Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM)

A new multiscale simulation approach is introduced that couples atomistic-scale simulations using molecular dynamics (MD) with continuum-scale simulations using the recently developed material point method (MPM). In MPM, material continuum is represented by a finite collection of material points carrying all relevant physical characteristics, such as mass, acceleration, velocity, strain and stress. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A silicon single crystal under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. The coupled MD/MPM simulations show that silicon under nanometric tension experiences, with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress–strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in the rest of the material.     

Discrete dislocation dynamics: an important recent break-through in the modelling of dislocation collective behaviour

Recent results obtained by 3D discrete Dislocation Dynamics (DD) simulations are reviewed. Firstly, in the case of fatigued AISI 316L stainless steel, it is shown how DD simulations can both explain the formation of persistent slip bands and give a criterion for crack initiation. The same study is performed in the case of precipitate hardened metals where the precipitate size plays a crucial role. Secondly, we show how molecular dynamics (MD) simulations can feed the DD simulations for two applications. The first concerns the modelling of BCC Fe for which the dislocation mobility is derived from MD simulations. The second considers the modelling of irradiated stainless steels (FCC), where MD is used to define the local rules of interactions between dislocations and Frank loops. To cite this article: M.C. Fivel, C. R. Physique 9 (2008).     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Strain Rate Sensitivities of Face-Centred-Cubic Metals Using Molecular Dynamics Simulation

We use dislocation theory and molecular dynamics （MD） simulations to investigate the effect of atom properties on the macroscopic strain rate sensitivity of f cc metals. A method to analyse such effect is proposed. The stress dependence of dislocation velocity is identified as the key of such study and is obtained via 2-D MD simulations on the motion of an individual dislocation in an fcc metal. Combining the simulation results with Orowan＇s relationship, it is concluded that strain rate sensitivities of fcc metals are mainly dependent on their atomic mass rather than the interatomic potential. The order of strain rate sensitivities of five fcc metals obtained by analysing is consistent with the experimental results available.     

Cross-slip in face-centered cubic metals: a general Escaig stress-dependent activation energy line tension model

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the energy barrier for cross-slip is essential to construct reliable cross-slip rules in dislocation models. In this work, we employ a line tension model for cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier under Escaig stresses. The analysis shows that the activation energy is proportional to the stacking fault energy, the unstressed dissociation width and a typical length for cross-slip along the dislocation line. Linearisation of the interaction forces between the partial dislocations yields that this typical length is related to the dislocation length that bows towards constriction during cross-slip. We show that the application of Escaig stresses on both the primary and the cross-slip planes varies the typical length for cross-slip and we propose a stress-dependent closed form expression for the activation energy for cross-slip in a large range of stresses. This analysis results in a stress-dependent activation volume, corresponding to the typical volume surrounding the stressed dislocation at constriction. The expression proposed here is shown to be in agreement with previous models, and to capture qualitatively the essentials found in atomistic simulations. The activation energy function can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality.     

An empirical model for free surface energy of strained solids at different temperature regimes

We have developed an empirical formulation, based on the elastic theory, to calculate the variation of the surface free energy when a crystal is strained in the elastic regime. The model permits to obtain the variation of the surface energy at different strains and temperatures when are known the thermal dependence on the bulk and surface elastic constants. Molecular dynamics (MD) simulations were performed using the three low index surfaces of Al, to validate the accuracy of the model. The comparison between the empirical model and the MD simulations shows a good agreement for temperatures ranging between 0 and 900 K, and for deformation between −2% and 2%.     

First principles calculation of CH<Subscript>4</Subscript> decomposition on nickel (111) surface

The mechanism of the CH₄ decomposition on the nickel (111) surface is investigatedby first principles calculations. The activation energy of each reaction is calculatedusing nudged elastic band method. The activation energy of hydrogen dissociation from aCH₂ fragment isfound much lower than the one of a CH₃ fragment. This result is consistent with the fact,observed in our previous molecular dynamics (MD) simulations, that the CH₃ fragment is dissociated into aCH fragment and two hydrogen atoms spontaneously. The effects of finite temperatureat 1500 K on the decomposition reaction of a CH₄ molecule and its fragments are also investigated usingconstraint MD method. While the temperature effects are barely visible inCH₄ andCH₂ dissociationprocesses, they reduce the activation free energy of hydrogen dissociation fromCH₃ and CHfragments largely.     

Computational determination of radiation damage effects on DNA structure

Molecular dynamics (MD) studies of several radiation originated lesions on the DNA molecules are presented. The pyrimidine lesions (cytosinyl radical, thymine dimer, thymine glycol) and purine lesion (8-oxoguanine) were subjected to the MD simulations for several hundred picoseconds using MD simulation code AMBER 5.0 (4.0). The simulations were performed for fully dissolved solute molecules in water. Significant structural changes in the DNA double helical structure were observed in all cases which may be categorized as: a) the breaking of hydrogen bonds network between complementary bases and resulted opening of the double helix (cytosinyl, radical, 8-oxoguanine); b) the sharp bending of the DNA helix centered at the lesion site (thymine dimer, thymine glycol); and c) the flippingout of adenine on the strand complementary to the lesion (8-oxoguanine). These changes related to the overall collapsing of the double helical structure around the lesion, are expected to facilitate the docking of the repair enzyme into the DNA in the formation of DNA-enzyme complex. The stable DNA-enzyme complex is a necessary condition for the onset of the enzymatic repair process. In addition to structural changes, specific values of electrostatic interaction energy were determined at several lesion sites (thymine dimer, thymine glycol and 8-oxoguanine). This lesion-specific electrostatic energy is a factor that enables repair enzyme to discriminate lesion from the native site during the scanning of the DNA surface.     

Determination of the activation energy by stochastic analyses of molecular dynamics simulations of dislocation processes

An investigation is reported of the probability and the probability density of thermal activation of stress-driven dislocation processes, as simulated using molecular dynamics (MD). Stochastic analyses of the survival probability are found to lead to simple relationships between the loading history and the distribution of the interaction time and strength. It is shown that the determination of the activation energy associated to a thermally activated event can be achieved by a reduction of the stochastic process to a process obeying the Poisson's distribution, preserving the activation probability at the survival time. The method is applied to the kink-pair mechanism for screw dislocations in iron. Predictions are compared with experimental results and with other methods reported in the literature, which allows the difference in the approximations and in the assumptions considered in these models to be underlined.     

Atomic simulation of the dynamic properties for a double period structure with 90° partial dislocation in Si

The dynamic properties of a double period (DP) structure with a 90° partial dislocation were investigated by atomic simulation methods in Si. By the use of molecular dynamics (MD) method, the motion sequences of kinks and reconstruction defect (RD) of DP structure were obtained. Based on the conjugate gradients (CG) results and tight-binding (TB) potential, the formation energies E_f of kinks were computed. In addition, the migration barriers W_m of kinks were also calculated via nudged elastic band (NEB) method with TB potential. The results show that E_f is smaller than W_m, which means that the migration barrier of kink dominates the motion of DP structure. According to the activation energies of short dislocation segments (2.17 eV) and long dislocation segments (1.61 eV), we predict that the experimental results may be between these two values.     

基于多尺度分析的FCC金属应变率敏感性研究

 采用位错理论和分子动力学模拟研究了金属原子性质对其宏观应变率敏感性的影响。依据位错运动的Orowan关系,认为金属中位错速度对应力的依赖关系是此研究的关键,并分析提出研究金属原子性质与应变率敏感性关系的分析方法。构建了一个中等规模的二维分子动力学模型,应用此模型对单个位错在FCC金属中的运动进行模拟。综合位错理论分析和分子动力学模拟结果得出结论：影响金属应变率敏感性的原子性质是其原子量而不是其原子势。依据此结论分析得到的FCC金属应变率敏感性排序与试验结果相符。     

Simulation of the interaction between an edge dislocation and ⟨111⟩ interstitial dislocation loops in α-iron

ABSTRACT

The dependence of the interactions of intermediate-size ½<111> self-interstitial atom (SIA) loops with an edge dislocation on strain rate and temperature was investigated by molecular dynamics (MD) simulations for the interatomic potential derived by Ackland et al. (A97). For low temperatures (T?=?1?K), the mechanisms of the interactions were in agreement with recent literature. It was shown that a second passing of the dislocation through the loop led to a different mechanism than the one that occurred upon first passing. Since these mechanisms are associated with different SIA loop sizes, and since the loop lost a number of SIAs upon first interaction, it was deduced that the dividing threshold between large and small loops (rendering them strong or weak obstacles, respectively) is at the vicinity of the loop size studied (169 SIAs). For higher temperatures (T?=?300?K), the strain rate dependence proved strong: for low strain rates, the dislocation absorbed the loop as a double super-jog almost immediately and continued its glide unimpeded. For a high strain rate, the dislocation was initially pinned due to the formation of an almost sessile segment leading to high critical stress.     

高压下液态硝基甲烷的分子动力学模拟

 对高压下液态硝基甲烷的性质进行经典和基于第一性原理计算的Car-Parrinello分子动力学（CPMD）模拟。利用经典势的分子动力学（MD）模拟研究了高压压缩状态下液态硝基甲烷的结构和热力学性质,得到了高达14.2 GPa压力下的理论Hugoniot数据。对于一些热力学函数,如总能和粒子速度,经典势模拟给出了很好的总趋势,基本特征和实验观测一致。但是在给定的密度下,经典模拟预言的Hugoniot压力偏高。在几个选定的密度下,进行了CPMD模拟,得到了二体相关函数、速度自相关函数、振动光谱和其它的热力学性质,并与经典模拟结果进行了比较。对二体相关函数的分析表明经典势的短程部分的刚性可能太强,从而导致了比实验值高的理论压力值。对于某些二体相关函数,CPMD模拟和经典模拟结果差别很大,可以归结为量子效应。当压力增高时,量子模拟得到的振动光谱向高频部分移动的现象与实验观测相符合。     

Void growth via atomistic simulation: will the formation of shear loops still grow a void under different thermo-mechanical constraints?

Abstract

Molecular dynamics (MD) simulations under different mechanical and thermal constraints are carried out with a nanovoid embedded inside a single-crystal, face-centred-cubic copper. The dislocation emission angles measured from MD plots under 0.1 K, uniaxial-strain simulation are in line with the theoretical model. The dislocation density calculated from simulation is qualitatively consistent with the experimental measurement in terms of a saturation feature. The ‘relatively farthest-travelled’ atoms are employed to reflect the correlation between the dislocation structure and the void growth. At a smaller scale, the incomplete shear dislocation loops on the slip plane contribute to the local material transport. At a larger scale, the dislocation structures formed by those incomplete shear loops further facilitate the growth of nanovoid. Compared to the uniaxial-strain case, the void growth under the uniaxial-stress is very limited. The uniaxial-strain loading results in an octahedron void shape. The uniaxial-stress loading turns the nanovoid into a prolate ellipsoid along the loading direction. In the simulation, the largest specimen contains 12 million atoms and the lowest strain rate applied is 2 × 10⁶ s^?1. Under all the different thermomechanical constraints concerned, the formation of incomplete shear dislocation loops are found capable of growing the void.     

Computing activation energies of non-thermal reactions

The chemistry in bulk gases involves reactions of nascent radicals that are almost invariably non-thermal. The energy requirements of reactions involving radicals depend on the reactions that produce them and the intra- and inter-molecular energy transfer they may undergo. Here, we extend the generalised Tolman activation energy (GTEa) method to non-thermal reactions in molecular dynamics (MD) simulations. We compute the energy requirements, which we refer to as chemical-activation energies (CE _a), of reactions of radicals formed by the decomposition of hydrogen peroxide. The equipartition theorem is adapted to compute average energies of small isolated systems with internal degrees of freedom in MD simulations with periodic boundary conditions, which is necessary for application of the GTEa method to non-thermal reactions. To illustrate the applicability of the GTEa method to non-thermal reactions, we present CE _a results for H₂O₂?+?OH → H₂O?+?HO₂, a key reaction in hydrogen combustion, as described by the ReaxFF force field. The OH radicals are the products of the self-dissociation of H₂O₂ and subsequent reactions. We define the chemical-activation energy for a back reaction (BCE _a) as the difference between the energy of the products and the average energy of the system. We show that the BCE _a and CEa are linearly correlated.     

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.     

新的相互作用势对MD模拟钙钛矿结构MgSiO3热力学性质的影响

通过分析势能曲线解释了钙钛矿结构MgSiO3熔化模拟过程中模拟熔化温度存在较大差异的原因，并进一步研究了对势参数在分子动力学模拟中的影响. 通过调整已有的经验势得到了一组新的势参数，以此来进行分子动力学研究，得到的常温常压下摩尔体积与Belonoshko和Dubrovinsky的结果符合较好，并且其状态方程、常压下热容和常压下热膨胀系数与他人的实验值都较好地吻合. 另外，所得到的熔化温度也与以前的研究进行了比较.     

How to identify dislocations in molecular dynamics simulations?

Dislocations are of great importance in revealing the underlying mechanisms of deformed solid crystals.With the development of computational facilities and technologies,the observations of dislocations at atomic level through numerical simulations are permitted.Molecular dynamics(MD)simulation suggests itself as a powerful tool for understanding and visualizing the creation of dislocations as well as the evolution of crystal defects.However,the numerical results from the large-scale MD simulations are not very illuminating by themselves and there exist various techniques for analyzing dislocations and the deformed crystal structures.Thus,it is a big challenge for the beginners in this community to choose a proper method to start their investigations.In this review,we summarized and discussed up to twelve existing structure characterization methods in MD simulations of deformed crystal solids.A comprehensive comparison was made between the advantages and disadvantages of these typical techniques.We also examined some of the recent advances in the dynamics of dislocations related to the hydraulic fracturing.It was found that the dislocation emission has a significant effect on the propagation and bifurcation of the crack tip in the hydraulic fracturing.