the Stone Wales defects. We simulate a set of displacement controlled tensile loading up to fracture of SWNTs with (6,6) armchair and (10, 0)…
For the fatigue life of thin-walled components, not only fatigue crack initiation, but also crack growth is decisive. The phase-field method for fracture is a powerful tool to simulate arbitrary crack phenomena. Recently, it has been applied to fatigue fracture. Those models pose an alternative to classical fracture-mechanical approaches for fatigue life estimation. In the first part of this paper, the parameters of a phase-field fatigue model are calibrated and its predictions are compared to results of fatigue crack growth experiments of aluminium sheet material. In the second part, compress…
We present a combined phase field and cohesive zone formulation for hydrogen embrittlement that resolves the polycrystalline microstructure of metals. Unlike previous studies, our deformation-diffusion-fracture modelling framework accounts for hydrogen-microstructure interactions and explicitly captures the interplay between bulk (transgranular) fracture and intergranular fracture, with the latter being facilitated by hydrogen through mechanisms such as grain boundary decohesion. We demonstrate the potential of the theoretical and computational formulation presented by simulating inter- and tr…
Atomistic modelling of magnetic materials provides unprecedented detail about the underlying physical processes that govern their macroscopic properties, and allows the simulation of complex effects such as surface anisotropy, ultrafast laser-induced spin dynamics, exchange bias, and mi- crostructural effects. Here we present the key methods used in atomistic spin models which are then applied to a range of magnetic problems. We detail the parallelisation strategies used which enable the routine simulation of extended systems with full atomistic resolution.
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of quasi-static fracture, fatigue damage and dynamic cracking. The finite element results obtained reveal the robustness of quasi-Newton monolithic schemes, with convergence readily attained under both stable and unstable cracking conditions. Moreover, since the solution method is unconditionally stable, very significant computational gains are observed relative to the …
Modeling dynamics fracture in materials involves usage of hydrodynamic codes which solve basic conservation laws of mass, energy and momentum in space and time. This requires appropriate models to handle elastic-plastic deformation, equation of state, material strength, and fracture. Nucleation and Growth (NAG) damage model is a micro-physical model which computes amount of damage in the material by accounting for phenomena like nucleation, growth and coalescence of voids or cracks. The NAG model involves several material model parameters, such as nucleation threshold, growth threshold, etc. T…
We carried out fully-atomistic reactive molecular dynamics simulations to study the elastic properties and fracture patterns of transition metal dichalcogenide (TMD) MoX2 (X=S, Se, Te) membranes, in their 2H and 1T phases, within the framework of the Stillinger-Weber potential. Results showed that the fracture mechanism of these membranes occurs through a fast crack propagation followed by their abrupt rupture into moieties. As a general trend, the translated arrangement of the chalcogen atoms in the 1T phase contributes to diminishing their structural stability when contrasted with the 2H one…
Transitions between bulk and interfacial fracture in diamond/$c$BN heterostructures
Tel Aviv University（特拉维夫大学）；Xi’an Jiaotong University（西安交通大学）；Inner Mongolia University of Science and Technology（内蒙古科技大学）；China Academy of Engineering Physics（中国工程物理研究院）
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of phase field-based multi-physics models in transforming the engineering assessment and design of structural components in hydrogen-containing environments. First, we present a theoretical and numerical framework coupling deformation, diffusion and fracture, which accounts for inertia effects.Several constitutive choices are considered for the crack density f…
Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace and (iii) hybrid scheme within quantum mechanics. Test calculations are done with upto 10$^6$ atoms using a standard workstation. As a practical nanoscale calculation, the dynamical fracture of nanocrystalline silicon was simulated.
Fracture of lithium-ion battery electrodes is found to contribute to capacity fade and reduce the lifespan of a battery. Traditional fracture models for batteries are restricted to consideration of a single, idealised particle; here, advanced X-ray computed tomography (CT) imaging, an electro-chemo-mechanical model and a phase field fracture framework are combined to predict the void-driven fracture in the electrode particles of a realistic battery electrode microstructure. The electrode is shown to exhibit a highly heterogeneous electrochemical and fracture response that depends on the partic…
We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force $F_{\rm a}$. The force $F_{\rm s}$ acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of $F_{\rm s}$ (the friction force) acting on Au nanoparticles increases linearly with the contact area, havi…
Ductility and Brittle Fracture of Tungsten by Disconnection Pile-up on Twin Boundaries
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California Irvine（加州大学尔湾分校）；University of California Los Angeles（加州大学洛杉矶分校）；Lehigh University（理海大学）；Northwestern University（西北大学）
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency. The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations. The results reveal an increase in …
Cycling of a metallic glass between ambient and cryogenic temperatures can induce higher-energy states characteristic of glass formation on faster cooling. This rejuvenation, unexpected because it occurs at small macroscopic strains and well below the temperatures of thermally induced structural change, is important, for example, in improving plasticity. Molecular-dynamics simulations elucidate the mechanisms by which thermal cycling can induce relaxation (reaching lower energy) as well as rejuvenation. Thermal cycling, over tens of cycles, drives local atomic rearrangements progressively eras…
